зеркало из https://github.com/mozilla/pjs.git
Stable drop of JavaScript interpreter code from SpiderMonkey140_BRANCH
This commit is contained in:
mccabe%netscape.com
Родитель
24ddb74d95
Коммит
ab3c1def59
|
|
@ -1,3 +1,4 @@
|
|||
*.pdb
|
||||
*.ncb
|
||||
*.opt
|
||||
*.plg
|
||||
|
|
|
|||
|
|
@ -82,7 +82,6 @@ EXPORTS = js.msg \
|
|||
jscntxt.h \
|
||||
jscompat.h \
|
||||
jsconfig.h \
|
||||
jscpucfg.h \
|
||||
jsdate.h \
|
||||
jsdbgapi.h \
|
||||
jsemit.h \
|
||||
|
|
@ -166,12 +165,6 @@ endif # sparc
|
|||
|
||||
INCLUDES += -I.
|
||||
|
||||
ifdef NSPR20
|
||||
INCLUDES += -I$(DIST)/include/nspr20/pr
|
||||
else
|
||||
INCLUDES += -I$(XPDIST)/public/nspr
|
||||
endif
|
||||
|
||||
ifndef NSBUILDROOT
|
||||
JSJAVA_STUBHEADERS = -I$(DEPTH)/sun-java/include/_gen \
|
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-I$(DEPTH)/sun-java/netscape/javascript/_jri \
|
||||
|
|
@ -197,6 +190,30 @@ ifeq ($(OS_ARCH), Linux)
|
|||
LDFLAGS += -ldl
|
||||
endif
|
||||
|
||||
FDLIBM_LIBRARY = fdlibm/$(OBJDIR)/libfdm.a
|
||||
JSMATH_PRELINK = $(OBJDIR)/jsmathtemp.o
|
||||
|
||||
# special rule for jsmath.o since we want to incrementally link
|
||||
# against fdlibm to pull in only what is needed
|
||||
$(OBJDIR)/jsmath.o: $(FDLIBM_LIBRARY) $(JSMATH_PRELINK)
|
||||
@$(MAKE_OBJDIR)
|
||||
ifneq (,$(filter OS2 WINNT,$(OS_ARCH)))
|
||||
ld -r -o $@ $(JSMATH_PRELINK) $(FDLIBM_LIBRARY)
|
||||
else
|
||||
ld -r -o $@ $(JSMATH_PRELINK) $(FDLIBM_LIBRARY)
|
||||
endif
|
||||
|
||||
$(JSMATH_PRELINK): jsmath.c jslibmath.h
|
||||
@$(MAKE_OBJDIR)
|
||||
ifneq (,$(filter OS2 WINNT,$(OS_ARCH)))
|
||||
$(CC) -Fo$@ -c $(CFLAGS) $<
|
||||
else
|
||||
$(CC) -o $@ -c $(CFLAGS) $<
|
||||
endif
|
||||
|
||||
$(FDLIBM_LIBRARY):
|
||||
cd fdlibm; $(MAKE)
|
||||
|
||||
# this requires clobbering and recompiling with XCFLAGS=-DJSFILE
|
||||
js:
|
||||
$(MAKE) clobber
|
||||
|
|
@ -218,6 +235,20 @@ endif
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|||
# hardwire dependencies on jsopcode.tbl
|
||||
jsopcode.h jsopcode.c: jsopcode.tbl
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|
||||
# Generate jsautocfg.h header
|
||||
$(OBJDIR)/jsautocfg.h: $(OBJDIR)/jscpucfg
|
||||
rm -f $@
|
||||
$(OBJDIR)/jscpucfg > $@
|
||||
|
||||
$(OBJDIR)/jscpucfg: $(OBJDIR)/jscpucfg.o
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$(CC) -o $@ $(OBJDIR)/jscpucfg.o
|
||||
|
||||
export:: $(OBJDIR)/jsautocfg.h
|
||||
$(INSTALL) -m 444 $(OBJDIR)/jsautocfg.h $(DIST)/include
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||||
|
||||
# Add to TARGETS so clobber rule works
|
||||
TARGETS += $(OBJDIR)/jsautocfg.h $(OBJDIR)/jscpucfg $(OBJDIR)/jscpucfg.o
|
||||
|
||||
# this section was put in the merged by danda into the
|
||||
# JAVA_*_MERGE section and normally would have
|
||||
# been removed. However it looks like it shouldn't have
|
||||
|
|
@ -231,24 +262,6 @@ $(OBJDIR)/js.o: js.c
|
|||
$(CC) -Fo$@ -c $(CFLAGS) $(JSJAVA_CFLAGS) js.c
|
||||
endif
|
||||
|
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clobber::
|
||||
rm -f $(OBJDIR)/jscpucfg $(OBJDIR)/jscpucfg.h
|
||||
|
||||
refdiff:
|
||||
@for f in `cat commfiles`; do \
|
||||
t=/tmp/refdiff.$$$$; \
|
||||
trap 'rm -f $$t' 0 1 2 15; \
|
||||
sed -f prconv.sed ../ref/$$f > $$t; \
|
||||
cmp -s $$t $$f; \
|
||||
if test $$? -ne 0; then \
|
||||
echo "=== $$f"; \
|
||||
diff $$f $$t; \
|
||||
fi; \
|
||||
rm -f $$t; \
|
||||
done
|
||||
|
||||
refconv:
|
||||
@for f in `cat commfiles`; do \
|
||||
echo "=== $$f"; \
|
||||
sed -f prconv.sed ../ref/$$f > $$f; \
|
||||
done
|
||||
|
||||
.PHONY: refdiff refconv
|
||||
|
|
|
|||
|
|
@ -27,6 +27,8 @@ ifdef MOZ_OJI
|
|||
DIRS = liveconnect
|
||||
endif
|
||||
|
||||
DIRS += fdlibm
|
||||
|
||||
LIBRARY_NAME = js
|
||||
|
||||
ifeq ($(subst /,_,$(shell uname -s)),OS2)
|
||||
|
|
@ -87,7 +89,6 @@ EXPORTS = js.msg \
|
|||
jscntxt.h \
|
||||
jscompat.h \
|
||||
jsconfig.h \
|
||||
jscpucfg.h \
|
||||
jsdate.h \
|
||||
jsdbgapi.h \
|
||||
jsemit.h \
|
||||
|
|
@ -198,6 +199,36 @@ ifeq ($(OS_ARCH), Linux)
|
|||
LDFLAGS += -ldl
|
||||
endif
|
||||
|
||||
FDLIBM_LIBRARY = fdlibm/libfdm.a
|
||||
JSMATH_PRELINK = jsmathtemp.o
|
||||
|
||||
# special rule for jsmath.o since we want to incrementally link
|
||||
# against fdlibm to pull in only what is needed
|
||||
jsmath.o: $(FDLIBM_LIBRARY) $(JSMATH_PRELINK)
|
||||
@$(MAKE_OBJDIR)
|
||||
ifneq (,$(filter OS2 WINNT,$(OS_ARCH)))
|
||||
ld -r -o $@ $(JSMATH_PRELINK) $(FDLIBM_LIBRARY)
|
||||
else
|
||||
ld -r -o $@ $(JSMATH_PRELINK) $(FDLIBM_LIBRARY)
|
||||
endif
|
||||
|
||||
$(JSMATH_PRELINK): jsmath.c
|
||||
@$(MAKE_OBJDIR)
|
||||
ifneq (,$(filter OS2 WINNT,$(OS_ARCH)))
|
||||
$(CC) -Fo$@ -c $(CFLAGS) $<
|
||||
else
|
||||
$(CC) -o $@ -c $(CFLAGS) $<
|
||||
endif
|
||||
|
||||
# ripped from $(topsrcdir)/config/rules.mk
|
||||
$(FDLIBM_LIBRARY):
|
||||
set -e; \
|
||||
set $(EXIT_ON_ERROR); \
|
||||
echo "cd $(@D); $(MAKE) $(@F)"; \
|
||||
oldDir=`pwd`; \
|
||||
cd $(@D); $(MAKE) $(@F); cd $$oldDir; \
|
||||
set +e;
|
||||
|
||||
# this requires clobbering and recompiling with XCFLAGS=-DJSFILE
|
||||
js:
|
||||
$(MAKE) clobber
|
||||
|
|
@ -219,6 +250,20 @@ endif
|
|||
# hardwire dependencies on jsopcode.tbl
|
||||
jsopcode.h jsopcode.c: jsopcode.tbl
|
||||
|
||||
# Generate jsautocfg.h header
|
||||
$(OBJDIR)/jsautocfg.h: $(OBJDIR)/jscpucfg
|
||||
rm -f $@
|
||||
$(OBJDIR)/jscpucfg > $@
|
||||
|
||||
$(OBJDIR)/jscpucfg: $(OBJDIR)/jscpucfg.o
|
||||
$(CC) -o $@ $(OBJDIR)/jscpucfg.o
|
||||
|
||||
export:: $(OBJDIR)/jsautocfg.h
|
||||
$(INSTALL) -m 444 $(OBJDIR)/jsautocfg.h $(DIST)/include
|
||||
|
||||
# Add to TARGETS so clobber rule works
|
||||
TARGETS += $(OBJDIR)/jsautocfg.h $(OBJDIR)/jscpucfg $(OBJDIR)/jscpucfg.o
|
||||
|
||||
# this section was put in the merged by danda into the
|
||||
# JAVA_*_MERGE section and normally would have
|
||||
# been removed. However it looks like it shouldn't have
|
||||
|
|
@ -231,25 +276,3 @@ $(OBJDIR)/js.o: js.c
|
|||
@$(MAKE_OBJDIR)
|
||||
$(CC) -Fo$@ -c $(CFLAGS) $(JSJAVA_CFLAGS) js.c
|
||||
endif
|
||||
|
||||
|
||||
refdiff:
|
||||
@for f in `cat commfiles`; do \
|
||||
t=/tmp/refdiff.$$$$; \
|
||||
trap 'rm -f $$t' 0 1 2 15; \
|
||||
sed -f prconv.sed ../ref/$$f > $$t; \
|
||||
cmp -s $$t $$f; \
|
||||
if test $$? -ne 0; then \
|
||||
echo "=== $$f"; \
|
||||
diff $$f $$t; \
|
||||
fi; \
|
||||
rm -f $$t; \
|
||||
done
|
||||
|
||||
refconv:
|
||||
@for f in `cat commfiles`; do \
|
||||
echo "=== $$f"; \
|
||||
sed -f prconv.sed ../ref/$$f > $$f; \
|
||||
done
|
||||
|
||||
.PHONY: refdiff refconv
|
||||
|
|
|
|||
|
|
@ -24,6 +24,12 @@ include config.mk
|
|||
|
||||
#NS_USE_NATIVE = 1
|
||||
|
||||
ifdef USE_MSVC
|
||||
OTHER_LIBS += fdlibm/$(OBJDIR)/fdlibm.lib
|
||||
else
|
||||
OTHER_LIBS += -Lfdlibm/$(OBJDIR) -lfdm
|
||||
endif
|
||||
|
||||
ifdef JS_THREADSAFE
|
||||
DEFINES += -DJS_THREADSAFE
|
||||
INCLUDES += -I../../dist/$(OBJDIR)/include
|
||||
|
|
@ -32,15 +38,16 @@ OTHER_LIBS += ../../dist/$(OBJDIR)/lib/libnspr21.lib
|
|||
else
|
||||
OTHER_LIBS += -L../../dist/$(OBJDIR)/lib -lnspr21
|
||||
endif
|
||||
else
|
||||
# Look in OBJDIR to find prcpucfg.h
|
||||
INCLUDES += -I$(OBJDIR)
|
||||
endif
|
||||
|
||||
ifdef JS_NO_THIN_LOCKS
|
||||
DEFINES += -DJS_USE_ONLY_NSPR_LOCKS
|
||||
endif
|
||||
|
||||
ifdef JS_HAS_FILE_OBJECT
|
||||
DEFINES += -DJS_HAS_FILE_OBJECT
|
||||
endif
|
||||
|
||||
#
|
||||
# XCFLAGS may be set in the environment or on the gmake command line
|
||||
#
|
||||
|
|
@ -81,6 +88,7 @@ JS_HFILES = \
|
|||
jsfun.h \
|
||||
jsgc.h \
|
||||
jsinterp.h \
|
||||
jslibmath.h \
|
||||
jslock.h \
|
||||
jsmath.h \
|
||||
jsnum.h \
|
||||
|
|
@ -146,14 +154,20 @@ JS_CFILES = \
|
|||
prmjtime.c \
|
||||
$(NULL)
|
||||
|
||||
PREDIRS += fdlibm
|
||||
ifdef JS_LIVECONNECT
|
||||
DIRS = liveconnect
|
||||
DIRS += liveconnect
|
||||
endif
|
||||
|
||||
ifdef JS_PERLCONNECT
|
||||
JS_CFILES += jsperl.c
|
||||
endif
|
||||
|
||||
ifdef JS_HAS_FILE_OBJECT
|
||||
JS_CFILES += jsfile.c
|
||||
JS_HFILES += jsfile.h
|
||||
endif
|
||||
|
||||
LIB_CFILES = $(JS_CFILES)
|
||||
LIB_ASFILES := $(wildcard *_$(OS_ARCH).s)
|
||||
PROG_CFILES = js.c
|
||||
|
|
@ -168,6 +182,12 @@ SHARED_LIBRARY = $(OBJDIR)/libjs.so
|
|||
PROGRAM = $(OBJDIR)/js
|
||||
endif
|
||||
|
||||
ifdef USE_MSVC
|
||||
FDLIBM_LIBRARY = fdlibm.lib
|
||||
else
|
||||
FDLIBM_LIBRARY = libfdm.a
|
||||
endif
|
||||
|
||||
include rules.mk
|
||||
|
||||
MOZ_DEPTH = ../..
|
||||
|
|
@ -177,7 +197,7 @@ nsinstall-target:
|
|||
cd ../../config; $(MAKE) OBJDIR=$(OBJDIR) OBJDIR_NAME=$(OBJDIR)
|
||||
ifdef USE_MSVC
|
||||
$(PROGRAM): $(PROG_OBJS) $(LIBRARY)
|
||||
link.exe -out:"$@" $(EXE_LINK_FLAGS) $?
|
||||
link.exe -out:"$@" $(EXE_LINK_FLAGS) $^
|
||||
else
|
||||
$(PROGRAM): $(PROG_OBJS) $(LIBRARY)
|
||||
$(CC) -o $@ $(CFLAGS) $(PROG_OBJS) $(LIBRARY) $(LDFLAGS) $(OTHER_LIBS)
|
||||
|
|
@ -187,18 +207,21 @@ $(PROGRAM).pure: $(PROG_OBJS) $(LIBRARY)
|
|||
purify $(PUREFLAGS) \
|
||||
$(CC) -o $@ $(PURE_OS_CFLAGS) $(PROG_OBJS) $(LIBRARY) $(LDFLAGS) $(OTHER_LIBS)
|
||||
|
||||
$(HFILES) $(CFILES): $(OBJDIR)/jscpucfg.h
|
||||
ifndef PREBUILT_CPUCFG
|
||||
$(HFILES) $(CFILES): $(OBJDIR)/jsautocfg.h
|
||||
|
||||
ifdef PREBUILT_CPUCFG
|
||||
$(OBJDIR)/jscpucfg.h: jscpucfg.h
|
||||
cp jscpucfg.h $(OBJDIR)
|
||||
else
|
||||
$(OBJDIR)/jscpucfg.h: $(OBJDIR)/jscpucfg
|
||||
$(OBJDIR)/jsautocfg.h: $(OBJDIR)/jscpucfg
|
||||
rm -f $@
|
||||
$(OBJDIR)/jscpucfg > $@
|
||||
|
||||
$(OBJDIR)/jscpucfg: $(OBJDIR)/jscpucfg.o
|
||||
$(CC) -o $@ $(OBJDIR)/jscpucfg.o
|
||||
|
||||
# Look in OBJDIR to find jsautocfg.h
|
||||
INCLUDES += -I$(OBJDIR)
|
||||
|
||||
# Add to TARGETS for clobber rule
|
||||
TARGETS += $(OBJDIR)/jsautocfg.h $(OBJDIR)/jscpucfg $(OBJDIR)/jscpucfg.o
|
||||
endif
|
||||
|
||||
#
|
||||
|
|
|
|||
|
|
@ -1,128 +1,208 @@
|
|||
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
|
||||
<HTML>
|
||||
<HEAD>
|
||||
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
|
||||
<META NAME="GENERATOR" CONTENT="Mozilla/4.5b2 [en] (WinNT; I) [Netscape]">
|
||||
<TITLE>JavaScript Reference Implementation (JSRef) README</TITLE>
|
||||
</HEAD>
|
||||
<BODY>
|
||||
<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="GENERATOR" content="Mozilla/4.5 [en] (WinNT; I) [Netscape]">
|
||||
<title>JavaScript Reference Implementation (JSRef) README</title>
|
||||
</head>
|
||||
<body>
|
||||
|
||||
<H2>
|
||||
Introduction</H2>
|
||||
This is the README file for the <SPAN CLASS=LXRSHORTDESC>JavaScript Reference (JSRef) implementation.</SPAN>
|
||||
It consists of build conventions and instructions, source code conventions,
|
||||
a design walk-through, and a brief file-by-file description of the source.
|
||||
<P><SPAN CLASS=LXRLONGDESC>JSRef builds a library or DLL containing the JavaScript runtime (compiler,
|
||||
interpreter, decompiler, garbage collector, atom manager, standard classes).
|
||||
It then compiles a small "shell" program and links that with the library
|
||||
to make an interpreter that can be used interactively and with test .js
|
||||
files to run scripts. The code has no dependencies on the Navigator.</SPAN>
|
||||
<P><I>Quick start tip</I>: skip to "Using the JS API" below, build js,
|
||||
and play with the object named "it" (start by setting 'it.noisy = true').
|
||||
<H2>
|
||||
Build conventions</H2>
|
||||
<h2>
|
||||
Table of Contents</h2>
|
||||
|
||||
<UL>
|
||||
<LI>
|
||||
On Windows, use MSDEV4.2 or 5.0. Use either the js.mdp project file
|
||||
to build with the IDE or '<TT>nmake -f js.mak</TT>' to build from the command-line</LI>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="#Introduction">Introduction</a></li>
|
||||
|
||||
<LI>
|
||||
On Mac, use CodeWarrior 3.x (<TT>JSRef.mcp</TT> in the <TT>js/src/macbuild</TT>
|
||||
subdirectory)</LI>
|
||||
<li>
|
||||
<a href="#Build">Build conventions (standalone JS engine and shell)</a></li>
|
||||
|
||||
<LI>
|
||||
On Unix, use vendor cc or <A HREF="ftp://prep.ai.mit.edu/pub/gnu">gcc</A>
|
||||
for compiling, and use '<TT>gmake -f Makefile.ref</TT>' for building. To
|
||||
compile optimized code, pass
|
||||
<TT>BUILD_OPT=1</TT> on the nmake/gmake command
|
||||
line or preset it in the environment or makefile. The C preprocessor macro
|
||||
<TT>DEBUG</TT>
|
||||
will be undefined, and <TT>NDEBUG </TT>(archaic Unix-ism for "No Debugging")
|
||||
will be defined. Without <TT>BUILD_OPT</TT>, <TT>DEBUG</TT> is predefined
|
||||
and
|
||||
<TT>NDEBUG</TT> is undefined. On Unix, your own debug flag, <TT>DEBUG_$USER</TT>,
|
||||
will be defined or undefined as <TT>BUILD_OPT</TT> is unset or set.</LI>
|
||||
<li>
|
||||
<a href="#Debugging">Debugging notes</a></li>
|
||||
|
||||
<LI>
|
||||
To add C compiler options from the make command line, set <TT>XCFLAGS=-Dfoo</TT>.
|
||||
To predefine -D or -U options in the makefile, set <TT>DEFINES</TT>. To
|
||||
predefine -I options in the makefile, set INCLUDES.</LI>
|
||||
<li>
|
||||
<a href="#Conventions">Naming and coding conventions</a></li>
|
||||
|
||||
<LI>
|
||||
To turn on GC instrumentation, define <TT>JS_GCMETER</TT>.</LI>
|
||||
<li>
|
||||
<a href="#JSAPI">Using the JS API</a></li>
|
||||
|
||||
<LI>
|
||||
To enable multi-threaded execution, define <TT>JS_THREADSAFE</TT> and flesh
|
||||
out the stubs and required headers in <I>jslock.c</I> and <I>jslock.h</I>.
|
||||
See the JS API docs for more.</LI>
|
||||
<li>
|
||||
<a href="#Design">Design walk-through</a></li>
|
||||
</ul>
|
||||
|
||||
<LI>
|
||||
To turn on the arena package's instrumentation, define <TT>JS_ARENAMETER</TT>.</LI>
|
||||
<h2>
|
||||
<a NAME="Introduction"></a>Introduction</h2>
|
||||
This is the README file for the <span CLASS=LXRSHORTDESC>JavaScript
|
||||
Reference (JSRef) implementation.</span> It consists of build conventions
|
||||
and instructions, source code conventions, a design walk-through, and a
|
||||
brief file-by-file description of the source.
|
||||
<p><span CLASS=LXRLONGDESC>JSRef builds a library or DLL containing the
|
||||
JavaScript runtime (compiler, interpreter, decompiler, garbage collector,
|
||||
atom manager, standard classes). It then compiles a small "shell" program
|
||||
and links that with the library to make an interpreter that can be used
|
||||
interactively and with test .js files to run scripts. The code has
|
||||
no dependencies on the Navigator code.</span>
|
||||
<p><i>Quick start tip</i>: skip to "Using the JS API" below, build the
|
||||
js shell, and play with the object named "it" (start by setting 'it.noisy
|
||||
= true').
|
||||
<h2>
|
||||
<a NAME="Build"></a>Build conventions (standalone JS engine and shell)</h2>
|
||||
These build directions refer only to building the standalone JavaScript
|
||||
engine and shell. To build within the browser, refer to the <a href="http://www.mozilla.org/docs/">build
|
||||
directions</a> on the mozilla.org website.
|
||||
<p>By default, all platforms build a version of the JS engine that is <i>not</i>
|
||||
threadsafe. If you require thread-safety, you must also populate
|
||||
the <tt>mozilla/dist</tt> directory with <a href="http://www.mozilla.org/docs/tplist/catCode/nsprdesc.htm">NSPR</a>
|
||||
headers and libraries. (NSPR implements a portable threading library,
|
||||
among other things. The source is downloadable via <a href="http://www.mozilla.org/cvs.html">CVS</a>
|
||||
from <tt><a href="http://cvs-mirror.mozilla.org/webtools/lxr/source/nsprpub">mozilla/nsprpub</a></tt>.)
|
||||
Next, you must define <tt>JS_THREADSAFE</tt> when building the JS engine,
|
||||
either on the command-line (gmake/nmake) or in a universal header file.
|
||||
<h3>
|
||||
Windows</h3>
|
||||
|
||||
<LI>
|
||||
To turn on the hash table package's metering, define <TT>JS_HASHMETER</TT>.</LI>
|
||||
</UL>
|
||||
<ul>
|
||||
<li>
|
||||
Use MSVC 4.2 or 5.0.</li>
|
||||
|
||||
<H2>
|
||||
Naming and coding conventions</H2>
|
||||
<li>
|
||||
For building from the IDE use <tt>js/src/js.mdp</tt>. (<tt>js.mdp</tt>
|
||||
is an MSVC4.2 project file, but if you load it into MSVC5, it will be converted
|
||||
to the newer project file format.) <font color="#CC0000">NOTE: makefile.win
|
||||
is an nmake file used only for building the JS-engine in the Mozilla browser.
|
||||
Don't attempt to use it to build the standalone JS-engine.</font></li>
|
||||
|
||||
<UL>
|
||||
<LI>
|
||||
Public function names begin with <TT>JS_</TT> followed by capitalized "intercaps",
|
||||
e.g. <TT>JS_NewObject</TT>.</LI>
|
||||
<li>
|
||||
If you prefer to build from the command-line, use '<tt>nmake -f js.mak</tt>'</li>
|
||||
|
||||
<LI>
|
||||
Extern but library-private function names use a <TT>js_</TT> prefix and
|
||||
mixed case, e.g. <TT>js_LookupSymbol</TT>.</LI>
|
||||
<li>
|
||||
Executable shell <tt>js.exe</tt> and runtime library <tt>js32.dll</tt>
|
||||
are created in either <tt>js/src/Debug</tt> or <tt>js/src/Release</tt>.</li>
|
||||
</ul>
|
||||
|
||||
<LI>
|
||||
Most static function names have unprefixed, mixed-case names: <TT>GetChar</TT>.</LI>
|
||||
<h3>
|
||||
Macintosh</h3>
|
||||
|
||||
<LI>
|
||||
<ul>
|
||||
<li>
|
||||
Use CodeWarrior 3.x</li>
|
||||
|
||||
<li>
|
||||
Load the project file <tt>js:src:macbuild:JSRef.mcp </tt>and select "Make"
|
||||
from the menu.</li>
|
||||
</ul>
|
||||
|
||||
<h3>
|
||||
Unix</h3>
|
||||
|
||||
<ul>
|
||||
<li>
|
||||
Use '<tt>gmake -f Makefile.ref</tt>' to build. To compile optimized code,
|
||||
pass <tt>BUILD_OPT=1</tt> on the gmake command line or preset it in the
|
||||
environment or <tt>Makefile.ref</tt>. <font color="#CC0000">NOTE:
|
||||
Do not attempt to use Makefile to build the standalone JavaScript engine.
|
||||
This file is used only for building the JS-engine in the Mozilla browser.</font></li>
|
||||
|
||||
<li>
|
||||
<font color="#000000">Each platform on which JS is built must have a <tt>*.mk</tt>
|
||||
configuration file in the <tt>js/src/config</tt> directory. The configuration
|
||||
file specifies the compiler/linker to be used and allows for customization
|
||||
of command-line options. To date, the build system has been tested
|
||||
on Solaris, AIX, HP/UX, OSF, IRIX, x86 Linux and Windows NT.</font></li>
|
||||
|
||||
<li>
|
||||
<font color="#000000">Most platforms will work with either the vendor compiler
|
||||
</font>or
|
||||
<a href="ftp://prep.ai.mit.edu/pub/gnu">gcc</a>.
|
||||
(Except that HP builds only work using the native compiler. gcc won't
|
||||
link correctly with shared libraries on that platform. If someone
|
||||
knows a way to fix this, <a href="mailto:wynholds@netscape.com">let us
|
||||
know</a>.)</li>
|
||||
|
||||
<li>
|
||||
<font color="#000000">If you define <tt>JS_LIVECONNECT</tt>, gmake will
|
||||
descend into the liveconnect directory and build <a href="http://cvs-mirror.mozilla.org/webtools/lxr/source/js/src/liveconnect/README.html">LiveConnect</a>
|
||||
after building the JS engine.</font></li>
|
||||
|
||||
<li>
|
||||
To build a binary drop (a zip'ed up file of headers, libraries, binaries),
|
||||
check out <tt>mozilla/config</tt> and <tt>mozilla/nsprpub/config</tt>.
