зеркало из https://github.com/mozilla/gecko-dev.git
Backed out 3 changesets (bug 1760633
) for causing Spidermonkey bustages. CLOSED TREE
Backed out changeset 527f857a91f8 (bug1760633
) Backed out changeset ee8ecdac4be5 (bug1760633
) Backed out changeset addec3dc0f80 (bug1760633
)
This commit is contained in:
Родитель
43336c5845
Коммит
94f1cf5515
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@ -17,7 +17,7 @@ origin:
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|||
|
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# Revision to pull in
|
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# Must be a long or short commit SHA (long preferred)
|
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revision: bd5e624a861433dee76fe00a8acedc9564425332
|
||||
revision: 369ea0520a3061c07400d7cd32172efb6af39815
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|
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license: "BSD-2-Clause"
|
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license-file: LICENSE
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|
|
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@ -1,7 +1,7 @@
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|||
diff --git a/fdlibm.h b/fdlibm.h
|
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--- a/fdlibm.h
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+++ b/fdlibm.h
|
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@@ -12,504 +12,66 @@
|
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@@ -12,504 +12,51 @@
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/*
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||||
* from: @(#)fdlibm.h 5.1 93/09/24
|
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* $FreeBSD$
|
||||
|
@ -130,7 +130,7 @@ diff --git a/fdlibm.h b/fdlibm.h
|
|||
-#define M_LN2 0.69314718055994530942 /* log e2 */
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||||
-#define M_LN10 2.30258509299404568402 /* log e10 */
|
||||
-#define M_PI 3.14159265358979323846 /* pi */
|
||||
#define M_PI_2 1.57079632679489661923 /* pi/2 */
|
||||
-#define M_PI_2 1.57079632679489661923 /* pi/2 */
|
||||
-#define M_PI_4 0.78539816339744830962 /* pi/4 */
|
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-#define M_1_PI 0.31830988618379067154 /* 1/pi */
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-#define M_2_PI 0.63661977236758134308 /* 2/pi */
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||||
|
@ -256,7 +256,7 @@ diff --git a/fdlibm.h b/fdlibm.h
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|||
double cbrt(double);
|
||||
-double erf(double);
|
||||
-double erfc(double);
|
||||
double exp2(double);
|
||||
-double exp2(double);
|
||||
double expm1(double);
|
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-double fma(double, double, double);
|
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double hypot(double, double);
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|
@ -330,20 +330,20 @@ diff --git a/fdlibm.h b/fdlibm.h
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-
|
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-/* float versions of ANSI/POSIX functions */
|
||||
-#if __ISO_C_VISIBLE >= 1999
|
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float acosf(float);
|
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float asinf(float);
|
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float atanf(float);
|
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-float acosf(float);
|
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-float asinf(float);
|
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-float atanf(float);
|
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-float atan2f(float, float);
|
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float cosf(float);
|
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float sinf(float);
|
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float tanf(float);
|
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-float cosf(float);
|
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-float sinf(float);
|
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-float tanf(float);
|
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-
|
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-float coshf(float);
|
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-float sinhf(float);
|
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-float tanhf(float);
|
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-
|
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float exp2f(float);
|
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float expf(float);
|
||||
-float exp2f(float);
|
||||
-float expf(float);
|
||||
-float expm1f(float);
|
||||
-float frexpf(float, int *); /* fundamentally !__pure2 */
|
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-int ilogbf(float) __pure2;
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|
@ -351,15 +351,14 @@ diff --git a/fdlibm.h b/fdlibm.h
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-float log10f(float);
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-float log1pf(float);
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-float log2f(float);
|
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float logf(float);
|
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-float logf(float);
|
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-float modff(float, float *); /* fundamentally !__pure2 */
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-
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float powf(float, float);
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float sqrtf(float);
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-float powf(float, float);
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-float sqrtf(float);
|
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|
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float ceilf(float);
|
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-float fabsf(float) __pure2;
|
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+float fabsf(float);
|
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float floorf(float);
|
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-float fmodf(float, float);
|
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-float roundf(float);
|
||||
|
@ -387,7 +386,7 @@ diff --git a/fdlibm.h b/fdlibm.h
|
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-float remquof(float, float, int *);
|
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float rintf(float);
|
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-float scalblnf(float, long);
|
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float scalbnf(float, int);
|
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-float scalbnf(float, int);
|
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float truncf(float);
|
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|
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-float fdimf(float, float);
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|
|
|
@ -1,6 +1,7 @@
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--- a/fdlibm.h 2022-12-13 14:27:29.092805897 -0500
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+++ b/fdlibm.h 2022-12-13 14:27:37.444836016 -0500
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@@ -9,18 +9,21 @@
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diff --git a/fdlibm.h b/fdlibm.h
|
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--- a/fdlibm.h
|
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+++ b/fdlibm.h
|
||||
@@ -9,18 +9,18 @@
|
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* ====================================================
|
||||
*/
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@ -14,24 +15,21 @@
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+#ifndef mozilla_imported_fdlibm_h
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+#define mozilla_imported_fdlibm_h
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|
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+#ifndef M_PI_2
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#define M_PI_2 1.57079632679489661923 /* pi/2 */
|
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+#endif
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+
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double acos(double);
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double asin(double);
|
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double atan(double);
|
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double atan2(double, double);
|
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double cos(double);
|
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double sin(double);
|
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@@ -69,9 +72,9 @@
|
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double tan(double);
|
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@@ -54,9 +54,9 @@ double scalbn(double, int);
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double trunc(double);
|
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|
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float ceilf(float);
|
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float fabsf(float);
|
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float floorf(float);
|
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float nearbyintf(float);
|
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float rintf(float);
|
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float scalbnf(float, int);
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float truncf(float);
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|
||||
-#endif /* !_MATH_H_ */
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+#endif /* !mozilla_imported_fdlibm_h */
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+#endif /* mozilla_imported_fdlibm_h */
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|
|
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@ -1,6 +1,7 @@
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--- a/fdlibm.h 2022-12-13 14:28:36.393051585 -0500
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+++ b/fdlibm.h 2022-12-13 14:28:47.533092878 -0500
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@@ -12,19 +12,21 @@
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diff --git a/fdlibm.h b/fdlibm.h
|
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--- a/fdlibm.h
|
||||
+++ b/fdlibm.h
|
||||
@@ -12,16 +12,18 @@
|
||||
/*
|
||||
* from: @(#)fdlibm.h 5.1 93/09/24
|
||||
* $FreeBSD$
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||||
|
@ -11,10 +12,6 @@
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|||
|
||||
+namespace fdlibm {
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||||
+
|
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#ifndef M_PI_2
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#define M_PI_2 1.57079632679489661923 /* pi/2 */
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#endif
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|
||||
double acos(double);
|
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double asin(double);
|
||||
double atan(double);
|
||||
|
@ -22,15 +19,16 @@
|
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double cos(double);
|
||||
double sin(double);
|
||||
double tan(double);
|
||||
@@ -69,9 +71,11 @@
|
||||
|
||||
@@ -54,9 +56,11 @@ double scalbn(double, int);
|
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double trunc(double);
|
||||
|
||||
float ceilf(float);
|
||||
float fabsf(float);
|
||||
float floorf(float);
|
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float nearbyintf(float);
|
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float rintf(float);
|
||||
float scalbnf(float, int);
|
||||
float truncf(float);
|
||||
|
||||
+} /* namespace fdlibm */
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||||
+
|
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#endif /* !mozilla_imported_fdlibm_h */
|
||||
#endif /* mozilla_imported_fdlibm_h */
|
||||
|
|
|
@ -866,327 +866,3 @@ diff --git a/s_truncf.cpp b/s_truncf.cpp
|
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truncf(float x)
|
||||
{
|
||||
int32_t i0,j0;
|
||||
--- a/e_acosf.cpp 2022-12-11 21:15:50.058431053 -0500
|
||||
+++ b/e_acosf.cpp_new 2022-12-11 21:13:10.532515637 -0500
|
||||
@@ -12,15 +12,14 @@
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */
|
||||
static volatile float
|
||||
--- a/e_asinf.cpp 2022-12-11 21:15:50.486437124 -0500
|
||||
+++ b/e_asinf.cpp_new 2022-12-11 21:13:07.876498396 -0500
|
||||
@@ -12,15 +12,14 @@
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.6666586697e-01,
|
||||
--- a/e_expf.cpp 2022-12-11 21:15:51.250447960 -0500
|
||||
+++ b/e_expf.cpp_new 2022-12-11 21:13:05.212481099 -0500
|
||||
@@ -14,15 +14,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
|
||||
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
|
||||
--- a/e_logf.cpp 2022-12-11 21:15:51.978458278 -0500
|
||||
+++ b/e_logf.cpp_new 2022-12-11 21:13:02.644464418 -0500
|
||||
@@ -12,15 +12,14 @@
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
|
||||
--- a/e_powf.cpp 2022-12-11 21:15:52.242462016 -0500
|
||||
+++ b/e_powf.cpp_new 2022-12-11 21:13:00.164448306 -0500
|
||||
@@ -12,15 +12,14 @@
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
||||
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
||||
zero = 0.0,
|
||||
--- a/e_rem_pio2f.cpp 2022-12-11 21:15:52.626467454 -0500
|
||||
+++ b/e_rem_pio2f.cpp_new 2022-12-11 21:12:57.300429693 -0500
|
||||
@@ -22,15 +22,14 @@
|
||||
* return the remainder of x rem pi/2 in *y
|
||||
* use double precision for everything except passing x
|
||||
* use __kernel_rem_pio2() for large x
|
||||
*/
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 25 bits of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
*/
|
||||
--- a/e_sqrtf.cpp 2022-12-11 21:15:52.922471645 -0500
|
||||
+++ b/e_sqrtf.cpp_new 2022-12-11 21:12:54.596412113 -0500
|
||||
@@ -13,15 +13,14 @@
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef lint
|
||||
static char rcsid[] = "$FreeBSD$";
|
||||
#endif
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef USE_BUILTIN_SQRTF
|
||||
float
|
||||
__ieee754_sqrtf(float x)
|
||||
{
|
||||
return (__builtin_sqrtf(x));
|
||||
--- a/k_cosf.cpp 2022-12-11 21:15:53.178475268 -0500
|
||||
+++ b/k_cosf.cpp_new 2022-12-11 21:12:52.012395309 -0500
|
||||
@@ -15,15 +15,14 @@
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_COSDF
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
|
||||
static const double
|
||||
one = 1.0,
|
||||
C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */
|
||||
C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */
|
||||
--- a/k_expf.cpp 2022-12-11 21:15:53.434478888 -0500
|
||||
+++ b/k_expf.cpp_new 2022-12-11 21:12:49.012375792 -0500
|
||||
@@ -27,15 +27,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <complex.h>
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const uint32_t k = 235; /* constant for reduction */
|
||||
static const float kln2 = 162.88958740F; /* k * ln2 */
|
||||
|
||||
/*
|
||||
* See k_exp.c for details.
