2019-02-07 11:53:11 +03:00
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/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to David M. Gay (dmg at acm dot org,
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* with " at " changed at "@" and " dot " changed to "."). */
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/* On a machine with IEEE extended-precision registers, it is
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* necessary to specify double-precision (53-bit) rounding precision
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* before invoking strtod or dtoa. If the machine uses (the equivalent
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* of) Intel 80x87 arithmetic, the call
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* _control87(PC_53, MCW_PC);
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* does this with many compilers. Whether this or another call is
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* appropriate depends on the compiler; for this to work, it may be
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* necessary to #include "float.h" or another system-dependent header
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* file.
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*/
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/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
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*
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* This strtod returns a nearest machine number to the input decimal
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* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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* broken by the IEEE round-even rule. Otherwise ties are broken by
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* biased rounding (add half and chop).
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*
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* Inspired loosely by William D. Clinger's paper "How to Read Floating
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* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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*
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* Modifications:
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*
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* 1. We only require IEEE, IBM, or VAX double-precision
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* arithmetic (not IEEE double-extended).
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* 2. We get by with floating-point arithmetic in a case that
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* Clinger missed -- when we're computing d * 10^n
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* for a small integer d and the integer n is not too
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* much larger than 22 (the maximum integer k for which
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* we can represent 10^k exactly), we may be able to
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* compute (d*10^k) * 10^(e-k) with just one roundoff.
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* 3. Rather than a bit-at-a-time adjustment of the binary
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* result in the hard case, we use floating-point
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* arithmetic to determine the adjustment to within
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* one bit; only in really hard cases do we need to
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* compute a second residual.
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* 4. Because of 3., we don't need a large table of powers of 10
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* for ten-to-e (just some small tables, e.g. of 10^k
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* for 0 <= k <= 22).
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*/
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/*
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* #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
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* significant byte has the lowest address.
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* #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
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* significant byte has the lowest address.
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* #define Long int on machines with 32-bit ints and 64-bit longs.
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* #define IBM for IBM mainframe-style floating-point arithmetic.
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* #define VAX for VAX-style floating-point arithmetic (D_floating).
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* #define No_leftright to omit left-right logic in fast floating-point
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* computation of dtoa.
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* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
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* and strtod and dtoa should round accordingly.
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* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
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* and Honor_FLT_ROUNDS is not #defined.
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* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
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* that use extended-precision instructions to compute rounded
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* products and quotients) with IBM.
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* #define ROUND_BIASED for IEEE-format with biased rounding.
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* #define Inaccurate_Divide for IEEE-format with correctly rounded
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* products but inaccurate quotients, e.g., for Intel i860.
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* #define NO_LONG_LONG on machines that do not have a "long long"
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* integer type (of >= 64 bits). On such machines, you can
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* #define Just_16 to store 16 bits per 32-bit Long when doing
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* high-precision integer arithmetic. Whether this speeds things
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* up or slows things down depends on the machine and the number
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* being converted. If long long is available and the name is
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* something other than "long long", #define Llong to be the name,
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* and if "unsigned Llong" does not work as an unsigned version of
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* Llong, #define #ULLong to be the corresponding unsigned type.
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* #define KR_headers for old-style C function headers.
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* #define Bad_float_h if your system lacks a float.h or if it does not
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* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
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* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
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* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
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* if memory is available and otherwise does something you deem
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* appropriate. If MALLOC is undefined, malloc will be invoked
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* directly -- and assumed always to succeed.
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* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
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* memory allocations from a private pool of memory when possible.
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* When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
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* unless #defined to be a different length. This default length
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* suffices to get rid of MALLOC calls except for unusual cases,
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* such as decimal-to-binary conversion of a very long string of
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* digits. The longest string dtoa can return is about 751 bytes
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* long. For conversions by strtod of strings of 800 digits and
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* all dtoa conversions in single-threaded executions with 8-byte
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* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
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* pointers, PRIVATE_MEM >= 7112 appears adequate.
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* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
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* Infinity and NaN (case insensitively). On some systems (e.g.,
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* some HP systems), it may be necessary to #define NAN_WORD0
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* appropriately -- to the most significant word of a quiet NaN.
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* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
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* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
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* strtod also accepts (case insensitively) strings of the form
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* NaN(x), where x is a string of hexadecimal digits and spaces;
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* if there is only one string of hexadecimal digits, it is taken
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* for the 52 fraction bits of the resulting NaN; if there are two
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* or more strings of hex digits, the first is for the high 20 bits,
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* the second and subsequent for the low 32 bits, with intervening
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* white space ignored; but if this results in none of the 52
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* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
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* and NAN_WORD1 are used instead.
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* #define MULTIPLE_THREADS if the system offers preemptively scheduled
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* multiple threads. In this case, you must provide (or suitably
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* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
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* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
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* in pow5mult, ensures lazy evaluation of only one copy of high
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* powers of 5; omitting this lock would introduce a small
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* probability of wasting memory, but would otherwise be harmless.)
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* You must also invoke freedtoa(s) to free the value s returned by
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* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
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* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
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* avoids underflows on inputs whose result does not underflow.
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* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
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* floating-point numbers and flushes underflows to zero rather
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* than implementing gradual underflow, then you must also #define
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* Sudden_Underflow.
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* #define YES_ALIAS to permit aliasing certain double values with
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* arrays of ULongs. This leads to slightly better code with
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* some compilers and was always used prior to 19990916, but it
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* is not strictly legal and can cause trouble with aggressively
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* optimizing compilers (e.g., gcc 2.95.1 under -O2).