|
||||
Use '<tt>gmake -f Makefile.ref nsinstall-target all export ship</tt>'</li>
|
||||
</ul>
|
||||
|
||||
<h2>
|
||||
<a NAME="Debugging"></a>Debugging notes</h2>
|
||||
|
||||
<ul>
|
||||
<li>
|
||||
To turn on GC instrumentation, define <tt>JS_GCMETER</tt>.</li>
|
||||
|
||||
<li>
|
||||
To turn on the arena package's instrumentation, define <tt>JS_ARENAMETER</tt>.</li>
|
||||
|
||||
<li>
|
||||
To turn on the hash table package's metering, define <tt>JS_HASHMETER</tt>.</li>
|
||||
</ul>
|
||||
|
||||
<h2>
|
||||
<a NAME="Conventions"></a>Naming and coding conventions</h2>
|
||||
|
||||
<ul>
|
||||
<li>
|
||||
Public function names begin with <tt>JS_</tt> followed by capitalized "intercaps",
|
||||
e.g. <tt>JS_NewObject</tt>.</li>
|
||||
|
||||
<li>
|
||||
Extern but library-private function names use a <tt>js_</tt> prefix and
|
||||
mixed case, e.g. <tt>js_LookupSymbol</tt>.</li>
|
||||
|
||||
<li>
|
||||
Most static function names have unprefixed, mixed-case names: <tt>GetChar</tt>.</li>
|
||||
|
||||
<li>
|
||||
But static native methods of JS objects have lowercase, underscore-separated
|
||||
or intercaps names, e.g., <TT>str_indexOf</TT>.</LI>
|
||||
or intercaps names, e.g., <tt>str_indexOf</tt>.</li>
|
||||
|
||||
<LI>
|
||||
<li>
|
||||
And library-private and static data use underscores, not intercaps (but
|
||||
library-private data do use a <TT>js_</TT> prefix).</LI>
|
||||
library-private data do use a <tt>js_</tt> prefix).</li>
|
||||
|
||||
<LI>
|
||||
Scalar type names are lowercase and js-prefixed: <TT>jsdouble</TT>.</LI>
|
||||
<li>
|
||||
Scalar type names are lowercase and js-prefixed: <tt>jsdouble</tt>.</li>
|
||||
|
||||
<LI>
|
||||
Aggregate type names are JS-prefixed and mixed-case: <TT>JSObject.</TT></LI>
|
||||
<li>
|
||||
Aggregate type names are JS-prefixed and mixed-case: <tt>JSObject.</tt></li>
|
||||
|
||||
<LI>
|
||||
Macros are generally <TT>ALL_CAPS </TT>and underscored, to call out potential
|
||||
<li>
|
||||
Macros are generally <tt>ALL_CAPS </tt>and underscored, to call out potential
|
||||
side effects, multiple uses of a formal argument, etc. - Four spaces of
|
||||
indentation per statement nesting level.</LI>
|
||||
indentation per statement nesting level.</li>
|
||||
|
||||
<LI>
|
||||
<li>
|
||||
Tabs are taken to be eight spaces, and an Emacs magic comment at the top
|
||||
of each file tries to help. If you're using MSVC or similar, you'll want
|
||||
to set tab width to 8, or convert these files to be space-filled.</LI>
|
||||
to set tab width to 8, or convert these files to be space-filled.</li>
|
||||
|
||||
<LI>
|
||||
DLL entry points have their return type expanded within a <TT>JS_PUBLIC_API()</TT>
|
||||
<li>
|
||||
DLL entry points have their return type expanded within a <tt>JS_PUBLIC_API()</tt>
|
||||
macro call, to get the right Windows secret type qualifiers in the right
|
||||
places for both 16- and 32-bit builds.</LI>
|
||||
places for both 16- and 32-bit builds.</li>
|
||||
|
||||
<LI>
|
||||
<li>
|
||||
Callback functions that might be called from a DLL are similarly macroized
|
||||
with <TT>JS_STATIC_DLL_CALLBACK</TT> (if the function otherwise would be
|
||||
static to hide its name) or <TT>JS_DLL_CALLBACK</TT> (this macro takes
|
||||
with <tt>JS_STATIC_DLL_CALLBACK</tt> (if the function otherwise would be
|
||||
static to hide its name) or <tt>JS_DLL_CALLBACK</tt> (this macro takes
|
||||
no type argument; it should be used after the return type and before the
|
||||
function name).</LI>
|
||||
</UL>
|
||||
function name).</li>
|
||||
</ul>
|
||||
|
||||
<H2>
|
||||
Using the JS API</H2>
|
||||
<h2>
|
||||
<a NAME="JSAPI"></a>Using the JS API</h2>
|
||||
|
||||
<H4>
|
||||
Starting up</H4>
|
||||
<h4>
|
||||
Starting up</h4>
|
||||
|
||||
<PRE><TT> /*
|
||||
<pre><tt> /*
|
||||
* Tune this to avoid wasting space for shallow stacks, while saving on
|
||||
* malloc overhead/fragmentation for deep or highly-variable stacks.
|
||||
*/
|
||||
|
|
@ -147,12 +227,12 @@ Starting up</H4>
|
|||
JSObject *globalObj;
|
||||
|
||||
globalObj = JS_NewObject(cx, &my_global_class, 0, 0);
|
||||
JS_InitStandardClasses(cx, globalObj);</TT></PRE>
|
||||
JS_InitStandardClasses(cx, globalObj);</tt></pre>
|
||||
|
||||
<H4>
|
||||
Defining objects and properties</H4>
|
||||
<h4>
|
||||
Defining objects and properties</h4>
|
||||
|
||||
<PRE><TT> /* Statically initialize a class to make "one-off" objects. */
|
||||
<pre><tt> /* Statically initialize a class to make "one-off" objects. */
|
||||
JSClass my_class = {
|
||||
"MyClass",
|
||||
|
||||
|
|
@ -214,12 +294,12 @@ Defining objects and properties</H4>
|
|||
}
|
||||
}
|
||||
return JS_TRUE;
|
||||
}</TT></PRE>
|
||||
}</tt></pre>
|
||||
|
||||
<H4>
|
||||
Defining functions</H4>
|
||||
<h4>
|
||||
Defining functions</h4>
|
||||
|
||||
<PRE><TT> /* Define a bunch of native functions first: */
|
||||
<pre><tt> /* Define a bunch of native functions first: */
|
||||
static JSBool
|
||||
my_abs(JSContext *cx, JSObject *obj, uintN argc, jsval *argv, jsval *rval)
|
||||
{
|
||||
|
|
@ -251,12 +331,12 @@ Defining functions</H4>
|
|||
* a prototype object, the methods will apply to all instances past and
|
||||
* future of the prototype's class (see below for classes).
|
||||
*/
|
||||
JS_DefineFunctions(cx, globalObj, my_functions);</TT></PRE>
|
||||
JS_DefineFunctions(cx, globalObj, my_functions);</tt></pre>
|
||||
|
||||
<H4>
|
||||
Defining classes</H4>
|
||||
<h4>
|
||||
Defining classes</h4>
|
||||
|
||||
<PRE><TT> /*
|
||||
<pre><tt> /*
|
||||
* This pulls together the above API elements by defining a constructor
|
||||
* function, a prototype object, and properties of the prototype and of
|
||||
* the constructor, all with one API call.
|
||||
|
|
@ -287,12 +367,12 @@ Defining classes</H4>
|
|||
my_props, my_methods,
|
||||
|
||||
/* class constructor properties and methods */
|
||||
my_static_props, my_static_methods);</TT></PRE>
|
||||
my_static_props, my_static_methods);</tt></pre>
|
||||
|
||||
<H4>
|
||||
Running scripts</H4>
|
||||
<h4>
|
||||
Running scripts</h4>
|
||||
|
||||
<PRE><TT> /* These should indicate source location for diagnostics. */
|
||||
<pre><tt> /* These should indicate source location for diagnostics. */
|
||||
char *filename;
|
||||
uintN lineno;
|
||||
|
||||
|
|
@ -320,12 +400,12 @@ Running scripts</H4>
|
|||
|
||||
ok = JS_ValueToNumber(cx, rval, &d);
|
||||
. . .
|
||||
}</TT></PRE>
|
||||
}</tt></pre>
|
||||
|
||||
<H4>
|
||||
Calling functions</H4>
|
||||
<h4>
|
||||
Calling functions</h4>
|
||||
|
||||
<PRE><TT> /* Call a global function named "foo" that takes no arguments. */
|
||||
<pre><tt> /* Call a global function named "foo" that takes no arguments. */
|
||||
ok = JS_CallFunctionName(cx, globalObj, "foo", 0, 0, &rval);
|
||||
|
||||
jsval argv[2];
|
||||
|
|
@ -333,43 +413,43 @@ Calling functions</H4>
|
|||
/* Call a function in obj's scope named "method", passing two arguments. */
|
||||
argv[0] = . . .;
|
||||
argv[1] = . . .;
|
||||
ok = JS_CallFunctionName(cx, obj, "method", 2, argv, &rval);</TT></PRE>
|
||||
ok = JS_CallFunctionName(cx, obj, "method", 2, argv, &rval);</tt></pre>
|
||||
|
||||
<H4>
|
||||
Shutting down</H4>
|
||||
<h4>
|
||||
Shutting down</h4>
|
||||
|
||||
<PRE><TT> /* For each context you've created: */
|
||||
<pre><tt> /* For each context you've created: */
|
||||
JS_DestroyContext(cx);
|
||||
|
||||
/* And finally: */
|
||||
JS_Finish(rt);</TT></PRE>
|
||||
JS_Finish(rt);</tt></pre>
|
||||
|
||||
<H4>
|
||||
Debugging API</H4>
|
||||
See the<TT> trap, untrap, watch, unwatch, line2pc</TT>, and <TT>pc2line</TT>
|
||||
commands in <TT>js.c</TT>. Also the (scant) comments in <I>jsdbgapi.h</I>.
|
||||
<H2>
|
||||
Design walk-through</H2>
|
||||
<h4>
|
||||
Debugging API</h4>
|
||||
See the<tt> trap, untrap, watch, unwatch, line2pc</tt>, and <tt>pc2line</tt>
|
||||
commands in <tt>js.c</tt>. Also the (scant) comments in <i>jsdbgapi.h</i>.
|
||||
<h2>
|
||||
<a NAME="Design"></a>Design walk-through</h2>
|
||||
This section must be brief for now -- it could easily turn into a book.
|
||||
<H4>
|
||||
JS "JavaScript Proper"</H4>
|
||||
<h4>
|
||||
JS "JavaScript Proper"</h4>
|
||||
JS modules declare and implement the JavaScript compiler, interpreter,
|
||||
decompiler, GC and atom manager, and standard classes.
|
||||
<P>JavaScript uses untyped bytecode and runtime type tagging of data values.
|
||||
The <TT>jsval</TT> type is a signed machine word that contains either a
|
||||
<p>JavaScript uses untyped bytecode and runtime type tagging of data values.
|
||||
The <tt>jsval</tt> type is a signed machine word that contains either a
|
||||
signed integer value (if the low bit is set), or a type-tagged pointer
|
||||
or boolean value (if the low bit is clear). Tagged pointers all refer to
|
||||
8-byte-aligned things in the GC heap.
|
||||
<P>Objects consist of a possibly shared structural description, called
|
||||
<p>Objects consist of a possibly shared structural description, called
|
||||
the map or scope; and unshared property values in a vector, called the
|
||||
slots. Object properties are associated with nonnegative integers stored
|
||||
in <TT>jsval</TT>'s, or with atoms (unique string descriptors) if named
|
||||
in <tt>jsval</tt>'s, or with atoms (unique string descriptors) if named
|
||||
by an identifier or a non-integral index expression.
|
||||
<P>Scripts contain bytecode, source annotations, and a pool of string,
|
||||
<p>Scripts contain bytecode, source annotations, and a pool of string,
|
||||
number, and identifier literals. Functions are objects that extend scripts
|
||||
or native functions with formal parameters, a literal syntax, and a distinct
|
||||
primitive type ("function").
|
||||
<P>The compiler consists of a recursive-descent parser and a random-logic
|
||||
<p>The compiler consists of a recursive-descent parser and a random-logic
|
||||
rather than table-driven lexical scanner. Semantic and lexical feedback
|
||||
are used to disambiguate hard cases such as missing semicolons, assignable
|
||||
expressions ("lvalues" in C parlance), etc. The parser generates bytecode
|
||||
|
|
@ -381,88 +461,89 @@ All state associated with an interpreter instance is passed through formal
|
|||
parameters to the interpreter entry point; most implicit state is collected
|
||||
in a type named JSContext. Therefore, all API and almost all other functions
|
||||
in JSRef take a JSContext pointer as their first argument.
|
||||
<P>The decompiler translates postfix bytecode into infix source by consulting
|
||||
<p>The decompiler translates postfix bytecode into infix source by consulting
|
||||
a separate byte-sized code, called source notes, to disambiguate bytecodes
|
||||
that result from more than one grammatical production.
|
||||
<P>The GC is a mark-and-sweep, non-conservative (perfect) collector. It
|
||||
<p>The GC is a mark-and-sweep, non-conservative (perfect) collector. It
|
||||
can allocate only fixed-sized things -- the current size is two machine
|
||||
words. It is used to hold JS object and string descriptors (but not property
|
||||
lists or string bytes), and double-precision floating point numbers. It
|
||||
runs automatically only when maxbytes (as passed to <TT>JS_Init()</TT>)
|
||||
runs automatically only when maxbytes (as passed to <tt>JS_Init()</tt>)
|
||||
bytes of GC things have been allocated and another thing-allocation request
|
||||
is made. JS API users should call <TT>JS_GC()</TT> or <TT>JS_MaybeGC()</TT>
|
||||
is made. JS API users should call <tt>JS_GC()</tt> or <tt>JS_MaybeGC()</tt>
|
||||
between script executions or from the branch callback, as often as necessary.
|
||||
<P>An important point about the GC's "perfection": you must add roots for
|
||||
<p>An important point about the GC's "perfection": you must add roots for
|
||||
new objects created by your native methods if you store references to them
|
||||
into a non-JS structure in the malloc heap or in static data. Also, if
|
||||
you make a new object in a native method, but do not store it through the
|
||||
<TT>rval</TT> result parameter (see math_abs in the "Using the JS API"
|
||||
section above) so that it is in a known root, the object is guaranteed
|
||||
to survive only until another new object is created. Either lock the first
|
||||
new object when making two in a row, or store it in a root you've added,
|
||||
or store it via rval.
|
||||
<P>The atom manager consists of a hash table associating strings uniquely
|
||||
<tt>rval</tt>
|
||||
result parameter (see math_abs in the "Using the JS API" section above)
|
||||
so that it is in a known root, the object is guaranteed to survive only
|
||||
until another new object is created. Either lock the first new object when
|
||||
making two in a row, or store it in a root you've added, or store it via
|
||||
rval.
|
||||
<p>The atom manager consists of a hash table associating strings uniquely
|
||||
with scanner/parser information such as keyword type, index in script or
|
||||
function literal pool, etc. Atoms play three roles in JSRef: as literals
|
||||
referred to by unaligned 16-bit immediate bytecode operands, as unique
|
||||
string descriptors for efficient property name hashing, and as members
|
||||
of the root GC set for perfect GC. This design therefore requires atoms
|
||||
to be manually reference counted, from script literal pools (<TT>JSAtomMap</TT>)
|
||||
and object symbol (<TT>JSSymbol</TT>) entry keys.
|
||||
<P>Native objects and methods for arrays, booleans, dates, functions, numbers,
|
||||
to be manually reference counted, from script literal pools (<tt>JSAtomMap</tt>)
|
||||
and object symbol (<tt>JSSymbol</tt>) entry keys.
|
||||
<p>Native objects and methods for arrays, booleans, dates, functions, numbers,
|
||||
and strings are implemented using the JS API and certain internal interfaces
|
||||
used as "fast paths".
|
||||
<P>In general, errors are signaled by false or unoverloaded-null return
|
||||
values, and are reported using <TT>JS_ReportError()</TT> or one of its
|
||||
<p>In general, errors are signaled by false or unoverloaded-null return
|
||||
values, and are reported using <tt>JS_ReportError()</tt> or one of its
|
||||
variants by the lowest level in order to provide the most detail. Client
|
||||
code can substitute its own error reporting function and suppress errors,
|
||||
or reflect them into Java or some other runtime system as exceptions, GUI
|
||||
dialogs, etc..
|
||||
<H2>
|
||||
File walk-through</H2>
|
||||
<h2>
|
||||
File walk-through (BADLY OUT OF DATE!)</h2>
|
||||
|
||||
<H4>
|
||||
jsapi.c, jsapi.h</H4>
|
||||
<h4>
|
||||
jsapi.c, jsapi.h</h4>
|
||||
The public API to be used by almost all client code. If your client
|
||||
code can't make do with <TT>jsapi.h</TT>, and must reach into a friend
|
||||
or private js* file, please let us know so we can extend <TT>jsapi.h</TT>
|
||||
code can't make do with <tt>jsapi.h</tt>, and must reach into a friend
|
||||
or private js* file, please let us know so we can extend <tt>jsapi.h</tt>
|
||||
to include what you need in a fashion that we can support over the long
|
||||
run.
|
||||
<H4>
|
||||
jspubtd.h, jsprvtd.h</H4>
|
||||
<h4>
|
||||
jspubtd.h, jsprvtd.h</h4>
|
||||
These files exist to group struct and scalar typedefs so they can be used
|
||||
everywhere without dragging in struct definitions from N different files.
|
||||
The <TT>jspubtd.h</TT> file contains public typedefs, and is included by
|
||||
<TT>jsapi.h</TT>. The <TT>jsprvtd.h</TT> file contains private typedefs
|
||||
and is included by various .h files that need type names, but not type
|
||||
sizes or declarations.
|
||||
<H4>
|
||||
jsdbgapi.c, jsdbgapi.h</H4>
|
||||
The <tt>jspubtd.h</tt> file contains public typedefs, and is included by
|
||||
<tt>jsapi.h</tt>.
|
||||
The <tt>jsprvtd.h</tt> file contains private typedefs and is included by
|
||||
various .h files that need type names, but not type sizes or declarations.
|
||||
<h4>
|
||||
jsdbgapi.c, jsdbgapi.h</h4>
|
||||
The Debugging API, still very much under development. Provided so far:
|
||||
<UL>
|
||||
<LI>
|
||||
<ul>
|
||||
<li>
|
||||
Traps, with which breakpoints, single-stepping, step over, step out, and
|
||||
so on can be implemented. The debugger will have to consult jsopcode.def
|
||||
on its own to figure out where to plant trap instructions to implement
|
||||
functions like step out, but a future jsdbgapi.h will provide convenience
|
||||
interfaces to do these things. At most one trap per bytecode can be set.
|
||||
When a script (<TT>JSScript</TT>) is destroyed, all traps set in its bytecode
|
||||
are cleared.</LI>
|
||||
When a script (<tt>JSScript</tt>) is destroyed, all traps set in its bytecode
|
||||
are cleared.</li>
|
||||
|
||||
<LI>
|
||||
<li>
|
||||
Watchpoints, for intercepting set operations on properties and running
|
||||
a debugger-supplied function that receives the old value and a pointer
|
||||
to the new one, which it can use to modify the new value being set.</LI>
|
||||
to the new one, which it can use to modify the new value being set.</li>
|
||||
|
||||
<LI>
|
||||
<li>
|
||||
Line number to PC and back mapping functions. The line-to-PC direction
|
||||
"rounds" toward the next bytecode generated from a line greater than or
|
||||
equal to the input line, and may return the PC of a for-loop update part,
|
||||
if given the line number of the loop body's closing brace. Any line after
|
||||
the last one in a script or function maps to a PC one byte beyond the last
|
||||
bytecode in the script. An example, from perfect.js:</LI>
|
||||
bytecode in the script. An example, from perfect.js:</li>
|
||||
|
||||
<PRE><TT>14 function perfect(n)
|
||||
<pre><tt>14 function perfect(n)
|
||||
15 {
|
||||
16 print("The perfect numbers up to " + n + " are:");
|
||||
17
|
||||
|
|
@ -482,10 +563,10 @@ bytecode in the script. An example, from perfect.js:</LI>
|
|||
31 }
|
||||
32 delete sumOfDivisors;
|
||||
33 print("That's all.");
|
||||
34 }</TT></PRE>
|
||||
34 }</tt></pre>
|
||||
The line number to PC and back mappings can be tested using the js program
|
||||
with the following script:
|
||||
<PRE><TT> load("perfect.js")
|
||||
<pre><tt> load("perfect.js")
|
||||
print(perfect)
|
||||
dis(perfect)
|
||||
|
||||
|
|
@ -494,9 +575,9 @@ with the following script:
|
|||
var pc = line2pc(perfect,ln)
|
||||
var ln2 = pc2line(perfect,pc)
|
||||
print("\tline " + ln + " => pc " + pc + " => line " + ln2)
|
||||
}</TT></PRE>
|
||||
}</tt></pre>
|
||||
The result of the for loop over lines 0 to 40 inclusive is:
|
||||
<PRE><TT> line 0 => pc 0 => line 16
|
||||
<pre><tt> line 0 => pc 0 => line 16
|
||||
line 1 => pc 0 => line 16
|
||||
line 2 => pc 0 => line 16
|
||||
line 3 => pc 0 => line 16
|
||||
|
|
@ -536,138 +617,139 @@ The result of the for loop over lines 0 to 40 inclusive is:
|
|||
line 37 => pc 172 => line 33
|
||||
line 38 => pc 172 => line 33
|
||||
line 39 => pc 172 => line 33
|
||||
line 40 => pc 172 => line 33</TT></PRE>
|
||||
</UL>
|
||||
line 40 => pc 172 => line 33</tt></pre>
|
||||
</ul>
|
||||
|
||||
<H4>
|
||||
jsconfig.h</H4>
|
||||
Various configuration macros defined as 0 or 1 depending on how <TT>JS_VERSION</TT>
|
||||
<h4>
|
||||
jsconfig.h</h4>
|
||||
Various configuration macros defined as 0 or 1 depending on how <tt>JS_VERSION</tt>
|
||||
is defined (as 10 for JavaScript 1.0, 11 for JavaScript 1.1, etc.). Not
|
||||
all macros are tested around related code yet. In particular, JS 1.0 support
|
||||
is missing from JSRef. JS 1.2 support will appear in a future JSRef release.
|
||||
<BR>
|
||||
<H4>
|
||||
js.c</H4>
|
||||
<br>
|
||||
<h4>
|
||||
js.c</h4>
|
||||
The "JS shell", a simple interpreter program that uses the JS API and more
|
||||
than a few internal interfaces (some of these internal interfaces could
|
||||
be replaced by <TT>jsapi.h</TT> calls). The js program built from this
|
||||
be replaced by <tt>jsapi.h</tt> calls). The js program built from this
|
||||
source provides a test vehicle for evaluating scripts and calling functions,
|
||||
trying out new debugger primitives, etc.
|
||||
<H4>
|
||||
jsarray.*, jsbool.*, jdsdate.*, jsfun.*, jsmath.*, jsnum.*, jsstr.*</H4>
|
||||
<h4>
|
||||
jsarray.*, jsbool.*, jdsdate.*, jsfun.*, jsmath.*, jsnum.*, jsstr.*</h4>
|
||||
These file pairs implement the standard classes and (where they exist)
|
||||
their underlying primitive types. They have similar structure, generally
|
||||
starting with class definitions and continuing with internal constructors,
|
||||
finalizers, and helper functions.
|
||||
<H4>
|
||||
jsobj.*, jsscope.*</H4>
|
||||
<h4>
|
||||
jsobj.*, jsscope.*</h4>
|
||||
These two pairs declare and implement the JS object system. All of the
|
||||
following happen here:
|
||||
<UL>
|
||||
<LI>
|
||||
creating objects by class and prototype, and finalizing objects;</LI>
|
||||
<ul>
|
||||
<li>
|
||||
creating objects by class and prototype, and finalizing objects;</li>
|
||||
|
||||
<LI>
|
||||
defining, looking up, getting, setting, and deleting properties;</LI>
|
||||
<li>
|
||||
defining, looking up, getting, setting, and deleting properties;</li>
|
||||
|
||||
<LI>
|
||||
creating and destroying properties and binding names to them.</LI>
|
||||
</UL>
|
||||
The details of an object map (scope) are mostly hidden in <TT>jsscope.[ch]</TT>,
|
||||
<li>
|
||||
creating and destroying properties and binding names to them.</li>
|
||||
</ul>
|
||||
The details of an object map (scope) are mostly hidden in <tt>jsscope.[ch]</tt>,
|
||||
where scopes start out as linked lists of symbols, and grow after some
|
||||
threshold into PR hash tables.
|
||||
<H4>
|
||||
jsatom.c, jsatom.h</H4>
|
||||
<h4>
|
||||
jsatom.c, jsatom.h</h4>
|
||||
The atom manager. Contains well-known string constants, their atoms, the
|
||||
global atom hash table and related state, the js_Atomize() function that
|
||||
turns a counted string of bytes into an atom, and literal pool (<TT>JSAtomMap</TT>)
|
||||
turns a counted string of bytes into an atom, and literal pool (<tt>JSAtomMap</tt>)
|
||||
methods.
|
||||
<H4>
|
||||
jsgc.c, jsgc.h</H4>
|
||||
<h4>
|
||||
jsgc.c, jsgc.h</h4>
|
||||
[TBD]
|
||||
<H4>
|
||||
jsinterp.*, jscntxt.*</H4>
|
||||
<h4>
|
||||
jsinterp.*, jscntxt.*</h4>
|
||||
The bytecode interpreter, and related functions such as Call and AllocStack,
|
||||
live in <I>jsinterp.c</I>. The JSContext constructor and destructor are
|
||||
factored out into <I>jscntxt.c</I> for minimal linking when the compiler
|
||||
live in <i>jsinterp.c</i>. The JSContext constructor and destructor are
|
||||
factored out into <i>jscntxt.c</i> for minimal linking when the compiler
|
||||
part of JS is split from the interpreter part into a separate program.
|
||||
<H4>
|
||||
jsemit.*, jsopcode.tbl, jsopcode.*, jsparse.*, jsscan.*, jsscript.*</H4>
|
||||
Compiler and decompiler modules. The <I>jsopcode.tbl</I> file is a C preprocessor
|
||||
<h4>
|
||||
jsemit.*, jsopcode.tbl, jsopcode.*, jsparse.*, jsscan.*, jsscript.*</h4>
|
||||
Compiler and decompiler modules. The <i>jsopcode.tbl</i> file is a C preprocessor
|
||||
source that defines almost everything there is to know about JS bytecodes.
|
||||
See its major comment for how to use it. For now, a debugger will use it
|
||||
and its dependents such as <I>jsopcode.h</I> directly, but over time we
|
||||
intend to extend <I>jsdbgapi.h</I> to hide uninteresting details and provide
|
||||
and its dependents such as <i>jsopcode.h</i> directly, but over time we
|
||||
intend to extend <i>jsdbgapi.h</i> to hide uninteresting details and provide
|
||||
conveniences. The code generator is split across paragraphs of code in
|
||||
<I>jsparse.c</I>, and the utility methods called on <TT>JSCodeGenerator</TT>
|
||||
appear in <I>jsemit.c</I>. Source notes generated by <I>jsparse.c</I> and
|
||||
<I>jsemit.c</I> are used in <I>jsscript.c</I> to map line number to program
|
||||
counter and back.
|
||||
<H4>
|
||||
jstypes.h, jslog2.c</H4>
|
||||
<i>jsparse.c</i>,
|
||||
and the utility methods called on <tt>JSCodeGenerator</tt> appear in <i>jsemit.c</i>.
|
||||
Source notes generated by <i>jsparse.c</i> and
|
||||
<i>jsemit.c</i> are used
|
||||
in <i>jsscript.c</i> to map line number to program counter and back.
|
||||
<h4>
|
||||
jstypes.h, jslog2.c</h4>
|
||||
Fundamental representation types and utility macros. This file alone among
|
||||
all .h files in JSRef must be included first by .c files. It is not nested
|
||||
in .h files, as other prerequisite .h files generally are, since it is
|
||||
also a direct dependency of most .c files and would be over-included if
|
||||
nested in addition to being directly included. The one "not-quite-a-macro
|
||||
macro" is the <TT>JS_CeilingLog2()</TT> function in <I>jslog2.c</I>.
|
||||
<H4>
|
||||
jsarena.c, jsarena.h</H4>
|
||||
macro" is the <tt>JS_CeilingLog2()</tt> function in <i>jslog2.c</i>.
|
||||
<h4>
|
||||
jsarena.c, jsarena.h</h4>
|
||||
Last-In-First-Out allocation macros that amortize malloc costs and allow
|
||||
for en-masse freeing. See the paper mentioned in prarena.h's major comment.
|
||||
<H4>
|
||||
jsutil.c, jsutil.h</H4>
|
||||
The <TT>JS_ASSERT</TT> macro is used throughout JSRef source as a proof
|
||||
<h4>
|
||||
jsutil.c, jsutil.h</h4>
|
||||
The <tt>JS_ASSERT</tt> macro is used throughout JSRef source as a proof
|
||||
device to make invariants and preconditions clear to the reader, and to
|
||||
hold the line during maintenance and evolution against regressions or violations
|
||||
of assumptions that it would be too expensive to test unconditionally at
|
||||
run-time. Certain assertions are followed by run-time tests that cope with
|
||||
assertion failure, but only where I'm too smart or paranoid to believe
|
||||
the assertion will never fail...