|
||||
--- a/k_sinf.cpp 2022-12-11 21:15:53.946486130 -0500
|
||||
+++ b/k_sinf.cpp_new 2022-12-11 21:12:46.020356322 -0500
|
||||
@@ -15,15 +15,14 @@
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_SINDF
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
|
||||
static const double
|
||||
S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
|
||||
S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
|
||||
S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
|
||||
--- a/k_tanf.cpp 2022-12-11 21:15:54.254490484 -0500
|
||||
+++ b/k_tanf.cpp_new 2022-12-11 21:12:42.972336479 -0500
|
||||
@@ -14,15 +14,14 @@
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_TANDF
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
|
||||
static const double
|
||||
T[] = {
|
||||
0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
|
||||
0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
|
||||
--- a/s_atanf.cpp 2022-12-11 21:15:54.670496364 -0500
|
||||
+++ b/s_atanf.cpp_new 2022-12-11 21:12:39.940316733 -0500
|
||||
@@ -12,15 +12,14 @@
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float atanhi[] = {
|
||||
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
|
||||
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
|
||||
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
|
||||
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
|
||||
--- a/s_cosf.cpp 2022-12-11 21:15:55.494508001 -0500
|
||||
+++ b/s_cosf.cpp_new 2022-12-11 21:12:37.396300160 -0500
|
||||
@@ -15,15 +15,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.c"
|
||||
#include "k_cosf.c"
|
||||
#include "k_sinf.c"
|
||||
--- a/s_exp2.cpp 2022-12-11 21:15:55.790512181 -0500
|
||||
+++ b/s_exp2.cpp_new 2022-12-11 21:12:34.476281131 -0500
|
||||
@@ -27,15 +27,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 8
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const double
|
||||
redux = 0x1.8p52 / TBLSIZE,
|
||||
--- a/s_exp2f.cpp 2022-12-11 21:15:55.926514101 -0500
|
||||
+++ b/s_exp2f.cpp_new 2022-12-11 21:12:30.644256149 -0500
|
||||
@@ -27,15 +27,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 4
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const float
|
||||
redux = 0x1.8p23f / TBLSIZE,
|
||||
--- a/s_fabsf.cpp 2022-12-11 21:15:56.202517995 -0500
|
||||
+++ b/s_fabsf.cpp_new 2022-12-11 21:12:27.244233973 -0500
|
||||
@@ -16,15 +16,14 @@
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
/*
|
||||
* fabsf(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
-#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
fabsf(float x)
|
||||
{
|
||||
u_int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
--- a/s_sinf.cpp 2022-12-11 21:15:57.618537960 -0500
|
||||
+++ b/s_sinf.cpp_new 2022-12-11 21:12:24.684217270 -0500
|
||||
@@ -15,15 +15,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.c"
|
||||
#include "k_cosf.c"
|
||||
#include "k_sinf.c"
|
||||
--- a/s_tanf.cpp 2022-12-11 21:15:57.930542357 -0500
|
||||
+++ b/s_tanf.cpp_new 2022-12-11 21:12:20.420189437 -0500
|
||||
@@ -15,15 +15,14 @@
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
-#include "math.h"
|
||||
#define INLINE_KERNEL_TANDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.c"
|
||||
#include "k_tanf.c"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
|
|
|
@ -1,7 +1,7 @@
|
|||
diff --git a/math_private.h b/math_private.h
|
||||
--- a/math_private.h
|
||||
+++ b/math_private.h
|
||||
@@ -867,16 +867,67 @@ irintl(long double x)
|
||||
@@ -867,16 +867,53 @@ irintl(long double x)
|
||||
#define __ieee754_j1f j1f
|
||||
#define __ieee754_y0f y0f
|
||||
#define __ieee754_y1f y1f
|
||||
|
@ -11,34 +11,22 @@ diff --git a/math_private.h b/math_private.h
|
|||
#define __ieee754_scalbf scalbf
|
||||
|
||||
+#define acos fdlibm::acos
|
||||
+#define acosf fdlibm::acosf
|
||||
+#define asin fdlibm::asin
|
||||
+#define asinf fdlibm::asinf
|
||||
+#define atan fdlibm::atan
|
||||
+#define atanf fdlibm::atanf
|
||||
+#define atan2 fdlibm::atan2
|
||||
+#define cos fdlibm::cos
|
||||
+#define cosf fdlibm::cosf
|
||||
+#define sin fdlibm::sin
|
||||
+#define sinf fdlibm::sinf
|
||||
+#define tan fdlibm::tan
|
||||
+#define tanf fdlibm::tanf
|
||||
+#define cosh fdlibm::cosh
|
||||
+#define sinh fdlibm::sinh
|
||||
+#define tanh fdlibm::tanh
|
||||
+#define exp fdlibm::exp
|
||||
+#define expf fdlibm::expf
|
||||
+#define exp2 fdlibm::exp2
|
||||
+#define exp2f fdlibm::exp2f
|
||||
+#define log fdlibm::log
|
||||
+#define logf fdlibm::logf
|
||||
+#define log10 fdlibm::log10
|
||||
+#define pow fdlibm::pow
|
||||
+#define powf fdlibm::powf
|
||||
+#define ceil fdlibm::ceil
|
||||
+#define ceilf fdlibm::ceilf
|
||||
+#define fabs fdlibm::fabs
|
||||
+#define fabsf fdlibm::fabsf
|
||||
+#define floor fdlibm::floor
|
||||
+#define acosh fdlibm::acosh
|
||||
+#define asinh fdlibm::asinh
|
||||
|
@ -51,7 +39,6 @@ diff --git a/math_private.h b/math_private.h
|
|||
+#define scalb fdlibm::scalb
|
||||
+#define copysign fdlibm::copysign
|
||||
+#define scalbn fdlibm::scalbn
|
||||
+#define scalbnf fdlibm::scalbnf
|
||||
+#define trunc fdlibm::trunc
|
||||
+#define truncf fdlibm::truncf
|
||||
+#define floorf fdlibm::floorf
|
||||
|
@ -59,7 +46,6 @@ diff --git a/math_private.h b/math_private.h
|
|||
+#define nearbyintf fdlibm::nearbyintf
|
||||
+#define rint fdlibm::rint
|
||||
+#define rintf fdlibm::rintf
|
||||
+#define sqrtf fdlibm::sqrtf
|
||||
+
|
||||
/* fdlibm kernel function */
|
||||
int __kernel_rem_pio2(double*,double*,int,int,int);
|
||||
|
|
|
@ -431,16 +431,3 @@ diff --git a/s_trunc.cpp b/s_trunc.cpp
|
|||
-#if LDBL_MANT_DIG == 53
|
||||
-__weak_reference(trunc, truncl);
|
||||
-#endif
|
||||
--- a/s_exp2.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_exp2.cpp_new 2022-12-11 21:20:57.490259247 -0500
|
||||
@@ -389,10 +389,6 @@
|
||||
return (r * 2.0 * 0x1p1023);
|
||||
return (r * twopk);
|
||||
} else {
|
||||
return (r * twopkp1000 * twom1000);
|
||||
}
|
||||
}
|
||||
-
|
||||
-#if (LDBL_MANT_DIG == 53)
|
||||
-__weak_reference(exp2, exp2l);
|
||||
-#endif
|
||||
|
|
|
@ -978,385 +978,3 @@ diff --git a/s_truncf.cpp b/s_truncf.cpp
|
|||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to truncf(x).
|
||||
--- a/e_acosf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_acosf.cpp_new 2022-12-11 21:23:31.863880382 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */
|
||||
--- a/e_asinf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_asinf.cpp_new 2022-12-11 21:23:31.875880502 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
/* coefficient for R(x^2) */
|
||||
--- a/e_expf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_expf.cpp_new 2022-12-11 21:23:31.895880703 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
--- a/e_logf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_logf.cpp_new 2022-12-11 21:23:31.935881104 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
--- a/e_powf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_powf.cpp_new 2022-12-11 21:23:31.971881465 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
||||
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
||||
--- a/e_rem_pio2f.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/e_rem_pio2f.cpp_new 2022-12-11 21:23:32.015881905 -0500
|
||||
@@ -10,16 +10,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
/* __ieee754_rem_pio2f(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in *y
|
||||
* use double precision for everything except passing x
|
||||
* use __kernel_rem_pio2() for large x
|
||||
*/
|
||||
--- b/k_cosf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/k_cosf.cpp_new 2022-12-11 21:23:32.051882266 -0500
|
||||
@@ -11,16 +11,16 @@
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_COSDF
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
|
||||
static const double
|
||||
one = 1.0,
|
||||
--- b/k_expf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/k_expf.cpp_new 2022-12-11 21:23:32.087882627 -0500
|
||||
@@ -22,16 +22,16 @@
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <complex.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const uint32_t k = 235; /* constant for reduction */
|
||||
static const float kln2 = 162.88958740F; /* k * ln2 */
|
||||
--- b/k_sinf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/k_sinf.cpp_new 2022-12-11 21:23:32.119882948 -0500
|
||||
@@ -11,16 +11,16 @@
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_SINDF
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
|
||||
static const double
|
||||
S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
|
||||
--- b/k_tanf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/k_tanf.cpp_new 2022-12-11 21:23:32.155883308 -0500
|
||||
@@ -10,16 +10,16 @@
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_TANDF
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
|
||||
static const double
|
||||
T[] = {
|
||||
--- a/s_atanf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_atanf.cpp_new 2022-12-11 21:23:32.199883749 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float atanhi[] = {
|
||||
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
|
||||
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
|
||||
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
|
||||
--- a/s_cosf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_cosf.cpp_new 2022-12-11 21:23:32.235884110 -0500
|
||||
@@ -10,16 +10,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
--- a/s_exp2.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_exp2.cpp_new 2022-12-11 21:23:32.275884511 -0500
|
||||
@@ -22,16 +22,16 @@
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 8
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
--- a/s_exp2f.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_exp2f.cpp_new 2022-12-11 21:23:32.311884872 -0500
|
||||
@@ -22,16 +22,16 @@
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 4
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
--- a/s_fabsf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_fabsf.cpp_new 2022-12-11 21:23:32.347885233 -0500
|
||||
@@ -9,16 +9,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
/*
|
||||
* fabsf(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
--- a/s_sinf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_sinf.cpp_new 2022-12-11 21:23:32.383885594 -0500
|
||||
@@ -10,16 +10,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
--- a/s_tanf.cpp 2022-12-11 21:20:40.290068458 -0500
|
||||
+++ b/s_tanf.cpp_new 2022-12-11 21:23:32.419885954 -0500
|
||||
@@ -10,16 +10,16 @@
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#include <sys/cdefs.h>
|
||||
-__FBSDID("$FreeBSD$");
|
||||
+//#include <sys/cdefs.h>
|
||||
+//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_TANDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.c"
|
||||
--- a/e_sqrtf.cpp 2022-12-13 14:30:13.113415455 -0500
|
||||
+++ b/e_sqrtf.cpp 2022-12-13 14:13:15.302434550 -0500
|
||||
@@ -8,19 +8,19 @@
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
-#ifndef lint
|
||||
-static char rcsid[] = "$FreeBSD$";
|
||||
-#endif
|
||||
+//#ifndef lint
|
||||
+//static char rcsid[] = "$FreeBSD$";
|
||||
+//#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef USE_BUILTIN_SQRTF
|
||||
float
|
||||
__ieee754_sqrtf(float x)
|
||||
{
|
||||
return (__builtin_sqrtf(x));
|
||||
|
|
|
@ -54,54 +54,3 @@ diff --git a/k_exp.cpp b/k_exp.cpp
|
|||
- return (CMPLX(c * exp_x * scale1 * scale2,
|
||||
- s * exp_x * scale1 * scale2));
|
||||
-}
|
||||
--- a/k_expf.cpp 2022-12-13 14:39:11.791594163 -0500
|
||||
+++ b/k_expf.cpp 2022-12-13 14:39:18.631622916 -0500
|
||||
@@ -24,18 +24,16 @@
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
-#include <complex.h>
|
||||
-
|
||||
#include "math_private.h"
|
||||
|
||||
static const uint32_t k = 235; /* constant for reduction */
|
||||
static const float kln2 = 162.88958740F; /* k * ln2 */
|
||||
|
||||
/*
|
||||
* See k_exp.c for details.