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* #define USE_LOCALE to use the current locale's decimal_point value.
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* #define SET_INEXACT if IEEE arithmetic is being used and extra
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* computation should be done to set the inexact flag when the
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* result is inexact and avoid setting inexact when the result
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* is exact. In this case, dtoa.c must be compiled in
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* an environment, perhaps provided by #include "dtoa.c" in a
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* suitable wrapper, that defines two functions,
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* int get_inexact(void);
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* void clear_inexact(void);
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* such that get_inexact() returns a nonzero value if the
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* inexact bit is already set, and clear_inexact() sets the
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* inexact bit to 0. When SET_INEXACT is #defined, strtod
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* also does extra computations to set the underflow and overflow
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* flags when appropriate (i.e., when the result is tiny and
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* inexact or when it is a numeric value rounded to +-infinity).
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* #define NO_ERRNO if strtod should not assign errno = ERANGE when
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* the result overflows to +-Infinity or underflows to 0.
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*/
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#ifdef WORDS_BIGENDIAN
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#define IEEE_BIG_ENDIAN
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#else
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#define IEEE_LITTLE_ENDIAN
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#endif
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#ifdef __vax__
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#define VAX
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#undef IEEE_BIG_ENDIAN
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#undef IEEE_LITTLE_ENDIAN
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#endif
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#if defined(__arm__) && !defined(__VFP_FP__)
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#define IEEE_BIG_ENDIAN
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#undef IEEE_LITTLE_ENDIAN
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#endif
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#undef Long
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#undef ULong
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2023-07-14 08:33:21 +03:00
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#include <assert.h>
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2021-01-10 09:46:23 +03:00
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#include <limits.h>
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2023-07-14 08:33:21 +03:00
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#include <stddef.h>
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#include <stdint.h>
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2021-01-10 09:46:23 +03:00
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#if (INT_MAX >> 30) && !(INT_MAX >> 31)
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2019-02-07 11:53:11 +03:00
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#define Long int
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#define ULong unsigned int
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2021-01-10 09:46:23 +03:00
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#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
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2019-02-07 11:53:11 +03:00
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#define Long long int
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#define ULong unsigned long int
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2021-01-10 09:46:23 +03:00
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#else
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#error No 32bit integer
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2019-02-07 11:53:11 +03:00
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#endif
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2023-07-14 08:33:21 +03:00
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#if defined(HAVE_LONG_LONG) && (HAVE_LONG_LONG)
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2019-02-07 11:53:11 +03:00
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#define Llong LONG_LONG
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#else
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#define NO_LONG_LONG
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#endif
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#ifdef DEBUG
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#include <stdio.h>
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#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
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#endif
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2021-01-10 09:46:23 +03:00
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#ifndef ISDIGIT
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#include <ctype.h>
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#define ISDIGIT(c) isdigit(c)
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#endif
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#include <errno.h>
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2019-02-07 11:53:11 +03:00
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#include <stdlib.h>
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#include <string.h>
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#ifdef USE_LOCALE
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#include <locale.h>
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#endif
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#ifdef MALLOC
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extern void *MALLOC(size_t);
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#else
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2023-07-14 08:33:21 +03:00
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#define MALLOC malloc
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2019-02-07 11:53:11 +03:00
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#endif
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#ifdef FREE
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extern void FREE(void*);
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#else
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2023-07-14 08:33:21 +03:00
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#define FREE free
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2019-02-07 11:53:11 +03:00
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#endif
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2021-01-10 09:46:23 +03:00
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#ifndef NO_SANITIZE
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#define NO_SANITIZE(x, y) y
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#endif
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2019-02-07 11:53:11 +03:00
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#ifndef Omit_Private_Memory
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#ifndef PRIVATE_MEM
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#define PRIVATE_MEM 2304
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#endif
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#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
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static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
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#endif
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#undef IEEE_Arith
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#undef Avoid_Underflow
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#ifdef IEEE_BIG_ENDIAN
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#define IEEE_Arith
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#endif
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#ifdef IEEE_LITTLE_ENDIAN
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#define IEEE_Arith
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#endif
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#ifdef Bad_float_h
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#ifdef IEEE_Arith
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#define DBL_DIG 15
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#define DBL_MAX_10_EXP 308
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#define DBL_MAX_EXP 1024
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#define FLT_RADIX 2
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#endif /*IEEE_Arith*/
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#ifdef IBM
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#define DBL_DIG 16
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#define DBL_MAX_10_EXP 75
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#define DBL_MAX_EXP 63
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#define FLT_RADIX 16
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#define DBL_MAX 7.2370055773322621e+75
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#endif
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#ifdef VAX
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#define DBL_DIG 16
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#define DBL_MAX_10_EXP 38
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#define DBL_MAX_EXP 127
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#define FLT_RADIX 2
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#define DBL_MAX 1.7014118346046923e+38
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#endif
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#ifndef LONG_MAX
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#define LONG_MAX 2147483647
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#endif
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#else /* ifndef Bad_float_h */
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#include <float.h>
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#endif /* Bad_float_h */
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#include <math.h>
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#ifdef __cplusplus
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extern "C" {
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#if 0
|
|
|
|
|
} /* satisfy cc-mode */
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifndef hexdigit
|
2021-01-10 09:46:23 +03:00
|
|
|
static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
|
2019-02-07 11:53:11 +03:00
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
|
|
|
|
|
Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
typedef union { double d; ULong L[2]; } U;
|
|
|
|
|
|
|
|
|
|
#ifdef YES_ALIAS
|
|
|
|
|
typedef double double_u;
|
|
|
|
|
# define dval(x) (x)
|
|
|
|
|
# ifdef IEEE_LITTLE_ENDIAN
|
|
|
|
|
# define word0(x) (((ULong *)&(x))[1])
|
|
|
|
|
# define word1(x) (((ULong *)&(x))[0])
|
|
|
|
|
# else
|
|
|
|
|
# define word0(x) (((ULong *)&(x))[0])
|
|
|
|
|
# define word1(x) (((ULong *)&(x))[1])
|
|
|
|
|
# endif
|
|
|
|
|
#else
|
|
|
|
|
typedef U double_u;
|
|
|
|
|
# ifdef IEEE_LITTLE_ENDIAN
|
|
|
|
|
# define word0(x) ((x).L[1])
|
|
|
|
|
# define word1(x) ((x).L[0])
|
|
|
|
|
# else
|
|
|
|
|
# define word0(x) ((x).L[0])
|
|
|
|
|
# define word1(x) ((x).L[1])
|
|
|
|
|
# endif
|
|
|
|
|
# define dval(x) ((x).d)
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
/* The following definition of Storeinc is appropriate for MIPS processors.