|
||||
<H4>
|
||||
jsclist.h</H4>
|
||||
<h4>
|
||||
jsclist.h</h4>
|
||||
Doubly-linked circular list struct and macros.
|
||||
<H4>
|
||||
jscpucfg.c</H4>
|
||||
This standalone program generates <I>jscpucfg.h</I>, a header file containing
|
||||
<h4>
|
||||
jscpucfg.c</h4>
|
||||
This standalone program generates <i>jscpucfg.h</i>, a header file containing
|
||||
bytes per word and other constants that depend on CPU architecture and
|
||||
C compiler type model. It tries to discover most of these constants by
|
||||
running its own experiments on the build host, so if you are cross-compiling,
|
||||
beware.
|
||||
<H4>
|
||||
prdtoa.c, prdtoa.h</H4>
|
||||
<h4>
|
||||
prdtoa.c, prdtoa.h</h4>
|
||||
David Gay's portable double-precision floating point to string conversion
|
||||
code, with Permission To Use notice included.
|
||||
<H4>
|
||||
prhash.c, prhash.h</H4>
|
||||
<h4>
|
||||
prhash.c, prhash.h</h4>
|
||||
Portable, extensible hash tables. These use multiplicative hash for strength
|
||||
reduction over division hash, yet with very good key distribution over
|
||||
power of two table sizes. Collisions resolve via chaining, so each entry
|
||||
burns a malloc and can fragment the heap.
|
||||
<H4>
|
||||
prlong.c, prlong.h</H4>
|
||||
<h4>
|
||||
prlong.c, prlong.h</h4>
|
||||
64-bit integer emulation, and compatible macros that use C's long long
|
||||
type where it exists (my last company mapped long long to a 128-bit type,
|
||||
but no real architecture does 128-bit ints yet).
|
||||
<H4>
|
||||
jsosdep.h</H4>
|
||||
<h4>
|
||||
jsosdep.h</h4>
|
||||
Annoying OS dependencies rationalized into a few "feature-test" macros
|
||||
such as <TT>JS_HAVE_LONG_LONG</TT>.
|
||||
<H4>
|
||||
jsprf.*</H4>
|
||||
such as <tt>JS_HAVE_LONG_LONG</tt>.
|
||||
<h4>
|
||||
jsprf.*</h4>
|
||||
Portable, buffer-overrun-resistant sprintf and friends. For no good reason
|
||||
save lack of time, the %e, %f, and %g formats cause your system's native
|
||||
sprintf, rather than <TT>JS_dtoa()</TT>, to be used. This bug doesn't affect
|
||||
JSRef, because it uses its own <TT>JS_dtoa()</TT> call in <I>jsnum.c</I>
|
||||
sprintf, rather than <tt>JS_dtoa()</tt>, to be used. This bug doesn't affect
|
||||
JSRef, because it uses its own <tt>JS_dtoa()</tt> call in <i>jsnum.c</i>
|
||||
to convert from double to string, but it's a bug that we'll fix later,
|
||||
and one you should be aware of if you intend to use a <TT>JS_*printf()</TT>
|
||||
and one you should be aware of if you intend to use a <tt>JS_*printf()</tt>
|
||||
function with your own floating type arguments - various vendor sprintf's
|
||||
mishandle NaN, +/-Inf, and some even print normal floating values inaccurately.
|
||||
<H4>
|
||||
prmjtime.c, prmjtime.h</H4>
|
||||
<h4>
|
||||
prmjtime.c, prmjtime.h</h4>
|
||||
Time functions. These interfaces are named in a way that makes local vs.
|
||||
universal time confusion likely. Caveat emptor, and we're working on it.
|
||||
To make matters worse, Java (and therefore JavaScript) uses "local" time
|
||||
numbers (offsets from the epoch) in its Date class.
|
||||
</BODY>
|
||||
</HTML>
|
||||
</body>
|
||||
</html>
|
||||
|
|
|
|||
|
|
@ -0,0 +1,12 @@
|
|||
mozilla/js/src/*
|
||||
mozilla/js/src/config/*
|
||||
mozilla/js/src/fdlibm/*
|
||||
mozilla/js/src/liveconnect/*
|
||||
mozilla/js/src/liveconnect/_jni/*
|
||||
mozilla/js/src/liveconnect/classes/*
|
||||
mozilla/js/src/liveconnect/classes/netscape/*
|
||||
mozilla/js/src/liveconnect/classes/netscape/javascript/*
|
||||
mozilla/js/src/liveconnect/config/*
|
||||
mozilla/js/src/liveconnect/macbuild/*
|
||||
mozilla/js/src/liveconnect/macbuild/JavaSession/*
|
||||
mozilla/js/src/macbuild/*
|
||||
|
|
@ -40,10 +40,8 @@ else
|
|||
INSTALL = $(DEPTH)/../../dist/$(OBJDIR)/bin/nsinstall
|
||||
endif
|
||||
|
||||
include $(DEPTH)/config/$(OS_CONFIG).mk
|
||||
|
||||
ifdef BUILD_OPT
|
||||
OPTIMIZER += -O
|
||||
OPTIMIZER = -O
|
||||
DEFINES += -UDEBUG -DNDEBUG -UDEBUG_$(shell whoami)
|
||||
OBJDIR_TAG = _OPT
|
||||
else
|
||||
|
|
@ -56,6 +54,8 @@ DEFINES += -DDEBUG -DDEBUG_$(shell whoami)
|
|||
OBJDIR_TAG = _DBG
|
||||
endif
|
||||
|
||||
include $(DEPTH)/config/$(OS_CONFIG).mk
|
||||
|
||||
# Name of the binary code directories
|
||||
OBJDIR = $(OS_CONFIG)$(OBJDIR_TAG).OBJ
|
||||
VPATH = $(OBJDIR)
|
||||
|
|
|
|||
|
|
@ -21,6 +21,8 @@
|
|||
|
||||
CC = xlC_r
|
||||
CCC = xlC_r
|
||||
CFLAGS += -qarch=com -qnoansialias -qinline+$(INLINES) -DXP_UNIX -DAIX -DAIXV3 -DSYSV
|
||||
OPTIMIZER = -O
|
||||
|
||||
RANLIB = ranlib
|
||||
|
||||
|
|
@ -31,12 +33,10 @@ CPU_ARCH = rs6000
|
|||
GFX_ARCH = x
|
||||
INLINES = js_compare_and_swap:js_fast_lock1:js_fast_unlock1:js_lock_get_slot:js_lock_set_slot:js_lock_scope1
|
||||
|
||||
OS_CFLAGS = -qarch=com -qinline+$(INLINES) -DXP_UNIX -DAIX -DAIXV3 -DSYSV
|
||||
OS_LIBS = -lbsd -lsvld -lm
|
||||
XLDFLAGS += -lbsd -lsvld -lm -lc_r
|
||||
#-lpthreads -lc_r
|
||||
|
||||
MKSHLIB = $(LD) -brtl -bM:SRE -bnoentry -bexpall -berok
|
||||
XLDFLAGS += -lc
|
||||
|
||||
ifdef JS_THREADSAFE
|
||||
XLDFLAGS += -ldl
|
||||
|
|
|
|||
|
|
@ -35,7 +35,7 @@ MKSHLIB = $(LD) -b
|
|||
CPU_ARCH = hppa
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DHPUX -DSYSV -D_SVID_GETTOD
|
||||
OS_CFLAGS = -DXP_UNIX -DHPUX -DSYSV
|
||||
OS_LIBS = -ldld
|
||||
|
||||
ifeq ($(OS_RELEASE),B.10)
|
||||
|
|
|
|||
|
|
@ -0,0 +1,53 @@
|
|||
#
|
||||
# The contents of this file are subject to the Netscape Public License
|
||||
# Version 1.0 (the "NPL"); you may not use this file except in
|
||||
# compliance with the NPL. You may obtain a copy of the NPL at
|
||||
# http://www.mozilla.org/NPL/
|
||||
#
|
||||
# Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
# for the specific language governing rights and limitations under the
|
||||
# NPL.
|
||||
#
|
||||
# The Initial Developer of this code under the NPL is Netscape
|
||||
# Communications Corporation. Portions created by Netscape are
|
||||
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
|
||||
# Reserved.
|
||||
#
|
||||
|
||||
#
|
||||
# Config stuff for HPUX
|
||||
#
|
||||
|
||||
# CC = gcc
|
||||
# CCC = g++
|
||||
# CFLAGS += -Wall -Wno-format -fPIC
|
||||
|
||||
CC = cc -Ae +Z
|
||||
CCC = CC -Ae +a1 +eh +Z
|
||||
|
||||
RANLIB = echo
|
||||
MKSHLIB = $(LD) -b
|
||||
|
||||
#.c.o:
|
||||
# $(CC) -c -MD $*.d $(CFLAGS) $<
|
||||
|
||||
CPU_ARCH = hppa
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DHPUX -DSYSV
|
||||
OS_LIBS = -ldld
|
||||
|
||||
ifeq ($(OS_RELEASE),B.10)
|
||||
PLATFORM_FLAGS += -DHPUX10 -Dhpux10
|
||||
PORT_FLAGS += -DRW_NO_OVERLOAD_SCHAR -DHAVE_MODEL_H
|
||||
ifeq ($(OS_VERSION),.10)
|
||||
PLATFORM_FLAGS += -DHPUX10_10
|
||||
endif
|
||||
ifeq ($(OS_VERSION),.20)
|
||||
PLATFORM_FLAGS += -DHPUX10_20
|
||||
endif
|
||||
ifeq ($(OS_VERSION),.30)
|
||||
PLATFORM_FLAGS += -DHPUX10_30
|
||||
endif
|
||||
endif
|
||||
|
|
@ -33,7 +33,7 @@ MKSHLIB = $(LD) -b
|
|||
CPU_ARCH = hppa
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DHPUX -DSYSV -D_SVID_GETTOD
|
||||
OS_CFLAGS = -DXP_UNIX -DHPUX -DSYSV
|
||||
OS_LIBS = -ldld
|
||||
|
||||
XLDFLAGS = -lpthread
|
||||
|
|
|
|||
|
|
@ -19,4 +19,4 @@
|
|||
# Config stuff for IRIX5.3
|
||||
#
|
||||
|
||||
include config/IRIX.mk
|
||||
include $(DEPTH)/config/IRIX.mk
|
||||
|
|
|
|||
|
|
@ -19,4 +19,4 @@
|
|||
# Config stuff for IRIX6.3
|
||||
#
|
||||
|
||||
include config/IRIX.mk
|
||||
include $(DEPTH)/config/IRIX.mk
|
||||
|
|
|
|||
|
|
@ -24,7 +24,7 @@ CCC = g++
|
|||
CFLAGS += -Wall -Wno-format
|
||||
|
||||
RANLIB = echo
|
||||
MKSHLIB = $(LD) -shared
|
||||
MKSHLIB = $(LD) -shared $(XMKSHLIBOPTS)
|
||||
|
||||
#.c.o:
|
||||
# $(CC) -c -MD $*.d $(CFLAGS) $<
|
||||
|
|
|
|||
|
|
@ -23,9 +23,15 @@
|
|||
# Initial DG/UX port by Marc Fraioli (fraioli@dg-rtp.dg.com)
|
||||
#
|
||||
|
||||
AS = as
|
||||
CC = gcc
|
||||
CCC = g++
|
||||
ifdef NS_USE_GCC
|
||||
CC = gcc
|
||||
CCC = g++
|
||||
CFLAGS += -mieee -Wall -Wno-format
|
||||
else
|
||||
CC = cc
|
||||
CCC = cxx
|
||||
CFLAGS += -ieee -std
|
||||
endif
|
||||
|
||||
RANLIB = echo
|
||||
MKSHLIB = $(LD) -shared -all -expect_unresolved "*"
|
||||
|
|
|
|||
|
|
@ -37,7 +37,7 @@ RANLIB = echo
|
|||
CPU_ARCH = sparc
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS -D_SVID_GETTOD
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS
|
||||
OS_LIBS = -lsocket -lnsl -ldl
|
||||
|
||||
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
|
||||
|
|
@ -46,28 +46,16 @@ HAVE_PURIFY = 1
|
|||
|
||||
NOSUCHFILE = /solaris-rm-f-sucks
|
||||
|
||||
ifndef JS_NO_ULTRA
|
||||
ULTRA_OPTIONS := -xarch=v8plus
|
||||
ULTRA_OPTIONSD := -DULTRA_SPARC
|
||||
ifeq ($(OS_CPUARCH),sun4u) # ultra sparc?
|
||||
ifeq ($(CC),gcc) # using gcc?
|
||||
ifndef JS_NO_ULTRA # do we want ultra?
|
||||
ifdef JS_THREADSAFE # only in thread-safe mode
|
||||
DEFINES += -DULTRA_SPARC
|
||||
DEFINES += -Wa,-xarch=v8plus,-DULTRA_SPARC
|
||||
else
|
||||
ULTRA_OPTIONS := -xarch=v8
|
||||
ULTRA_OPTIONSD :=
|
||||
endif
|
||||
|
||||
ifeq ($(OS_CPUARCH),sun4u)
|
||||
DEFINES += $(ULTRA_OPTIONSD)
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,$(ULTRA_OPTIONS),$(ULTRA_OPTIONSD)
|
||||
else
|
||||
ASFLAGS += $(ULTRA_OPTIONS) $(ULTRA_OPTIONSD)
|
||||
ASFLAGS += -xarch=v8plus -DULTRA_SPARC
|
||||
endif
|
||||
endif
|
||||
|
||||
ifeq ($(OS_CPUARCH),sun4m)
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,-xarch=v8
|
||||
else
|
||||
ASFLAGS += -xarch=v8
|
||||
endif
|
||||
endif
|
||||
|
||||
|
|
|
|||
|
|
@ -20,11 +20,15 @@
|
|||
#
|
||||
|
||||
AS = as
|
||||
ifndef NS_USE_NATIVE
|
||||
CC = gcc
|
||||
CCC = g++
|
||||
CFLAGS += -Wall -Wno-format
|
||||
else
|
||||
CC = cc
|
||||
CCC = CC
|
||||
endif
|
||||
|
||||
#CC = /opt/SUNWspro/SC3.0.1/bin/cc
|
||||
RANLIB = echo
|
||||
|
||||
#.c.o:
|
||||
|
|
@ -33,7 +37,7 @@ RANLIB = echo
|
|||
CPU_ARCH = sparc
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS -D_SVID_GETTOD
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS
|
||||
OS_LIBS = -lsocket -lnsl -ldl
|
||||
|
||||
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
|
||||
|
|
@ -42,22 +46,15 @@ HAVE_PURIFY = 1
|
|||
|
||||
NOSUCHFILE = /solaris-rm-f-sucks
|
||||
|
||||
ifndef JS_NO_ULTRA
|
||||
ULTRA_OPTIONS := -xarch=v8plus -DULTRA_SPARC
|
||||
ifeq ($(OS_CPUARCH),sun4u) # ultra sparc?
|
||||
ifeq ($(CC),gcc) # using gcc?
|
||||
ifndef JS_NO_ULTRA # do we want ultra?
|
||||
ifdef JS_THREADSAFE # only in thread-safe mode
|
||||
DEFINES += -DULTRA_SPARC
|
||||
DEFINES += -Wa,-xarch=v8plus,-DULTRA_SPARC
|
||||
else
|
||||
ULTRA_OPTIONS := -xarch=v8
|
||||
ASFLAGS += -xarch=v8plus -DULTRA_SPARC
|
||||
endif
|
||||
|
||||
ifeq ($(OS_CPUARCH),sun4u)
|
||||
ASFLAGS += $(ULTRA_OPTIONS)
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,$(ULTRA_OPTIONS)
|
||||
endif
|
||||
else
|
||||
ifeq ($(OS_CPUARCH),sun4m)
|
||||
ASFLAGS += -xarch=v8
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,-xarch=v8
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
|
|
|
|||
|
|
@ -37,7 +37,7 @@ RANLIB = echo
|
|||
CPU_ARCH = sparc
|
||||
GFX_ARCH = x
|
||||
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS -D_SVID_GETTOD
|
||||
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS
|
||||
OS_LIBS = -lsocket -lnsl -ldl
|
||||
|
||||
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
|
||||
|
|
@ -46,28 +46,16 @@ HAVE_PURIFY = 1
|
|||
|
||||
NOSUCHFILE = /solaris-rm-f-sucks
|
||||
|
||||
ifndef JS_NO_ULTRA
|
||||
ULTRA_OPTIONS := -xarch=v8plus
|
||||
ULTRA_OPTIONSD := -DULTRA_SPARC
|
||||
ifeq ($(OS_CPUARCH),sun4u) # ultra sparc?
|
||||
ifeq ($(CC),gcc) # using gcc?
|
||||
ifndef JS_NO_ULTRA # do we want ultra?
|
||||
ifdef JS_THREADSAFE # only in thread-safe mode
|
||||
DEFINES += -DULTRA_SPARC
|
||||
DEFINES += -Wa,-xarch=v8plus,-DULTRA_SPARC
|
||||
else
|
||||
ULTRA_OPTIONS := -xarch=v8
|
||||
ULTRA_OPTIONSD :=
|
||||
endif
|
||||
|
||||
ifeq ($(OS_CPUARCH),sun4u)
|
||||
DEFINES += $(ULTRA_OPTIONSD)
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,$(ULTRA_OPTIONS),$(ULTRA_OPTIONSD)
|
||||
else
|
||||
ASFLAGS += $(ULTRA_OPTIONS) $(ULTRA_OPTIONSD)
|
||||
ASFLAGS += -xarch=v8plus -DULTRA_SPARC
|
||||
endif
|
||||
endif
|
||||
|
||||
ifeq ($(OS_CPUARCH),sun4m)
|
||||
ifeq ($(CC),gcc)
|
||||
DEFINES += -Wa,-xarch=v8
|
||||
else
|
||||
ASFLAGS += -xarch=v8
|
||||
endif
|
||||
endif
|
||||
|
||||
|
|
|
|||
|
|
@ -28,7 +28,33 @@ RANLIB = echo
|
|||
CPU_ARCH = x86 # XXX fixme
|
||||
GFX_ARCH = win32
|
||||
|
||||
OS_CFLAGS = -DXP_PC -DWIN32 -D_WINDOWS -D_WIN32
|
||||
# MSVC compiler options for both debug/optimize
|
||||
# /nologo - suppress copyright message
|
||||
# /W3 - Warning level 3
|
||||
# /Gm - enable minimal rebuild
|
||||
# /Zi - put debug info in a Program Database (.pdb) file
|
||||
# /YX - automatic precompiled headers
|
||||
# /GX - enable C++ exception support
|
||||
WIN_CFLAGS = /nologo /W3 /Gm /Zi /Fp$(OBJDIR)/js.pch /Fd$(OBJDIR)/js32.pdb
|
||||
|
||||
# MSVC compiler options for debug builds
|
||||
# /MDd - link with MSVCRTD.LIB (Dynamically-linked, multi-threaded, debug C-runtime)
|
||||
# /Od - minimal optimization
|
||||
WIN_DEBUG_CFLAGS = /MDd /Od
|
||||
|
||||
# MSVC compiler options for release (optimized) builds
|
||||
# /MD - link with MSVCRT.LIB (Dynamically-linked, multi-threaded, debug C-runtime)
|
||||
# /O2 - Optimize for speed
|
||||
# /G5 - Optimize for Pentium
|
||||
WIN_OPT_CFLAGS = /MD /O2
|
||||
|
||||
ifdef BUILD_OPT
|
||||
OPTIMIZER = $(WIN_OPT_CFLAGS)
|
||||
else
|
||||
OPTIMIZER = $(WIN_DEBUG_CFLAGS)
|
||||
endif
|
||||
|
||||
OS_CFLAGS = -DXP_PC -DWIN32 -D_WINDOWS -D_WIN32 $(WIN_CFLAGS)
|
||||
JSDLL_CFLAGS = -DEXPORT_JS_API
|
||||
OS_LIBS = -lm -lc
|
||||
|
||||
|
|
@ -45,10 +71,6 @@ EXE_LINK_FLAGS=kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib\
|
|||
/subsystem:console /incremental:yes /debug\
|
||||
/machine:I386
|
||||
|
||||
ifdef JS_THREADSAFE
|
||||
LIB_LINK_FLAGS += $(DIST)/lib/libnspr21.lib
|
||||
endif
|
||||
|
||||
CAFEDIR = t:/cafe
|
||||
JCLASSPATH = $(CAFEDIR)/Java/Lib/classes.zip
|
||||
JAVAC = $(CAFEDIR)/Bin/sj.exe
|
||||
|
|
|
|||
|
|
@ -0,0 +1,6 @@
|
|||
*.pdb
|
||||
*.ncb
|
||||
*.opt
|
||||
*.plg
|
||||
Debug
|
||||
Release
|
||||
|
|
@ -0,0 +1,103 @@
|
|||
#
|
||||
# The contents of this file are subject to the Netscape Public License
|
||||
# Version 1.0 (the "License"); you may not use this file except in
|
||||
# compliance with the License. You may obtain a copy of the License at
|
||||
# http://www.mozilla.org/NPL/
|
||||
#
|
||||
# Software distributed under the License is distributed on an "AS IS"
|
||||
# basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
|
||||
# the License for the specific language governing rights and limitations
|
||||
# under the License.
|
||||
#
|
||||
# The Original Code is Mozilla Communicator client code.
|
||||
#
|
||||
# The Initial Developer of the Original Code is Netscape Communications
|
||||
# Corporation. Portions created by Netscape are Copyright (C) 1998
|
||||
# Netscape Communications Corporation. All Rights Reserved.
|
||||
#
|
||||
|
||||
DEPTH = ../../..
|
||||
topsrcdir = @top_srcdir@
|
||||
VPATH = @srcdir@
|
||||
srcdir = @srcdir@
|
||||
|
||||
include $(DEPTH)/config/autoconf.mk
|
||||
|
||||
#
|
||||
# Default IEEE libm
|
||||
#
|
||||
CFLAGS += -D_IEEE_LIBM
|
||||
|
||||
LIBRARY_NAME = fdm
|
||||
|
||||
MODULE = js
|
||||
|
||||
CSRCS = \
|
||||
e_acos.c \
|
||||
e_asin.c \
|
||||
e_atan2.c \
|
||||
e_exp.c \
|
||||
e_fmod.c \
|
||||
e_log.c \
|
||||
e_pow.c \
|
||||
e_rem_pio2.c \
|
||||
s_scalbn.c \
|
||||
e_sqrt.c \
|
||||
k_cos.c \
|
||||
k_sin.c \
|
||||
k_rem_pio2.c \
|
||||
k_tan.c \
|
||||
s_atan.c \
|
||||
s_ceil.c \
|
||||
s_copysign.c \
|
||||
s_cos.c \
|
||||
s_fabs.c \
|
||||
s_finite.c \
|
||||
s_floor.c \
|
||||
s_isnan.c \
|
||||
s_lib_version.c \
|
||||
s_sin.c \
|
||||
s_tan.c \
|
||||
w_acos.c \
|
||||
w_asin.c \
|
||||
w_atan2.c \
|
||||
w_exp.c \
|
||||
w_fmod.c \
|
||||
w_log.c \
|
||||
w_pow.c \
|
||||
w_sqrt.c \
|
||||
$(NULL)
|
||||
|
||||
EXPORTS = fdlibm.h
|
||||
|
||||
include $(topsrcdir)/config/rules.mk
|
||||
|
||||
# from mozilla/js/src/Makefile
|
||||
ifeq ($(CPU_ARCH),sparc)
|
||||
|
||||
ifndef JS_NO_ULTRA
|
||||
ULTRA_OPTIONS := -xarch=v8plus,-DULTRA_SPARC
|
||||
ULTRA_OPTIONSCC := -DULTRA_SPARC
|
||||
else
|
||||
ULTRA_OPTIONS := -xarch=v8
|
||||
ULTRA_OPTIONSCC :=
|
||||
endif
|
||||
|
||||
ifeq ($(shell uname -m),sun4u)
|
||||
ASFLAGS += -Wa,$(ULTRA_OPTIONS),-P,-L,-D_ASM,-D__STDC__=0 $(ULTRA_OPTIONSCC)
|
||||
else
|
||||
ASFLAGS += -Wa,-xarch=v8,-P,-L,-D_ASM,-D__STDC__=0
|
||||
endif
|
||||
|
||||
endif # sparc
|
||||
|
||||
ifeq ($(OS_ARCH), OSF1)
|
||||
LDFLAGS += -lc_r
|
||||
endif
|
||||
ifeq ($(OS_ARCH), SunOS)
|
||||
LDFLAGS += -lposix4 -ldl -lnsl -lsocket
|
||||
endif
|
||||
ifeq ($(OS_ARCH), Linux)
|
||||
LDFLAGS += -ldl
|
||||
endif
|
||||
# end from mozilla/js/src/Makefile
|
||||
|
|
@ -0,0 +1,167 @@
|
|||
#
|
||||
# The contents of this file are subject to the Netscape Public License
|
||||
# Version 1.0 (the "NPL"); you may not use this file except in
|
||||
# compliance with the NPL. You may obtain a copy of the NPL at
|
||||
# http://www.mozilla.org/NPL/
|
||||
#
|
||||
# Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
# for the specific language governing rights and limitations under the
|
||||
# NPL.
|
||||
#
|
||||
# The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
# Inc. Portions created by Netscape are
|
||||
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
|
||||
# Reserved.
|
||||
|
||||
#
|
||||
# @(#)Makefile 1.4 95/01/18
|
||||
#
|
||||
# ====================================================
|
||||
# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
#
|
||||
# Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
# Permission to use, copy, modify, and distribute this
|
||||
# software is freely granted, provided that this notice
|
||||
# is preserved.
|
||||
# ====================================================
|
||||
#
|
||||
#
|
||||
|
||||
#
|
||||
# There are two options in making libm at fdlibm compile time:
|
||||
# _IEEE_LIBM --- IEEE libm; smaller, and somewhat faster
|
||||
# _MULTI_LIBM --- Support multi-standard at runtime by
|
||||
# imposing wrapper functions defined in
|
||||
# fdlibm.h:
|
||||
# _IEEE_MODE -- IEEE
|
||||
# _XOPEN_MODE -- X/OPEN
|
||||
# _POSIX_MODE -- POSIX/ANSI
|
||||
# _SVID3_MODE -- SVID
|
||||
#
|
||||
# Here is how to set up CFLAGS to create the desired libm at
|
||||
# compile time:
|
||||
#
|
||||
# CFLAGS = -D_IEEE_LIBM ... IEEE libm (recommended)
|
||||
# CFLAGS = -D_SVID3_MODE ... Multi-standard supported
|
||||
# libm with SVID as the
|
||||
# default standard
|
||||
# CFLAGS = -D_XOPEN_MODE ... Multi-standard supported
|
||||
# libm with XOPEN as the
|
||||
# default standard
|
||||
# CFLAGS = -D_POSIX_MODE ... Multi-standard supported
|
||||
# libm with POSIX as the
|
||||
# default standard
|
||||
# CFLAGS = ... Multi-standard supported
|
||||
# libm with IEEE as the
|
||||
# default standard
|
||||
#
|
||||
# NOTE: if scalb's second arguement is an int, then one must
|
||||
# define _SCALB_INT in CFLAGS. The default prototype of scalb
|
||||
# is double scalb(double, double)
|
||||
#
|
||||
|
||||
DEPTH = ..