|
||||
*
|
||||
@@ -61,29 +59,8 @@
|
||||
float exp_x, scale;
|
||||
int ex_expt;
|
||||
|
||||
exp_x = __frexp_expf(x, &ex_expt);
|
||||
expt += ex_expt;
|
||||
SET_FLOAT_WORD(scale, (0x7f + expt) << 23);
|
||||
return (exp_x * scale);
|
||||
}
|
||||
-
|
||||
-float complex
|
||||
-__ldexp_cexpf(float complex z, int expt)
|
||||
-{
|
||||
- float c, exp_x, s, scale1, scale2, x, y;
|
||||
- int ex_expt, half_expt;
|
||||
-
|
||||
- x = crealf(z);
|
||||
- y = cimagf(z);
|
||||
- exp_x = __frexp_expf(x, &ex_expt);
|
||||
- expt += ex_expt;
|
||||
-
|
||||
- half_expt = expt / 2;
|
||||
- SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23);
|
||||
- half_expt = expt - half_expt;
|
||||
- SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
|
||||
-
|
||||
- sincosf(y, &s, &c);
|
||||
- return (CMPLXF(c * exp_x * scale1 * scale2,
|
||||
- s * exp_x * scale1 * scale2));
|
||||
-}
|
||||
|
|
|
@ -45,24 +45,3 @@ diff --git a/s_expm1.cpp b/s_expm1.cpp
|
|||
SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
|
||||
y = t-(e-x);
|
||||
y = y*twopk;
|
||||
--- a/s_exp2.cpp 2022-12-11 21:26:36.045643147 -0500
|
||||
+++ b/s_exp2.cpp_new 2022-12-11 21:28:42.058769925 -0500
|
||||
@@ -381,14 +381,16 @@
|
||||
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
|
||||
else
|
||||
INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0);
|
||||
r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
|
||||
|
||||
/* Scale by 2**(k>>20). */
|
||||
if(k >= -(1021 << 20)) {
|
||||
- if (k == 1024 << 20)
|
||||
- return (r * 2.0 * 0x1p1023);
|
||||
+ if (k == 1024 << 20) {
|
||||
+ double const_0x1p1023 = pow(2, 1023);
|
||||
+ return (r * 2.0 * const_0x1p1023);
|
||||
+ }
|
||||
return (r * twopk);
|
||||
} else {
|
||||
return (r * twopkp1000 * twom1000);
|
||||
}
|
||||
}
|
||||
|
|
|
@ -251,39 +251,3 @@ diff --git a/s_asinh.cpp b/s_asinh.cpp
|
|||
}
|
||||
if(hx>0) return w; else return -w;
|
||||
}
|
||||
--- a/e_asinf.cpp 2022-12-13 14:45:17.953154257 -0500
|
||||
+++ b/e_asinf.cpp 2022-12-13 14:45:03.425091710 -0500
|
||||
@@ -11,16 +11,18 @@
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
+#include <cmath>
|
||||
+
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.6666586697e-01,
|
||||
pS1 = -4.2743422091e-02,
|
||||
@@ -52,13 +54,13 @@
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabsf(x);
|
||||
t = w*(float)0.5;
|
||||
p = t*(pS0+t*(pS1+t*pS2));
|
||||
q = one+t*qS1;
|
||||
- s = sqrt(t);
|
||||
+ s = std::sqrt(t);
|
||||
w = p/q;
|
||||
t = pio2-2.0*(s+s*w);
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
|
|
|
@ -109,97 +109,3 @@ diff --git a/s_tan.cpp b/s_tan.cpp
|
|||
int32_t n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
--- a/s_cosf.cpp 2022-12-11 21:26:36.041643110 -0500
|
||||
+++ b/s_cosf.cpp 2022-12-11 21:34:08.197486828 -0500
|
||||
@@ -18,19 +18,19 @@
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
-#include "e_rem_pio2f.c"
|
||||
-#include "k_cosf.c"
|
||||
-#include "k_sinf.c"
|
||||
+#include "e_rem_pio2f.cpp"
|
||||
+#include "k_cosf.cpp"
|
||||
+#include "k_sinf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
--- a/s_sinf.cpp 2022-12-11 21:26:36.045643147 -0500
|
||||
+++ b/s_sinf.cpp 2022-12-11 21:33:52.741362926 -0500
|
||||
@@ -18,19 +18,19 @@
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
-#include "e_rem_pio2f.c"
|
||||
-#include "k_cosf.c"
|
||||
-#include "k_sinf.c"
|
||||
+#include "e_rem_pio2f.cpp"
|
||||
+#include "k_cosf.cpp"
|
||||
+#include "k_sinf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
--- a/s_tanf.cpp 2022-12-11 21:26:36.045643147 -0500
|
||||
+++ b/s_tanf.cpp 2022-12-11 21:33:45.269302886 -0500
|
||||
@@ -17,18 +17,18 @@
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_TANDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
-#include "e_rem_pio2f.c"
|
||||
-#include "k_tanf.c"
|
||||
+#include "e_rem_pio2f.cpp"
|
||||
+#include "k_tanf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
--- a/e_rem_pio2f.cpp 2022-12-13 14:50:12.582776365 -0500
|
||||
+++ b/e_rem_pio2f.cpp 2022-12-13 14:51:05.003200166 -0500
|
||||
@@ -35,17 +35,17 @@
|
||||
*/
|
||||
|
||||
static const double
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
|
||||
pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
|
||||
|
||||
#ifdef INLINE_REM_PIO2F
|
||||
-static __inline __always_inline
|
||||
+static inline
|
||||
#endif
|
||||
int
|
||||
__ieee754_rem_pio2f(float x, double *y)
|
||||
{
|
||||
double w,r,fn;
|
||||
double tx[1],ty[1];
|
||||
float z;
|
||||
int32_t e0,n,ix,hx;
|
||||
|
|
|
@ -19,47 +19,3 @@ diff --git a/math_private.h b/math_private.h
|
|||
* ix1 = *((1-n0)+(int*)&x); * low word of x *
|
||||
* to dig two 32 bit words out of the 64 bit IEEE floating point
|
||||
* value. That is non-ANSI, and, moreover, the gcc instruction
|
||||
diff --git a/e_rem_pio2f.cpp b/e_rem_pio2f.cpp
|
||||
--- a/e_rem_pio2f.cpp
|
||||
+++ b/e_rem_pio2f.cpp
|
||||
@@ -49,17 +49,17 @@ int
|
||||
double tx[1],ty[1];
|
||||
float z;
|
||||
int32_t e0,n,ix,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
/* 33+53 bit pi is good enough for medium size */
|
||||
if(ix<0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
|
||||
- fn = rnint((float_t)x*invpio2);
|
||||
+ fn = rnint((float)x*invpio2);
|
||||
n = irint(fn);
|
||||
r = x-fn*pio2_1;
|
||||
w = fn*pio2_1t;
|
||||
*y = r-w;
|
||||
return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
diff --git a/s_scalbnf.cpp b/s_scalbnf.cpp
|
||||
--- a/s_scalbnf.cpp
|
||||
+++ b/s_scalbnf.cpp
|
||||
@@ -7,17 +7,17 @@
|
||||
* for all contributors to musl.
|
||||
*/
|
||||
#include <math.h>
|
||||
#include <stdint.h>
|
||||
|
||||
float scalbnf(float x, int n)
|
||||
{
|
||||
union {float f; uint32_t i;} u;
|
||||
- float_t y = x;
|
||||
+ float y = x;
|
||||
|
||||
if (n > 127) {
|
||||
y *= 0x1p127f;
|
||||
n -= 127;
|
||||
if (n > 127) {
|
||||
y *= 0x1p127f;
|
||||
n -= 127;
|
||||
if (n > 127)
|
||||
|
|
|
@ -1,76 +0,0 @@
|
|||
/* e_acosf.c -- float version of e_acos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */
|
||||
static volatile float
|
||||
pio2_lo = 7.5497894159e-08; /* 0x33a22168 */
|
||||
static const float
|
||||
pS0 = 1.6666586697e-01,
|
||||
pS1 = -4.2743422091e-02,
|
||||
pS2 = -8.6563630030e-03,
|
||||
qS1 = -7.0662963390e-01;
|
||||
|
||||
float
|
||||
__ieee754_acosf(float x)
|
||||
{
|
||||
float z,p,q,r,w,s,c,df;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3f800000) { /* |x| >= 1 */
|
||||
if(ix==0x3f800000) { /* |x| == 1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3f000000) { /* |x| < 0.5 */
|
||||
if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*pS2));
|
||||
q = one+z*qS1;
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*(float)0.5;
|
||||
p = z*(pS0+z*(pS1+z*pS2));
|
||||
q = one+z*qS1;
|
||||
s = sqrtf(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - (float)2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
int32_t idf;
|
||||
z = (one-x)*(float)0.5;
|
||||
s = sqrtf(z);
|
||||
df = s;
|
||||
GET_FLOAT_WORD(idf,df);
|
||||
SET_FLOAT_WORD(df,idf&0xfffff000);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*pS2));
|
||||
q = one+z*qS1;
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return (float)2.0*(df+w);
|
||||
}
|
||||
}
|
|
@ -1,66 +0,0 @@
|
|||
/* e_asinf.c -- float version of e_asin.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <cmath>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.6666586697e-01,
|
||||
pS1 = -4.2743422091e-02,
|
||||
pS2 = -8.6563630030e-03,
|
||||
qS1 = -7.0662963390e-01;
|
||||
|
||||
static const double
|
||||
pio2 = 1.570796326794896558e+00;
|
||||
|
||||
float
|
||||
__ieee754_asinf(float x)
|
||||
{
|
||||
double s;
|
||||
float t,w,p,q;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3f800000) { /* |x| >= 1 */
|
||||
if(ix==0x3f800000) /* |x| == 1 */
|
||||
return x*pio2; /* asin(+-1) = +-pi/2 with inexact */
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3f000000) { /* |x|<0.5 */
|
||||
if(ix<0x39800000) { /* |x| < 2**-12 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
}
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*pS2));
|
||||
q = one+t*qS1;
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabsf(x);
|
||||
t = w*(float)0.5;
|
||||
p = t*(pS0+t*(pS1+t*pS2));
|
||||
q = one+t*qS1;
|
||||
s = std::sqrt(t);
|
||||
w = p/q;
|
||||
t = pio2-2.0*(s+s*w);
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
|
@ -1,97 +0,0 @@
|
|||
/* e_expf.c -- float version of e_exp.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
|
||||
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
|
||||
ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
|
||||
-6.9314575195e-01,}, /* 0xbf317200 */
|
||||
ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
|
||||
-1.4286067653e-06,}, /* 0xb5bfbe8e */
|
||||
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
|
||||
/*
|
||||
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
|
||||
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
|
||||
*/
|
||||
P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
|
||||
P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
|
||||
|
||||
static volatile float
|
||||
huge = 1.0e+30,
|
||||
twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
|
||||
|
||||
float
|
||||
__ieee754_expf(float x)
|
||||
{
|
||||
float y,hi=0.0,lo=0.0,c,t,twopk;
|
||||
int32_t k=0,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
||||
if(hx>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx==0x7f800000)
|
||||
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom100*twom100; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = invln2*x+halF[xsb];
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
STRICT_ASSIGN(float, x, hi - lo);
|
||||
}
|
||||
else if(hx < 0x39000000) { /* when |x|<2**-14 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
if(k >= -125)
|
||||
SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);
|
||||
else
|
||||
SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23);
|
||||
c = x - t*(P1+t*P2);
|
||||
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
|
||||
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
|
||||
if(k >= -125) {
|
||||
if(k==128) return y*2.0F*0x1p127F;
|
||||
return y*twopk;
|
||||
} else {
|
||||
return y*twopk*twom100;
|
||||
}
|
||||
}
|
|
@ -1,88 +0,0 @@
|
|||
/* e_logf.c -- float version of e_log.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
|
||||
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
|
||||
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
|
||||
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
|
||||
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
|
||||
|
||||
static const float zero = 0.0;
|
||||
static volatile float vzero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_logf(float x)
|
||||
{
|
||||
float hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,ix,i,j;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
k=0;
|
||||
if (ix < 0x00800000) { /* x < 2**-126 */
|
||||
if ((ix&0x7fffffff)==0)
|
||||
return -two25/vzero; /* log(+-0)=-inf */
|
||||
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
}
|
||||
if (ix >= 0x7f800000) return x+x;
|
||||
k += (ix>>23)-127;
|
||||
ix &= 0x007fffff;
|
||||
i = (ix+(0x95f64<<3))&0x800000;
|
||||
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
|
||||
k += (i>>23);
|
||||
f = x-(float)1.0;
|
||||
if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */
|
||||
if(f==zero) {
|
||||
if(k==0) {
|
||||
return zero;
|
||||
} else {
|
||||
dk=(float)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;
|
||||
}
|
||||
}
|
||||
R = f*f*((float)0.5-(float)0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(float)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/((float)2.0+f);