|
|
|
|
|
* An alternative that might be better on some machines is
|
|
|
|
|
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
|
|
|
|
|
*/
|
|
|
|
|
#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
|
|
|
|
|
#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
|
|
|
|
|
((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
|
|
|
|
|
#else
|
|
|
|
|
#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
|
|
|
|
|
((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
/* #define P DBL_MANT_DIG */
|
|
|
|
|
/* Ten_pmax = floor(P*log(2)/log(5)) */
|
|
|
|
|
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
|
|
|
|
|
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
|
|
|
|
|
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
|
|
|
|
|
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
#define Exp_shift 20
|
|
|
|
|
#define Exp_shift1 20
|
|
|
|
|
#define Exp_msk1 0x100000
|
|
|
|
|
#define Exp_msk11 0x100000
|
|
|
|
|
#define Exp_mask 0x7ff00000
|
|
|
|
|
#define P 53
|
|
|
|
|
#define Bias 1023
|
|
|
|
|
#define Emin (-1022)
|
|
|
|
|
#define Exp_1 0x3ff00000
|
|
|
|
|
#define Exp_11 0x3ff00000
|
|
|
|
|
#define Ebits 11
|
|
|
|
|
#define Frac_mask 0xfffff
|
|
|
|
|
#define Frac_mask1 0xfffff
|
|
|
|
|
#define Ten_pmax 22
|
|
|
|
|
#define Bletch 0x10
|
|
|
|
|
#define Bndry_mask 0xfffff
|
|
|
|
|
#define Bndry_mask1 0xfffff
|
|
|
|
|
#define LSB 1
|
|
|
|
|
#define Sign_bit 0x80000000
|
|
|
|
|
#define Log2P 1
|
|
|
|
|
#define Tiny0 0
|
|
|
|
|
#define Tiny1 1
|
|
|
|
|
#define Quick_max 14
|
|
|
|
|
#define Int_max 14
|
|
|
|
|
#ifndef NO_IEEE_Scale
|
|
|
|
|
#define Avoid_Underflow
|
|
|
|
|
#ifdef Flush_Denorm /* debugging option */
|
|
|
|
|
#undef Sudden_Underflow
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifndef Flt_Rounds
|
|
|
|
|
#ifdef FLT_ROUNDS
|
|
|
|
|
#define Flt_Rounds FLT_ROUNDS
|
|
|
|
|
#else
|
|
|
|
|
#define Flt_Rounds 1
|
|
|
|
|
#endif
|
|
|
|
|
#endif /*Flt_Rounds*/
|
|
|
|
|
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
#define Rounding rounding
|
|
|
|
|
#undef Check_FLT_ROUNDS
|
|
|
|
|
#define Check_FLT_ROUNDS
|
|
|
|
|
#else
|
|
|
|
|
#define Rounding Flt_Rounds
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#else /* ifndef IEEE_Arith */
|
|
|
|
|
#undef Check_FLT_ROUNDS
|
|
|
|
|
#undef Honor_FLT_ROUNDS
|
|
|
|
|
#undef SET_INEXACT
|
|
|
|
|
#undef Sudden_Underflow
|
|
|
|
|
#define Sudden_Underflow
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
#undef Flt_Rounds
|
|
|
|
|
#define Flt_Rounds 0
|
|
|
|
|
#define Exp_shift 24
|
|
|
|
|
#define Exp_shift1 24
|
|
|
|
|
#define Exp_msk1 0x1000000
|
|
|
|
|
#define Exp_msk11 0x1000000
|
|
|
|
|
#define Exp_mask 0x7f000000
|
|
|
|
|
#define P 14
|
|
|
|
|
#define Bias 65
|
|
|
|
|
#define Exp_1 0x41000000
|
|
|
|
|
#define Exp_11 0x41000000
|
|
|
|
|
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
|
|
|
|
|
#define Frac_mask 0xffffff
|
|
|
|
|
#define Frac_mask1 0xffffff
|
|
|
|
|
#define Bletch 4
|
|
|
|
|
#define Ten_pmax 22
|
|
|
|
|
#define Bndry_mask 0xefffff
|
|
|
|
|
#define Bndry_mask1 0xffffff
|
|
|
|
|
#define LSB 1
|
|
|
|
|
#define Sign_bit 0x80000000
|
|
|
|
|
#define Log2P 4
|
|
|
|
|
#define Tiny0 0x100000
|
|
|
|
|
#define Tiny1 0
|
|
|
|
|
#define Quick_max 14
|
|
|
|
|
#define Int_max 15
|
|
|
|
|
#else /* VAX */
|
|
|
|
|
#undef Flt_Rounds
|
|
|
|
|
#define Flt_Rounds 1
|
|
|
|
|
#define Exp_shift 23
|
|
|
|
|
#define Exp_shift1 7
|
|
|
|
|
#define Exp_msk1 0x80
|
|
|
|
|
#define Exp_msk11 0x800000
|
|
|
|
|
#define Exp_mask 0x7f80
|
|
|
|
|
#define P 56
|
|
|
|
|
#define Bias 129
|
|
|
|
|
#define Exp_1 0x40800000
|
|
|
|
|
#define Exp_11 0x4080
|
|
|
|
|
#define Ebits 8
|
|
|
|
|
#define Frac_mask 0x7fffff
|
|
|
|
|
#define Frac_mask1 0xffff007f
|
|
|
|
|
#define Ten_pmax 24
|
|
|
|
|
#define Bletch 2
|
|
|
|
|
#define Bndry_mask 0xffff007f
|
|
|
|
|
#define Bndry_mask1 0xffff007f
|
|
|
|
|
#define LSB 0x10000
|
|
|
|
|
#define Sign_bit 0x8000
|
|
|
|
|
#define Log2P 1
|
|
|
|
|
#define Tiny0 0x80
|
|
|
|
|
#define Tiny1 0
|
|
|
|
|
#define Quick_max 15
|
|
|
|
|
#define Int_max 15
|
|
|
|
|
#endif /* IBM, VAX */
|
|
|
|
|
#endif /* IEEE_Arith */
|
|
|
|
|
|
|
|
|
|
#ifndef IEEE_Arith
|
|
|
|
|
#define ROUND_BIASED
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifdef RND_PRODQUOT