|
||||
|
||||
include $(DEPTH)/config.mk
|
||||
|
||||
#
|
||||
# Default IEEE libm
|
||||
#
|
||||
CFLAGS += -DXP_UNIX $(OPTIMIZER) $(OS_CFLAGS) $(DEFINES) $(INCLUDES) \
|
||||
-DJSFILE $(XCFLAGS) -D_IEEE_LIBM
|
||||
|
||||
|
||||
|
||||
#CC = cc
|
||||
|
||||
INCFILES = fdlibm.h
|
||||
.INIT: $(INCFILES)
|
||||
.KEEP_STATE:
|
||||
FDLIBM_CFILES = \
|
||||
k_standard.c k_rem_pio2.c \
|
||||
k_cos.c k_sin.c k_tan.c \
|
||||
e_acos.c e_acosh.c e_asin.c e_atan2.c \
|
||||
e_atanh.c e_cosh.c e_exp.c e_fmod.c \
|
||||
e_gamma.c e_gamma_r.c e_hypot.c e_j0.c \
|
||||
e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c \
|
||||
e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \
|
||||
e_scalb.c e_sinh.c e_sqrt.c \
|
||||
w_acos.c w_acosh.c w_asin.c w_atan2.c \
|
||||
w_atanh.c w_cosh.c w_exp.c w_fmod.c \
|
||||
w_gamma.c w_gamma_r.c w_hypot.c w_j0.c \
|
||||
w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c \
|
||||
w_log.c w_log10.c w_pow.c w_remainder.c \
|
||||
w_scalb.c w_sinh.c w_sqrt.c \
|
||||
s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c \
|
||||
s_cos.c s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c \
|
||||
s_frexp.c s_ilogb.c s_isnan.c s_ldexp.c s_lib_version.c \
|
||||
s_log1p.c s_logb.c s_matherr.c s_modf.c s_nextafter.c \
|
||||
s_rint.c s_scalbn.c s_signgam.c s_significand.c s_sin.c \
|
||||
s_tan.c s_tanh.c
|
||||
|
||||
ifdef USE_MSVC
|
||||
FDLIBM_OBJS = $(addprefix $(OBJDIR)/, $(FDLIBM_CFILES:.c=.obj))
|
||||
else
|
||||
FDLIBM_OBJS = $(addprefix $(OBJDIR)/, $(FDLIBM_CFILES:.c=.o))
|
||||
endif
|
||||
|
||||
ifdef USE_MSVC
|
||||
LIBRARY = $(OBJDIR)/fdlibm.lib
|
||||
else
|
||||
LIBRARY = $(OBJDIR)/libfdm.a
|
||||
endif
|
||||
|
||||
define MAKE_OBJDIR
|
||||
if test ! -d $(@D); then rm -rf $(@D); mkdir $(@D); fi
|
||||
endef
|
||||
|
||||
all: $(LIBRARY)
|
||||
|
||||
export:
|
||||
|
||||
$(OBJDIR)/%: %.c
|
||||
@$(MAKE_OBJDIR)
|
||||
$(CC) -o $@ $(CFLAGS) $*.c $(LDFLAGS)
|
||||
|
||||
$(OBJDIR)/%.o: %.c
|
||||
@$(MAKE_OBJDIR)
|
||||
$(CC) -o $@ -c $(CFLAGS) $*.c
|
||||
|
||||
$(OBJDIR)/%.o: %.s
|
||||
@$(MAKE_OBJDIR)
|
||||
$(AS) -o $@ $(ASFLAGS) $*.s
|
||||
|
||||
# windows only
|
||||
$(OBJDIR)/%.obj: %.c
|
||||
@$(MAKE_OBJDIR)
|
||||
$(CC) -Fo$(OBJDIR)/ -c $(CFLAGS) $*.c
|
||||
|
||||
ifeq ($(OS_ARCH),OS2)
|
||||
$(LIBRARY): $(FDLIBM_OBJS)
|
||||
$(AR) $@ $? $(AR_OS2_SUFFIX)
|
||||
$(RANLIB) $@
|
||||
else
|
||||
ifdef USE_MSVC
|
||||
$(LIBRARY): $(FDLIBM_OBJS)
|
||||
lib.exe /out:"$@" $?
|
||||
else
|
||||
$(LIBRARY): $(FDLIBM_OBJS)
|
||||
$(AR) rv $@ $?
|
||||
$(RANLIB) $@
|
||||
endif
|
||||
endif
|
||||
|
||||
libfdm.a : $(FDLIBM_OBJS)
|
||||
$(AR) cru $(OBJDIR)/libfdm.a $(FDLIBM_OBJS)
|
||||
$(RANLIB) $(OBJDIR)/libfdm.a
|
||||
|
||||
clean:
|
||||
rm -rf $(FDLIBM_OBJS)
|
||||
|
||||
clobber:
|
||||
rm -rf $(FDLIBM_OBJS) $(LIBRARY) $(DEPENDENCIES)
|
||||
|
||||
SUFFIXES: .i
|
||||
%.i: %.c
|
||||
$(CC) -C -E $(CFLAGS) $< > $*.i
|
||||
|
|
@ -0,0 +1,121 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_acos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_acos(x)
|
||||
* Method :
|
||||
* acos(x) = pi/2 - asin(x)
|
||||
* acos(-x) = pi/2 + asin(x)
|
||||
* For |x|<=0.5
|
||||
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
|
||||
* For x>0.5
|
||||
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
|
||||
* = 2asin(sqrt((1-x)/2))
|
||||
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
|
||||
* = 2f + (2c + 2s*z*R(z))
|
||||
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
|
||||
* for f so that f+c ~ sqrt(z).
|
||||
* For x<-0.5
|
||||
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
|
||||
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
* Function needed: sqrt
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_acos(double x)
|
||||
#else
|
||||
double __ieee754_acos(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z,p,q,r,w,s,c,df;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3ff00000) { /* |x| >= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3fe00000) { /* |x| < 0.5 */
|
||||
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = fd_sqrt(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - 2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
z = (one-x)*0.5;
|
||||
s = fd_sqrt(z);
|
||||
df = s;
|
||||
__LO(df) = 0;
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return 2.0*(df+w);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,81 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_acosh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_acosh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
||||
* we have
|
||||
* acosh(x) := log(x)+ln2, if x is large; else
|
||||
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
|
||||
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
|
||||
*
|
||||
* Special cases:
|
||||
* acosh(x) is NaN with signal if x<1.
|
||||
* acosh(NaN) is NaN without signal.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_acosh(double x)
|
||||
#else
|
||||
double __ieee754_acosh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t;
|
||||
int hx;
|
||||
hx = __HI(x);
|
||||
if(hx<0x3ff00000) { /* x < 1 */
|
||||
return (x-x)/(x-x);
|
||||
} else if(hx >=0x41b00000) { /* x > 2**28 */
|
||||
if(hx >=0x7ff00000) { /* x is inf of NaN */
|
||||
return x+x;
|
||||
} else
|
||||
return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
|
||||
} else if(((hx-0x3ff00000)|__LO(x))==0) {
|
||||
return 0.0; /* acosh(1) = 0 */
|
||||
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
||||
t=x*x;
|
||||
return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one)));
|
||||
} else { /* 1<x<2 */
|
||||
t = x-one;
|
||||
return fd_log1p(t+fd_sqrt(2.0*t+t*t));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,130 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_asin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_asin(x)
|
||||
* Method :
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
||||
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
huge = 1.000e+300,
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_asin(double x)
|
||||
#else
|
||||
double __ieee754_asin(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w,p,q,c,r,s;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>= 0x3ff00000) { /* |x|>= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3fe00000) { /* |x|<0.5 */
|
||||
if(ix<0x3e400000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fd_fabs(x);
|
||||
t = w*0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = fd_sqrt(t);
|
||||
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
w = s;
|
||||
__LO(w) = 0;
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = 2.0*s*r-(pio2_lo-2.0*c);
|
||||
q = pio4_hi-2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,139 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_atan2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_atan2(y,x)
|
||||
* Method :
|
||||
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
||||
* 2. Reduce x to positive by (if x and y are unexceptional):
|
||||
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
||||
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
||||
*
|
||||
* Special cases:
|
||||
*
|
||||
* ATAN2((anything), NaN ) is NaN;
|
||||
* ATAN2(NAN , (anything) ) is NaN;
|
||||
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
||||
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
||||
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
||||
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
||||
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
||||
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
||||
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
||||
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
tiny = 1.0e-300,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
|
||||
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_atan2(double y, double x)
|
||||
#else
|
||||
double __ieee754_atan2(y,x)
|
||||
double y,x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int k,m,hx,hy,ix,iy;
|
||||
unsigned lx,ly;
|
||||
|
||||
hx = __HI(x); ix = hx&0x7fffffff;
|
||||
lx = __LO(x);
|
||||
hy = __HI(y); iy = hy&0x7fffffff;
|
||||
ly = __LO(y);
|
||||
if(((ix|((lx|-(int)lx)>>31))>0x7ff00000)||
|
||||
((iy|((ly|-(int)ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if((hx-0x3ff00000|lx)==0) return fd_atan(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if((iy|ly)==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7ff00000) {
|
||||
if(iy==0x7ff00000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>20;
|
||||
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=fd_atan(fd_fabs(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: __HI(z) ^= 0x80000000;
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,84 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_atanh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_atanh(x)
|
||||
* Method :
|
||||
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
|
||||
* 2.For x>=0.5
|
||||
* 1 2x x
|
||||
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
|
||||
* 2 1 - x 1 - x
|
||||
*
|
||||
* For x<0.5
|
||||
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
|
||||
*
|
||||
* Special cases:
|
||||
* atanh(x) is NaN if |x| > 1 with signal;
|
||||
* atanh(NaN) is that NaN with no signal;
|
||||
* atanh(+-1) is +-INF with signal.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, huge = 1e300;
|
||||
#else
|
||||
static double one = 1.0, huge = 1e300;
|
||||
#endif
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_atanh(double x)
|
||||
#else
|
||||
double __ieee754_atanh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t;
|
||||
int hx,ix;
|
||||
unsigned lx;
|
||||
hx = __HI(x); /* high word */
|
||||
lx = __LO(x); /* low word */
|
||||
ix = hx&0x7fffffff;
|
||||
if ((ix|((lx|(-(int)lx))>>31))>0x3ff00000) /* |x|>1 */
|
||||
return (x-x)/(x-x);
|
||||
if(ix==0x3ff00000)
|
||||
return x/zero;
|
||||
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
|
||||
__HI(x) = ix; /* x <- |x| */
|
||||
if(ix<0x3fe00000) { /* x < 0.5 */
|
||||
t = x+x;
|
||||
t = 0.5*fd_log1p(t+t*x/(one-x));
|
||||
} else
|
||||
t = 0.5*fd_log1p((x+x)/(one-x));
|
||||
if(hx>=0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,109 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_cosh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_cosh(x)
|
||||
* Method :
|
||||
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
|
||||
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
|
||||
* 2.
|
||||
* [ exp(x) - 1 ]^2
|
||||
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
|
||||
* 2*exp(x)
|
||||
*
|
||||
* exp(x) + 1/exp(x)
|
||||
* ln2/2 <= x <= 22 : cosh(x) := -------------------
|
||||
* 2
|
||||
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : cosh(x) := huge*huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* cosh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only cosh(0)=1 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef _WIN32
|
||||
#define huge myhuge
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, half=0.5, huge = 1.0e300;
|
||||
#else
|
||||
static double one = 1.0, half=0.5, huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_cosh(double x)
|
||||
#else
|
||||
double __ieee754_cosh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w;
|
||||
int ix;
|
||||
unsigned lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
ix = __HI(x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
|
||||
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
||||
if(ix<0x3fd62e43) {
|
||||
t = fd_expm1(fd_fabs(x));
|
||||
w = one+t;
|
||||
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
|
||||
return one+(t*t)/(w+w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
||||
if (ix < 0x40360000) {
|
||||
t = __ieee754_exp(fd_fabs(x));
|
||||
return half*t+half/t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
|
||||
if (ix < 0x40862E42) return half*__ieee754_exp(fd_fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
|
||||
if (ix<0x408633CE ||
|
||||
(ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
|
||||
w = __ieee754_exp(half*fd_fabs(x));
|
||||
t = half*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge*huge;
|
||||
}
|
||||
|
|
@ -0,0 +1,173 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_exp.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_exp(x)
|
||||
* Returns the exponential of x.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2.
|
||||
*
|
||||
* Here r will be represented as r = hi-lo for better
|
||||
* accuracy.
|
||||
*
|
||||
* 2. Approximation of exp(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Write
|
||||
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
||||
* We use a special Reme algorithm on [0,0.34658] to generate
|
||||
* a polynomial of degree 5 to approximate R. The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
huge = 1.0e+300,
|
||||
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
|
||||
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
|
||||
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_exp(double x) /* default IEEE double exp */
|
||||
#else
|
||||
double __ieee754_exp(x) /* default IEEE double exp */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,hi,lo,c,t;
|
||||
int k,xsb;
|
||||
unsigned hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
if(((hx&0xfffff)|__LO(x))!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom1000*twom1000; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = (int)(invln2*x+halF[xsb]);
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-2.0)-x);
|
||||
else y = one-((lo-(x*c)/(2.0-c))-hi);
|
||||
if(k >= -1021) {
|
||||
__HI(y) += (k<<20); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
__HI(y) += ((k+1000)<<20);/* add k to y's exponent */
|
||||
return y*twom1000;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,156 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_fmod.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __ieee754_fmod(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#else
|
||||
static double one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_fmod(double x, double y)
|
||||
#else
|
||||
double __ieee754_fmod(x,y)
|
||||
double x,y ;
|
||||
#endif
|
||||
{
|
||||
int n,hx,hy,hz,ix,iy,sx,i;
|
||||
unsigned lx,ly,lz;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
hy = __HI(y); /* high word of y */
|
||||
ly = __LO(y); /* low word of y */
|
||||
sx = hx&0x80000000; /* sign of x */
|
||||
hx ^=sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
|
||||
((hy|((ly|-(int)ly)>>31))>0x7ff00000)) /* or y is NaN */
|
||||
return (x*y)/(x*y);
|
||||
if(hx<=hy) {
|
||||
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
|
||||
if(lx==ly)
|
||||
return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
|
||||
}
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if(hx<0x00100000) { /* subnormal x */
|
||||
if(hx==0) {
|
||||
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
|
||||
} else {
|
||||
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
|
||||
}
|
||||
} else ix = (hx>>20)-1023;
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if(hy<0x00100000) { /* subnormal y */
|
||||
if(hy==0) {
|
||||
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
|
||||
} else {
|
||||
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
|
||||
}
|
||||
} else iy = (hy>>20)-1023;
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if(ix >= -1022)
|
||||
hx = 0x00100000|(0x000fffff&hx);
|
||||
else { /* subnormal x, shift x to normal */
|
||||
n = -1022-ix;
|
||||
if(n<=31) {
|
||||
hx = (hx<<n)|(lx>>(32-n));
|
||||
lx <<= n;
|
||||
} else {
|
||||
hx = lx<<(n-32);
|
||||
lx = 0;
|
||||
}
|
||||
}
|
||||
if(iy >= -1022)
|
||||
hy = 0x00100000|(0x000fffff&hy);
|
||||
else { /* subnormal y, shift y to normal */
|
||||
n = -1022-iy;
|
||||
if(n<=31) {
|
||||
hy = (hy<<n)|(ly>>(32-n));
|
||||
ly <<= n;
|
||||
} else {
|
||||
hy = ly<<(n-32);
|
||||
ly = 0;
|
||||
}
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while(n--) {
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
|
||||
else {
|
||||
if((hz|lz)==0) /* return sign(x)*0 */
|
||||
return Zero[(unsigned)sx>>31];
|
||||
hx = hz+hz+(lz>>31); lx = lz+lz;
|
||||
}
|
||||
}
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz>=0) {hx=hz;lx=lz;}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if((hx|lx)==0) /* return sign(x)*0 */
|
||||
return Zero[(unsigned)sx>>31];
|
||||
while(hx<0x00100000) { /* normalize x */
|
||||
hx = hx+hx+(lx>>31); lx = lx+lx;
|
||||
iy -= 1;
|
||||
}
|
||||
if(iy>= -1022) { /* normalize output */
|
||||
hx = ((hx-0x00100000)|((iy+1023)<<20));
|
||||
__HI(x) = hx|sx;
|
||||
__LO(x) = lx;
|
||||
} else { /* subnormal output */
|
||||
n = -1022 - iy;
|
||||
if(n<=20) {
|
||||
lx = (lx>>n)|((unsigned)hx<<(32-n));
|
||||
hx >>= n;
|
||||
} else if (n<=31) {
|
||||
lx = (hx<<(32-n))|(lx>>n); hx = sx;
|
||||
} else {
|
||||
lx = hx>>(n-32); hx = sx;
|
||||
}
|
||||
__HI(x) = hx|sx;
|
||||
__LO(x) = lx;
|
||||
x *= one; /* create necessary signal */
|
||||
}
|
||||
return x; /* exact output */
|
||||
}
|
||||
|
|
@ -0,0 +1,49 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_gamma.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_gamma(x)
|
||||
* Return the logarithm of the Gamma function of x.
|
||||
*
|
||||
* Method: call __ieee754_gamma_r
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_gamma(double x)
|
||||
#else
|
||||
double __ieee754_gamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return __ieee754_gamma_r(x,&signgam);
|
||||
}
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_gamma_r.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_gamma_r(x, signgamp)
|
||||
* Reentrant version of the logarithm of the Gamma function
|
||||
* with user provide pointer for the sign of Gamma(x).
|
||||
*
|
||||
* Method: See __ieee754_lgamma_r
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_gamma_r(double x, int *signgamp)
|
||||
#else
|
||||
double __ieee754_gamma_r(x,signgamp)
|
||||
double x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
return __ieee754_lgamma_r(x,signgamp);
|
||||
}
|
||||
|
|
@ -0,0 +1,131 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_hypot.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_hypot(x,y)
|
||||
*
|
||||
* Method :
|
||||
* If (assume round-to-nearest) z=x*x+y*y
|
||||
* has error less than sqrt(2)/2 ulp, than
|
||||
* sqrt(z) has error less than 1 ulp (exercise).
|
||||
*
|
||||
* So, compute sqrt(x*x+y*y) with some care as
|
||||
* follows to get the error below 1 ulp:
|
||||
*
|
||||
* Assume x>y>0;
|
||||
* (if possible, set rounding to round-to-nearest)
|
||||
* 1. if x > 2y use
|
||||
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
|
||||
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
|
||||
* 2. if x <= 2y use
|
||||
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
|
||||
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
|
||||
* y1= y with lower 32 bits chopped, y2 = y-y1.
|
||||
*
|
||||
* NOTE: scaling may be necessary if some argument is too
|
||||
* large or too tiny
|
||||
*
|
||||
* Special cases:
|
||||
* hypot(x,y) is INF if x or y is +INF or -INF; else
|
||||
* hypot(x,y) is NAN if x or y is NAN.
|
||||
*
|
||||
* Accuracy:
|
||||
* hypot(x,y) returns sqrt(x^2+y^2) with error less
|
||||
* than 1 ulps (units in the last place)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_hypot(double x, double y)
|
||||
#else
|
||||
double __ieee754_hypot(x,y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double a=x,b=y,t1,t2,y1,y2,w;
|
||||
int j,k,ha,hb;
|
||||
|
||||
ha = __HI(x)&0x7fffffff; /* high word of x */
|
||||
hb = __HI(y)&0x7fffffff; /* high word of y */
|
||||
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
|
||||
__HI(a) = ha; /* a <- |a| */
|
||||
__HI(b) = hb; /* b <- |b| */
|
||||
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
|
||||
k=0;
|
||||
if(ha > 0x5f300000) { /* a>2**500 */
|
||||
if(ha >= 0x7ff00000) { /* Inf or NaN */
|
||||
w = a+b; /* for sNaN */
|
||||
if(((ha&0xfffff)|__LO(a))==0) w = a;
|
||||
if(((hb^0x7ff00000)|__LO(b))==0) w = b;
|
||||
return w;
|
||||
}
|
||||
/* scale a and b by 2**-600 */
|
||||
ha -= 0x25800000; hb -= 0x25800000; k += 600;
|
||||
__HI(a) = ha;
|
||||
__HI(b) = hb;
|
||||
}
|
||||
if(hb < 0x20b00000) { /* b < 2**-500 */
|
||||
if(hb <= 0x000fffff) { /* subnormal b or 0 */
|
||||
if((hb|(__LO(b)))==0) return a;
|
||||
t1=0;
|
||||
__HI(t1) = 0x7fd00000; /* t1=2^1022 */
|
||||
b *= t1;
|
||||
a *= t1;
|
||||
k -= 1022;
|
||||
} else { /* scale a and b by 2^600 */
|
||||
ha += 0x25800000; /* a *= 2^600 */
|
||||
hb += 0x25800000; /* b *= 2^600 */
|
||||
k -= 600;
|
||||
__HI(a) = ha;
|
||||
__HI(b) = hb;
|
||||
}
|
||||
}
|
||||
/* medium size a and b */
|
||||
w = a-b;
|
||||
if (w>b) {
|
||||
t1 = 0;
|
||||
__HI(t1) = ha;
|
||||
t2 = a-t1;
|
||||
w = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
|
||||
} else {
|
||||
a = a+a;
|
||||
y1 = 0;
|
||||
__HI(y1) = hb;
|
||||
y2 = b - y1;
|
||||
t1 = 0;
|
||||
__HI(t1) = ha+0x00100000;
|
||||
t2 = a - t1;
|
||||
w = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
|
||||
}
|
||||
if(k!=0) {
|
||||
t1 = 1.0;
|
||||
__HI(t1) += (k<<20);
|
||||
return t1*w;
|
||||
} else return w;
|
||||
}
|
||||
|
|
@ -0,0 +1,494 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_j0.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_j0(x), __ieee754_y0(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j0(x):
|
||||
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
|
||||
* 2. Reduce x to |x| since j0(x)=j0(-x), and
|
||||
* for x in (0,2)
|
||||
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
|
||||
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
|
||||
* for x in (2,inf)
|
||||
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* as follow:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (cos(x) + sin(x))
|
||||
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j0(nan)= nan
|
||||
* j0(0) = 1
|
||||
* j0(inf) = 0
|
||||
*
|
||||
* Method -- y0(x):
|
||||
* 1. For x<2.
|
||||
* Since
|
||||
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
|
||||
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
|
||||
* We use the following function to approximate y0,
|
||||
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
|
||||
* where
|
||||
* U(z) = u00 + u01*z + ... + u06*z^6
|
||||
* V(z) = 1 + v01*z + ... + v04*z^4
|
||||
* with absolute approximation error bounded by 2**-72.
|
||||
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
|
||||
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
|
||||
* 2. For x>=2.
|
||||
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* by the method mentioned above.
|
||||
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pzero(double), qzero(double);
|
||||
#else
|
||||
static double pzero(), qzero();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0, 2.00] */
|
||||
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
|
||||
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
|
||||
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
|
||||
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
|
||||
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
|
||||
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
|
||||
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
|
||||
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_j0(double x)
|
||||
#else
|
||||
double __ieee754_j0(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v;
|
||||
int hx,ix;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/(x*x);
|
||||
x = fd_fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = fd_sin(x);
|
||||
c = fd_cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -fd_cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<0x3f200000) { /* |x| < 2**-13 */
|
||||
if(huge+x>one) { /* raise inexact if x != 0 */
|
||||
if(ix<0x3e400000) return one; /* |x|<2**-27 */
|
||||
else return one - 0.25*x*x;
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(R02+z*(R03+z*(R04+z*R05)));
|
||||
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
|
||||
if(ix < 0x3FF00000) { /* |x| < 1.00 */
|
||||
return one + z*(-0.25+(r/s));
|
||||
} else {
|
||||
u = 0.5*x;
|
||||
return((one+u)*(one-u)+z*(r/s));
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
|
||||
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
|
||||
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
|
||||
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
|
||||
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
|
||||
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
|
||||
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
|
||||
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
|
||||
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
|
||||
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
|
||||
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_y0(double x)
|
||||
#else
|
||||
double __ieee754_y0(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int hx,ix,lx;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = 0x7fffffff&hx;
|
||||
lx = __LO(x);
|
||||
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
|
||||
* where x0 = x-pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) + cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
s = fd_sin(x);
|
||||
c = fd_cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -fd_cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3e400000) { /* x < 2**-27 */
|
||||
return(u00 + tpi*__ieee754_log(x));
|
||||
}
|
||||
z = x*x;
|
||||
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
||||
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
|
||||
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
|
||||
}
|
||||
|
||||
/* The asymptotic expansions of pzero is
|
||||
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
|
||||
* For x >= 2, We approximate pzero by
|
||||
* pzero(x) = 1 + (R/S)
|
||||
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
|
||||
* S = 1 + pS0*s^2 + ... + pS4*s^10
|
||||
* and
|
||||
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
|
||||
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
|
||||
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
|
||||
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
|
||||
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS8[5] = {
|
||||
#else
|
||||
static double pS8[5] = {
|
||||
#endif
|
||||
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
|
||||
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
|
||||
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
|
||||
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
|
||||
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
|
||||
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
|
||||
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
|
||||
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
|
||||
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
|
||||
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS5[5] = {
|
||||
#else
|
||||
static double pS5[5] = {
|
||||
#endif
|
||||
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
|
||||
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
|
||||
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
|
||||
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
|
||||
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
|
||||
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
|
||||
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
|
||||
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
|
||||
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
|
||||
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS3[5] = {
|
||||
#else
|
||||
static double pS3[5] = {
|
||||
#endif
|
||||
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
|
||||
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
|
||||
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
|
||||
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
|
||||
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
|
||||
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
|
||||
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
|
||||
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
|
||||
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
|
||||
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS2[5] = {
|
||||
#else
|
||||
static double pS2[5] = {
|
||||
#endif
|
||||
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
|
||||
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
|
||||
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
|
||||
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
|
||||
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pzero(double x)
|
||||
#else
|
||||
static double pzero(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double z,r,s;
|
||||
int ix;
|
||||
ix = 0x7fffffff&__HI(x);
|
||||
if(ix>=0x40200000) {p = pR8; q= pS8;}
|
||||
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
|
||||
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
|
||||
else if(ix>=0x40000000){p = pR2; q= pS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qzero is
|
||||
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pzero by
|
||||
* qzero(x) = s*(-1.25 + (R/S))
|
||||
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
|
||||
* S = 1 + qS0*s^2 + ... + qS5*s^12
|
||||
* and
|
||||
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
|
||||
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
|
||||
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
|
||||
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
|
||||
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS8[6] = {
|
||||
#else
|
||||
static double qS8[6] = {
|
||||
#endif
|
||||
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
|
||||
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
|
||||
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
|
||||
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
|
||||
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
|
||||
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
|
||||
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
|
||||
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
|
||||
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
|
||||
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
|
||||
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS5[6] = {
|
||||
#else
|
||||
static double qS5[6] = {
|
||||
#endif
|
||||
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
|
||||
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
|
||||
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
|
||||
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
|
||||
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
|
||||
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
|
||||
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
|
||||
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
|
||||
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
|
||||
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
|
||||
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS3[6] = {
|
||||
#else
|
||||
static double qS3[6] = {
|
||||
#endif
|
||||
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
|
||||
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
|
||||
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
|
||||
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
|
||||
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
|
||||
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
|
||||
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
|
||||
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
|
||||
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
|
||||
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
|
||||
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS2[6] = {
|
||||
#else
|
||||
static double qS2[6] = {
|
||||
#endif
|
||||
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
|
||||
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
|
||||
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
|
||||
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
|
||||
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
|
||||
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double qzero(double x)
|
||||
#else
|
||||
static double qzero(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double s,r,z;
|
||||
int ix;
|
||||
ix = 0x7fffffff&__HI(x);
|
||||
if(ix>=0x40200000) {p = qR8; q= qS8;}
|
||||
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
|
||||
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
|
||||
else if(ix>=0x40000000){p = qR2; q= qS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (-.125 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,493 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_j1.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_j1(x), __ieee754_y1(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j1(x):
|
||||
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
|
||||
* 2. Reduce x to |x| since j1(x)=-j1(-x), and
|
||||
* for x in (0,2)
|
||||
* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
|
||||
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
|
||||
* for x in (2,inf)
|
||||
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* as follow:
|
||||
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (sin(x) + cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j1(nan)= nan
|
||||
* j1(0) = 0
|
||||
* j1(inf) = 0
|
||||
*
|
||||
* Method -- y1(x):
|
||||
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
|
||||
* 2. For x<2.
|
||||
* Since
|
||||
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
|
||||
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
|
||||
* We use the following function to approximate y1,
|
||||
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
|
||||
* where for x in [0,2] (abs err less than 2**-65.89)
|
||||
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
|
||||
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
|
||||
* Note: For tiny x, 1/x dominate y1 and hence
|
||||
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
|
||||
* 3. For x>=2.