|
||||
dk = (float)k;
|
||||
z = s*s;
|
||||
i = ix-(0x6147a<<3);
|
||||
w = z*z;
|
||||
j = (0x6b851<<3)-ix;
|
||||
t1= w*(Lg2+w*Lg4);
|
||||
t2= z*(Lg1+w*Lg3);
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=(float)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);
|
||||
}
|
||||
}
|
|
@ -1,251 +0,0 @@
|
|||
/* e_powf.c -- float version of e_pow.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
||||
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
||||
zero = 0.0,
|
||||
half = 0.5,
|
||||
qrtr = 0.25,
|
||||
thrd = 3.33333343e-01, /* 0x3eaaaaab */
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two24 = 16777216.0, /* 0x4b800000 */
|
||||
huge = 1.0e30,
|
||||
tiny = 1.0e-30,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 6.0000002384e-01, /* 0x3f19999a */
|
||||
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
||||
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
||||
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
||||
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
||||
L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
||||
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
||||
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
||||
P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
||||
lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
||||
lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
||||
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
||||
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
||||
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
||||
cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
|
||||
cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
|
||||
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
||||
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
||||
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
||||
|
||||
float
|
||||
__ieee754_powf(float x, float y)
|
||||
{
|
||||
float z,ax,z_h,z_l,p_h,p_l;
|
||||
float y1,t1,t2,r,s,sn,t,u,v,w;
|
||||
int32_t i,j,k,yisint,n;
|
||||
int32_t hx,hy,ix,iy,is;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if(iy==0) return one;
|
||||
|
||||
/* x==1: 1**y = 1, even if y is NaN */
|
||||
if (hx==0x3f800000) return one;
|
||||
|
||||
/* y!=zero: result is NaN if either arg is NaN */
|
||||
if(ix > 0x7f800000 ||
|
||||
iy > 0x7f800000)
|
||||
return nan_mix(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>=0x4b800000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3f800000) {
|
||||
k = (iy>>23)-0x7f; /* exponent */
|
||||
j = iy>>(23-k);
|
||||
if((j<<(23-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if (iy==0x7f800000) { /* y is +-inf */
|
||||
if (ix==0x3f800000)
|
||||
return one; /* (-1)**+-inf is NaN */
|
||||
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3f800000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3f000000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return __ieee754_sqrtf(x);
|
||||
}
|
||||
|
||||
ax = fabsf(x);
|
||||
/* special value of x */
|
||||
if(ix==0x7f800000||ix==0||ix==0x3f800000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3f800000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
n = ((u_int32_t)hx>>31)-1;
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if((n|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x4d000000) { /* if |y| > 2**27 */
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3f7ffff6) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
|
||||
if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*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 = ax-1; /* t has 20 trailing zeros */
|
||||
w = (t*t)*(half-t*(thrd-t*qrtr));
|
||||
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
float s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00800000)
|
||||
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
|
||||
n += ((ix)>>23)-0x7f;
|
||||
j = ix&0x007fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3f800000; /* normalize ix */
|
||||
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00800000;}
|
||||
SET_FLOAT_WORD(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;
|
||||
GET_FLOAT_WORD(is,s_h);
|
||||
SET_FLOAT_WORD(s_h,is&0xfffff000);
|
||||
/* t_h=ax+bp[k] High */
|
||||
is = ((ix>>1)&0xfffff000)|0x20000000;
|
||||
SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
|
||||
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+s2+r;
|
||||
GET_FLOAT_WORD(is,t_h);
|
||||
SET_FLOAT_WORD(t_h,is&0xfffff000);
|
||||
t_l = r-((t_h-3)-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;
|
||||
GET_FLOAT_WORD(is,p_h);
|
||||
SET_FLOAT_WORD(p_h,is&0xfffff000);
|
||||
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 = n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
GET_FLOAT_WORD(is,y);
|
||||
SET_FLOAT_WORD(y1,is&0xfffff000);
|
||||
p_l = (y-y1)*t1+y*t2;
|
||||
p_h = y1*t1;
|
||||
z = p_l+p_h;
|
||||
GET_FLOAT_WORD(j,z);
|
||||
if (j>0x43000000) /* if z > 128 */
|
||||
return sn*huge*huge; /* overflow */
|
||||
else if (j==0x43000000) { /* if z == 128 */
|
||||
if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
|
||||
}
|
||||
else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
|
||||
return sn*tiny*tiny; /* underflow */
|
||||
else if (j==0xc3160000){ /* z == -150 */
|
||||
if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>23)-0x7f;
|
||||
n = 0;
|
||||
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00800000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
|
||||
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
|
||||
n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
GET_FLOAT_WORD(is,t);
|
||||
SET_FLOAT_WORD(t,is&0xffff8000);
|
||||
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);
|
||||
GET_FLOAT_WORD(j,z);
|
||||
j += (n<<23);
|
||||
if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
|
||||
else SET_FLOAT_WORD(z,j);
|
||||
return sn*z;
|
||||
}
|
|
@ -1,77 +0,0 @@
|
|||
/* e_rem_pio2f.c -- float version of e_rem_pio2.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Debugged and optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
/* __ieee754_rem_pio2f(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in *y
|
||||
* use double precision for everything except passing x
|
||||
* use __kernel_rem_pio2() for large x
|
||||
*/
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 25 bits of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
*/
|
||||
|
||||
static const double
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
|
||||
pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
|
||||
|
||||
#ifdef INLINE_REM_PIO2F
|
||||
static inline
|
||||
#endif
|
||||
int
|
||||
__ieee754_rem_pio2f(float x, double *y)
|
||||
{
|
||||
double w,r,fn;
|
||||
double tx[1],ty[1];
|
||||
float z;
|
||||
int32_t e0,n,ix,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
/* 33+53 bit pi is good enough for medium size */
|
||||
if(ix<0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
|
||||
fn = rnint((float)x*invpio2);
|
||||
n = irint(fn);
|
||||
r = x-fn*pio2_1;
|
||||
w = fn*pio2_1t;
|
||||
*y = r-w;
|
||||
return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7f800000) { /* x is inf or NaN */
|
||||
*y=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(|x|)-23) */
|
||||
e0 = (ix>>23)-150; /* e0 = ilogb(|x|)-23; */
|
||||
SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
|
||||
tx[0] = z;
|
||||
n = __kernel_rem_pio2(tx,ty,e0,1,0);
|
||||
if(hx<0) {*y = -ty[0]; return -n;}
|
||||
*y = ty[0]; return n;
|
||||
}
|
|
@ -1,96 +0,0 @@
|
|||
/* e_sqrtf.c -- float version of e_sqrt.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#ifndef lint
|
||||
//static char rcsid[] = "$FreeBSD$";
|
||||
//#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef USE_BUILTIN_SQRTF
|
||||
float
|
||||
__ieee754_sqrtf(float x)
|
||||
{
|
||||
return (__builtin_sqrtf(x));
|
||||
}
|
||||
#else
|
||||
static const float one = 1.0, tiny=1.0e-30;
|
||||
|
||||
float
|
||||
__ieee754_sqrtf(float x)
|
||||
{
|
||||
float z;
|
||||
int32_t sign = (int)0x80000000;
|
||||
int32_t ix,s,q,m,t,i;
|
||||
u_int32_t r;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix&0x7f800000)==0x7f800000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix<=0) {
|
||||
if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix>>23);
|
||||
if(m==0) { /* subnormal x */
|
||||
for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
|
||||
m -= i-1;
|
||||
}
|
||||
m -= 127; /* unbias exponent */
|
||||
ix = (ix&0x007fffff)|0x00800000;
|
||||
if(m&1) /* odd m, double x to make it even */
|
||||
ix += ix;
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix += ix;
|
||||
q = s = 0; /* q = sqrt(x) */
|
||||
r = 0x01000000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s+r;
|
||||
if(t<=ix) {
|
||||
s = t+r;
|
||||
ix -= t;
|
||||
q += r;
|
||||
}
|
||||
ix += ix;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if(ix!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (z>one)
|
||||
q += 2;
|
||||
else
|
||||
q += (q&1);
|
||||
}
|
||||
}
|
||||
ix = (q>>1)+0x3f000000;
|
||||
ix += (m <<23);
|
||||
SET_FLOAT_WORD(z,ix);
|
||||
return z;
|
||||
}
|
||||
#endif
|
|
@ -19,10 +19,6 @@
|
|||
|
||||
namespace fdlibm {
|
||||
|
||||
#ifndef M_PI_2
|
||||
#define M_PI_2 1.57079632679489661923 /* pi/2 */
|
||||
#endif
|
||||
|
||||
double acos(double);
|
||||
double asin(double);
|
||||
double atan(double);
|
||||
|
@ -49,7 +45,6 @@ double acosh(double);
|
|||
double asinh(double);
|
||||
double atanh(double);
|
||||
double cbrt(double);
|
||||
double exp2(double);
|
||||
double expm1(double);
|
||||
double hypot(double, double);
|
||||
double log1p(double);
|
||||
|
@ -59,26 +54,13 @@ double copysign(double, double);
|
|||
double nearbyint(double);
|
||||
double scalbn(double, int);
|
||||
double trunc(double);
|
||||
float acosf(float);
|
||||
float asinf(float);
|
||||
float atanf(float);
|
||||
float cosf(float);
|
||||
float sinf(float);
|
||||
float tanf(float);
|
||||
float exp2f(float);
|
||||
float expf(float);
|
||||
float logf(float);
|
||||
float powf(float, float);
|
||||
float sqrtf(float);
|
||||
|
||||
float ceilf(float);
|
||||
float fabsf(float);
|
||||
float floorf(float);
|
||||
float nearbyintf(float);
|
||||
float rintf(float);
|
||||
float scalbnf(float, int);
|
||||
float truncf(float);
|
||||
|
||||
} /* namespace fdlibm */
|
||||
|
||||
#endif /* !mozilla_imported_fdlibm_h */
|
||||
#endif /* mozilla_imported_fdlibm_h */
|
||||
|
|
|
@ -1,45 +0,0 @@
|
|||
/* k_cosf.c -- float version of k_cos.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Debugged and optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_COSDF
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
|
||||
static const double
|
||||
one = 1.0,
|
||||
C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */
|
||||
C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */
|
||||
C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */
|
||||
C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */
|
||||
|
||||
#ifdef INLINE_KERNEL_COSDF
|
||||
static __inline
|
||||
#endif
|
||||
float
|
||||
__kernel_cosdf(double x)
|
||||
{
|
||||
double r, w, z;
|
||||
|
||||
/* Try to optimize for parallel evaluation as in k_tanf.c. */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
r = C2+z*C3;
|
||||
return ((one+z*C0) + w*C1) + (w*z)*r;
|
||||
}
|
|
@ -1,66 +0,0 @@
|
|||
/*-
|
||||
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
|
||||
*
|
||||
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const uint32_t k = 235; /* constant for reduction */
|
||||
static const float kln2 = 162.88958740F; /* k * ln2 */
|
||||
|
||||
/*
|
||||
* See k_exp.c for details.