|
|
|
|
|
#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
|
|
|
|
|
#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
|
|
|
|
|
extern double rnd_prod(double, double), rnd_quot(double, double);
|
|
|
|
|
#else
|
|
|
|
|
#define rounded_product(a,b) ((a) *= (b))
|
|
|
|
|
#define rounded_quotient(a,b) ((a) /= (b))
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
|
|
|
|
|
#define Big1 0xffffffff
|
|
|
|
|
|
|
|
|
|
#ifndef Pack_32
|
|
|
|
|
#define Pack_32
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#define FFFFFFFF 0xffffffffUL
|
|
|
|
|
|
|
|
|
|
#ifdef NO_LONG_LONG
|
|
|
|
|
#undef ULLong
|
|
|
|
|
#ifdef Just_16
|
|
|
|
|
#undef Pack_32
|
|
|
|
|
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
|
|
|
|
|
* This makes some inner loops simpler and sometimes saves work
|
|
|
|
|
* during multiplications, but it often seems to make things slightly
|
|
|
|
|
* slower. Hence the default is now to store 32 bits per Long.
|
|
|
|
|
*/
|
|
|
|
|
#endif
|
|
|
|
|
#else /* long long available */
|
|
|
|
|
#ifndef Llong
|
|
|
|
|
#define Llong long long
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef ULLong
|
|
|
|
|
#define ULLong unsigned Llong
|
|
|
|
|
#endif
|
|
|
|
|
#endif /* NO_LONG_LONG */
|
|
|
|
|
|
|
|
|
|
#define MULTIPLE_THREADS 1
|
|
|
|
|
|
|
|
|
|
#ifndef MULTIPLE_THREADS
|
|
|
|
|
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
|
|
|
|
|
#define FREE_DTOA_LOCK(n) /*nothing*/
|
|
|
|
|
#else
|
|
|
|
|
#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
|
|
|
|
|
#define FREE_DTOA_LOCK(n) /*unused right now*/
|
|
|
|
|
#endif
|
|
|
|
|
|
2021-01-10 11:36:18 +03:00
|
|
|
#ifndef ATOMIC_PTR_CAS
|
2023-07-14 08:33:21 +03:00
|
|
|
#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (void *)(old))
|
2021-01-10 11:36:18 +03:00
|
|
|
#endif
|
|
|
|
|
#ifndef LIKELY
|
|
|
|
|
#define LIKELY(x) (x)
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef UNLIKELY
|
|
|
|
|
#define UNLIKELY(x) (x)
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef ASSUME
|
|
|
|
|
#define ASSUME(x) (void)(x)
|
|
|
|
|
#endif
|
|
|
|
|
|
2019-02-07 11:53:11 +03:00
|
|
|
#define Kmax 15
|
|
|
|
|
|
|
|
|
|
struct Bigint {
|
|
|
|
|
struct Bigint *next;
|
|
|
|
|
int k, maxwds, sign, wds;
|
|
|
|
|
ULong x[1];
|
|
|
|
|
};
|
|
|
|
|
|
|
|
|
|
typedef struct Bigint Bigint;
|
|
|
|
|
|
|
|
|
|
static Bigint *freelist[Kmax+1];
|
|
|
|
|
|
2021-02-10 09:24:23 +03:00
|
|
|
#define BLOCKING_BIGINT ((Bigint *)(-1))
|
|
|
|
|
|
2019-02-07 11:53:11 +03:00
|
|
|
static Bigint *
|
|
|
|
|
Balloc(int k)
|
|
|
|
|
{
|
|
|
|
|
int x;
|
|
|
|
|
Bigint *rv;
|
|
|
|
|
#ifndef Omit_Private_Memory
|
|
|
|
|
size_t len;
|
|
|
|
|
#endif
|
|
|
|
|
|
2021-01-10 11:36:18 +03:00
|
|
|
rv = 0;
|
2019-02-07 11:53:11 +03:00
|
|
|
ACQUIRE_DTOA_LOCK(0);
|
2021-01-10 11:36:18 +03:00
|
|
|
if (k <= Kmax) {
|
|
|
|
|
rv = freelist[k];
|
|
|
|
|
while (rv) {
|
|
|
|
|
Bigint *rvn = rv;
|
2021-02-10 09:24:23 +03:00
|
|
|
rv = ATOMIC_PTR_CAS(freelist[k], rv, BLOCKING_BIGINT);
|
|
|
|
|
if (LIKELY(rv != BLOCKING_BIGINT && rvn == rv)) {
|
|
|
|
|
rvn = ATOMIC_PTR_CAS(freelist[k], BLOCKING_BIGINT, rv->next);
|
|
|
|
|
assert(rvn == BLOCKING_BIGINT);
|
2021-01-10 11:36:18 +03:00
|
|
|
ASSUME(rv);
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
2021-01-10 11:36:18 +03:00
|
|
|
if (!rv) {
|
2019-02-07 11:53:11 +03:00
|
|
|
x = 1 << k;
|
|
|
|
|
#ifdef Omit_Private_Memory
|
|
|
|
|
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
|
|
|
|
|
#else
|
|
|
|
|
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
|
|
|
|
|
/sizeof(double);
|
2021-01-10 11:36:18 +03:00
|
|
|
if (k <= Kmax) {
|
|
|
|
|
double *pnext = pmem_next;
|
|
|
|
|
while (pnext - private_mem + len <= PRIVATE_mem) {
|
|
|
|
|
double *p = pnext;
|
|
|
|
|
pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
|
|
|
|
|
if (LIKELY(p == pnext)) {
|
|
|
|
|
rv = (Bigint*)pnext;
|
|
|
|
|
ASSUME(rv);
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
2021-01-10 11:36:18 +03:00
|
|
|
if (!rv)
|
2019-02-07 11:53:11 +03:00
|
|
|
rv = (Bigint*)MALLOC(len*sizeof(double));
|
|
|
|
|
#endif
|
|
|
|
|
rv->k = k;
|
|
|
|
|
rv->maxwds = x;
|
|
|
|
|
}
|
|
|
|
|
FREE_DTOA_LOCK(0);
|
|
|
|
|
rv->sign = rv->wds = 0;
|
|
|
|
|
return rv;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static void