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* by method mentioned above.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pone(double), qone(double);
|
||||
#else
|
||||
static double pone(), qone();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0,2] */
|
||||
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
|
||||
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
|
||||
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
|
||||
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
|
||||
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
|
||||
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
|
||||
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
|
||||
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
|
||||
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_j1(double x)
|
||||
#else
|
||||
double __ieee754_j1(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v,y;
|
||||
int hx,ix;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/x;
|
||||
y = fd_fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = fd_sin(y);
|
||||
c = fd_cos(y);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure y+y not overflow */
|
||||
z = fd_cos(y+y);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
|
||||
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(y);
|
||||
else {
|
||||
u = pone(y); v = qone(y);
|
||||
z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(y);
|
||||
}
|
||||
if(hx<0) return -z;
|
||||
else return z;
|
||||
}
|
||||
if(ix<0x3e400000) { /* |x|<2**-27 */
|
||||
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(r00+z*(r01+z*(r02+z*r03)));
|
||||
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
|
||||
r *= x;
|
||||
return(x*0.5+r/s);
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double U0[5] = {
|
||||
#else
|
||||
static double U0[5] = {
|
||||
#endif
|
||||
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
|
||||
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
|
||||
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
|
||||
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
|
||||
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double V0[5] = {
|
||||
#else
|
||||
static double V0[5] = {
|
||||
#endif
|
||||
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
|
||||
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
|
||||
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
|
||||
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
|
||||
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_y1(double x)
|
||||
#else
|
||||
double __ieee754_y1(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int hx,ix,lx;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = 0x7fffffff&hx;
|
||||
lx = __LO(x);
|
||||
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = fd_sin(x);
|
||||
c = fd_cos(x);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = fd_cos(x+x);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
|
||||
* where x0 = x-3pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (cos(x) + sin(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
|
||||
else {
|
||||
u = pone(x); v = qone(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3c900000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
z = x*x;
|
||||
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
|
||||
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
|
||||
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
|
||||
}
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of pone is
|
||||
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* pone(x) = 1 + (R/S)
|
||||
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
|
||||
* S = 1 + ps0*s^2 + ... + ps4*s^10
|
||||
* and
|
||||
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
|
||||
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
|
||||
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
|
||||
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
|
||||
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps8[5] = {
|
||||
#else
|
||||
static double ps8[5] = {
|
||||
#endif
|
||||
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
|
||||
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
|
||||
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
|
||||
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
|
||||
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
|
||||
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
|
||||
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
|
||||
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
|
||||
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
|
||||
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps5[5] = {
|
||||
#else
|
||||
static double ps5[5] = {
|
||||
#endif
|
||||
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
|
||||
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
|
||||
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
|
||||
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
|
||||
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr3[6] = {
|
||||
#else
|
||||
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
|
||||
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
|
||||
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
|
||||
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
|
||||
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
|
||||
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps3[5] = {
|
||||
#else
|
||||
static double ps3[5] = {
|
||||
#endif
|
||||
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
|
||||
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
|
||||
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
|
||||
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
|
||||
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
|
||||
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
|
||||
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
|
||||
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
|
||||
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
|
||||
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps2[5] = {
|
||||
#else
|
||||
static double ps2[5] = {
|
||||
#endif
|
||||
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
|
||||
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
|
||||
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
|
||||
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
|
||||
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pone(double x)
|
||||
#else
|
||||
static double pone(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double z,r,s;
|
||||
int ix;
|
||||
ix = 0x7fffffff&__HI(x);
|
||||
if(ix>=0x40200000) {p = pr8; q= ps8;}
|
||||
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
|
||||
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
|
||||
else if(ix>=0x40000000){p = pr2; q= ps2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* qone(x) = s*(0.375 + (R/S))
|
||||
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
|
||||
* S = 1 + qs1*s^2 + ... + qs6*s^12
|
||||
* and
|
||||
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
|
||||
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
|
||||
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
|
||||
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
|
||||
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs8[6] = {
|
||||
#else
|
||||
static double qs8[6] = {
|
||||
#endif
|
||||
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
|
||||
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
|
||||
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
|
||||
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
|
||||
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
|
||||
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
|
||||
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
|
||||
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
|
||||
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
|
||||
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
|
||||
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs5[6] = {
|
||||
#else
|
||||
static double qs5[6] = {
|
||||
#endif
|
||||
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
|
||||
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
|
||||
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
|
||||
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
|
||||
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
|
||||
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr3[6] = {
|
||||
#else
|
||||
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
|
||||
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
|
||||
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
|
||||
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
|
||||
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
|
||||
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs3[6] = {
|
||||
#else
|
||||
static double qs3[6] = {
|
||||
#endif
|
||||
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
|
||||
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
|
||||
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
|
||||
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
|
||||
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
|
||||
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
|
||||
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
|
||||
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
|
||||
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
|
||||
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
|
||||
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs2[6] = {
|
||||
#else
|
||||
static double qs2[6] = {
|
||||
#endif
|
||||
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
|
||||
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
|
||||
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
|
||||
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
|
||||
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
|
||||
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double qone(double x)
|
||||
#else
|
||||
static double qone(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double s,r,z;
|
||||
int ix;
|
||||
ix = 0x7fffffff&__HI(x);
|
||||
if(ix>=0x40200000) {p = qr8; q= qs8;}
|
||||
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
|
||||
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
|
||||
else if(ix>=0x40000000){p = qr2; q= qs2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (.375 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,288 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_jn.c 1.4 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __ieee754_jn(n, x), __ieee754_yn(n, x)
|
||||
* floating point Bessel's function of the 1st and 2nd kind
|
||||
* of order n
|
||||
*
|
||||
* Special cases:
|
||||
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
||||
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
|
||||
* Note 2. About jn(n,x), yn(n,x)
|
||||
* For n=0, j0(x) is called,
|
||||
* for n=1, j1(x) is called,
|
||||
* for n<x, forward recursion us used starting
|
||||
* from values of j0(x) and j1(x).
|
||||
* for n>x, a continued fraction approximation to
|
||||
* j(n,x)/j(n-1,x) is evaluated and then backward
|
||||
* recursion is used starting from a supposed value
|
||||
* for j(n,x). The resulting value of j(0,x) is
|
||||
* compared with the actual value to correct the
|
||||
* supposed value of j(n,x).
|
||||
*
|
||||
* yn(n,x) is similar in all respects, except
|
||||
* that forward recursion is used for all
|
||||
* values of n>1.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
|
||||
|
||||
static double zero = 0.00000000000000000000e+00;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_jn(int n, double x)
|
||||
#else
|
||||
double __ieee754_jn(n,x)
|
||||
int n; double x;
|
||||
#endif
|
||||
{
|
||||
int i,hx,ix,lx, sgn;
|
||||
double a, b, temp, di;
|
||||
double z, w;
|
||||
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
hx = __HI(x);
|
||||
ix = 0x7fffffff&hx;
|
||||
lx = __LO(x);
|
||||
/* if J(n,NaN) is NaN */
|
||||
if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
x = -x;
|
||||
hx ^= 0x80000000;
|
||||
}
|
||||
if(n==0) return(__ieee754_j0(x));
|
||||
if(n==1) return(__ieee754_j1(x));
|
||||
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fd_fabs(x);
|
||||
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
|
||||
b = zero;
|
||||
else if((double)n<=x) {
|
||||
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = fd_cos(x)+fd_sin(x); break;
|
||||
case 1: temp = -fd_cos(x)+fd_sin(x); break;
|
||||
case 2: temp = -fd_cos(x)-fd_sin(x); break;
|
||||
case 3: temp = fd_cos(x)-fd_sin(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/fd_sqrt(x);
|
||||
} else {
|
||||
a = __ieee754_j0(x);
|
||||
b = __ieee754_j1(x);
|
||||
for(i=1;i<n;i++){
|
||||
temp = b;
|
||||
b = b*((double)(i+i)/x) - a; /* avoid underflow */
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(ix<0x3e100000) { /* x < 2**-29 */
|
||||
/* x is tiny, return the first Taylor expansion of J(n,x)
|
||||
* J(n,x) = 1/n!*(x/2)^n - ...
|
||||
*/
|
||||
if(n>33) /* underflow */
|
||||
b = zero;
|
||||
else {
|
||||
temp = x*0.5; b = temp;
|
||||
for (a=one,i=2;i<=n;i++) {
|
||||
a *= (double)i; /* a = n! */
|
||||
b *= temp; /* b = (x/2)^n */
|
||||
}
|
||||
b = b/a;
|
||||
}
|
||||
} else {
|
||||
/* use backward recurrence */
|
||||
/* x x^2 x^2
|
||||
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
|
||||
* 2n - 2(n+1) - 2(n+2)
|
||||
*
|
||||
* 1 1 1
|
||||
* (for large x) = ---- ------ ------ .....
|
||||
* 2n 2(n+1) 2(n+2)
|
||||
* -- - ------ - ------ -
|
||||
* x x x
|
||||
*
|
||||
* Let w = 2n/x and h=2/x, then the above quotient
|
||||
* is equal to the continued fraction:
|
||||
* 1
|
||||
* = -----------------------
|
||||
* 1
|
||||
* w - -----------------
|
||||
* 1
|
||||
* w+h - ---------
|
||||
* w+2h - ...
|
||||
*
|
||||
* To determine how many terms needed, let
|
||||
* Q(0) = w, Q(1) = w(w+h) - 1,
|
||||
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
|
||||
* When Q(k) > 1e4 good for single
|
||||
* When Q(k) > 1e9 good for double
|
||||
* When Q(k) > 1e17 good for quadruple
|
||||
*/
|
||||
/* determine k */
|
||||
double t,v;
|
||||
double q0,q1,h,tmp; int k,m;
|
||||
w = (n+n)/(double)x; h = 2.0/(double)x;
|
||||
q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
|
||||
while(q1<1.0e9) {
|
||||
k += 1; z += h;
|
||||
tmp = z*q1 - q0;
|
||||
q0 = q1;
|
||||
q1 = tmp;
|
||||
}
|
||||
m = n+n;
|
||||
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
|
||||
a = t;
|
||||
b = one;
|
||||
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
|
||||
* Hence, if n*(log(2n/x)) > ...
|
||||
* single 8.8722839355e+01
|
||||
* double 7.09782712893383973096e+02
|
||||
* long double 1.1356523406294143949491931077970765006170e+04
|
||||
* then recurrent value may overflow and the result is
|
||||
* likely underflow to zero
|
||||
*/
|
||||
tmp = n;
|
||||
v = two/x;
|
||||
tmp = tmp*__ieee754_log(fd_fabs(v*tmp));
|
||||
if(tmp<7.09782712893383973096e+02) {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
}
|
||||
} else {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
/* scale b to avoid spurious overflow */
|
||||
if(b>1e100) {
|
||||
a /= b;
|
||||
t /= b;
|
||||
b = one;
|
||||
}
|
||||
}
|
||||
}
|
||||
b = (t*__ieee754_j0(x)/b);
|
||||
}
|
||||
}
|
||||
if(sgn==1) return -b; else return b;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_yn(int n, double x)
|
||||
#else
|
||||
double __ieee754_yn(n,x)
|
||||
int n; double x;
|
||||
#endif
|
||||
{
|
||||
int i,hx,ix,lx;
|
||||
int sign;
|
||||
double a, b, temp;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = 0x7fffffff&hx;
|
||||
lx = __LO(x);
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
sign = 1;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
sign = 1 - ((n&1)<<1);
|
||||
}
|
||||
if(n==0) return(__ieee754_y0(x));
|
||||
if(n==1) return(sign*__ieee754_y1(x));
|
||||
if(ix==0x7ff00000) return zero;
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = fd_sin(x)-fd_cos(x); break;
|
||||
case 1: temp = -fd_sin(x)-fd_cos(x); break;
|
||||
case 2: temp = -fd_sin(x)+fd_cos(x); break;
|
||||
case 3: temp = fd_sin(x)+fd_cos(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/fd_sqrt(x);
|
||||
} else {
|
||||
a = __ieee754_y0(x);
|
||||
b = __ieee754_y1(x);
|
||||
/* quit if b is -inf */
|
||||
for(i=1;i<n&&(__HI(b) != 0xfff00000);i++){
|
||||
temp = b;
|
||||
b = ((double)(i+i)/x)*b - a;
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
if(sign>0) return b; else return -b;
|
||||
}
|
||||
|
|
@ -0,0 +1,49 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_lgamma.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_lgamma(x)
|
||||
* Return the logarithm of the Gamma function of x.
|
||||
*
|
||||
* Method: call __ieee754_lgamma_r
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_lgamma(double x)
|
||||
#else
|
||||
double __ieee754_lgamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return __ieee754_lgamma_r(x,&signgam);
|
||||
}
|
||||
|
|
@ -0,0 +1,320 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_lgamma_r.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_lgamma_r(x, signgamp)
|
||||
* Reentrant version of the logarithm of the Gamma function
|
||||
* with user provide pointer for the sign of Gamma(x).
|
||||
*
|
||||
* Method:
|
||||
* 1. Argument Reduction for 0 < x <= 8
|
||||
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
|
||||
* reduce x to a number in [1.5,2.5] by
|
||||
* lgamma(1+s) = log(s) + lgamma(s)
|
||||
* for example,
|
||||
* lgamma(7.3) = log(6.3) + lgamma(6.3)
|
||||
* = log(6.3*5.3) + lgamma(5.3)
|
||||
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
|
||||
* 2. Polynomial approximation of lgamma around its
|
||||
* minimun ymin=1.461632144968362245 to maintain monotonicity.
|
||||
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
|
||||
* Let z = x-ymin;
|
||||
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
|
||||
* where
|
||||
* poly(z) is a 14 degree polynomial.
|
||||
* 2. Rational approximation in the primary interval [2,3]
|
||||
* We use the following approximation:
|
||||
* s = x-2.0;
|
||||
* lgamma(x) = 0.5*s + s*P(s)/Q(s)
|
||||
* with accuracy
|
||||
* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
|
||||
* Our algorithms are based on the following observation
|
||||
*
|
||||
* zeta(2)-1 2 zeta(3)-1 3
|
||||
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
|
||||
* 2 3
|
||||
*
|
||||
* where Euler = 0.5771... is the Euler constant, which is very
|
||||
* close to 0.5.
|
||||
*
|
||||
* 3. For x>=8, we have
|
||||
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
|
||||
* (better formula:
|
||||
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
|
||||
* Let z = 1/x, then we approximation
|
||||
* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
|
||||
* by
|
||||
* 3 5 11
|
||||
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
|
||||
* where
|
||||
* |w - f(z)| < 2**-58.74
|
||||
*
|
||||
* 4. For negative x, since (G is gamma function)
|
||||
* -x*G(-x)*G(x) = pi/sin(pi*x),
|
||||
* we have
|
||||
* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
|
||||
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
|
||||
* Hence, for x<0, signgam = sign(sin(pi*x)) and
|
||||
* lgamma(x) = log(|Gamma(x)|)
|
||||
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
|
||||
* Note: one should avoid compute pi*(-x) directly in the
|
||||
* computation of sin(pi*(-x)).
|
||||
*
|
||||
* 5. Special Cases
|
||||
* lgamma(2+s) ~ s*(1-Euler) for tiny s
|
||||
* lgamma(1)=lgamma(2)=0
|
||||
* lgamma(x) ~ -log(x) for tiny x
|
||||
* lgamma(0) = lgamma(inf) = inf
|
||||
* lgamma(-integer) = +-inf
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
|
||||
a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
|
||||
a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
|
||||
a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
|
||||
a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
|
||||
a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
|
||||
a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
|
||||
a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
|
||||
a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
|
||||
a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
|
||||
a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
|
||||
a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
|
||||
tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
|
||||
tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
|
||||
t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
|
||||
t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
|
||||
t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
|
||||
t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
|
||||
t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
|
||||
t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
|
||||
t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
|
||||
t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
|
||||
t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
|
||||
t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
|
||||
t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
|
||||
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
|
||||
t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
|
||||
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
|
||||
t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
|
||||
u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
|
||||
u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
|
||||
u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
|
||||
u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
|
||||
u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
|
||||
v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
|
||||
v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
|
||||
v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
|
||||
v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
|
||||
v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
|
||||
s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
|
||||
s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
|
||||
s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
|
||||
s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
|
||||
s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
|
||||
s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
|
||||
r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
|
||||
r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
|
||||
r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
|
||||
r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
|
||||
r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
|
||||
r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
|
||||
w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
|
||||
w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
|
||||
w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
|
||||
w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
|
||||
w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
|
||||
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
|
||||
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
|
||||
|
||||
static double zero= 0.00000000000000000000e+00;
|
||||
|
||||
#ifdef __STDC__
|
||||
static double sin_pi(double x)
|
||||
#else
|
||||
static double sin_pi(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,z;
|
||||
int n,ix;
|
||||
|
||||
ix = 0x7fffffff&__HI(x);
|
||||
|
||||
if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = fd_floor(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= 0.5;
|
||||
y = 2.0*(y - fd_floor(y)); /* y = |x| mod 2.0 */
|
||||
n = (int) (y*4.0);
|
||||
} else {
|
||||
if(ix>=0x43400000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x43300000) z = y+two52; /* exact */
|
||||
n = __LO(z)&1; /* lower word of z */
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sin(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
|
||||
default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_lgamma_r(double x, int *signgamp)
|
||||
#else
|
||||
double __ieee754_lgamma_r(x,signgamp)
|
||||
double x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,lx,ix;
|
||||
|
||||
hx = __HI(x);
|
||||
lx = __LO(x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
if((ix|lx)==0) return one/zero;
|
||||
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_log(-x);
|
||||
} else return -__ieee754_log(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pi(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_log(pi/fd_fabs(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_log(x);
|
||||
if(ix>=0x3FE76944) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x40200000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(double)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+2.0); /* FALLTHRU */
|
||||
r += __ieee754_log(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x43900000) {
|
||||
t = __ieee754_log(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_log(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
|
|
@ -0,0 +1,155 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_log.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_log(x)
|
||||
* Return the logrithm of x
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* 2. Approximation of log(1+f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
||||
* (the values of Lg1 to Lg7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lg1*s +...+Lg7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log(1+f) = f - s*(f - R) (if f is not too large)
|
||||
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
||||
*
|
||||
* 3. Finally, log(x) = k*ln2 + log(1+f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log(x) is NaN with signal if x < 0 (including -INF) ;
|
||||
* log(+INF) is +INF; log(0) is -INF with signal;
|
||||
* log(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_log(double x)
|
||||
#else
|
||||
double __ieee754_log(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int k,hx,i,j;
|
||||
unsigned lx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
hx = __HI(x); /* high word of x */
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx+0x95f64)&0x100000;
|
||||
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
|
||||
k += (i>>20);
|
||||
f = x-1.0;
|
||||
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||||
if(f==zero) if(k==0) return zero; else {dk=(double)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
R = f*f*(0.5-0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(double)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
dk = (double)k;
|
||||
z = s*s;
|
||||
i = hx-0x6147a;
|
||||
w = z*z;
|
||||
j = 0x6b851-hx;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,107 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_log10.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_log10(x)
|
||||
* Return the base 10 logarithm of x
|
||||
*
|
||||
* Method :
|
||||
* Let log10_2hi = leading 40 bits of log10(2) and
|
||||
* log10_2lo = log10(2) - log10_2hi,
|
||||
* ivln10 = 1/log(10) rounded.
|
||||
* Then
|
||||
* n = ilogb(x),
|
||||
* if(n<0) n = n+1;
|
||||
* x = scalbn(x,-n);
|
||||
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
||||
*
|
||||
* Note 1:
|
||||
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
||||
* mode must set to Round-to-Nearest.
|
||||
* Note 2:
|
||||
* [1/log(10)] rounded to 53 bits has error .198 ulps;
|
||||
* log10 is monotonic at all binary break points.
|
||||
*
|
||||
* Special cases:
|
||||
* log10(x) is NaN with signal if x < 0;
|
||||
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
|
||||
* log10(NaN) is that NaN with no signal;
|
||||
* log10(10**N) = N for N=0,1,...,22.
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following constants.
|
||||
* The decimal values may be used, provided that the compiler will convert
|
||||
* from decimal to binary accurately enough to produce the hexadecimal values
|
||||
* shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
|
||||
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
|
||||
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_log10(double x)
|
||||
#else
|
||||
double __ieee754_log10(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,z;
|
||||
int i,k,hx;
|
||||
unsigned lx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
hx = __HI(x); /* high word of x */
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
i = ((unsigned)k&0x80000000)>>31;
|
||||
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
|
||||
y = (double)(k+i);
|
||||
__HI(x) = hx;
|
||||
z = y*log10_2lo + ivln10*__ieee754_log(x);
|
||||
return z+y*log10_2hi;
|
||||
}
|
||||
|
|
@ -0,0 +1,325 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_pow.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_pow(x,y) return x**y
|
||||
*
|
||||
* n
|
||||
* Method: Let x = 2 * (1+f)
|
||||
* 1. Compute and return log2(x) in two pieces:
|
||||
* log2(x) = w1 + w2,
|
||||
* where w1 has 53-24 = 29 bit trailing zeros.
|
||||
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
|
||||
* arithmetic, where |y'|<=0.5.
|
||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||
*
|
||||
* Special cases:
|
||||
* 1. (anything) ** 0 is 1
|
||||
* 2. (anything) ** 1 is itself
|
||||
* 3. (anything) ** NAN is NAN
|
||||
* 4. NAN ** (anything except 0) is NAN
|
||||
* 5. +-(|x| > 1) ** +INF is +INF
|
||||
* 6. +-(|x| > 1) ** -INF is +0
|
||||
* 7. +-(|x| < 1) ** +INF is +0
|
||||
* 8. +-(|x| < 1) ** -INF is +INF
|
||||
* 9. +-1 ** +-INF is NAN
|
||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||
*
|
||||
* Accuracy:
|
||||
* pow(x,y) returns x**y nearly rounded. In particular
|
||||
* pow(integer,integer)
|
||||
* always returns the correct integer provided it is
|
||||
* representable.
|
||||
*
|
||||
* Constants :
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
|
||||
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
|
||||
huge = 1.0e300,
|
||||
tiny = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_pow(double x, double y)
|
||||
#else
|
||||
double __ieee754_pow(x,y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double z,ax,z_h,z_l,p_h,p_l;
|
||||
double y1,t1,t2,r,s,t,u,v,w;
|
||||
int i,j,k,yisint,n;
|
||||
int hx,hy,ix,iy;
|
||||
unsigned lx,ly;
|
||||
|
||||
hx = __HI(x); lx = __LO(x);
|
||||
hy = __HI(y); ly = __LO(y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if((iy|ly)==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
|
||||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x43400000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3ff00000) {
|
||||
k = (iy>>20)-0x3ff; /* exponent */
|
||||
if(k>20) {
|
||||
j = ly>>(52-k);
|
||||
if((j<<(52-k))==(int)ly) yisint = 2-(j&1);
|
||||
} else if(ly==0) {
|
||||
j = iy>>(20-k);
|
||||
if((j<<(20-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if(ly==0) {
|
||||
if (iy==0x7ff00000) { /* y is +-inf */
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3ff00000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3fe00000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return fd_sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fd_fabs(x);
|
||||
/* special value of x */
|
||||
if(lx==0) {
|
||||
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3ff00000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1) {
|
||||
#ifdef HPUX
|
||||
__HI(z) ^= 1<<31; /* some HPUXes cannot negate 0.. */
|
||||
#else
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
#endif
|
||||
}
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x41e00000) { /* if |y| > 2**31 */
|
||||
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
||||
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = x-1; /* t has 20 trailing zeros */
|
||||
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
__LO(t1) = 0;
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
double s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00100000)
|
||||
{ax *= two53; n -= 53; ix = __HI(ax); }
|
||||
n += ((ix)>>20)-0x3ff;
|
||||
j = ix&0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3ff00000; /* normalize ix */
|
||||
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00100000;}
|
||||
__HI(ax) = ix;
|
||||
|
||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
s = u*v;
|
||||
s_h = s;
|
||||
__LO(s_h) = 0;
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = s*s;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+s);
|
||||
s2 = s_h*s_h;
|
||||
t_h = 3.0+s2+r;
|
||||
__LO(t_h) = 0;
|
||||
t_l = r-((t_h-3.0)-s2);
|
||||
/* u+v = s*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*s;
|
||||
/* 2/(3log2)*(s+...) */
|
||||
p_h = u+v;
|
||||
__LO(p_h) = 0;
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
__LO(t1) = 0;
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if((((hx>>31)+1)|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
y1 = y;
|
||||
__LO(y1) = 0;
|
||||
p_l = (y-y1)*t1+y*t2;
|
||||
p_h = y1*t1;
|
||||
z = p_l+p_h;
|
||||
j = __HI(z);
|
||||
i = __LO(z);
|
||||
if (j>=0x40900000) { /* z >= 1024 */
|
||||
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else {
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
||||
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
else {
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>20)-0x3ff;
|
||||
n = 0;
|
||||
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00100000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
__HI(t) = (n&~(0x000fffff>>k));
|
||||
n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
__LO(t) = 0;
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
j = __HI(z);
|
||||
j += (n<<20);
|
||||
if((j>>20)<=0) z = fd_scalbn(z,n); /* subnormal output */
|
||||
else __HI(z) += (n<<20);
|
||||
return s*z;
|
||||
}
|
||||
|
|
@ -0,0 +1,191 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_rem_pio2.c 1.4 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_rem_pio2(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2()
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const int two_over_pi[] = {
|
||||
#else
|
||||
static int two_over_pi[] = {
|
||||
#endif
|
||||
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
||||
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
||||
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
||||
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
||||
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
||||
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
||||
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
||||
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
||||
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
||||
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
||||
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int npio2_hw[] = {
|
||||
#else
|
||||
static int npio2_hw[] = {
|
||||
#endif
|
||||
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
||||
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
||||
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
||||
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
||||
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
||||
0x404858EB, 0x404921FB,
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 33 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 33 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 33 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
||||
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
||||
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
||||
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
||||
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
||||
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __ieee754_rem_pio2(double x, double *y)
|
||||
#else
|
||||
int __ieee754_rem_pio2(x,y)
|
||||
double x,y[];
|
||||
#endif
|
||||
{
|
||||
double z,w,t,r,fn;
|
||||
double tx[3];
|
||||
int e0,i,j,nx,n,ix,hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
||||
t = fd_fabs(x);
|
||||
n = (int) (t*invpio2+half);
|
||||
fn = (double)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
||||
if(n<32&&ix!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
j = ix>>20;
|
||||
y[0] = r-w;
|
||||
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
||||
if(i>16) { /* 2nd iteration needed, good to 118 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
||||
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-23) */
|
||||
__LO(z) = __LO(x);
|
||||
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
|
||||
__HI(z) = ix - (e0<<20);
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (double)((int)(z));
|
||||
z = (z-tx[i])*two24;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
|
|
@ -0,0 +1,93 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_remainder.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_remainder(x,p)
|
||||
* Return :
|
||||
* returns x REM p = x - [x/p]*p as if in infinite
|
||||
* precise arithmetic, where [x/p] is the (infinite bit)
|
||||
* integer nearest x/p (in half way case choose the even one).