|
||||
*
|
||||
* Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7
|
||||
* Output: 2**127 <= y < 2**128
|
||||
*/
|
||||
static float
|
||||
__frexp_expf(float x, int *expt)
|
||||
{
|
||||
float exp_x;
|
||||
uint32_t hx;
|
||||
|
||||
exp_x = expf(x - kln2);
|
||||
GET_FLOAT_WORD(hx, exp_x);
|
||||
*expt = (hx >> 23) - (0x7f + 127) + k;
|
||||
SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23));
|
||||
return (exp_x);
|
||||
}
|
||||
|
||||
float
|
||||
__ldexp_expf(float x, int expt)
|
||||
{
|
||||
float exp_x, scale;
|
||||
int ex_expt;
|
||||
|
||||
exp_x = __frexp_expf(x, &ex_expt);
|
||||
expt += ex_expt;
|
||||
SET_FLOAT_WORD(scale, (0x7f + expt) << 23);
|
||||
return (exp_x * scale);
|
||||
}
|
|
@ -1,45 +0,0 @@
|
|||
/* k_sinf.c -- float version of k_sin.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_SINDF
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
|
||||
static const double
|
||||
S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
|
||||
S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
|
||||
S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
|
||||
S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */
|
||||
|
||||
#ifdef INLINE_KERNEL_SINDF
|
||||
static __inline
|
||||
#endif
|
||||
float
|
||||
__kernel_sindf(double x)
|
||||
{
|
||||
double r, s, w, z;
|
||||
|
||||
/* Try to optimize for parallel evaluation as in k_tanf.c. */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
r = S3+z*S4;
|
||||
s = z*x;
|
||||
return (x + s*(S1+z*S2)) + s*w*r;
|
||||
}
|
|
@ -1,65 +0,0 @@
|
|||
/* k_tanf.c -- float version of k_tan.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#ifndef INLINE_KERNEL_TANDF
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
|
||||
static const double
|
||||
T[] = {
|
||||
0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
|
||||
0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
|
||||
0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
|
||||
0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
|
||||
0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
|
||||
0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
|
||||
};
|
||||
|
||||
#ifdef INLINE_KERNEL_TANDF
|
||||
static __inline
|
||||
#endif
|
||||
float
|
||||
__kernel_tandf(double x, int iy)
|
||||
{
|
||||
double z,r,w,s,t,u;
|
||||
|
||||
z = x*x;
|
||||
/*
|
||||
* Split up the polynomial into small independent terms to give
|
||||
* opportunities for parallel evaluation. The chosen splitting is
|
||||
* micro-optimized for Athlons (XP, X64). It costs 2 multiplications
|
||||
* relative to Horner's method on sequential machines.
|
||||
*
|
||||
* We add the small terms from lowest degree up for efficiency on
|
||||
* non-sequential machines (the lowest degree terms tend to be ready
|
||||
* earlier). Apart from this, we don't care about order of
|
||||
* operations, and don't need to care since we have precision to
|
||||
* spare. However, the chosen splitting is good for accuracy too,
|
||||
* and would give results as accurate as Horner's method if the
|
||||
* small terms were added from highest degree down.
|
||||
*/
|
||||
r = T[4]+z*T[5];
|
||||
t = T[2]+z*T[3];
|
||||
w = z*z;
|
||||
s = z*x;
|
||||
u = T[0]+z*T[1];
|
||||
r = (x+s*u)+(s*w)*(t+w*r);
|
||||
if(iy==1) return r;
|
||||
else return -1.0/r;
|
||||
}
|
|
@ -871,34 +871,22 @@ irintl(long double x)
|
|||
#define __ieee754_scalbf scalbf
|
||||
|
||||
#define acos fdlibm::acos
|
||||
#define acosf fdlibm::acosf
|
||||
#define asin fdlibm::asin
|
||||
#define asinf fdlibm::asinf
|
||||
#define atan fdlibm::atan
|
||||
#define atanf fdlibm::atanf
|
||||
#define atan2 fdlibm::atan2
|
||||
#define cos fdlibm::cos
|
||||
#define cosf fdlibm::cosf
|
||||
#define sin fdlibm::sin
|
||||
#define sinf fdlibm::sinf
|
||||
#define tan fdlibm::tan
|
||||
#define tanf fdlibm::tanf
|
||||
#define cosh fdlibm::cosh
|
||||
#define sinh fdlibm::sinh
|
||||
#define tanh fdlibm::tanh
|
||||
#define exp fdlibm::exp
|
||||
#define expf fdlibm::expf
|
||||
#define exp2 fdlibm::exp2
|
||||
#define exp2f fdlibm::exp2f
|
||||
#define log fdlibm::log
|
||||
#define logf fdlibm::logf
|
||||
#define log10 fdlibm::log10
|
||||
#define pow fdlibm::pow
|
||||
#define powf fdlibm::powf
|
||||
#define ceil fdlibm::ceil
|
||||
#define ceilf fdlibm::ceilf
|
||||
#define fabs fdlibm::fabs
|
||||
#define fabsf fdlibm::fabsf
|
||||
#define floor fdlibm::floor
|
||||
#define acosh fdlibm::acosh
|
||||
#define asinh fdlibm::asinh
|
||||
|
@ -911,7 +899,6 @@ irintl(long double x)
|
|||
#define scalb fdlibm::scalb
|
||||
#define copysign fdlibm::copysign
|
||||
#define scalbn fdlibm::scalbn
|
||||
#define scalbnf fdlibm::scalbnf
|
||||
#define trunc fdlibm::trunc
|
||||
#define truncf fdlibm::truncf
|
||||
#define floorf fdlibm::floorf
|
||||
|
@ -919,7 +906,6 @@ irintl(long double x)
|
|||
#define nearbyintf fdlibm::nearbyintf
|
||||
#define rint fdlibm::rint
|
||||
#define rintf fdlibm::rintf
|
||||
#define sqrtf fdlibm::sqrtf
|
||||
|
||||
/* fdlibm kernel function */
|
||||
int __kernel_rem_pio2(double*,double*,int,int,int);
|
||||
|
|
|
@ -34,47 +34,32 @@ if CONFIG['CC_TYPE'] == 'clang-cl':
|
|||
# variables (e.g. almost every source file defines a `one` and a `huge`).
|
||||
SOURCES += [
|
||||
'e_acos.cpp',
|
||||
'e_acosf.cpp',
|
||||
'e_acosh.cpp',
|
||||
'e_asin.cpp',
|
||||
'e_asinf.cpp',
|
||||
'e_atan2.cpp',
|
||||
'e_atanh.cpp',
|
||||
'e_cosh.cpp',
|
||||
'e_exp.cpp',
|
||||
'e_expf.cpp',
|
||||
'e_hypot.cpp',
|
||||
'e_log.cpp',
|
||||
'e_log10.cpp',
|
||||
'e_log2.cpp',
|
||||
'e_logf.cpp',
|
||||
'e_pow.cpp',
|
||||
'e_powf.cpp',
|
||||
'e_sinh.cpp',
|
||||
'e_sqrtf.cpp',
|
||||
'k_cos.cpp',
|
||||
'k_cosf.cpp',
|
||||
'k_exp.cpp',
|
||||
'k_expf.cpp',
|
||||
'k_rem_pio2.cpp',
|
||||
'k_sin.cpp',
|
||||
'k_sinf.cpp',
|
||||
'k_tan.cpp',
|
||||
'k_tanf.cpp',
|
||||
's_asinh.cpp',
|
||||
's_atan.cpp',
|
||||
's_atanf.cpp',
|
||||
's_cbrt.cpp',
|
||||
's_ceil.cpp',
|
||||
's_ceilf.cpp',
|
||||
# 's_copysign.cpp', # Unused file.
|
||||
's_cos.cpp',
|
||||
's_cosf.cpp',
|
||||
's_exp2.cpp',
|
||||
's_exp2f.cpp',
|
||||
's_expm1.cpp',
|
||||
's_fabs.cpp',
|
||||
's_fabsf.cpp',
|
||||
's_floor.cpp',
|
||||
's_floorf.cpp',
|
||||
's_log1p.cpp',
|
||||
|
@ -83,9 +68,7 @@ SOURCES += [
|
|||
's_rintf.cpp',
|
||||
's_scalbn.cpp',
|
||||
's_sin.cpp',
|
||||
's_sinf.cpp',
|
||||
's_tan.cpp',
|
||||
's_tanf.cpp',
|
||||
's_tanh.cpp',
|
||||
's_trunc.cpp',
|
||||
's_truncf.cpp',
|
||||
|
|
|
@ -1,91 +0,0 @@
|
|||
/* s_atanf.c -- float version of s_atan.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
static const float atanhi[] = {
|
||||
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
|
||||
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
|
||||
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
|
||||
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
|
||||
};
|
||||
|
||||
static const float atanlo[] = {
|
||||
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
|
||||
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
|
||||
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
|
||||
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
|
||||
};
|
||||
|
||||
static const float aT[] = {
|
||||
3.3333328366e-01,
|
||||
-1.9999158382e-01,
|
||||
1.4253635705e-01,
|
||||
-1.0648017377e-01,
|
||||
6.1687607318e-02,
|
||||
};
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
huge = 1.0e30;
|
||||
|
||||
float
|
||||
atanf(float x)
|
||||
{
|
||||
float w,s1,s2,z;
|
||||
int32_t ix,hx,id;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x4c800000) { /* if |x| >= 2**26 */
|
||||
if(ix>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3];
|
||||
else return -atanhi[3]-*(volatile float *)&atanlo[3];
|
||||