|
|
|
|
|
Bfree(Bigint *v)
|
|
|
|
|
{
|
2021-01-10 11:36:18 +03:00
|
|
|
Bigint *vn;
|
2019-02-07 11:53:11 +03:00
|
|
|
if (v) {
|
|
|
|
|
if (v->k > Kmax) {
|
|
|
|
|
FREE(v);
|
|
|
|
|
return;
|
|
|
|
|
}
|
|
|
|
|
ACQUIRE_DTOA_LOCK(0);
|
2021-01-10 11:36:18 +03:00
|
|
|
do {
|
2021-02-10 09:24:23 +03:00
|
|
|
do {
|
|
|
|
|
vn = ATOMIC_PTR_CAS(freelist[v->k], 0, 0);
|
|
|
|
|
} while (UNLIKELY(vn == BLOCKING_BIGINT));
|
|
|
|
|
v->next = vn;
|
2021-01-10 11:36:18 +03:00
|
|
|
} while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
|
2019-02-07 11:53:11 +03:00
|
|
|
FREE_DTOA_LOCK(0);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
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|
|
#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
|
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|
|
(y)->wds*sizeof(Long) + 2*sizeof(int))
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static Bigint *
|
|
|
|
|
multadd(Bigint *b, int m, int a) /* multiply by m and add a */
|
|
|
|
|
{
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int i, wds;
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|
|
ULong *x;
|
|
|
|
|
#ifdef ULLong
|
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|
|
ULLong carry, y;
|
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|
|
#else
|
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|
|
ULong carry, y;
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|
|
#ifdef Pack_32
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|
|
ULong xi, z;
|
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|
|
#endif
|
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|
|
#endif
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|
|
Bigint *b1;
|
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|
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wds = b->wds;
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x = b->x;
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i = 0;
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|
carry = a;
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|
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|
do {
|
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|
|
#ifdef ULLong
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|
|
y = *x * (ULLong)m + carry;
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|
carry = y >> 32;
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|
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|
*x++ = (ULong)(y & FFFFFFFF);
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|
#else
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|
|
#ifdef Pack_32
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|
xi = *x;
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|
y = (xi & 0xffff) * m + carry;
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|
z = (xi >> 16) * m + (y >> 16);
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|
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|
carry = z >> 16;
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|
|
*x++ = (z << 16) + (y & 0xffff);
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|
#else
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|
y = *x * m + carry;
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|
carry = y >> 16;
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|
*x++ = y & 0xffff;
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#endif
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|
#endif
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|
|
|
} while (++i < wds);
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|
|
|
if (carry) {
|
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|
|
|
if (wds >= b->maxwds) {
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|
|
|
b1 = Balloc(b->k+1);
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|
|
|
Bcopy(b1, b);
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|
|
|
Bfree(b);
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|
b = b1;
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|
}
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|
b->x[wds++] = (ULong)carry;
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|
b->wds = wds;
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}