|
||||
* Method :
|
||||
* Based on fmod() return x-[x/p]chopped*p exactlp.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_remainder(double x, double p)
|
||||
#else
|
||||
double __ieee754_remainder(x,p)
|
||||
double x,p;
|
||||
#endif
|
||||
{
|
||||
int hx,hp;
|
||||
unsigned sx,lx,lp;
|
||||
double p_half;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
hp = __HI(p); /* high word of p */
|
||||
lp = __LO(p); /* low word of p */
|
||||
sx = hx&0x80000000;
|
||||
hp &= 0x7fffffff;
|
||||
hx &= 0x7fffffff;
|
||||
|
||||
/* purge off exception values */
|
||||
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
|
||||
if((hx>=0x7ff00000)|| /* x not finite */
|
||||
((hp>=0x7ff00000)&& /* p is NaN */
|
||||
(((hp-0x7ff00000)|lp)!=0)))
|
||||
return (x*p)/(x*p);
|
||||
|
||||
|
||||
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
|
||||
if (((hx-hp)|(lx-lp))==0) return zero*x;
|
||||
x = fd_fabs(x);
|
||||
p = fd_fabs(p);
|
||||
if (hp<0x00200000) {
|
||||
if(x+x>p) {
|
||||
x-=p;
|
||||
if(x+x>=p) x -= p;
|
||||
}
|
||||
} else {
|
||||
p_half = 0.5*p;
|
||||
if(x>p_half) {
|
||||
x-=p;
|
||||
if(x>=p_half) x -= p;
|
||||
}
|
||||
}
|
||||
__HI(x) ^= sx;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,67 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_scalb.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __ieee754_scalb(x, fn) is provide for
|
||||
* passing various standard test suite. One
|
||||
* should use scalbn() instead.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef _SCALB_INT
|
||||
#ifdef __STDC__
|
||||
double __ieee754_scalb(double x, int fn)
|
||||
#else
|
||||
double __ieee754_scalb(x,fn)
|
||||
double x; int fn;
|
||||
#endif
|
||||
#else
|
||||
#ifdef __STDC__
|
||||
double __ieee754_scalb(double x, double fn)
|
||||
#else
|
||||
double __ieee754_scalb(x,fn)
|
||||
double x, fn;
|
||||
#endif
|
||||
#endif
|
||||
{
|
||||
#ifdef _SCALB_INT
|
||||
return fd_scalbn(x,fn);
|
||||
#else
|
||||
if (fd_isnan(x)||fd_isnan(fn)) return x*fn;
|
||||
if (!fd_finite(fn)) {
|
||||
if(fn>0.0) return x*fn;
|
||||
else return x/(-fn);
|
||||
}
|
||||
if (fd_rint(fn)!=fn) return (fn-fn)/(fn-fn);
|
||||
if ( fn > 65000.0) return fd_scalbn(x, 65000);
|
||||
if (-fn > 65000.0) return fd_scalbn(x,-65000);
|
||||
return fd_scalbn(x,(int)fn);
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)e_sinh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_sinh(x)
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : sinh(x) := x*shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0)=0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, shuge = 1.0e307;
|
||||
#else
|
||||
static double one = 1.0, shuge = 1.0e307;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sinh(double x)
|
||||
#else
|
||||
double __ieee754_sinh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w,h;
|
||||
int ix,jx;
|
||||
unsigned lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
jx = __HI(x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x+x;
|
||||
|
||||
h = 0.5;
|
||||
if (jx<0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix<0x3e300000) /* |x|<2**-28 */
|
||||
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = fd_expm1(fd_fabs(x));
|
||||
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
|
||||
return h*(t+t/(t+one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x40862E42) return h*__ieee754_exp(fd_fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
|
||||
if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
|
||||
w = __ieee754_exp(0.5*fd_fabs(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*shuge;
|
||||
}
|
||||
|
|
@ -0,0 +1,466 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
/* @(#)e_sqrt.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, tiny=1.0e-300;
|
||||
#else
|
||||
static double one = 1.0, tiny=1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sqrt(double x)
|
||||
#else
|
||||
double __ieee754_sqrt(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int sign = (int)0x80000000;
|
||||
unsigned r,t1,s1,ix1,q1;
|
||||
int ix0,s0,q,m,t,i;
|
||||
|
||||
ix0 = __HI(x); /* high word of x */
|
||||
ix1 = __LO(x); /* low word of x */
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix0&0x7ff00000)==0x7ff00000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix0<=0) {
|
||||
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix0<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0>>20);
|
||||
if(m==0) { /* subnormal x */
|
||||
while(ix0==0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1>>11); ix1 <<= 21;
|
||||
}
|
||||
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
|
||||
m -= i-1;
|
||||
ix0 |= (ix1>>(32-i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0&0x000fffff)|0x00100000;
|
||||
if(m&1){ /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s0+r;
|
||||
if(t<=ix0) {
|
||||
s0 = t+r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while(r!=0) {
|
||||
t1 = s1+r;
|
||||
t = s0;
|
||||
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
|
||||
s1 = t1+r;
|
||||
if(((int)(t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
|
||||
ix0 -= t;
|
||||
if (ix1 < t1) ix0 -= 1;
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if((ix0|ix1)!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
|
||||
else if (z>one) {
|
||||
if (q1==(unsigned)0xfffffffe) q+=1;
|
||||
q1+=2;
|
||||
} else
|
||||
q1 += (q1&1);
|
||||
}
|
||||
}
|
||||
ix0 = (q>>1)+0x3fe00000;
|
||||
ix1 = q1>>1;
|
||||
if ((q&1)==1) ix1 |= sign;
|
||||
ix0 += (m <<20);
|
||||
__HI(z) = ix0;
|
||||
__LO(z) = ix1;
|
||||
return z;
|
||||
}
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper then the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
|
||||
*/
|
||||
|
||||
|
|
@ -0,0 +1,242 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)fdlibm.h 1.5 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
|
||||
/* Modified defines start here.. */
|
||||
#ifdef _WIN32
|
||||
#define huge myhuge
|
||||
#define __LITTLE_ENDIAN
|
||||
#endif
|
||||
|
||||
/* End here. The rest is the standard file. */
|
||||
|
||||
#ifdef __NEWVALID /* special setup for Sun test regime */
|
||||
#if defined(i386) || defined(i486) || \
|
||||
defined(intel) || defined(x86) || defined(i86pc)
|
||||
#define __LITTLE_ENDIAN
|
||||
#endif
|
||||
#endif
|
||||
|
||||
|
||||
#ifdef __LITTLE_ENDIAN
|
||||
#define __HI(x) *(1+(int*)&x)
|
||||
#define __LO(x) *(int*)&x
|
||||
#define __HIp(x) *(1+(int*)x)
|
||||
#define __LOp(x) *(int*)x
|
||||
#else
|
||||
#define __HI(x) *(int*)&x
|
||||
#define __LO(x) *(1+(int*)&x)
|
||||
#define __HIp(x) *(int*)x
|
||||
#define __LOp(x) *(1+(int*)x)
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
#define __P(p) p
|
||||
#else
|
||||
#define __P(p) ()
|
||||
#endif
|
||||
|
||||
/*
|
||||
* ANSI/POSIX
|
||||
*/
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#define MAXFLOAT ((float)3.40282346638528860e+38)
|
||||
|
||||
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
|
||||
|
||||
#define _LIB_VERSION_TYPE enum fdversion
|
||||
#define _LIB_VERSION _fdlib_version
|
||||
|
||||
/* if global variable _LIB_VERSION is not desirable, one may
|
||||
* change the following to be a constant by:
|
||||
* #define _LIB_VERSION_TYPE const enum version
|
||||
* In that case, after one initializes the value _LIB_VERSION (see
|
||||
* s_lib_version.c) during compile time, it cannot be modified
|
||||
* in the middle of a program
|
||||
*/
|
||||
extern _LIB_VERSION_TYPE _LIB_VERSION;
|
||||
|
||||
#define _IEEE_ fdlibm_ieee
|
||||
#define _SVID_ fdlibm_svid
|
||||
#define _XOPEN_ fdlibm_xopen
|
||||
#define _POSIX_ fdlibm_posix
|
||||
|
||||
struct exception {
|
||||
int type;
|
||||
char *name;
|
||||
double arg1;
|
||||
double arg2;
|
||||
double retval;
|
||||
};
|
||||
|
||||
#define HUGE MAXFLOAT
|
||||
|
||||
/*
|
||||
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
|
||||
* (one may replace the following line by "#include <values.h>")
|
||||
*/
|
||||
|
||||
#define X_TLOSS 1.41484755040568800000e+16
|
||||
|
||||
#define DOMAIN 1
|
||||
#define SING 2
|
||||
#define OVERFLOW 3
|
||||
#define UNDERFLOW 4
|
||||
#define TLOSS 5
|
||||
#define PLOSS 6
|
||||
|
||||
/*
|
||||
* ANSI/POSIX
|
||||
*/
|
||||
|
||||
extern double fd_acos __P((double));
|
||||
extern double fd_asin __P((double));
|
||||
extern double fd_atan __P((double));
|
||||
extern double fd_atan2 __P((double, double));
|
||||
extern double fd_cos __P((double));
|
||||
extern double fd_sin __P((double));
|
||||
extern double fd_tan __P((double));
|
||||
|
||||
extern double fd_cosh __P((double));
|
||||
extern double fd_sinh __P((double));
|
||||
extern double fd_tanh __P((double));
|
||||
|
||||
extern double fd_exp __P((double));
|
||||
extern double fd_frexp __P((double, int *));
|
||||
extern double fd_ldexp __P((double, int));
|
||||
extern double fd_log __P((double));
|
||||
extern double fd_log10 __P((double));
|
||||
extern double fd_modf __P((double, double *));
|
||||
|
||||
extern double fd_pow __P((double, double));
|
||||
extern double fd_sqrt __P((double));
|
||||
|
||||
extern double fd_ceil __P((double));
|
||||
extern double fd_fabs __P((double));
|
||||
extern double fd_floor __P((double));
|
||||
extern double fd_fmod __P((double, double));
|
||||
|
||||
extern double fd_erf __P((double));
|
||||
extern double fd_erfc __P((double));
|
||||
extern double fd_gamma __P((double));
|
||||
extern double fd_hypot __P((double, double));
|
||||
extern int fd_isnan __P((double));
|
||||
extern int fd_finite __P((double));
|
||||
extern double fd_j0 __P((double));
|
||||
extern double fd_j1 __P((double));
|
||||
extern double fd_jn __P((int, double));
|
||||
extern double fd_lgamma __P((double));
|
||||
extern double fd_y0 __P((double));
|
||||
extern double fd_y1 __P((double));
|
||||
extern double fd_yn __P((int, double));
|
||||
|
||||
extern double fd_acosh __P((double));
|
||||
extern double fd_asinh __P((double));
|
||||
extern double fd_atanh __P((double));
|
||||
extern double fd_cbrt __P((double));
|
||||
extern double fd_logb __P((double));
|
||||
extern double fd_nextafter __P((double, double));
|
||||
extern double fd_remainder __P((double, double));
|
||||
#ifdef _SCALB_INT
|
||||
extern double fd_scalb __P((double, int));
|
||||
#else
|
||||
extern double fd_scalb __P((double, double));
|
||||
#endif
|
||||
|
||||
extern int fd_matherr __P((struct exception *));
|
||||
|
||||
/*
|
||||
* IEEE Test Vector
|
||||
*/
|
||||
extern double significand __P((double));
|
||||
|
||||
/*
|
||||
* Functions callable from C, intended to support IEEE arithmetic.
|
||||
*/
|
||||
extern double fd_copysign __P((double, double));
|
||||
extern int fd_ilogb __P((double));
|
||||
extern double fd_rint __P((double));
|
||||
extern double fd_scalbn __P((double, int));
|
||||
|
||||
/*
|
||||
* BSD math library entry points
|
||||
*/
|
||||
extern double fd_expm1 __P((double));
|
||||
extern double fd_log1p __P((double));
|
||||
|
||||
/*
|
||||
* Reentrant version of gamma & lgamma; passes signgam back by reference
|
||||
* as the second argument; user must allocate space for signgam.
|
||||
*/
|
||||
#ifdef _REENTRANT
|
||||
extern double gamma_r __P((double, int *));
|
||||
extern double lgamma_r __P((double, int *));
|
||||
#endif /* _REENTRANT */
|
||||
|
||||
/* ieee style elementary functions */
|
||||
extern double __ieee754_sqrt __P((double));
|
||||
extern double __ieee754_acos __P((double));
|
||||
extern double __ieee754_acosh __P((double));
|
||||
extern double __ieee754_log __P((double));
|
||||
extern double __ieee754_atanh __P((double));
|
||||
extern double __ieee754_asin __P((double));
|
||||
extern double __ieee754_atan2 __P((double,double));
|
||||
extern double __ieee754_exp __P((double));
|
||||
extern double __ieee754_cosh __P((double));
|
||||
extern double __ieee754_fmod __P((double,double));
|
||||
extern double __ieee754_pow __P((double,double));
|
||||
extern double __ieee754_lgamma_r __P((double,int *));
|
||||
extern double __ieee754_gamma_r __P((double,int *));
|
||||
extern double __ieee754_lgamma __P((double));
|
||||
extern double __ieee754_gamma __P((double));
|
||||
extern double __ieee754_log10 __P((double));
|
||||
extern double __ieee754_sinh __P((double));
|
||||
extern double __ieee754_hypot __P((double,double));
|
||||
extern double __ieee754_j0 __P((double));
|
||||
extern double __ieee754_j1 __P((double));
|
||||
extern double __ieee754_y0 __P((double));
|
||||
extern double __ieee754_y1 __P((double));
|
||||
extern double __ieee754_jn __P((int,double));
|
||||
extern double __ieee754_yn __P((int,double));
|
||||
extern double __ieee754_remainder __P((double,double));
|
||||
extern int __ieee754_rem_pio2 __P((double,double*));
|
||||
#ifdef _SCALB_INT
|
||||
extern double __ieee754_scalb __P((double,int));
|
||||
#else
|
||||
extern double __ieee754_scalb __P((double,double));
|
||||
#endif
|
||||
|
||||
/* fdlibm kernel function */
|
||||
extern double __kernel_standard __P((double,double,int));
|
||||
extern double __kernel_sin __P((double,double,int));
|
||||
extern double __kernel_cos __P((double,double));
|
||||
extern double __kernel_tan __P((double,double,int));
|
||||
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
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|
|
@ -0,0 +1,108 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)k_cos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __kernel_cos( x, y )
|
||||
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
|
||||
* 3. cos(x) is approximated by a polynomial of degree 14 on
|
||||
* [0,pi/4]
|
||||
* 4 14
|
||||
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
|
||||
* where the remez error is
|
||||
*
|
||||
* | 2 4 6 8 10 12 14 | -58
|
||||
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
|
||||
* | |
|
||||
*
|
||||
* 4 6 8 10 12 14
|
||||
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
|
||||
* cos(x) = 1 - x*x/2 + r
|
||||
* since cos(x+y) ~ cos(x) - sin(x)*y
|
||||
* ~ cos(x) - x*y,
|
||||
* a correction term is necessary in cos(x) and hence
|
||||
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
|
||||
* For better accuracy when x > 0.3, let qx = |x|/4 with
|
||||
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
|
||||
* Then
|
||||
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
|
||||
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
|
||||
* magnitude of the latter is at least a quarter of x*x/2,
|
||||
* thus, reducing the rounding error in the subtraction.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
|
||||
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
|
||||
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
|
||||
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
|
||||
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
|
||||
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_cos(double x, double y)
|
||||
#else
|
||||
double __kernel_cos(x, y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
double a,hz,z,r,qx;
|
||||
int ix;
|
||||
ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x3e400000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3FD33333) /* if |x| < 0.3 */
|
||||
return one - (0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3fe90000) { /* x > 0.78125 */
|
||||
qx = 0.28125;
|
||||
} else {
|
||||
__HI(qx) = ix-0x00200000; /* x/4 */
|
||||
__LO(qx) = 0;
|
||||
}
|
||||
hz = 0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,332 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)k_rem_pio2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
* double x[],y[]; int e0,nx,prec; int ipio2[];
|
||||
*
|
||||
* __kernel_rem_pio2 return the last three digits of N with
|
||||
* y = x - N*pi/2
|
||||
* so that |y| < pi/2.
|
||||
*
|
||||
* The method is to compute the integer (mod 8) and fraction parts of
|
||||
* (2/pi)*x without doing the full multiplication. In general we
|
||||
* skip the part of the product that are known to be a huge integer (
|
||||
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
||||
* independent of the exponent of the input.
|
||||
*
|
||||
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
||||
*
|
||||
* Input parameters:
|
||||
* x[] The input value (must be positive) is broken into nx
|
||||
* pieces of 24-bit integers in double precision format.
|
||||
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
||||
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
||||
* match x's up to 24 bits.
|
||||
*
|
||||
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
||||
* e0 = ilogb(z)-23
|
||||
* z = scalbn(z,-e0)
|
||||
* for i = 0,1,2
|
||||
* x[i] = floor(z)
|
||||
* z = (z-x[i])*2**24
|
||||
*
|
||||
*
|
||||
* y[] ouput result in an array of double precision numbers.
|
||||
* The dimension of y[] is:
|
||||
* 24-bit precision 1
|
||||
* 53-bit precision 2
|
||||
* 64-bit precision 2
|
||||
* 113-bit precision 3
|
||||
* The actual value is the sum of them. Thus for 113-bit
|
||||
* precison, one may have to do something like:
|
||||
*
|
||||
* long double t,w,r_head, r_tail;
|
||||
* t = (long double)y[2] + (long double)y[1];
|
||||
* w = (long double)y[0];
|
||||
* r_head = t+w;
|
||||
* r_tail = w - (r_head - t);
|
||||
*
|
||||
* e0 The exponent of x[0]
|
||||
*
|
||||
* nx dimension of x[]
|
||||
*
|
||||
* prec an integer indicating the precision:
|
||||
* 0 24 bits (single)
|
||||
* 1 53 bits (double)
|
||||
* 2 64 bits (extended)
|
||||
* 3 113 bits (quad)
|
||||
*
|
||||
* ipio2[]
|
||||
* integer array, contains the (24*i)-th to (24*i+23)-th
|
||||
* bit of 2/pi after binary point. The corresponding
|
||||
* floating value is
|
||||
*
|
||||
* ipio2[i] * 2^(-24(i+1)).
|
||||
*
|
||||
* External function:
|
||||
* double scalbn(), floor();
|
||||
*
|
||||
*
|
||||
* Here is the description of some local variables:
|
||||
*
|
||||
* jk jk+1 is the initial number of terms of ipio2[] needed
|
||||
* in the computation. The recommended value is 2,3,4,
|
||||
* 6 for single, double, extended,and quad.
|
||||
*
|
||||
* jz local integer variable indicating the number of
|
||||
* terms of ipio2[] used.
|
||||
*
|
||||
* jx nx - 1
|
||||
*
|
||||
* jv index for pointing to the suitable ipio2[] for the
|
||||
* computation. In general, we want
|
||||
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
||||
* is an integer. Thus
|
||||
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
||||
* Hence jv = max(0,(e0-3)/24).
|
||||
*
|
||||
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
||||
*
|
||||
* q[] double array with integral value, representing the
|
||||
* 24-bits chunk of the product of x and 2/pi.
|
||||
*
|
||||
* q0 the corresponding exponent of q[0]. Note that the
|
||||
* exponent for q[i] would be q0-24*i.
|
||||
*
|
||||
* PIo2[] double precision array, obtained by cutting pi/2
|
||||
* into 24 bits chunks.
|
||||
*
|
||||
* f[] ipio2[] in floating point
|
||||
*
|
||||
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
||||
*
|
||||
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
||||
*
|
||||
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
||||
* it also indicates the *sign* of the result.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
||||
#else
|
||||
static int init_jk[] = {2,3,4,6};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double PIo2[] = {
|
||||
#else
|
||||
static double PIo2[] = {
|
||||
#endif
|
||||
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
||||
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
||||
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
||||
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
||||
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
||||
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
||||
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
||||
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
|
||||
#else
|
||||
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
double x[], y[]; int e0,nx,prec; int ipio2[];
|
||||
#endif
|
||||
{
|
||||
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
double z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/24; if(jv<0) jv=0;
|
||||
q0 = e0-24*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (double)((int)(twon24* z));
|
||||
iq[i] = (int)(z-two24*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = fd_scalbn(z,q0); /* actual value of z */
|
||||
z -= 8.0*fd_floor(z*0.125); /* trim off integer >= 8 */
|
||||
n = (int) z;
|
||||
z -= (double)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(24-q0)); n += i;
|
||||
iq[jz-1] -= i<<(24-q0);
|
||||
ih = iq[jz-1]>>(23-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>23;
|
||||
else if(z>=0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x1000000- j;
|
||||
}
|
||||
} else iq[i] = 0xffffff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7fffff; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3fffff; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= fd_scalbn(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (double) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==0.0) {
|
||||
jz -= 1; q0 -= 24;
|
||||
while(iq[jz]==0) { jz--; q0-=24;}
|
||||
} else { /* break z into 24-bit if necessary */
|
||||
z = fd_scalbn(z,-q0);
|
||||
if(z>=two24) {
|
||||
fw = (double)((int)(twon24*z));
|
||||
iq[jz] = (int)(z-two24*fw);
|
||||
jz += 1; q0 += 24;
|
||||
iq[jz] = (int) fw;
|
||||
} else iq[jz] = (int) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = fd_scalbn(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(double)iq[i]; fw*=twon24;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
|
|
@ -0,0 +1,90 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)k_sin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __kernel_sin( x, y, iy)
|
||||
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
|
||||
* 3. sin(x) is approximated by a polynomial of degree 13 on
|
||||
* [0,pi/4]
|
||||
* 3 13
|
||||
* sin(x) ~ x + S1*x + ... + S6*x
|
||||
* where
|
||||
*
|
||||
* |sin(x) 2 4 6 8 10 12 | -58
|
||||
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* 4. sin(x+y) = sin(x) + sin'(x')*y
|
||||
* ~ sin(x) + (1-x*x/2)*y
|
||||
* For better accuracy, let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
|
||||
* then 3 2
|
||||
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
|
||||
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
|
||||
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
|
||||
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
|
||||
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
|
||||
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_sin(double x, double y, int iy)
|
||||
#else
|
||||
double __kernel_sin(x, y, iy)
|
||||
double x,y; int iy; /* iy=0 if y is zero */
|
||||
#endif
|
||||
{
|
||||
double z,r,v;
|
||||
int ix;
|
||||
ix = __HI(x)&0x7fffffff; /* high word of x */
|
||||
if(ix<0x3e400000) /* |x| < 2**-27 */
|
||||
{if((int)x==0) return x;} /* generate inexact */
|
||||
z = x*x;
|
||||
v = z*x;
|
||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||
if(iy==0) return x+v*(S1+z*r);
|
||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||
}
|
||||
|
|
@ -0,0 +1,758 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)k_standard.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/* XXX ugly hack to get msvc to link without error. */
|
||||
#if _LIB_VERSION == _IEEE_
|
||||
int errno;
|
||||
# define EDOM 0
|
||||
# define ERANGE 0
|
||||
#else
|
||||
# include <errno.h>
|
||||
#endif
|
||||
|
||||
|
||||
#ifndef _USE_WRITE
|
||||
#include <stdio.h> /* fputs(), stderr */
|
||||
#define WRITE2(u,v) fputs(u, stderr)
|
||||
#else /* !defined(_USE_WRITE) */
|
||||
#include <unistd.h> /* write */
|
||||
#define WRITE2(u,v) write(2, u, v)
|
||||
#undef fflush
|
||||
#endif /* !defined(_USE_WRITE) */
|
||||
|
||||
static double zero = 0.0; /* used as const */
|
||||
|
||||
/*
|
||||
* Standard conformance (non-IEEE) on exception cases.
|
||||
* Mapping:
|
||||
* 1 -- acos(|x|>1)
|
||||
* 2 -- asin(|x|>1)
|
||||
* 3 -- atan2(+-0,+-0)
|
||||
* 4 -- hypot overflow
|
||||
* 5 -- cosh overflow
|
||||
* 6 -- exp overflow
|
||||
* 7 -- exp underflow
|
||||
* 8 -- y0(0)
|
||||
* 9 -- y0(-ve)
|
||||
* 10-- y1(0)
|
||||
* 11-- y1(-ve)
|
||||
* 12-- yn(0)
|
||||
* 13-- yn(-ve)
|
||||
* 14-- lgamma(finite) overflow
|
||||
* 15-- lgamma(-integer)
|
||||
* 16-- log(0)
|
||||
* 17-- log(x<0)
|
||||
* 18-- log10(0)
|
||||
* 19-- log10(x<0)
|
||||
* 20-- pow(0.0,0.0)
|
||||
* 21-- pow(x,y) overflow
|
||||
* 22-- pow(x,y) underflow
|
||||
* 23-- pow(0,negative)
|
||||
* 24-- pow(neg,non-integral)
|
||||
* 25-- sinh(finite) overflow
|
||||
* 26-- sqrt(negative)
|
||||
* 27-- fmod(x,0)
|
||||
* 28-- remainder(x,0)
|
||||
* 29-- acosh(x<1)
|
||||
* 30-- atanh(|x|>1)
|
||||
* 31-- atanh(|x|=1)
|
||||
* 32-- scalb overflow
|
||||
* 33-- scalb underflow
|
||||
* 34-- j0(|x|>X_TLOSS)
|
||||
* 35-- y0(x>X_TLOSS)
|
||||
* 36-- j1(|x|>X_TLOSS)
|
||||
* 37-- y1(x>X_TLOSS)
|
||||
* 38-- jn(|x|>X_TLOSS, n)
|
||||
* 39-- yn(x>X_TLOSS, n)
|
||||
* 40-- gamma(finite) overflow
|
||||
* 41-- gamma(-integer)
|
||||
* 42-- pow(NaN,0.0)
|
||||
*/
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_standard(double x, double y, int type)
|
||||
#else
|
||||
double __kernel_standard(x,y,type)
|
||||
double x,y; int type;
|
||||
#endif
|
||||
{
|
||||
struct exception exc;
|
||||
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
|
||||
#define HUGE_VAL inf
|
||||
double inf = 0.0;
|
||||
|
||||
__HI(inf) = 0x7ff00000; /* set inf to infinite */
|
||||
#endif
|
||||
|
||||
#ifdef _USE_WRITE
|
||||
(void) fflush(stdout);
|
||||
#endif
|
||||
exc.arg1 = x;
|
||||
exc.arg2 = y;
|
||||
switch(type) {
|
||||
case 1:
|
||||
/* acos(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "acos";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("acos: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 2:
|
||||
/* asin(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "asin";
|
||||
exc.retval = zero;
|
||||
if(_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("asin: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 3:
|
||||
/* atan2(+-0,+-0) */
|
||||
exc.arg1 = y;
|
||||
exc.arg2 = x;
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "atan2";
|
||||
exc.retval = zero;
|
||||
if(_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atan2: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 4:
|
||||
/* hypot(finite,finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "hypot";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 5:
|
||||
/* cosh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "cosh";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 6:
|
||||
/* exp(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "exp";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 7:
|
||||
/* exp(finite) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "exp";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 8:
|
||||
/* y0(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "y0";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 9:
|
||||
/* y0(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "y0";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 10:
|
||||
/* y1(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "y1";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 11:
|
||||
/* y1(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "y1";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 12:
|
||||
/* yn(n,0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "yn";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 13:
|
||||
/* yn(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "yn";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 14:
|
||||
/* lgamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "lgamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 15:
|
||||
/* lgamma(-integer) or lgamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "lgamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("lgamma: SING error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 16:
|
||||
/* log(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "log";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log: SING error\n", 16);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 17:
|
||||
/* log(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "log";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log: DOMAIN error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 18:
|
||||
/* log10(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "log10";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log10: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 19:
|
||||
/* log10(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "log10";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log10: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 20:
|
||||
/* pow(0.0,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
(void) WRITE2("pow(0,0): DOMAIN error\n", 23);
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 21:
|
||||
/* pow(x,y) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
exc.retval = HUGE;
|
||||
y *= 0.5;
|
||||
if(x<zero&&fd_rint(y)!=y) exc.retval = -HUGE;
|
||||
} else {
|
||||
exc.retval = HUGE_VAL;
|
||||
y *= 0.5;
|
||||
if(x<zero&&fd_rint(y)!=y) exc.retval = -HUGE_VAL;
|
||||
}
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 22:
|
||||
/* pow(x,y) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "pow";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 23:
|
||||
/* 0**neg */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 24:
|
||||
/* neg**non-integral */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero; /* X/Open allow NaN */
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 25:
|
||||
/* sinh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "sinh";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = ( (x>zero) ? HUGE : -HUGE);
|
||||
else
|
||||
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 26:
|
||||
/* sqrt(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "sqrt";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("sqrt: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 27:
|
||||
/* fmod(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "fmod";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = x;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("fmod: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 28:
|
||||
/* remainder(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "remainder";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("remainder: DOMAIN error\n", 24);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 29:
|
||||
/* acosh(x<1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "acosh";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("acosh: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 30:
|
||||
/* atanh(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "atanh";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atanh: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 31:
|
||||
/* atanh(|x|=1) */
|
||||
exc.type = SING;
|
||||
exc.name = "atanh";
|
||||
exc.retval = x/zero; /* sign(x)*inf */
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atanh: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 32:
|
||||
/* scalb overflow; SVID also returns +-HUGE_VAL */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "scalb";
|
||||
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 33:
|
||||
/* scalb underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "scalb";
|
||||
exc.retval = fd_copysign(zero,x);
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 34:
|
||||
/* j0(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "j0";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 35:
|
||||
/* y0(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "y0";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 36:
|
||||
/* j1(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "j1";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 37:
|
||||
/* y1(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "y1";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 38:
|
||||
/* jn(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "jn";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 39:
|
||||
/* yn(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "yn";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 40:
|
||||
/* gamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "gamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 41:
|
||||
/* gamma(-integer) or gamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "gamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("gamma: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 42:
|
||||
/* pow(NaN,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
exc.retval = x;
|
||||
if (_LIB_VERSION == _IEEE_ ||
|
||||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
|
||||
else if (!fd_matherr(&exc)) {
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
}
|
||||
return exc.retval;
|
||||
}
|
||||
|
|
@ -0,0 +1,141 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)k_tan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __kernel_tan( x, y, k )
|
||||
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input k indicates whether tan (if k=1) or
|
||||
* -1/tan (if k= -1) is returned.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
|
||||
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
|
||||
* [0,0.67434]
|
||||
* 3 27
|
||||
* tan(x) ~ x + T1*x + ... + T13*x
|
||||
* where
|
||||
*
|
||||
* |tan(x) 2 4 26 | -59.2
|
||||
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* Note: tan(x+y) = tan(x) + tan'(x)*y
|
||||
* ~ tan(x) + (1+x*x)*y
|
||||
* Therefore, for better accuracy in computing tan(x+y), let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
|
||||
* then
|
||||
* 3 2
|
||||
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
|
||||
*
|
||||
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
|
||||
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
|
||||
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
|
||||
T[] = {
|
||||
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
|
||||
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
|
||||
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
|
||||
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
|
||||
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
|
||||
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
|
||||
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
|
||||
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
|
||||
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
|
||||
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
|
||||
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
|
||||
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
|
||||
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_tan(double x, double y, int iy)
|
||||
#else
|
||||
double __kernel_tan(x, y, iy)
|
||||
double x,y; int iy;
|
||||
#endif
|
||||
{
|
||||
double z,r,v,w,s;
|
||||
int ix,hx;
|
||||
hx = __HI(x); /* high word of x */
|
||||
ix = hx&0x7fffffff; /* high word of |x| */
|
||||
if(ix<0x3e300000) /* x < 2**-28 */
|
||||
{if((int)x==0) { /* generate inexact */
|
||||
if(((ix|__LO(x))|(iy+1))==0) return one/fd_fabs(x);
|
||||
else return (iy==1)? x: -one/x;
|
||||
}
|
||||
}
|
||||
if(ix>=0x3FE59428) { /* |x|>=0.6744 */
|
||||
if(hx<0) {x = -x; y = -y;}
|
||||
z = pio4-x;
|
||||
w = pio4lo-y;
|
||||
x = z+w; y = 0.0;
|
||||
}
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||
*/
|
||||
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
|
||||
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
|
||||
s = z*x;
|
||||
r = y + z*(s*(r+v)+y);
|
||||
r += T[0]*s;
|
||||
w = x+r;
|
||||
if(ix>=0x3FE59428) {
|
||||
v = (double)iy;
|
||||
return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
|
||||
}
|
||||
if(iy==1) return w;
|
||||
else { /* if allow error up to 2 ulp,
|
||||
simply return -1.0/(x+r) here */
|
||||
/* compute -1.0/(x+r) accurately */
|
||||
double a,t;
|
||||
z = w;
|
||||
__LO(z) = 0;
|
||||
v = r-(z - x); /* z+v = r+x */
|
||||
t = a = -1.0/w; /* a = -1.0/w */
|
||||
__LO(t) = 0;
|
||||
s = 1.0+t*z;
|
||||
return t+a*(s+t*v);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
#// The contents of this file are subject to the Netscape Public License
|
||||
#// Version 1.0 (the "NPL"); you may not use this file except in
|
||||
#// compliance with the NPL. You may obtain a copy of the NPL at
|
||||
#// http://www.mozilla.org/NPL/
|
||||
#//
|
||||
#// Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
#// WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
#// for the specific language governing rights and limitations under the
|
||||
#// NPL.