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
|
||||
if (ix < 0x39800000) { /* |x| < 2**-12 */
|
||||
if(huge+x>one) return x; /* raise inexact */
|
||||
}
|
||||
id = -1;
|
||||
} else {
|
||||
x = fabsf(x);
|
||||
if (ix < 0x3f980000) { /* |x| < 1.1875 */
|
||||
if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
|
||||
id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x401c0000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
|
||||
} else { /* 2.4375 <= |x| < 2**26 */
|
||||
id = 3; x = -(float)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]));
|
||||
s2 = w*(aT[1]+w*aT[3]);
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
|
@ -1,86 +0,0 @@
|
|||
/* s_cosf.c -- float version of s_cos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.cpp"
|
||||
#include "k_cosf.cpp"
|
||||
#include "k_sinf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
float
|
||||
cosf(float x)
|
||||
{
|
||||
double y;
|
||||
int32_t n, hx, ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx & 0x7fffffff;
|
||||
|
||||
if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
|
||||
if(ix<0x39800000) /* |x| < 2**-12 */
|
||||
if(((int)x)==0) return 1.0; /* 1 with inexact if x != 0 */
|
||||
return __kernel_cosdf(x);
|
||||
}
|
||||
if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */
|
||||
if(ix>0x4016cbe3) /* |x| ~> 3*pi/4 */
|
||||
return -__kernel_cosdf(x + (hx > 0 ? -c2pio2 : c2pio2));
|
||||
else {
|
||||
if(hx>0)
|
||||
return __kernel_sindf(c1pio2 - x);
|
||||
else
|
||||
return __kernel_sindf(x + c1pio2);
|
||||
}
|
||||
}
|
||||
if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */
|
||||
if(ix>0x40afeddf) /* |x| ~> 7*pi/4 */
|
||||
return __kernel_cosdf(x + (hx > 0 ? -c4pio2 : c4pio2));
|
||||
else {
|
||||
if(hx>0)
|
||||
return __kernel_sindf(x - c3pio2);
|
||||
else
|
||||
return __kernel_sindf(-c3pio2 - x);
|
||||
}
|
||||
}
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x;
|
||||
|
||||
/* general argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,&y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cosdf(y);
|
||||
case 1: return __kernel_sindf(-y);
|
||||
case 2: return -__kernel_cosdf(y);
|
||||
default:
|
||||
return __kernel_sindf(y);
|
||||
}
|
||||
}
|
||||
}
|
|
@ -1,396 +0,0 @@
|
|||
/*-
|
||||
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
|
||||
*
|
||||
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 8
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const double
|
||||
redux = 0x1.8p52 / TBLSIZE,
|
||||
P1 = 0x1.62e42fefa39efp-1,
|
||||
P2 = 0x1.ebfbdff82c575p-3,
|
||||
P3 = 0x1.c6b08d704a0a6p-5,
|
||||
P4 = 0x1.3b2ab88f70400p-7,
|
||||
P5 = 0x1.5d88003875c74p-10;
|
||||
|
||||
static volatile double
|
||||
huge = 0x1p1000,
|
||||
twom1000 = 0x1p-1000;
|
||||
|
||||
static const double tbl[TBLSIZE * 2] = {
|
||||
/* exp2(z + eps) eps */
|
||||
0x1.6a09e667f3d5dp-1, 0x1.9880p-44,
|
||||
0x1.6b052fa751744p-1, 0x1.8000p-50,
|
||||
0x1.6c012750bd9fep-1, -0x1.8780p-45,
|
||||
0x1.6cfdcddd476bfp-1, 0x1.ec00p-46,
|
||||
0x1.6dfb23c651a29p-1, -0x1.8000p-50,
|
||||
0x1.6ef9298593ae3p-1, -0x1.c000p-52,
|
||||
0x1.6ff7df9519386p-1, -0x1.fd80p-45,
|
||||
0x1.70f7466f42da3p-1, -0x1.c880p-45,
|
||||
0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46,
|
||||
0x1.72f8286eacf05p-1, -0x1.8300p-44,
|
||||
0x1.73f9a48a58152p-1, -0x1.0c00p-47,
|
||||
0x1.74fbd35d7ccfcp-1, 0x1.f880p-45,
|
||||
0x1.75feb564267f1p-1, 0x1.3e00p-47,
|
||||
0x1.77024b1ab6d48p-1, -0x1.7d00p-45,
|
||||
0x1.780694fde5d38p-1, -0x1.d000p-50,
|
||||
0x1.790b938ac1d00p-1, 0x1.3000p-49,
|
||||
0x1.7a11473eb0178p-1, -0x1.d000p-49,
|
||||
0x1.7b17b0976d060p-1, 0x1.0400p-45,
|
||||
0x1.7c1ed0130c133p-1, 0x1.0000p-53,
|
||||
0x1.7d26a62ff8636p-1, -0x1.6900p-45,
|
||||
0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47,
|
||||
0x1.7f3878491c3e8p-1, -0x1.4580p-45,
|
||||
0x1.80427543e1b4ep-1, 0x1.3000p-44,
|
||||
0x1.814d2add1071ap-1, 0x1.f000p-47,
|
||||
0x1.82589994ccd7ep-1, -0x1.1c00p-45,
|
||||
0x1.8364c1eb942d0p-1, 0x1.9d00p-45,
|
||||
0x1.8471a4623cab5p-1, 0x1.7100p-43,
|
||||
0x1.857f4179f5bbcp-1, 0x1.2600p-45,
|
||||
0x1.868d99b4491afp-1, -0x1.2c40p-44,
|
||||
0x1.879cad931a395p-1, -0x1.3000p-45,
|
||||
0x1.88ac7d98a65b8p-1, -0x1.a800p-45,
|
||||
0x1.89bd0a4785800p-1, -0x1.d000p-49,
|
||||
0x1.8ace5422aa223p-1, 0x1.3280p-44,
|
||||
0x1.8be05bad619fap-1, 0x1.2b40p-43,
|
||||
0x1.8cf3216b54383p-1, -0x1.ed00p-45,
|
||||
0x1.8e06a5e08664cp-1, -0x1.0500p-45,
|
||||
0x1.8f1ae99157807p-1, 0x1.8280p-45,
|
||||
0x1.902fed0282c0ep-1, -0x1.cb00p-46,
|
||||
0x1.9145b0b91ff96p-1, -0x1.5e00p-47,
|
||||
0x1.925c353aa2ff9p-1, 0x1.5400p-48,
|
||||
0x1.93737b0cdc64ap-1, 0x1.7200p-46,
|
||||
0x1.948b82b5f98aep-1, -0x1.9000p-47,
|
||||
0x1.95a44cbc852cbp-1, 0x1.5680p-45,
|
||||
0x1.96bdd9a766f21p-1, -0x1.6d00p-44,
|
||||
0x1.97d829fde4e2ap-1, -0x1.1000p-47,
|
||||
0x1.98f33e47a23a3p-1, 0x1.d000p-45,
|
||||
0x1.9a0f170ca0604p-1, -0x1.8a40p-44,
|
||||
0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44,
|
||||
0x1.9c49182a3f15bp-1, 0x1.6b80p-45,
|
||||
0x1.9d674194bb8c5p-1, -0x1.c000p-49,
|
||||
0x1.9e86319e3238ep-1, 0x1.7d00p-46,
|
||||
0x1.9fa5e8d07f302p-1, 0x1.6400p-46,
|
||||
0x1.a0c667b5de54dp-1, -0x1.5000p-48,
|
||||
0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47,
|
||||
0x1.a309bec4a2e27p-1, 0x1.ad80p-45,
|
||||
0x1.a42c980460a5dp-1, -0x1.af00p-46,
|
||||
0x1.a5503b23e259bp-1, 0x1.b600p-47,
|
||||
0x1.a674a8af46213p-1, 0x1.8880p-44,
|
||||
0x1.a799e1330b3a7p-1, 0x1.1200p-46,
|
||||
0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47,
|
||||
0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45,
|
||||
0x1.ab0e521356fb8p-1, 0x1.b700p-45,
|
||||
0x1.ac36bbfd3f381p-1, 0x1.9000p-50,
|
||||
0x1.ad5ff3a3c2780p-1, 0x1.4000p-49,
|
||||
0x1.ae89f995ad2a3p-1, -0x1.c900p-45,
|
||||
0x1.afb4ce622f367p-1, 0x1.6500p-46,
|
||||
0x1.b0e07298db790p-1, 0x1.fd40p-45,
|
||||
0x1.b20ce6c9a89a9p-1, 0x1.2700p-46,
|
||||
0x1.b33a2b84f1a4bp-1, 0x1.d470p-43,
|
||||
0x1.b468415b747e7p-1, -0x1.8380p-44,
|
||||
0x1.b59728de5593ap-1, 0x1.8000p-54,
|
||||
0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47,
|
||||
0x1.b7f76f2fb5e50p-1, 0x1.e800p-50,
|
||||
0x1.b928cf22749b2p-1, -0x1.4c00p-47,
|
||||
0x1.ba5b030a10603p-1, -0x1.d700p-47,
|
||||
0x1.bb8e0b79a6f66p-1, 0x1.d900p-47,
|
||||
0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47,
|
||||
0x1.bdf69c3f3a16fp-1, -0x1.f780p-46,
|
||||
0x1.bf2c25bd71db8p-1, -0x1.0a00p-46,
|
||||
0x1.c06286141b2e9p-1, -0x1.1400p-46,
|
||||
0x1.c199bdd8552e0p-1, 0x1.be00p-47,
|
||||
0x1.c2d1cd9fa64eep-1, -0x1.9400p-47,
|
||||
0x1.c40ab5fffd02fp-1, -0x1.ed00p-47,
|
||||
0x1.c544778fafd15p-1, 0x1.9660p-44,
|
||||
0x1.c67f12e57d0cbp-1, -0x1.a100p-46,
|
||||
0x1.c7ba88988c1b6p-1, -0x1.8458p-42,
|
||||
0x1.c8f6d9406e733p-1, -0x1.a480p-46,
|
||||
0x1.ca3405751c4dfp-1, 0x1.b000p-51,
|
||||
0x1.cb720dcef9094p-1, 0x1.1400p-47,
|
||||
0x1.ccb0f2e6d1689p-1, 0x1.0200p-48,
|
||||
0x1.cdf0b555dc412p-1, 0x1.3600p-48,
|
||||
0x1.cf3155b5bab3bp-1, -0x1.6900p-47,
|
||||
0x1.d072d4a0789bcp-1, 0x1.9a00p-47,
|
||||
0x1.d1b532b08c8fap-1, -0x1.5e00p-46,
|
||||
0x1.d2f87080d8a85p-1, 0x1.d280p-46,
|
||||
0x1.d43c8eacaa203p-1, 0x1.1a00p-47,
|
||||
0x1.d5818dcfba491p-1, 0x1.f000p-50,
|
||||
0x1.d6c76e862e6a1p-1, -0x1.3a00p-47,
|
||||
0x1.d80e316c9834ep-1, -0x1.cd80p-47,
|
||||
0x1.d955d71ff6090p-1, 0x1.4c00p-48,
|
||||
0x1.da9e603db32aep-1, 0x1.f900p-48,
|
||||
0x1.dbe7cd63a8325p-1, 0x1.9800p-49,
|
||||
0x1.dd321f301b445p-1, -0x1.5200p-48,
|
||||
0x1.de7d5641c05bfp-1, -0x1.d700p-46,
|
||||
0x1.dfc97337b9aecp-1, -0x1.6140p-46,
|
||||
0x1.e11676b197d5ep-1, 0x1.b480p-47,
|
||||
0x1.e264614f5a3e7p-1, 0x1.0ce0p-43,
|
||||
0x1.e3b333b16ee5cp-1, 0x1.c680p-47,
|
||||
0x1.e502ee78b3fb4p-1, -0x1.9300p-47,
|
||||
0x1.e653924676d68p-1, -0x1.5000p-49,