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|
return b;
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}
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static Bigint *
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|
|
|
s2b(const char *s, int nd0, int nd, ULong y9)
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|
|
|
{
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|
|
Bigint *b;
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|
|
|
int i, k;
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|
|
Long x, y;
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x = (nd + 8) / 9;
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|
for (k = 0, y = 1; x > y; y <<= 1, k++) ;
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|
|
#ifdef Pack_32
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|
|
b = Balloc(k);
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|
|
b->x[0] = y9;
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|
|
|
b->wds = 1;
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|
|
#else
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|
|
b = Balloc(k+1);
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|
|
b->x[0] = y9 & 0xffff;
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|
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
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|
#endif
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|
i = 9;
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|
if (9 < nd0) {
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|
s += 9;
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|
do {
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|
b = multadd(b, 10, *s++ - '0');
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|
|
|
} while (++i < nd0);
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|
|
s++;
|
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|
|
}
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|
|
else
|
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|
|
s += 10;
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|
|
for (; i < nd; i++)
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|
|
b = multadd(b, 10, *s++ - '0');
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|
return b;
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|
|
}
|
|
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|
|
|
|
|
|
|
static int
|
|
|
|
|
hi0bits(register ULong x)
|
|
|
|
|
{
|
|
|
|
|
register int k = 0;
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|
|
|
|
|
|
|
|
if (!(x & 0xffff0000)) {
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|
|
k = 16;
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|
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|
|
x <<= 16;
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|
|
|
|
}
|
|
|
|
|
if (!(x & 0xff000000)) {
|
|
|
|
|
k += 8;
|
|
|
|
|
x <<= 8;
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|
|
|
|
}
|
|
|
|
|
if (!(x & 0xf0000000)) {
|
|
|
|
|
k += 4;
|
|
|
|
|
x <<= 4;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 0xc0000000)) {
|
|
|
|
|
k += 2;
|
|
|
|
|
x <<= 2;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 0x80000000)) {
|
|
|
|
|
k++;
|
|
|
|
|
if (!(x & 0x40000000))
|
|
|
|
|
return 32;
|
|
|
|
|
}
|
|
|
|
|
return k;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static int
|
|
|
|
|
lo0bits(ULong *y)
|
|
|
|
|
{
|
|
|
|
|
register int k;
|
|
|
|
|
register ULong x = *y;
|
|
|
|
|
|
|
|
|
|
if (x & 7) {
|
|
|
|
|
if (x & 1)
|
|
|
|
|
return 0;
|
|
|
|
|
if (x & 2) {
|
|
|
|
|
*y = x >> 1;
|
|
|
|
|
return 1;
|
|
|
|
|
}
|
|
|
|
|
*y = x >> 2;
|
|
|
|
|
return 2;
|
|
|
|
|
}
|
|
|
|
|
k = 0;
|
|
|
|
|
if (!(x & 0xffff)) {
|
|
|
|
|
k = 16;
|
|
|
|
|
x >>= 16;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 0xff)) {
|
|
|
|
|
k += 8;
|
|
|
|
|
x >>= 8;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 0xf)) {
|
|
|
|
|
k += 4;
|
|
|
|
|
x >>= 4;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 0x3)) {
|
|
|
|
|
k += 2;
|
|
|
|
|
x >>= 2;
|
|
|
|
|
}
|
|
|
|
|
if (!(x & 1)) {
|
|
|
|
|
k++;
|
|
|
|
|
x >>= 1;
|
|
|
|
|
if (!x)
|
|
|
|
|
return 32;
|
|
|
|
|
}
|
|
|
|
|
*y = x;
|
|
|
|
|
return k;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
|