|
||||
#//
|
||||
#// The Initial Developer of this code under the NPL is Netscape
|
||||
#// Communications Corporation. Portions created by Netscape are
|
||||
#// Copyright (C) 1998 Netscape Communications Corporation. All Rights
|
||||
#// Reserved.
|
||||
|
||||
#//------------------------------------------------------------------------
|
||||
#//
|
||||
#// Specify the depth of the current directory relative to the
|
||||
#// root of NS
|
||||
#//
|
||||
#//------------------------------------------------------------------------
|
||||
DEPTH=..\..\..
|
||||
include <$(DEPTH)\config\config.mak>
|
||||
|
||||
#//------------------------------------------------------------------------
|
||||
#//
|
||||
#// Define any Public Make Variables here: (ie. PDFFILE, MAPFILE, ...)
|
||||
#//
|
||||
#//------------------------------------------------------------------------
|
||||
|
||||
LIBRARY_NAME = fdlibm
|
||||
|
||||
#//------------------------------------------------------------------------
|
||||
#//
|
||||
#// Define the files necessary to build the target (ie. OBJS)
|
||||
#//
|
||||
#//------------------------------------------------------------------------
|
||||
OBJS = \
|
||||
.\$(OBJDIR)\e_atan2.obj \
|
||||
.\$(OBJDIR)\e_pow.obj \
|
||||
.\$(OBJDIR)\e_sqrt.obj \
|
||||
.\$(OBJDIR)\k_standard.obj \
|
||||
.\$(OBJDIR)\s_atan.obj \
|
||||
.\$(OBJDIR)\s_copysign.obj \
|
||||
.\$(OBJDIR)\s_fabs.obj \
|
||||
.\$(OBJDIR)\s_finite.obj \
|
||||
.\$(OBJDIR)\s_isnan.obj \
|
||||
.\$(OBJDIR)\s_matherr.obj \
|
||||
.\$(OBJDIR)\s_rint.obj \
|
||||
.\$(OBJDIR)\s_scalbn.obj \
|
||||
.\$(OBJDIR)\w_atan2.obj \
|
||||
.\$(OBJDIR)\w_pow.obj \
|
||||
.\$(OBJDIR)\w_sqrt.obj \
|
||||
.\$(OBJDIR)\s_lib_version.obj \
|
||||
$(NULL)
|
||||
|
||||
#//------------------------------------------------------------------------
|
||||
#//
|
||||
#// Include the common makefile rules
|
||||
#//
|
||||
#//------------------------------------------------------------------------
|
||||
include <$(DEPTH)\config\rules.mak>
|
||||
|
||||
export:: $(LIBRARY)
|
||||
|
||||
#//------------------------------------------------------------------------
|
||||
#//
|
||||
#// Standalone js.exe interpreter
|
||||
#//
|
||||
#//------------------------------------------------------------------------
|
||||
|
||||
#//PROGRAM = $(OBJDIR)\js.exe
|
||||
#//js: $(PROGRAM)
|
||||
#//
|
||||
#//$(PROGRAM): $(OBJDIR)\js.obj $(LIBRARY)
|
||||
#// @$(MAKE_OBJDIR)
|
||||
#// $(link) /debug /out:$(PROGRAM) $(OBJDIR)\js.obj $(DIST)\lib\pr3240.lib $(LIBRARY) $(LDFLAGS)
|
||||
#//
|
||||
#//$(OBJDIR)\js.obj: js.c
|
||||
#// $(CC) /Fo$(OBJDIR)\js.obj js.c $(CFLAGS) -DJSFILE
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_asinh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* asinh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
|
||||
* we have
|
||||
* asinh(x) := x if 1+x*x=1,
|
||||
* := sign(x)*(log(x)+ln2)) for large |x|, else
|
||||
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
|
||||
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
huge= 1.00000000000000000000e+300;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_asinh(double x)
|
||||
#else
|
||||
double fd_asinh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
|
||||
if(ix< 0x3e300000) { /* |x|<2**-28 */
|
||||
if(huge+x>one) return x; /* return x inexact except 0 */
|
||||
}
|
||||
if(ix>0x41b00000) { /* |x| > 2**28 */
|
||||
w = __ieee754_log(fd_fabs(x))+ln2;
|
||||
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
|
||||
t = fd_fabs(x);
|
||||
w = __ieee754_log(2.0*t+one/(fd_sqrt(x*x+one)+t));
|
||||
} else { /* 2.0 > |x| > 2**-28 */
|
||||
t = x*x;
|
||||
w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
|
||||
}
|
||||
if(hx>0) return w; else return -w;
|
||||
}
|
||||
|
|
@ -0,0 +1,150 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_atan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* atan(x)
|
||||
* Method
|
||||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||||
* is further reduced to one of the following intervals and the
|
||||
* arctangent of t is evaluated by the corresponding formula:
|
||||
*
|
||||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double atanhi[] = {
|
||||
#else
|
||||
static double atanhi[] = {
|
||||
#endif
|
||||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double atanlo[] = {
|
||||
#else
|
||||
static double atanlo[] = {
|
||||
#endif
|
||||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double aT[] = {
|
||||
#else
|
||||
static double aT[] = {
|
||||
#endif
|
||||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
huge = 1.0e300;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_atan(double x)
|
||||
#else
|
||||
double fd_atan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double w,s1,s2,z;
|
||||
int ix,hx,id;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
||||
if(ix>0x7ff00000||
|
||||
(ix==0x7ff00000&&(__LO(x)!=0)))
|
||||
return x+x; /* NaN */
|
||||
if(hx>0) return atanhi[3]+atanlo[3];
|
||||
else return -atanhi[3]-atanlo[3];
|
||||
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
||||
if (ix < 0x3e200000) { /* |x| < 2^-29 */
|
||||
if(huge+x>one) return x; /* raise inexact */
|
||||
}
|
||||
id = -1;
|
||||
} else {
|
||||
x = fd_fabs(x);
|
||||
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
||||
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
|
||||
id = 0; x = (2.0*x-one)/(2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-1.5)/(one+1.5*x);
|
||||
} else { /* 2.4375 <= |x| < 2^66 */
|
||||
id = 3; x = -1.0/x;
|
||||
}
|
||||
}}
|
||||
/* end of argument reduction */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
||||
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,103 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_cbrt.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/* cbrt(x)
|
||||
* Return cube root of x
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const unsigned
|
||||
#else
|
||||
static unsigned
|
||||
#endif
|
||||
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
|
||||
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
|
||||
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
|
||||
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
|
||||
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
|
||||
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_cbrt(double x)
|
||||
#else
|
||||
double fd_cbrt(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx;
|
||||
double r,s,t=0.0,w;
|
||||
unsigned sign;
|
||||
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
sign=hx&0x80000000; /* sign= sign(x) */
|
||||
hx ^=sign;
|
||||
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
|
||||
if((hx|__LO(x))==0)
|
||||
return(x); /* cbrt(0) is itself */
|
||||
|
||||
__HI(x) = hx; /* x <- |x| */
|
||||
/* rough cbrt to 5 bits */
|
||||
if(hx<0x00100000) /* subnormal number */
|
||||
{__HI(t)=0x43500000; /* set t= 2**54 */
|
||||
t*=x; __HI(t)=__HI(t)/3+B2;
|
||||
}
|
||||
else
|
||||
__HI(t)=hx/3+B1;
|
||||
|
||||
|
||||
/* new cbrt to 23 bits, may be implemented in single precision */
|
||||
r=t*t/x;
|
||||
s=C+r*t;
|
||||
t*=G+F/(s+E+D/s);
|
||||
|
||||
/* chopped to 20 bits and make it larger than cbrt(x) */
|
||||
__LO(t)=0; __HI(t)+=0x00000001;
|
||||
|
||||
|
||||
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
|
||||
s=t*t; /* t*t is exact */
|
||||
r=x/s;
|
||||
w=t+t;
|
||||
r=(r-t)/(w+r); /* r-s is exact */
|
||||
t=t+t*r;
|
||||
|
||||
/* retore the sign bit */
|
||||
__HI(t) |= sign;
|
||||
return(t);
|
||||
}
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_ceil.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* ceil(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to ceil(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double huge = 1.0e300;
|
||||
#else
|
||||
static double huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_ceil(double x)
|
||||
#else
|
||||
double fd_ceil(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,i1,j0;
|
||||
unsigned i,j;
|
||||
i0 = __HI(x);
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0<0) {i0=0x80000000;i1=0;}
|
||||
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) i0 += (0x00100000)>>j0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) {
|
||||
if(j0==20) i0+=1;
|
||||
else {
|
||||
j = i1 + (1<<(52-j0));
|
||||
if((int)j<i1) i0+=1; /* got a carry */
|
||||
i1 = j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,47 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_copysign.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* copysign(double x, double y)
|
||||
* copysign(x,y) returns a value with the magnitude of x and
|
||||
* with the sign bit of y.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_copysign(double x, double y)
|
||||
#else
|
||||
double fd_copysign(x,y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_cos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* cos(x)
|
||||
* Return cosine function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_sin ... sine function on [-pi/4,pi/4]
|
||||
* __kernel_cos ... cosine function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_cos(double x)
|
||||
#else
|
||||
double fd_cos(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cos(y[0],y[1]);
|
||||
case 1: return -__kernel_sin(y[0],y[1],1);
|
||||
case 2: return -__kernel_cos(y[0],y[1]);
|
||||
default:
|
||||
return __kernel_sin(y[0],y[1],1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,326 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_erf.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* double erf(double x)
|
||||
* double erfc(double x)
|
||||
* x
|
||||
* 2 |\
|
||||
* erf(x) = --------- | exp(-t*t)dt
|
||||
* sqrt(pi) \|
|
||||
* 0
|
||||
*
|
||||
* erfc(x) = 1-erf(x)
|
||||
* Note that
|
||||
* erf(-x) = -erf(x)
|
||||
* erfc(-x) = 2 - erfc(x)
|
||||
*
|
||||
* Method:
|
||||
* 1. For |x| in [0, 0.84375]
|
||||
* erf(x) = x + x*R(x^2)
|
||||
* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
|
||||
* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
|
||||
* where R = P/Q where P is an odd poly of degree 8 and
|
||||
* Q is an odd poly of degree 10.
|
||||
* -57.90
|
||||
* | R - (erf(x)-x)/x | <= 2
|
||||
*
|
||||
*
|
||||
* Remark. The formula is derived by noting
|
||||
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
|
||||
* and that
|
||||
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
|
||||
* is close to one. The interval is chosen because the fix
|
||||
* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
|
||||
* near 0.6174), and by some experiment, 0.84375 is chosen to
|
||||
* guarantee the error is less than one ulp for erf.
|
||||
*
|
||||
* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
|
||||
* c = 0.84506291151 rounded to single (24 bits)
|
||||
* erf(x) = sign(x) * (c + P1(s)/Q1(s))
|
||||
* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
|
||||
* 1+(c+P1(s)/Q1(s)) if x < 0
|
||||
* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
|
||||
* Remark: here we use the taylor series expansion at x=1.
|
||||
* erf(1+s) = erf(1) + s*Poly(s)
|
||||
* = 0.845.. + P1(s)/Q1(s)
|
||||
* That is, we use rational approximation to approximate
|
||||
* erf(1+s) - (c = (single)0.84506291151)
|
||||
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
|
||||
* where
|
||||
* P1(s) = degree 6 poly in s
|
||||
* Q1(s) = degree 6 poly in s
|
||||
*
|
||||
* 3. For x in [1.25,1/0.35(~2.857143)],
|
||||
* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
|
||||
* erf(x) = 1 - erfc(x)
|
||||
* where
|
||||
* R1(z) = degree 7 poly in z, (z=1/x^2)
|
||||
* S1(z) = degree 8 poly in z
|
||||
*
|
||||
* 4. For x in [1/0.35,28]
|
||||
* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
|
||||
* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
|
||||
* = 2.0 - tiny (if x <= -6)
|
||||
* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
|
||||
* erf(x) = sign(x)*(1.0 - tiny)
|
||||
* where
|
||||
* R2(z) = degree 6 poly in z, (z=1/x^2)
|
||||
* S2(z) = degree 7 poly in z
|
||||
*
|
||||
* Note1:
|
||||
* To compute exp(-x*x-0.5625+R/S), let s be a single
|
||||
* precision number and s := x; then
|
||||
* -x*x = -s*s + (s-x)*(s+x)
|
||||
* exp(-x*x-0.5626+R/S) =
|
||||
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
|
||||
* Note2:
|
||||
* Here 4 and 5 make use of the asymptotic series
|
||||
* exp(-x*x)
|
||||
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
|
||||
* x*sqrt(pi)
|
||||
* We use rational approximation to approximate
|
||||
* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
|
||||
* Here is the error bound for R1/S1 and R2/S2
|
||||
* |R1/S1 - f(x)| < 2**(-62.57)
|
||||
* |R2/S2 - f(x)| < 2**(-61.52)
|
||||
*
|
||||
* 5. For inf > x >= 28
|
||||
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
|
||||
* erfc(x) = tiny*tiny (raise underflow) if x > 0
|
||||
* = 2 - tiny if x<0
|
||||
*
|
||||
* 7. Special case:
|
||||
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
|
||||
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
|
||||
* erfc/erf(NaN) is NaN
|
||||
*/
|
||||
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
tiny = 1e-300,
|
||||
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
|
||||
/* c = (float)0.84506291151 */
|
||||
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
|
||||
/*
|
||||
* Coefficients for approximation to erf on [0,0.84375]
|
||||
*/
|
||||
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
|
||||
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
|
||||
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
|
||||
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
|
||||
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
|
||||
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
|
||||
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
|
||||
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
|
||||
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
|
||||
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
|
||||
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
|
||||
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
|
||||
/*
|
||||
* Coefficients for approximation to erf in [0.84375,1.25]
|
||||
*/
|
||||
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
|
||||
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
|
||||
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
|
||||
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
|
||||
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
|
||||
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
|
||||
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
|
||||
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
|
||||
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
|
||||
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
|
||||
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
|
||||
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
|
||||
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1.25,1/0.35]
|
||||
*/
|
||||
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
|
||||
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
|
||||
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
|
||||
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
|
||||
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
|
||||
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
|
||||
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
|
||||
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
|
||||
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
|
||||
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
|
||||
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
|
||||
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
|
||||
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
|
||||
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
|
||||
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
|
||||
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1/.35,28]
|
||||
*/
|
||||
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
|
||||
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
|
||||
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
|
||||
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
|
||||
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
|
||||
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
|
||||
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
|
||||
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
|
||||
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
|
||||
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
|
||||
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
|
||||
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
|
||||
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
|
||||
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_erf(double x)
|
||||
#else
|
||||
double fd_erf(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx,ix,i;
|
||||
double R,S,P,Q,s,y,z,r;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) { /* erf(nan)=nan */
|
||||
i = ((unsigned)hx>>31)<<1;
|
||||
return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
|
||||
}
|
||||
|
||||
if(ix < 0x3feb0000) { /* |x|<0.84375 */
|
||||
if(ix < 0x3e300000) { /* |x|<2**-28 */
|
||||
if (ix < 0x00800000)
|
||||
return 0.125*(8.0*x+efx8*x); /*avoid underflow */
|
||||
return x + efx*x;
|
||||
}
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
return x + x*y;
|
||||
}
|
||||
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fd_fabs(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
|
||||
}
|
||||
if (ix >= 0x40180000) { /* inf>|x|>=6 */
|
||||
if(hx>=0) return one-tiny; else return tiny-one;
|
||||
}
|
||||
x = fd_fabs(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/0.35 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
z = x;
|
||||
__LO(z) = 0;
|
||||
r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
|
||||
if(hx>=0) return one-r/x; else return r/x-one;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double erfc(double x)
|
||||
#else
|
||||
double erfc(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx,ix;
|
||||
double R,S,P,Q,s,y,z,r;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) { /* erfc(nan)=nan */
|
||||
/* erfc(+-inf)=0,2 */
|
||||
return (double)(((unsigned)hx>>31)<<1)+one/x;
|
||||
}
|
||||
|
||||
if(ix < 0x3feb0000) { /* |x|<0.84375 */
|
||||
if(ix < 0x3c700000) /* |x|<2**-56 */
|
||||
return one-x;
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
if(hx < 0x3fd00000) { /* x<1/4 */
|
||||
return one-(x+x*y);
|
||||
} else {
|
||||
r = x*y;
|
||||
r += (x-half);
|
||||
return half - r ;
|
||||
}
|
||||
}
|
||||
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fd_fabs(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) {
|
||||
z = one-erx; return z - P/Q;
|
||||
} else {
|
||||
z = erx+P/Q; return one+z;
|
||||
}
|
||||
}
|
||||
if (ix < 0x403c0000) { /* |x|<28 */
|
||||
x = fd_fabs(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/.35 ~ 2.857143 */
|
||||
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
z = x;
|
||||
__LO(z) = 0;
|
||||
r = __ieee754_exp(-z*z-0.5625)*
|
||||
__ieee754_exp((z-x)*(z+x)+R/S);
|
||||
if(hx>0) return r/x; else return two-r/x;
|
||||
} else {
|
||||
if(hx>0) return tiny*tiny; else return two-tiny;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,232 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_expm1.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* expm1(x)
|
||||
* Returns exp(x)-1, the exponential of x minus 1.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
|
||||
*
|
||||
* Here a correction term c will be computed to compensate
|
||||
* the error in r when rounded to a floating-point number.
|
||||
*
|
||||
* 2. Approximating expm1(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Since
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
|
||||
* we define R1(r*r) by
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
|
||||
* That is,
|
||||
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
|
||||
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
|
||||
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
|
||||
* We use a special Reme algorithm on [0,0.347] to generate
|
||||
* a polynomial of degree 5 in r*r to approximate R1. The
|
||||
* maximum error of this polynomial approximation is bounded
|
||||
* by 2**-61. In other words,
|
||||
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
|
||||
* where Q1 = -1.6666666666666567384E-2,
|
||||
* Q2 = 3.9682539681370365873E-4,
|
||||
* Q3 = -9.9206344733435987357E-6,
|
||||
* Q4 = 2.5051361420808517002E-7,
|
||||
* Q5 = -6.2843505682382617102E-9;
|
||||
* (where z=r*r, and the values of Q1 to Q5 are listed below)
|
||||
* with error bounded by
|
||||
* | 5 | -61
|
||||
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
|
||||
* | |
|
||||
*
|
||||
* expm1(r) = exp(r)-1 is then computed by the following
|
||||
* specific way which minimize the accumulation rounding error:
|
||||
* 2 3
|
||||
* r r [ 3 - (R1 + R1*r/2) ]
|
||||
* expm1(r) = r + --- + --- * [--------------------]
|
||||
* 2 2 [ 6 - r*(3 - R1*r/2) ]
|
||||
*
|
||||
* To compensate the error in the argument reduction, we use
|
||||
* expm1(r+c) = expm1(r) + c + expm1(r)*c
|
||||
* ~ expm1(r) + c + r*c
|
||||
* Thus c+r*c will be added in as the correction terms for
|
||||
* expm1(r+c). Now rearrange the term to avoid optimization
|
||||
* screw up:
|
||||
* ( 2 2 )
|
||||
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
|
||||
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
|
||||
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
|
||||
* ( )
|
||||
*
|
||||
* = r - E
|
||||
* 3. Scale back to obtain expm1(x):
|
||||
* From step 1, we have
|
||||
* expm1(x) = either 2^k*[expm1(r)+1] - 1
|
||||
* = or 2^k*[expm1(r) + (1-2^-k)]
|
||||
* 4. Implementation notes:
|
||||
* (A). To save one multiplication, we scale the coefficient Qi
|
||||
* to Qi*2^i, and replace z by (x^2)/2.
|
||||
* (B). To achieve maximum accuracy, we compute expm1(x) by
|
||||
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
|
||||
* (ii) if k=0, return r-E
|
||||
* (iii) if k=-1, return 0.5*(r-E)-0.5
|
||||
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
|
||||
* else return 1.0+2.0*(r-E);
|
||||
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
|
||||
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
|
||||
* (vii) return 2^k(1-((E+2^-k)-r))
|
||||
*
|
||||
* Special cases:
|
||||
* expm1(INF) is INF, expm1(NaN) is NaN;
|
||||
* expm1(-INF) is -1, and
|
||||
* for finite argument, only expm1(0)=0 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
huge = 1.0e+300,
|
||||
tiny = 1.0e-300,
|
||||
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
|
||||
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
|
||||
/* scaled coefficients related to expm1 */
|
||||
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
|
||||
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
|
||||
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
|
||||
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
|
||||
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_expm1(double x)
|
||||
#else
|
||||
double fd_expm1(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,hi,lo,c,t,e,hxs,hfx,r1;
|
||||
int k,xsb;
|
||||
unsigned hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
xsb = hx&0x80000000; /* sign bit of x */
|
||||
if(xsb==0) y=x; else y= -x; /* y = |x| */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out huge and non-finite argument */
|
||||
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
if(((hx&0xfffff)|__LO(x))!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
}
|
||||
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
|
||||
if(x+tiny<0.0) /* raise inexact */
|
||||
return tiny-one; /* return -1 */
|
||||
}
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
if(xsb==0)
|
||||
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
|
||||
else
|
||||
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
|
||||
} else {
|
||||
k = (int)(invln2*x+((xsb==0)?0.5:-0.5));
|
||||
t = k;
|
||||
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
||||
lo = t*ln2_lo;
|
||||
}
|
||||
x = hi - lo;
|
||||
c = (hi-x)-lo;
|
||||
}
|
||||
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
|
||||
t = huge+x; /* return x with inexact flags when x!=0 */
|
||||
return x - (t-(huge+x));
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
hfx = 0.5*x;
|
||||
hxs = x*hfx;
|
||||
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
|
||||
t = 3.0-r1*hfx;
|
||||
e = hxs*((r1-t)/(6.0 - x*t));
|
||||
if(k==0) return x - (x*e-hxs); /* c is 0 */
|
||||
else {
|
||||
e = (x*(e-c)-c);
|
||||
e -= hxs;
|
||||
if(k== -1) return 0.5*(x-e)-0.5;
|
||||
if(k==1)
|
||||
if(x < -0.25) return -2.0*(e-(x+0.5));
|
||||
else return one+2.0*(x-e);
|
||||
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
|
||||
y = one-(e-x);
|
||||
__HI(y) += (k<<20); /* add k to y's exponent */
|
||||
return y-one;
|
||||
}
|
||||
t = one;
|
||||
if(k<20) {
|
||||
__HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
|
||||
y = t-(e-x);
|
||||
__HI(y) += (k<<20); /* add k to y's exponent */
|
||||
} else {
|
||||
__HI(t) = ((0x3ff-k)<<20); /* 2^-k */
|
||||
y = x-(e+t);
|
||||
y += one;
|
||||
__HI(y) += (k<<20); /* add k to y's exponent */
|
||||
}
|
||||
}
|
||||
return y;
|
||||
}
|
||||
|
|
@ -0,0 +1,45 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_fabs.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* fabs(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_fabs(double x)
|
||||
#else
|
||||
double fd_fabs(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
__HI(x) &= 0x7fffffff;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,47 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_finite.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* finite(x) returns 1 is x is finite, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int fd_finite(double x)
|
||||
#else
|
||||
int fd_finite(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx;
|
||||
hx = __HI(x);
|
||||
return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31;
|
||||
}
|
||||
|
|
@ -0,0 +1,95 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_floor.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* floor(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floor(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double huge = 1.0e300;
|
||||
#else
|
||||
static double huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_floor(double x)
|
||||
#else
|
||||
double fd_floor(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,i1,j0;
|
||||
unsigned i,j;
|
||||
i0 = __HI(x);
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0>=0) {i0=i1=0;}
|
||||
else if(((i0&0x7fffffff)|i1)!=0)
|
||||
{ i0=0xbff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) i0 += (0x00100000)>>j0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) {
|
||||
if(j0==20) i0+=1;
|
||||
else {
|
||||
j = i1+(1<<(52-j0));
|
||||
if((int)j<i1) i0 +=1 ; /* got a carry */
|
||||
i1=j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,72 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_frexp.c 1.4 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* for non-zero x
|
||||
* x = frexp(arg,&exp);
|
||||
* return a double fp quantity x such that 0.5 <= |x| <1.0
|
||||
* and the corresponding binary exponent "exp". That is
|
||||
* arg = x*2^exp.