|
||||
0x1.e7a51fbc74c44p-1, -0x1.7f80p-47,
|
||||
0x1.e8f7977cdb726p-1, -0x1.3700p-48,
|
||||
0x1.ea4afa2a490e8p-1, 0x1.5d00p-49,
|
||||
0x1.eb9f4867ccae4p-1, 0x1.61a0p-46,
|
||||
0x1.ecf482d8e680dp-1, 0x1.5500p-48,
|
||||
0x1.ee4aaa2188514p-1, 0x1.6400p-51,
|
||||
0x1.efa1bee615a13p-1, -0x1.e800p-49,
|
||||
0x1.f0f9c1cb64106p-1, -0x1.a880p-48,
|
||||
0x1.f252b376bb963p-1, -0x1.c900p-45,
|
||||
0x1.f3ac948dd7275p-1, 0x1.a000p-53,
|
||||
0x1.f50765b6e4524p-1, -0x1.4f00p-48,
|
||||
0x1.f6632798844fdp-1, 0x1.a800p-51,
|
||||
0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48,
|
||||
0x1.f91d802243c82p-1, -0x1.4600p-50,
|
||||
0x1.fa7c1819e908ep-1, -0x1.b0c0p-47,
|
||||
0x1.fbdba3692d511p-1, -0x1.0e00p-51,
|
||||
0x1.fd3c22b8f7194p-1, -0x1.0de8p-46,
|
||||
0x1.fe9d96b2a23eep-1, 0x1.e430p-49,
|
||||
0x1.0000000000000p+0, 0x0.0000p+0,
|
||||
0x1.00b1afa5abcbep+0, -0x1.3400p-52,
|
||||
0x1.0163da9fb3303p+0, -0x1.2170p-46,
|
||||
0x1.02168143b0282p+0, 0x1.a400p-52,
|
||||
0x1.02c9a3e77806cp+0, 0x1.f980p-49,
|
||||
0x1.037d42e11bbcap+0, -0x1.7400p-51,
|
||||
0x1.04315e86e7f89p+0, 0x1.8300p-50,
|
||||
0x1.04e5f72f65467p+0, -0x1.a3f0p-46,
|
||||
0x1.059b0d315855ap+0, -0x1.2840p-47,
|
||||
0x1.0650a0e3c1f95p+0, 0x1.1600p-48,
|
||||
0x1.0706b29ddf71ap+0, 0x1.5240p-46,
|
||||
0x1.07bd42b72a82dp+0, -0x1.9a00p-49,
|
||||
0x1.0874518759bd0p+0, 0x1.6400p-49,
|
||||
0x1.092bdf66607c8p+0, -0x1.0780p-47,
|
||||
0x1.09e3ecac6f383p+0, -0x1.8000p-54,
|
||||
0x1.0a9c79b1f3930p+0, 0x1.fa00p-48,
|
||||
0x1.0b5586cf988fcp+0, -0x1.ac80p-48,
|
||||
0x1.0c0f145e46c8ap+0, 0x1.9c00p-50,
|
||||
0x1.0cc922b724816p+0, 0x1.5200p-47,
|
||||
0x1.0d83b23395dd8p+0, -0x1.ad00p-48,
|
||||
0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46,
|
||||
0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47,
|
||||
0x1.0fb66affed2f0p+0, -0x1.d300p-47,
|
||||
0x1.1073028d7234bp+0, 0x1.1500p-48,
|
||||
0x1.11301d0125b5bp+0, 0x1.c000p-49,
|
||||
0x1.11edbab5e2af9p+0, 0x1.6bc0p-46,
|
||||
0x1.12abdc06c31d5p+0, 0x1.8400p-49,
|
||||
0x1.136a814f2047dp+0, -0x1.ed00p-47,
|
||||
0x1.1429aaea92de9p+0, 0x1.8e00p-49,
|
||||
0x1.14e95934f3138p+0, 0x1.b400p-49,
|
||||
0x1.15a98c8a58e71p+0, 0x1.5300p-47,
|
||||
0x1.166a45471c3dfp+0, 0x1.3380p-47,
|
||||
0x1.172b83c7d5211p+0, 0x1.8d40p-45,
|
||||
0x1.17ed48695bb9fp+0, -0x1.5d00p-47,
|
||||
0x1.18af9388c8d93p+0, -0x1.c880p-46,
|
||||
0x1.1972658375d66p+0, 0x1.1f00p-46,
|
||||
0x1.1a35beb6fcba7p+0, 0x1.0480p-46,
|
||||
0x1.1af99f81387e3p+0, -0x1.7390p-43,
|
||||
0x1.1bbe084045d54p+0, 0x1.4e40p-45,
|
||||
0x1.1c82f95281c43p+0, -0x1.a200p-47,
|
||||
0x1.1d4873168b9b2p+0, 0x1.3800p-49,
|
||||
0x1.1e0e75eb44031p+0, 0x1.ac00p-49,
|
||||
0x1.1ed5022fcd938p+0, 0x1.1900p-47,
|
||||
0x1.1f9c18438cdf7p+0, -0x1.b780p-46,
|
||||
0x1.2063b88628d8fp+0, 0x1.d940p-45,
|
||||
0x1.212be3578a81ep+0, 0x1.8000p-50,
|
||||
0x1.21f49917ddd41p+0, 0x1.b340p-45,
|
||||
0x1.22bdda2791323p+0, 0x1.9f80p-46,
|
||||
0x1.2387a6e7561e7p+0, -0x1.9c80p-46,
|
||||
0x1.2451ffb821427p+0, 0x1.2300p-47,
|
||||
0x1.251ce4fb2a602p+0, -0x1.3480p-46,
|
||||
0x1.25e85711eceb0p+0, 0x1.2700p-46,
|
||||
0x1.26b4565e27d16p+0, 0x1.1d00p-46,
|
||||
0x1.2780e341de00fp+0, 0x1.1ee0p-44,
|
||||
0x1.284dfe1f5633ep+0, -0x1.4c00p-46,
|
||||
0x1.291ba7591bb30p+0, -0x1.3d80p-46,
|
||||
0x1.29e9df51fdf09p+0, 0x1.8b00p-47,
|
||||
0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45,
|
||||
0x1.2b87fd0dada3ap+0, 0x1.a340p-45,
|
||||
0x1.2c57e39771af9p+0, -0x1.0800p-46,
|
||||
0x1.2d285a6e402d9p+0, -0x1.ed00p-47,
|
||||
0x1.2df961f641579p+0, -0x1.4200p-48,
|
||||
0x1.2ecafa93e2ecfp+0, -0x1.4980p-45,
|
||||
0x1.2f9d24abd8822p+0, -0x1.6300p-46,
|
||||
0x1.306fe0a31b625p+0, -0x1.2360p-44,
|
||||
0x1.31432edeea50bp+0, -0x1.0df8p-40,
|
||||
0x1.32170fc4cd7b8p+0, -0x1.2480p-45,
|
||||
0x1.32eb83ba8e9a2p+0, -0x1.5980p-45,
|
||||
0x1.33c08b2641766p+0, 0x1.ed00p-46,
|
||||
0x1.3496266e3fa27p+0, -0x1.c000p-50,
|
||||
0x1.356c55f929f0fp+0, -0x1.0d80p-44,
|
||||
0x1.36431a2de88b9p+0, 0x1.2c80p-45,
|
||||
0x1.371a7373aaa39p+0, 0x1.0600p-45,
|
||||
0x1.37f26231e74fep+0, -0x1.6600p-46,
|
||||
0x1.38cae6d05d838p+0, -0x1.ae00p-47,
|
||||
0x1.39a401b713ec3p+0, -0x1.4720p-43,
|
||||
0x1.3a7db34e5a020p+0, 0x1.8200p-47,
|
||||
0x1.3b57fbfec6e95p+0, 0x1.e800p-44,
|
||||
0x1.3c32dc313a8f2p+0, 0x1.f800p-49,
|
||||
0x1.3d0e544ede122p+0, -0x1.7a00p-46,
|
||||
0x1.3dea64c1234bbp+0, 0x1.6300p-45,
|
||||
0x1.3ec70df1c4eccp+0, -0x1.8a60p-43,
|
||||
0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44,
|
||||
0x1.40822c367a0bbp+0, 0x1.5b80p-45,
|
||||
0x1.4160a21f72e95p+0, 0x1.ec00p-46,
|
||||
0x1.423fb27094646p+0, -0x1.3600p-46,
|
||||
0x1.431f5d950a920p+0, 0x1.3980p-45,
|
||||
0x1.43ffa3f84b9ebp+0, 0x1.a000p-48,
|
||||
0x1.44e0860618919p+0, -0x1.6c00p-48,
|
||||
0x1.45c2042a7d201p+0, -0x1.bc00p-47,
|
||||
0x1.46a41ed1d0016p+0, -0x1.2800p-46,
|
||||
0x1.4786d668b3326p+0, 0x1.0e00p-44,
|
||||
0x1.486a2b5c13c00p+0, -0x1.d400p-45,
|
||||
0x1.494e1e192af04p+0, 0x1.c200p-47,
|
||||
0x1.4a32af0d7d372p+0, -0x1.e500p-46,
|
||||
0x1.4b17dea6db801p+0, 0x1.7800p-47,
|
||||
0x1.4bfdad53629e1p+0, -0x1.3800p-46,
|
||||
0x1.4ce41b817c132p+0, 0x1.0800p-47,
|
||||
0x1.4dcb299fddddbp+0, 0x1.c700p-45,
|
||||
0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46,
|
||||
0x1.4f9b2769d2d02p+0, 0x1.9200p-46,
|
||||
0x1.508417f4531c1p+0, -0x1.8c00p-47,
|
||||
0x1.516daa2cf662ap+0, -0x1.a000p-48,
|
||||
0x1.5257de83f51eap+0, 0x1.a080p-43,
|
||||
0x1.5342b569d4edap+0, -0x1.6d80p-45,
|
||||
0x1.542e2f4f6ac1ap+0, -0x1.2440p-44,
|
||||
0x1.551a4ca5d94dbp+0, 0x1.83c0p-43,
|
||||
0x1.56070dde9116bp+0, 0x1.4b00p-45,
|
||||
0x1.56f4736b529dep+0, 0x1.15a0p-43,
|
||||
0x1.57e27dbe2c40ep+0, -0x1.9e00p-45,
|
||||
0x1.58d12d497c76fp+0, -0x1.3080p-45,
|
||||
0x1.59c0827ff0b4cp+0, 0x1.dec0p-43,
|
||||
0x1.5ab07dd485427p+0, -0x1.4000p-51,
|
||||
0x1.5ba11fba87af4p+0, 0x1.0080p-44,
|
||||
0x1.5c9268a59460bp+0, -0x1.6c80p-45,
|
||||
0x1.5d84590998e3fp+0, 0x1.69a0p-43,
|
||||
0x1.5e76f15ad20e1p+0, -0x1.b400p-46,
|
||||
0x1.5f6a320dcebcap+0, 0x1.7700p-46,
|
||||
0x1.605e1b976dcb8p+0, 0x1.6f80p-45,
|
||||
0x1.6152ae6cdf715p+0, 0x1.1000p-47,
|
||||
0x1.6247eb03a5531p+0, -0x1.5d00p-46,
|
||||
0x1.633dd1d1929b5p+0, -0x1.2d00p-46,
|
||||
0x1.6434634ccc313p+0, -0x1.a800p-49,
|
||||
0x1.652b9febc8efap+0, -0x1.8600p-45,
|
||||
0x1.6623882553397p+0, 0x1.1fe0p-40,
|
||||
0x1.671c1c708328ep+0, -0x1.7200p-44,
|
||||
0x1.68155d44ca97ep+0, 0x1.6800p-49,
|
||||
0x1.690f4b19e9471p+0, -0x1.9780p-45,
|
||||
};
|
||||
|
||||
/*
|
||||
* exp2(x): compute the base 2 exponential of x
|
||||
*
|
||||
* Accuracy: Peak error < 0.503 ulp for normalized results.
|
||||
*
|
||||
* Method: (accurate tables)
|
||||
*
|
||||
* Reduce x:
|
||||
* x = 2**k + y, for integer k and |y| <= 1/2.
|
||||
* Thus we have exp2(x) = 2**k * exp2(y).
|
||||
*
|
||||
* Reduce y:
|
||||
* y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
|
||||
* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
|
||||
* with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
|
||||
*
|
||||
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
|
||||
* a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
|
||||
* The values in exp2t[] and eps[] are chosen such that
|
||||
* exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
|
||||
* that exp2t[i] is accurate to 2**-64.
|
||||
*
|
||||
* Note that the range of i is +-TBLSIZE/2, so we actually index the tables
|
||||
* by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are
|
||||
* virtual tables, interleaved in the real table tbl[].
|
||||
*
|
||||
* This method is due to Gal, with many details due to Gal and Bachelis:
|
||||
*
|
||||
* Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library
|
||||
* for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991).