i2b(int i)
|
|
|
|
|
{
|
|
|
|
|
Bigint *b;
|
|
|
|
|
|
|
|
|
|
b = Balloc(1);
|
|
|
|
|
b->x[0] = i;
|
|
|
|
|
b->wds = 1;
|
|
|
|
|
return b;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
|
mult(Bigint *a, Bigint *b)
|
|
|
|
|
{
|
|
|
|
|
Bigint *c;
|
|
|
|
|
int k, wa, wb, wc;
|
|
|
|
|
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
|
|
|
|
ULong y;
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
ULLong carry, z;
|
|
|
|
|
#else
|
|
|
|
|
ULong carry, z;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
ULong z2;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
if (a->wds < b->wds) {
|
|
|
|
|
c = a;
|
|
|
|
|
a = b;
|
|
|
|
|
b = c;
|
|
|
|
|
}
|
|
|
|
|
k = a->k;
|
|
|
|
|
wa = a->wds;
|
|
|
|
|
wb = b->wds;
|
|
|
|
|
wc = wa + wb;
|
|
|
|
|
if (wc > a->maxwds)
|
|
|
|
|
k++;
|
|
|
|
|
c = Balloc(k);
|
|
|
|
|
for (x = c->x, xa = x + wc; x < xa; x++)
|
|
|
|
|
*x = 0;
|
|
|
|
|
xa = a->x;
|
|
|
|
|
xae = xa + wa;
|
|
|
|
|
xb = b->x;
|
|
|
|
|
xbe = xb + wb;
|
|
|
|
|
xc0 = c->x;
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
for (; xb < xbe; xc0++) {
|
|
|
|
|
if ((y = *xb++) != 0) {
|
|
|
|
|
x = xa;
|
|
|
|
|
xc = xc0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
do {
|
|
|
|
|
z = *x++ * (ULLong)y + *xc + carry;
|
|
|
|
|
carry = z >> 32;
|
|
|
|
|
*xc++ = (ULong)(z & FFFFFFFF);
|
|
|
|
|
} while (x < xae);
|
|
|
|
|
*xc = (ULong)carry;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
for (; xb < xbe; xb++, xc0++) {
|
|
|
|
|
if ((y = *xb & 0xffff) != 0) {
|
|
|
|
|
x = xa;
|
|
|
|
|
xc = xc0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
do {
|
|
|
|
|
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
|
|
|
|
|
carry = z >> 16;
|
|
|
|
|
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
|
|
|
|
|
carry = z2 >> 16;
|
|
|
|
|
Storeinc(xc, z2, z);
|
|
|
|
|
} while (x < xae);
|
|
|
|
|
*xc = (ULong)carry;
|
|
|
|
|
}
|
|
|
|
|
if ((y = *xb >> 16) != 0) {
|
|
|
|
|
x = xa;
|
|
|
|
|
xc = xc0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
z2 = *xc;
|
|
|
|
|
do {
|
|
|
|
|
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
|
|
|
|
|
carry = z >> 16;
|
|
|
|
|
Storeinc(xc, z, z2);
|
|
|
|
|
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
|
|
|
|
|
carry = z2 >> 16;
|
|
|
|
|
} while (x < xae);
|
|
|
|
|
*xc = z2;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
for (; xb < xbe; xc0++) {
|
|
|
|
|
if (y = *xb++) {
|
|
|
|
|
x = xa;
|
|
|
|
|
xc = xc0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
do {
|
|
|
|
|
z = *x++ * y + *xc + carry;
|
|
|
|
|
carry = z >> 16;
|
|
|
|
|
*xc++ = z & 0xffff;
|
|
|
|
|
} while (x < xae);
|
|
|
|
|
*xc = (ULong)carry;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
|
|
|
|
|
c->wds = wc;
|
|
|
|
|
return c;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static Bigint *p5s;
|
|
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
|
pow5mult(Bigint *b, int k)
|
|
|
|
|
{
|
|
|
|
|
Bigint *b1, *p5, *p51;
|
2021-01-10 11:36:18 +03:00
|
|
|
Bigint *p5tmp;
|
2019-02-07 11:53:11 +03:00
|
|
|
int i;
|
2021-01-10 10:32:47 +03:00
|
|
|
static const int p05[3] = { 5, 25, 125 };
|
2019-02-07 11:53:11 +03:00
|
|
|
|
|
|
|
|
if ((i = k & 3) != 0)
|
|
|
|
|
b = multadd(b, p05[i-1], 0);
|
|
|
|
|
|
|
|
|
|
if (!(k >>= 2))
|
|
|
|
|
return b;
|
|
|
|
|
if (!(p5 = p5s)) {
|
|
|
|
|
/* first time */
|
|
|
|
|
ACQUIRE_DTOA_LOCK(1);
|
|
|
|
|
if (!(p5 = p5s)) {
|
2021-01-10 11:36:18 +03:00
|
|
|
p5 = i2b(625);
|
2019-02-07 11:53:11 +03:00
|
|
|
p5->next = 0;
|
2021-01-10 11:36:18 +03:00
|
|
|
p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
|
|
|
|
|
if (UNLIKELY(p5tmp)) {
|
|
|
|
|
Bfree(p5);
|
|
|
|
|
p5 = p5tmp;
|
|
|
|
|
}
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
|
|
|
|
FREE_DTOA_LOCK(1);
|
|
|
|
|
}
|
|
|
|
|
for (;;) {
|
|
|
|
|
if (k & 1) {
|
|
|
|
|
b1 = mult(b, p5);
|
|
|
|
|
Bfree(b);
|
|
|
|
|
b = b1;
|
|
|
|
|
}
|
|
|
|
|
if (!(k >>= 1))
|
|
|
|
|
break;
|
|
|
|
|
if (!(p51 = p5->next)) {
|
|
|
|
|
ACQUIRE_DTOA_LOCK(1);
|
|
|
|
|
if (!(p51 = p5->next)) {
|
2021-01-10 11:36:18 +03:00
|
|
|
p51 = mult(p5,p5);
|
2019-02-07 11:53:11 +03:00
|
|
|
p51->next = 0;
|
2021-01-10 11:36:18 +03:00
|
|
|
p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
|
|
|
|
|
if (UNLIKELY(p5tmp)) {
|
|
|
|
|
Bfree(p51);
|