|
||||
* If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
|
||||
* with *exp=0.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_frexp(double x, int *eptr)
|
||||
#else
|
||||
double fd_frexp(x, eptr)
|
||||
double x; int *eptr;
|
||||
#endif
|
||||
{
|
||||
int hx, ix, lx;
|
||||
hx = __HI(x);
|
||||
ix = 0x7fffffff&hx;
|
||||
lx = __LO(x);
|
||||
*eptr = 0;
|
||||
if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
|
||||
if (ix<0x00100000) { /* subnormal */
|
||||
x *= two54;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
*eptr = -54;
|
||||
}
|
||||
*eptr += (ix>>20)-1022;
|
||||
hx = (hx&0x800fffff)|0x3fe00000;
|
||||
__HI(x) = hx;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_ilogb.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* ilogb(double x)
|
||||
* return the binary exponent of non-zero x
|
||||
* ilogb(0) = 0x80000001
|
||||
* ilogb(inf/NaN) = 0x7fffffff (no signal is raised)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int fd_ilogb(double x)
|
||||
#else
|
||||
int fd_ilogb(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx,lx,ix;
|
||||
|
||||
hx = (__HI(x))&0x7fffffff; /* high word of x */
|
||||
if(hx<0x00100000) {
|
||||
lx = __LO(x);
|
||||
if((hx|lx)==0)
|
||||
return 0x80000001; /* ilogb(0) = 0x80000001 */
|
||||
else /* subnormal x */
|
||||
if(hx==0) {
|
||||
for (ix = -1043; lx>0; lx<<=1) ix -=1;
|
||||
} else {
|
||||
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
|
||||
}
|
||||
return ix;
|
||||
}
|
||||
else if (hx<0x7ff00000) return (hx>>20)-1023;
|
||||
else return 0x7fffffff;
|
||||
}
|
||||
|
|
@ -0,0 +1,50 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_isnan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* isnan(x) returns 1 is x is nan, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int fd_isnan(double x)
|
||||
#else
|
||||
int fd_isnan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx,lx;
|
||||
hx = (__HI(x)&0x7fffffff);
|
||||
lx = __LO(x);
|
||||
hx |= (unsigned)(lx|(-lx))>>31;
|
||||
hx = 0x7ff00000 - hx;
|
||||
return ((unsigned)(hx))>>31;
|
||||
}
|
||||
|
|
@ -0,0 +1,44 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_ldexp.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#include <errno.h>
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_ldexp(double value, int exp)
|
||||
#else
|
||||
double fd_ldexp(value, exp)
|
||||
double value; int exp;
|
||||
#endif
|
||||
{
|
||||
if(!fd_finite(value)||value==0.0) return value;
|
||||
value = fd_scalbn(value,exp);
|
||||
if(!fd_finite(value)||value==0.0) errno = ERANGE;
|
||||
return value;
|
||||
}
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_lib_version.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* MACRO for standards
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/*
|
||||
* define and initialize _LIB_VERSION
|
||||
*/
|
||||
#ifdef _POSIX_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
|
||||
#else
|
||||
#ifdef _XOPEN_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
|
||||
#else
|
||||
#ifdef _SVID3_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
|
||||
#else /* default _IEEE_MODE */
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
|
||||
#endif
|
||||
#endif
|
||||
#endif
|
||||
|
|
@ -0,0 +1,181 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_log1p.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* double log1p(double x)
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* 1+x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* Note. If k=0, then f=x is exact. However, if k!=0, then f
|
||||
* may not be representable exactly. In that case, a correction
|
||||
* term is need. Let u=1+x rounded. Let c = (1+x)-u, then
|
||||
* log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
|
||||
* and add back the correction term c/u.
|
||||
* (Note: when x > 2**53, one can simply return log(x))
|
||||
*
|
||||
* 2. Approximation of log1p(f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
|
||||
* (the values of Lp1 to Lp7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lp1*s +...+Lp7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log1p(f) = f - (hfsq - s*(hfsq+R)).
|
||||
*
|
||||
* 3. Finally, log1p(x) = k*ln2 + log1p(f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log1p(x) is NaN with signal if x < -1 (including -INF) ;
|
||||
* log1p(+INF) is +INF; log1p(-1) is -INF with signal;
|
||||
* log1p(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*
|
||||
* Note: Assuming log() return accurate answer, the following
|
||||
* algorithm can be used to compute log1p(x) to within a few ULP:
|
||||
*
|
||||
* u = 1+x;
|
||||
* if(u==1.0) return x ; else
|
||||
* return log(u)*(x/(u-1.0));
|
||||
*
|
||||
* See HP-15C Advanced Functions Handbook, p.193.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_log1p(double x)
|
||||
#else
|
||||
double fd_log1p(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double hfsq,f,c,s,z,R,u;
|
||||
int k,hx,hu,ax;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
ax = hx&0x7fffffff;
|
||||
|
||||
k = 1;
|
||||
if (hx < 0x3FDA827A) { /* x < 0.41422 */
|
||||
if(ax>=0x3ff00000) { /* x <= -1.0 */
|
||||
if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
|
||||
else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
|
||||
}
|
||||
if(ax<0x3e200000) { /* |x| < 2**-29 */
|
||||
if(two54+x>zero /* raise inexact */
|
||||
&&ax<0x3c900000) /* |x| < 2**-54 */
|
||||
return x;
|
||||
else
|
||||
return x - x*x*0.5;
|
||||
}
|
||||
if(hx>0||hx<=((int)0xbfd2bec3)) {
|
||||
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
if(k!=0) {
|
||||
if(hx<0x43400000) {
|
||||
u = 1.0+x;
|
||||
hu = __HI(u); /* high word of u */
|
||||
k = (hu>>20)-1023;
|
||||
c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
|
||||
c /= u;
|
||||
} else {
|
||||
u = x;
|
||||
hu = __HI(u); /* high word of u */
|
||||
k = (hu>>20)-1023;
|
||||
c = 0;
|
||||
}
|
||||
hu &= 0x000fffff;
|
||||
if(hu<0x6a09e) {
|
||||
__HI(u) = hu|0x3ff00000; /* normalize u */
|
||||
} else {
|
||||
k += 1;
|
||||
__HI(u) = hu|0x3fe00000; /* normalize u/2 */
|
||||
hu = (0x00100000-hu)>>2;
|
||||
}
|
||||
f = u-1.0;
|
||||
}
|
||||
hfsq=0.5*f*f;
|
||||
if(hu==0) { /* |f| < 2**-20 */
|
||||
if(f==zero) if(k==0) return zero;
|
||||
else {c += k*ln2_lo; return k*ln2_hi+c;}
|
||||
R = hfsq*(1.0-0.66666666666666666*f);
|
||||
if(k==0) return f-R; else
|
||||
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
z = s*s;
|
||||
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
|
||||
}
|
||||
|
|
@ -0,0 +1,54 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_logb.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* double logb(x)
|
||||
* IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
|
||||
* Use ilogb instead.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_logb(double x)
|
||||
#else
|
||||
double fd_logb(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int lx,ix;
|
||||
ix = (__HI(x))&0x7fffffff; /* high |x| */
|
||||
lx = __LO(x); /* low x */
|
||||
if((ix|lx)==0) return -1.0/fd_fabs(x);
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
if((ix>>=20)==0) /* IEEE 754 logb */
|
||||
return -1022.0;
|
||||
else
|
||||
return (double) (ix-1023);
|
||||
}
|
||||
|
|
@ -0,0 +1,42 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_matherr.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int fd_matherr(struct exception *x)
|
||||
#else
|
||||
int fd_matherr(x)
|
||||
struct exception *x;
|
||||
#endif
|
||||
{
|
||||
int n=0;
|
||||
if(x->arg1!=x->arg1) return 0;
|
||||
return n;
|
||||
}
|
||||
|
|
@ -0,0 +1,96 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_modf.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* modf(double x, double *iptr)
|
||||
* return fraction part of x, and return x's integral part in *iptr.
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
*
|
||||
* Exception:
|
||||
* No exception.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0;
|
||||
#else
|
||||
static double one = 1.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_modf(double x, double *iptr)
|
||||
#else
|
||||
double fd_modf(x, iptr)
|
||||
double x,*iptr;
|
||||
#endif
|
||||
{
|
||||
int i0,i1,j0;
|
||||
unsigned i;
|
||||
i0 = __HI(x); /* high x */
|
||||
i1 = __LO(x); /* low x */
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */
|
||||
if(j0<20) { /* integer part in high x */
|
||||
if(j0<0) { /* |x|<1 */
|
||||
__HIp(iptr) = i0&0x80000000;
|
||||
__LOp(iptr) = 0; /* *iptr = +-0 */
|
||||
return x;
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) { /* x is integral */
|
||||
*iptr = x;
|
||||
__HI(x) &= 0x80000000;
|
||||
__LO(x) = 0; /* return +-0 */
|
||||
return x;
|
||||
} else {
|
||||
__HIp(iptr) = i0&(~i);
|
||||
__LOp(iptr) = 0;
|
||||
return x - *iptr;
|
||||
}
|
||||
}
|
||||
} else if (j0>51) { /* no fraction part */
|
||||
*iptr = x*one;
|
||||
__HI(x) &= 0x80000000;
|
||||
__LO(x) = 0; /* return +-0 */
|
||||
return x;
|
||||
} else { /* fraction part in low x */
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) { /* x is integral */
|
||||
*iptr = x;
|
||||
__HI(x) &= 0x80000000;
|
||||
__LO(x) = 0; /* return +-0 */
|
||||
return x;
|
||||
} else {
|
||||
__HIp(iptr) = i0;
|
||||
__LOp(iptr) = i1&(~i);
|
||||
return x - *iptr;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_nextafter.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* IEEE functions
|
||||
* nextafter(x,y)
|
||||
* return the next machine floating-point number of x in the
|
||||
* direction toward y.
|
||||
* Special cases:
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_nextafter(double x, double y)
|
||||
#else
|
||||
double fd_nextafter(x,y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
int hx,hy,ix,iy;
|
||||
unsigned lx,ly;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
hy = __HI(y); /* high word of y */
|
||||
ly = __LO(y); /* low word of y */
|
||||
ix = hx&0x7fffffff; /* |x| */
|
||||
iy = hy&0x7fffffff; /* |y| */
|
||||
|
||||
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
|
||||
((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
|
||||
return x+y;
|
||||
if(x==y) return x; /* x=y, return x */
|
||||
if((ix|lx)==0) { /* x == 0 */
|
||||
__HI(x) = hy&0x80000000; /* return +-minsubnormal */
|
||||
__LO(x) = 1;
|
||||
y = x*x;
|
||||
if(y==x) return y; else return x; /* raise underflow flag */
|
||||
}
|
||||
if(hx>=0) { /* x > 0 */
|
||||
if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
|
||||
if(lx==0) hx -= 1;
|
||||
lx -= 1;
|
||||
} else { /* x < y, x += ulp */
|
||||
lx += 1;
|
||||
if(lx==0) hx += 1;
|
||||
}
|
||||
} else { /* x < 0 */
|
||||
if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
|
||||
if(lx==0) hx -= 1;
|
||||
lx -= 1;
|
||||
} else { /* x > y, x += ulp */
|
||||
lx += 1;
|
||||
if(lx==0) hx += 1;
|
||||
}
|
||||
}
|
||||
hy = hx&0x7ff00000;
|
||||
if(hy>=0x7ff00000) return x+x; /* overflow */
|
||||
if(hy<0x00100000) { /* underflow */
|
||||
y = x*x;
|
||||
if(y!=x) { /* raise underflow flag */
|
||||
__HI(y) = hx; __LO(y) = lx;
|
||||
return y;
|
||||
}
|
||||
}
|
||||
__HI(x) = hx; __LO(x) = lx;
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,100 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_rint.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* rint(x)
|
||||
* Return x rounded to integral value according to the prevailing
|
||||
* rounding mode.
|
||||
* Method:
|
||||
* Using floating addition.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to rint(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
TWO52[2]={
|
||||
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_rint(double x)
|
||||
#else
|
||||
double fd_rint(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,j0,sx;
|
||||
unsigned i,i1;
|
||||
double w,t;
|
||||
i0 = __HI(x);
|
||||
sx = (i0>>31)&1;
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) {
|
||||
if(((i0&0x7fffffff)|i1)==0) return x;
|
||||
i1 |= (i0&0x0fffff);
|
||||
i0 &= 0xfffe0000;
|
||||
i0 |= ((i1|-(int)i1)>>12)&0x80000;
|
||||
__HI(x)=i0;
|
||||
w = TWO52[sx]+x;
|
||||
t = w-TWO52[sx];
|
||||
i0 = __HI(t);
|
||||
__HI(t) = (i0&0x7fffffff)|(sx<<31);
|
||||
return t;
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
i>>=1;
|
||||
if(((i0&i)|i1)!=0) {
|
||||
if(j0==19) i1 = 0x40000000; else
|
||||
i0 = (i0&(~i))|((0x20000)>>j0);
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
i>>=1;
|
||||
if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
w = TWO52[sx]+x;
|
||||
return w-TWO52[sx];
|
||||
}
|
||||
|
|
@ -0,0 +1,79 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_scalbn.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* scalbn (double x, int n)
|
||||
* scalbn(x,n) returns x* 2**n computed by exponent
|
||||
* manipulation rather than by actually performing an
|
||||
* exponentiation or a multiplication.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
|
||||
huge = 1.0e+300,
|
||||
tiny = 1.0e-300;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_scalbn (double x, int n)
|
||||
#else
|
||||
double fd_scalbn (x,n)
|
||||
double x; int n;
|
||||
#endif
|
||||
{
|
||||
int k,hx,lx;
|
||||
hx = __HI(x);
|
||||
lx = __LO(x);
|
||||
k = (hx&0x7ff00000)>>20; /* extract exponent */
|
||||
if (k==0) { /* 0 or subnormal x */
|
||||
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
|
||||
x *= two54;
|
||||
hx = __HI(x);
|
||||
k = ((hx&0x7ff00000)>>20) - 54;
|
||||
if (n< -50000) return tiny*x; /*underflow*/
|
||||
}
|
||||
if (k==0x7ff) return x+x; /* NaN or Inf */
|
||||
k = k+n;
|
||||
if (k > 0x7fe) return huge*fd_copysign(huge,x); /* overflow */
|
||||
if (k > 0) /* normal result */
|
||||
{__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
|
||||
if (k <= -54)
|
||||
if (n > 50000) /* in case integer overflow in n+k */
|
||||
return huge*fd_copysign(huge,x); /*overflow*/
|
||||
else return tiny*fd_copysign(tiny,x); /*underflow*/
|
||||
k += 54; /* subnormal result */
|
||||
__HI(x) = (hx&0x800fffff)|(k<<20);
|
||||
return x*twom54;
|
||||
}
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
#include "fdlibm.h"
|
||||
int signgam = 0;
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_significand.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* significand(x) computes just
|
||||
* scalb(x, (double) -ilogb(x)),
|
||||
* for exercising the fraction-part(F) IEEE 754-1985 test vector.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_significand(double x)
|
||||
#else
|
||||
double fd_significand(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return __ieee754_scalb(x,(double) -fd_ilogb(x));
|
||||
}
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_sin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* sin(x)
|
||||
* Return sine function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_sin ... sine function on [-pi/4,pi/4]
|
||||
* __kernel_cos ... cose function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_sin(double x)
|
||||
#else
|
||||
double fd_sin(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
|
||||
|
||||
/* sin(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_sin(y[0],y[1],1);
|
||||
case 1: return __kernel_cos(y[0],y[1]);
|
||||
case 2: return -__kernel_sin(y[0],y[1],1);
|
||||
default:
|
||||
return -__kernel_cos(y[0],y[1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,88 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_tan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* tan(x)
|
||||
* Return tangent function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_tan ... tangent function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_tan(double x)
|
||||
#else
|
||||
double fd_tan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
|
||||
|
||||
/* tan(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x; /* NaN */
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
|
||||
-1 -- n odd */
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)s_tanh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* Tanh(x)
|
||||
* Return the Hyperbolic Tangent of x
|
||||
*
|
||||
* Method :
|
||||
* x -x
|
||||
* e - e
|
||||
* 0. tanh(x) is defined to be -----------
|
||||
* x -x
|
||||
* e + e
|
||||
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
||||
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
||||
* -t
|
||||
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
||||
* t + 2
|
||||
* 2
|
||||
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
||||
* t + 2
|
||||
* 22.0 < x <= INF : tanh(x) := 1.
|
||||
*
|
||||
* Special cases:
|
||||
* tanh(NaN) is NaN;
|
||||
* only tanh(0)=0 is exact for finite argument.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one=1.0, two=2.0, tiny = 1.0e-300;
|
||||
#else
|
||||
static double one=1.0, two=2.0, tiny = 1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_tanh(double x)
|
||||
#else
|
||||
double fd_tanh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,z;
|
||||
int jx,ix;
|
||||
|
||||
/* High word of |x|. */
|
||||
jx = __HI(x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) {
|
||||
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
||||
else return one/x-one; /* tanh(NaN) = NaN */
|
||||
}
|
||||
|
||||
/* |x| < 22 */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix<0x3c800000) /* |x|<2**-55 */
|
||||
return x*(one+x); /* tanh(small) = small */
|
||||
if (ix>=0x3ff00000) { /* |x|>=1 */
|
||||
t = fd_expm1(two*fd_fabs(x));
|
||||
z = one - two/(t+two);
|
||||
} else {
|
||||
t = fd_expm1(-two*fd_fabs(x));
|
||||
z= -t/(t+two);
|
||||
}
|
||||
/* |x| > 22, return +-1 */
|
||||
} else {
|
||||
z = one - tiny; /* raised inexact flag */
|
||||
}
|
||||
return (jx>=0)? z: -z;
|
||||
}
|
||||
|
|
@ -0,0 +1,55 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_acos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrap_acos(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_acos(double x) /* wrapper acos */
|
||||
#else
|
||||
double fd_acos(x) /* wrapper acos */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_acos(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_acos(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
if(fd_fabs(x)>1.0) {
|
||||
return __kernel_standard(x,x,1); /* acos(|x|>1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,55 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_acosh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper acosh(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_acosh(double x) /* wrapper acosh */
|
||||
#else
|
||||
double fd_acosh(x) /* wrapper acosh */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_acosh(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_acosh(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
if(x<1.0) {
|
||||
return __kernel_standard(x,x,29); /* acosh(x<1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,57 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_asin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper asin(x)
|
||||
*/
|
||||
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_asin(double x) /* wrapper asin */
|
||||
#else
|
||||
double fd_asin(x) /* wrapper asin */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_asin(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_asin(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
if(fd_fabs(x)>1.0) {
|
||||
return __kernel_standard(x,x,2); /* asin(|x|>1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,56 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_atan2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper atan2(y,x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_atan2(double y, double x) /* wrapper atan2 */
|
||||
#else
|
||||
double fd_atan2(y,x) /* wrapper atan2 */
|
||||
double y,x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_atan2(y,x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_atan2(y,x);
|
||||
if(_LIB_VERSION == _IEEE_||fd_isnan(x)||fd_isnan(y)) return z;
|
||||
if(x==0.0&&y==0.0) {
|
||||
return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_atanh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
/*
|
||||
* wrapper atanh(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_atanh(double x) /* wrapper atanh */
|
||||
#else
|
||||
double fd_atanh(x) /* wrapper atanh */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_atanh(x);
|
||||
#else
|
||||
double z,y;
|
||||
z = __ieee754_atanh(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
y = fd_fabs(x);
|
||||
if(y>=1.0) {
|
||||
if(y>1.0)
|
||||
return __kernel_standard(x,x,30); /* atanh(|x|>1) */
|
||||
else
|
||||
return __kernel_standard(x,x,31); /* atanh(|x|==1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,54 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_cosh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper cosh(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_cosh(double x) /* wrapper cosh */
|
||||
#else
|
||||
double fd_cosh(x) /* wrapper cosh */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_cosh(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_cosh(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
if(fd_fabs(x)>7.10475860073943863426e+02) {
|
||||
return __kernel_standard(x,x,5); /* cosh overflow */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,65 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_exp.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper exp(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_exp(double x) /* wrapper exp */
|
||||
#else
|
||||
double fd_exp(x) /* wrapper exp */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_exp(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_exp(x);
|
||||
if(_LIB_VERSION == _IEEE_) return z;
|
||||
if(fd_finite(x)) {
|
||||
if(x>o_threshold)
|
||||
return __kernel_standard(x,x,6); /* exp overflow */
|
||||
else if(x<u_threshold)
|
||||
return __kernel_standard(x,x,7); /* exp underflow */
|
||||
}
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,55 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_fmod.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper fmod(x,y)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_fmod(double x, double y) /* wrapper fmod */
|
||||
#else
|
||||
double fd_fmod(x,y) /* wrapper fmod */
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_fmod(x,y);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_fmod(x,y);
|
||||
if(_LIB_VERSION == _IEEE_ ||fd_isnan(y)||fd_isnan(x)) return z;
|
||||
if(y==0.0) {
|
||||
return __kernel_standard(x,y,27); /* fmod(x,0) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_gamma.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* double gamma(double x)
|
||||
* Return the logarithm of the Gamma function of x.
|
||||
*
|
||||
* Method: call gamma_r
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_gamma(double x)
|
||||
#else
|
||||
double fd_gamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_gamma_r(x,&signgam);
|
||||
#else
|
||||
double y;
|
||||
y = __ieee754_gamma_r(x,&signgam);
|
||||
if(_LIB_VERSION == _IEEE_) return y;
|
||||
if(!fd_finite(y)&&fd_finite(x)) {
|
||||
if(fd_floor(x)==x&&x<=0.0)
|
||||
return __kernel_standard(x,x,41); /* gamma pole */
|
||||
else
|
||||
return __kernel_standard(x,x,40); /* gamma overflow */
|
||||
} else
|
||||
return y;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_gamma_r.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper double gamma_r(double x, int *signgamp)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_gamma_r(double x, int *signgamp) /* wrapper lgamma_r */
|
||||
#else
|
||||
double fd_gamma_r(x,signgamp) /* wrapper lgamma_r */
|
||||
double x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_gamma_r(x,signgamp);
|
||||
#else
|
||||
double y;
|
||||
y = __ieee754_gamma_r(x,signgamp);
|
||||
if(_LIB_VERSION == _IEEE_) return y;
|
||||
if(!fd_finite(y)&&fd_finite(x)) {
|
||||
if(fd_floor(x)==x&&x<=0.0)
|
||||
return __kernel_standard(x,x,41); /* gamma pole */
|
||||
else
|
||||
return __kernel_standard(x,x,40); /* gamma overflow */
|
||||
} else
|
||||
return y;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,55 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_hypot.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper hypot(x,y)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_hypot(double x, double y)/* wrapper hypot */
|
||||
#else
|
||||
double fd_hypot(x,y) /* wrapper hypot */
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_hypot(x,y);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_hypot(x,y);
|
||||
if(_LIB_VERSION == _IEEE_) return z;
|
||||
if((!fd_finite(z))&&fd_finite(x)&&fd_finite(y))
|
||||
return __kernel_standard(x,y,4); /* hypot overflow */
|
||||
else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,81 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_j0.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper j0(double x), y0(double x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_j0(double x) /* wrapper j0 */
|
||||
#else
|
||||
double fd_j0(x) /* wrapper j0 */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_j0(x);
|
||||
#else
|
||||
double z = __ieee754_j0(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x)) return z;
|
||||
if(fd_fabs(x)>X_TLOSS) {
|
||||
return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double y0(double x) /* wrapper y0 */
|
||||
#else
|
||||
double y0(x) /* wrapper y0 */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_y0(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_y0(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x) ) return z;
|
||||
if(x <= 0.0){
|
||||
if(x==0.0)
|
||||
/* d= -one/(x-x); */
|
||||
return __kernel_standard(x,x,8);
|
||||
else
|
||||
/* d = zero/(x-x); */
|
||||
return __kernel_standard(x,x,9);
|
||||
}
|
||||
if(x>X_TLOSS) {
|
||||
return __kernel_standard(x,x,35); /* y0(x>X_TLOSS) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,82 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_j1.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper of j1,y1
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_j1(double x) /* wrapper j1 */
|
||||
#else
|
||||
double fd_j1(x) /* wrapper j1 */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_j1(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_j1(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x) ) return z;
|
||||
if(fd_fabs(x)>X_TLOSS) {
|
||||
return __kernel_standard(x,x,36); /* j1(|x|>X_TLOSS) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double y1(double x) /* wrapper y1 */
|
||||
#else
|
||||
double y1(x) /* wrapper y1 */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_y1(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_y1(x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x) ) return z;
|
||||
if(x <= 0.0){
|
||||
if(x==0.0)
|
||||
/* d= -one/(x-x); */
|
||||
return __kernel_standard(x,x,10);
|
||||
else
|
||||
/* d = zero/(x-x); */
|
||||
return __kernel_standard(x,x,11);
|
||||
}
|
||||
if(x>X_TLOSS) {
|
||||
return __kernel_standard(x,x,37); /* y1(x>X_TLOSS) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,104 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_jn.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper jn(int n, double x), yn(int n, double x)
|
||||
* floating point Bessel's function of the 1st and 2nd kind
|
||||
* of order n
|
||||
*
|
||||
* Special cases:
|
||||
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
||||
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
|
||||
* Note 2. About jn(n,x), yn(n,x)
|
||||
* For n=0, j0(x) is called,
|
||||
* for n=1, j1(x) is called,
|
||||
* for n<x, forward recursion us used starting
|
||||
* from values of j0(x) and j1(x).
|
||||
* for n>x, a continued fraction approximation to
|
||||
* j(n,x)/j(n-1,x) is evaluated and then backward
|
||||
* recursion is used starting from a supposed value
|
||||
* for j(n,x). The resulting value of j(0,x) is
|
||||
* compared with the actual value to correct the
|
||||
* supposed value of j(n,x).
|
||||
*
|
||||
* yn(n,x) is similar in all respects, except
|
||||
* that forward recursion is used for all
|
||||
* values of n>1.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_jn(int n, double x) /* wrapper jn */
|
||||
#else
|
||||
double fd_jn(n,x) /* wrapper jn */
|
||||
double x; int n;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_jn(n,x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_jn(n,x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x) ) return z;
|
||||
if(fd_fabs(x)>X_TLOSS) {
|
||||
return __kernel_standard((double)n,x,38); /* jn(|x|>X_TLOSS,n) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double yn(int n, double x) /* wrapper yn */
|
||||
#else
|
||||
double yn(n,x) /* wrapper yn */
|
||||
double x; int n;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_yn(n,x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_yn(n,x);
|
||||
if(_LIB_VERSION == _IEEE_ || fd_isnan(x) ) return z;
|
||||
if(x <= 0.0){
|
||||
if(x==0.0)
|
||||
/* d= -one/(x-x); */
|
||||
return __kernel_standard((double)n,x,12);
|
||||
else
|
||||
/* d = zero/(x-x); */
|
||||
return __kernel_standard((double)n,x,13);
|
||||
}
|
||||
if(x>X_TLOSS) {
|
||||
return __kernel_standard((double)n,x,39); /* yn(x>X_TLOSS,n) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
|
||||
*
|
||||
* The contents of this file are subject to the Netscape Public License
|
||||
* Version 1.0 (the "NPL"); you may not use this file except in
|
||||
* compliance with the NPL. You may obtain a copy of the NPL at
|
||||
* http://www.mozilla.org/NPL/
|
||||
*
|
||||
* Software distributed under the NPL is distributed on an "AS IS" basis,
|
||||
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
|
||||
* for the specific language governing rights and limitations under the
|
||||
* NPL.
|
||||
*
|
||||
* The Initial Developer of this code under the NPL is Sun Microsystems,
|
||||
* Inc. Portions created by Netscape are Copyright (C) 1998 Netscape
|
||||
* Communications Corporation. All Rights Reserved.
|
||||
*/
|
||||
|
||||
/* @(#)w_lgamma.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* double lgamma(double x)
|
||||
* Return the logarithm of the Gamma function of x.
|
||||
*
|
||||
* Method: call __ieee754_lgamma_r
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#ifdef __STDC__
|
||||
double fd_lgamma(double x)
|
||||
#else
|
||||
double fd_lgamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_lgamma_r(x,&signgam);
|
||||
#else
|
||||
double y;
|
||||
y = __ieee754_lgamma_r(x,&signgam);
|
||||
if(_LIB_VERSION == _IEEE_) return y;
|
||||
if(!fd_finite(y)&&fd_finite(x)) {
|
||||
if(fd_floor(x)==x&&x<=0.0)
|
||||
return __kernel_standard(x,x,15); /* lgamma pole */
|
||||
else
|
||||
return __kernel_standard(x,x,14); /* lgamma overflow */
|
||||
} else
|
||||
return y;
|
||||
#endif
|
||||
}
|
||||
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