|
||||
*/
|
||||
double
|
||||
exp2(double x)
|
||||
{
|
||||
double r, t, twopk, twopkp1000, z;
|
||||
uint32_t hx, ix, lx, i0;
|
||||
int k;
|
||||
|
||||
/* Filter out exceptional cases. */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if(ix >= 0x40900000) { /* |x| >= 1024 */
|
||||
if(ix >= 0x7ff00000) {
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0)
|
||||
return (x + x); /* x is NaN or +Inf */
|
||||
else
|
||||
return (0.0); /* x is -Inf */
|
||||
}
|
||||
if(x >= 0x1.0p10)
|
||||
return (huge * huge); /* overflow */
|
||||
if(x <= -0x1.0ccp10)
|
||||
return (twom1000 * twom1000); /* underflow */
|
||||
} else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */
|
||||
return (1.0 + x);
|
||||
}
|
||||
|
||||
/* Reduce x, computing z, i0, and k. */
|
||||
STRICT_ASSIGN(double, t, x + redux);
|
||||
GET_LOW_WORD(i0, t);
|
||||
i0 += TBLSIZE / 2;
|
||||
k = (i0 >> TBLBITS) << 20;
|
||||
i0 = (i0 & (TBLSIZE - 1)) << 1;
|
||||
t -= redux;
|
||||
z = x - t;
|
||||
|
||||
/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
|
||||
t = tbl[i0]; /* exp2t[i0] */
|
||||
z -= tbl[i0 + 1]; /* eps[i0] */
|
||||
if (k >= -(1021 << 20))
|
||||
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
|
||||
else
|
||||
INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0);
|
||||
r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
|
||||
|
||||
/* Scale by 2**(k>>20). */
|
||||
if(k >= -(1021 << 20)) {
|
||||
if (k == 1024 << 20) {
|
||||
double const_0x1p1023 = pow(2, 1023);
|
||||
return (r * 2.0 * const_0x1p1023);
|
||||
}
|
||||
return (r * twopk);
|
||||
} else {
|
||||
return (r * twopkp1000 * twom1000);
|
||||
}
|
||||
}
|
|
@ -1,138 +0,0 @@
|
|||
/*-
|
||||
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
|
||||
*
|
||||
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 4
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const float
|
||||
redux = 0x1.8p23f / TBLSIZE,
|
||||
P1 = 0x1.62e430p-1f,
|
||||
P2 = 0x1.ebfbe0p-3f,
|
||||
P3 = 0x1.c6b348p-5f,
|
||||
P4 = 0x1.3b2c9cp-7f;
|
||||
|
||||
static volatile float
|
||||
huge = 0x1p100f,
|
||||
twom100 = 0x1p-100f;
|
||||
|
||||
static const double exp2ft[TBLSIZE] = {
|
||||
0x1.6a09e667f3bcdp-1,
|
||||
0x1.7a11473eb0187p-1,
|
||||
0x1.8ace5422aa0dbp-1,
|
||||
0x1.9c49182a3f090p-1,
|
||||
0x1.ae89f995ad3adp-1,
|
||||
0x1.c199bdd85529cp-1,
|
||||
0x1.d5818dcfba487p-1,
|
||||
0x1.ea4afa2a490dap-1,
|
||||
0x1.0000000000000p+0,
|
||||
0x1.0b5586cf9890fp+0,
|
||||
0x1.172b83c7d517bp+0,
|
||||
0x1.2387a6e756238p+0,
|
||||
0x1.306fe0a31b715p+0,
|
||||
0x1.3dea64c123422p+0,
|
||||
0x1.4bfdad5362a27p+0,
|
||||
0x1.5ab07dd485429p+0,
|
||||
};
|
||||
|
||||
/*
|
||||
* exp2f(x): compute the base 2 exponential of x
|
||||
*
|
||||
* Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
|
||||
*
|
||||
* Method: (equally-spaced tables)
|
||||
*
|
||||
* Reduce x:
|
||||
* x = 2**k + y, for integer k and |y| <= 1/2.
|
||||
* Thus we have exp2f(x) = 2**k * exp2(y).
|
||||
*
|
||||
* Reduce y:
|
||||
* y = i/TBLSIZE + z for integer i near y * TBLSIZE.
|
||||
* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
|
||||
* with |z| <= 2**-(TBLSIZE+1).
|
||||
*
|
||||
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
|
||||
* degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
|
||||
* Using double precision for everything except the reduction makes
|
||||
* roundoff error insignificant and simplifies the scaling step.
|
||||
*
|
||||
* This method is due to Tang, but I do not use his suggested parameters:
|
||||
*
|
||||
* Tang, P. Table-driven Implementation of the Exponential Function
|
||||
* in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
|
||||
*/
|
||||
float
|
||||
exp2f(float x)
|
||||
{
|
||||
double tv, twopk, u, z;
|
||||
float t;
|
||||
uint32_t hx, ix, i0;
|
||||
int32_t k;
|
||||
|
||||
/* Filter out exceptional cases. */
|
||||
GET_FLOAT_WORD(hx, x);
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if(ix >= 0x43000000) { /* |x| >= 128 */
|
||||
if(ix >= 0x7f800000) {
|
||||
if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
|
||||
return (x + x); /* x is NaN or +Inf */
|
||||
else
|
||||
return (0.0); /* x is -Inf */
|
||||
}
|
||||
if(x >= 0x1.0p7f)
|
||||
return (huge * huge); /* overflow */
|
||||
if(x <= -0x1.2cp7f)
|
||||
return (twom100 * twom100); /* underflow */
|
||||
} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
|
||||
return (1.0f + x);
|
||||
}
|
||||
|
||||
/* Reduce x, computing z, i0, and k. */
|
||||
STRICT_ASSIGN(float, t, x + redux);
|
||||
GET_FLOAT_WORD(i0, t);
|
||||
i0 += TBLSIZE / 2;
|
||||
k = (i0 >> TBLBITS) << 20;
|
||||
i0 &= TBLSIZE - 1;
|
||||
t -= redux;
|
||||
z = x - t;
|
||||
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
|
||||
|
||||
/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
|
||||
tv = exp2ft[i0];
|
||||
u = tv * z;
|
||||
tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
|
||||
|
||||
/* Scale by 2**(k>>20). */
|
||||
return (tv * twopk);
|
||||
}
|
|
@ -1,32 +0,0 @@
|
|||
/* s_fabsf.c -- float version of s_fabs.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
/*
|
||||
* fabsf(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
fabsf(float x)
|
||||
{
|
||||
u_int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(x,ix&0x7fffffff);
|
||||
return x;
|
||||
}
|
|
@ -1,41 +0,0 @@
|
|||
/*
|
||||
* Copyright (c) 2005-2020 Rich Felker, et al.
|
||||
*
|
||||
* SPDX-License-Identifier: MIT
|
||||
*
|
||||
* Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
|
||||
* for all contributors to musl.
|
||||
*/
|
||||
#include <math.h>
|
||||
#include <stdint.h>
|
||||
|
||||
float scalbnf(float x, int n)
|
||||
{
|
||||
union {float f; uint32_t i;} u;
|
||||
float y = x;
|
||||
|
||||
if (n > 127) {
|
||||
y *= 0x1p127f;
|
||||
n -= 127;
|
||||
if (n > 127) {
|
||||
y *= 0x1p127f;
|
||||
n -= 127;
|
||||
if (n > 127)
|
||||
n = 127;
|
||||
}
|
||||
} else if (n < -126) {
|
||||
y *= 0x1p-126f * 0x1p24f;
|
||||
n += 126 - 24;
|
||||
if (n < -126) {
|
||||
y *= 0x1p-126f * 0x1p24f;
|
||||
n += 126 - 24;
|
||||
if (n < -126)
|
||||
n = -126;
|
||||
}
|
||||
}
|
||||
u.i = (uint32_t)(0x7f+n)<<23;
|
||||
x = y * u.f;
|
||||
return x;
|
||||
}
|
||||
|
||||
__strong_reference(scalbnf, ldexpf);
|
|
@ -1,84 +0,0 @@
|
|||
/* s_sinf.c -- float version of s_sin.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_COSDF
|
||||
#define INLINE_KERNEL_SINDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.cpp"
|
||||
#include "k_cosf.cpp"
|
||||
#include "k_sinf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
float
|
||||
sinf(float x)
|
||||
{
|
||||
double y;
|
||||
int32_t n, hx, ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx & 0x7fffffff;
|
||||
|
||||
if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
|
||||
if(ix<0x39800000) /* |x| < 2**-12 */
|
||||
if(((int)x)==0) return x; /* x with inexact if x != 0 */
|
||||
return __kernel_sindf(x);
|
||||
}
|
||||
if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */
|
||||
if(ix<=0x4016cbe3) { /* |x| ~<= 3pi/4 */
|
||||
if(hx>0)
|
||||
return __kernel_cosdf(x - s1pio2);
|
||||
else
|
||||
return -__kernel_cosdf(x + s1pio2);
|
||||
} else
|
||||
return __kernel_sindf((hx > 0 ? s2pio2 : -s2pio2) - x);
|
||||
}
|
||||
if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */
|
||||
if(ix<=0x40afeddf) { /* |x| ~<= 7*pi/4 */
|
||||
if(hx>0)
|
||||
return -__kernel_cosdf(x - s3pio2);
|
||||
else
|
||||
return __kernel_cosdf(x + s3pio2);
|
||||
} else
|
||||
return __kernel_sindf(x + (hx > 0 ? -s4pio2 : s4pio2));
|
||||
}
|
||||
|
||||
/* sin(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x;
|
||||
|
||||
/* general argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,&y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_sindf(y);
|
||||
case 1: return __kernel_cosdf(y);
|
||||
case 2: return __kernel_sindf(-y);
|
||||
default:
|
||||
return -__kernel_cosdf(y);
|
||||
}
|
||||
}
|
||||
}
|
|
@ -1,71 +0,0 @@
|
|||
/* s_tanf.c -- float version of s_tan.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
* Optimized by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
//#include <sys/cdefs.h>
|
||||
//__FBSDID("$FreeBSD$");
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#define INLINE_KERNEL_TANDF
|
||||
#define INLINE_REM_PIO2F
|
||||
#include "math_private.h"
|
||||
#include "e_rem_pio2f.cpp"
|
||||
#include "k_tanf.cpp"
|
||||
|
||||
/* Small multiples of pi/2 rounded to double precision. */
|
||||
static const double
|
||||
t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
|
||||
t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
|
||||
t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
|
||||
t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
|
||||
|
||||
float
|
||||
tanf(float x)
|
||||
{
|
||||
double y;
|
||||
int32_t n, hx, ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx & 0x7fffffff;
|
||||
|
||||
if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
|
||||
if(ix<0x39800000) /* |x| < 2**-12 */
|
||||
if(((int)x)==0) return x; /* x with inexact if x != 0 */
|
||||
return __kernel_tandf(x,1);
|
||||
}
|
||||
if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */
|
||||
if(ix<=0x4016cbe3) /* |x| ~<= 3pi/4 */
|
||||
return __kernel_tandf(x + (hx>0 ? -t1pio2 : t1pio2), -1);
|
||||
else
|
||||
return __kernel_tandf(x + (hx>0 ? -t2pio2 : t2pio2), 1);
|
||||
}
|
||||
if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */
|
||||
if(ix<=0x40afeddf) /* |x| ~<= 7*pi/4 */
|
||||
return __kernel_tandf(x + (hx>0 ? -t3pio2 : t3pio2), -1);
|
||||
else
|
||||
return __kernel_tandf(x + (hx>0 ? -t4pio2 : t4pio2), 1);
|
||||
}
|
||||
|
||||
/* tan(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x;
|
||||
|
||||
/* general argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,&y);
|
||||
/* integer parameter: 1 -- n even; -1 -- n odd */
|
||||
return __kernel_tandf(y,1-((n&1)<<1));
|
||||
}
|
||||
}
|
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