|
|
|
|
p51 = p5tmp;
|
|
|
|
|
}
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
|
|
|
|
FREE_DTOA_LOCK(1);
|
|
|
|
|
}
|
|
|
|
|
p5 = p51;
|
|
|
|
|
}
|
|
|
|
|
return b;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
|
lshift(Bigint *b, int k)
|
|
|
|
|
{
|
|
|
|
|
int i, k1, n, n1;
|
|
|
|
|
Bigint *b1;
|
|
|
|
|
ULong *x, *x1, *xe, z;
|
|
|
|
|
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
n = k >> 5;
|
|
|
|
|
#else
|
|
|
|
|
n = k >> 4;
|
|
|
|
|
#endif
|
|
|
|
|
k1 = b->k;
|
|
|
|
|
n1 = n + b->wds + 1;
|
|
|
|
|
for (i = b->maxwds; n1 > i; i <<= 1)
|
|
|
|
|
k1++;
|
|
|
|
|
b1 = Balloc(k1);
|
|
|
|
|
x1 = b1->x;
|
|
|
|
|
for (i = 0; i < n; i++)
|
|
|
|
|
*x1++ = 0;
|
|
|
|
|
x = b->x;
|
|
|
|
|
xe = x + b->wds;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
if (k &= 0x1f) {
|
|
|
|
|
k1 = 32 - k;
|
|
|
|
|
z = 0;
|
|
|
|
|
do {
|
|
|
|
|
*x1++ = *x << k | z;
|
|
|
|
|
z = *x++ >> k1;
|
|
|
|
|
} while (x < xe);
|
|
|
|
|
if ((*x1 = z) != 0)
|
|
|
|
|
++n1;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
if (k &= 0xf) {
|
|
|
|
|
k1 = 16 - k;
|
|
|
|
|
z = 0;
|
|
|
|
|
do {
|
|
|
|
|
*x1++ = *x << k & 0xffff | z;
|
|
|
|
|
z = *x++ >> k1;
|
|
|
|
|
} while (x < xe);
|
|
|
|
|
if (*x1 = z)
|
|
|
|
|
++n1;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
else
|
|
|
|
|
do {
|
|
|
|
|
*x1++ = *x++;
|
|
|
|
|
} while (x < xe);
|
|
|
|
|
b1->wds = n1 - 1;
|
|
|
|
|
Bfree(b);
|
|
|
|
|
return b1;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static int
|
|
|
|
|
cmp(Bigint *a, Bigint *b)
|
|
|
|
|
{
|
|
|
|
|
ULong *xa, *xa0, *xb, *xb0;
|
|
|
|
|
int i, j;
|
|
|
|
|
|
|
|
|
|
i = a->wds;
|
|
|
|
|
j = b->wds;
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
if (i > 1 && !a->x[i-1])
|
|
|
|
|
Bug("cmp called with a->x[a->wds-1] == 0");
|
|
|
|
|
if (j > 1 && !b->x[j-1])
|
|
|
|
|
Bug("cmp called with b->x[b->wds-1] == 0");
|
|
|
|
|
#endif
|
|
|
|
|
if (i -= j)
|
|
|
|
|
return i;
|
|
|
|
|
xa0 = a->x;
|
|
|
|
|
xa = xa0 + j;
|
|
|
|
|
xb0 = b->x;
|
|
|
|
|
xb = xb0 + j;
|
|
|
|
|
for (;;) {
|
|
|
|
|
if (*--xa != *--xb)
|
|
|
|
|
return *xa < *xb ? -1 : 1;
|
|
|
|
|
if (xa <= xa0)
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
return 0;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
|
|
|
|
|
static Bigint *
|
|
|
|
|
diff(Bigint *a, Bigint *b)
|
|
|
|
|
{
|
|
|
|
|
Bigint *c;
|
|
|
|
|
int i, wa, wb;
|
|
|
|
|
ULong *xa, *xae, *xb, *xbe, *xc;
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
ULLong borrow, y;
|
|
|
|
|
#else
|
|
|
|
|
ULong borrow, y;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
ULong z;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
i = cmp(a,b);
|
|
|
|
|
if (!i) {
|
|
|
|
|
c = Balloc(0);
|
|
|
|
|
c->wds = 1;
|
|
|
|
|
c->x[0] = 0;
|
|
|
|
|
return c;
|
|
|
|
|
}
|
|
|
|
|
if (i < 0) {
|
|
|
|
|
c = a;
|
|
|
|
|
a = b;
|
|
|
|
|
b = c;
|
|
|
|
|
i = 1;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
i = 0;
|
|
|
|
|
c = Balloc(a->k);
|
|
|
|
|
c->sign = i;
|
|
|
|
|
wa = a->wds;
|
|
|
|
|
xa = a->x;
|
|
|
|
|
xae = xa + wa;
|
|
|
|
|
wb = b->wds;
|
|
|
|
|
xb = b->x;
|
|
|
|
|
xbe = xb + wb;
|
|
|
|
|
xc = c->x;
|
|
|
|
|
borrow = 0;
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
do {
|
|
|
|
|
y = (ULLong)*xa++ - *xb++ - borrow;
|
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
|
|
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
|
|
|
|
} while (xb < xbe);
|
|
|
|
|
while (xa < xae) {
|
|
|
|
|
y = *xa++ - borrow;
|
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
|
|
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
do {
|
|
|
|
|
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
|
Storeinc(xc, z, y);
|
|
|
|
|
} while (xb < xbe);
|
|
|
|
|
while (xa < xae) {
|
|
|
|
|
y = (*xa & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
z = (*xa++ >> 16) - borrow;
|
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
|
Storeinc(xc, z, y);
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
do {
|
|
|
|
|
y = *xa++ - *xb++ - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
*xc++ = y & 0xffff;
|
|
|
|
|
} while (xb < xbe);
|
|
|
|
|
while (xa < xae) {
|
|
|
|
|
y = *xa++ - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
*xc++ = y & 0xffff;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
while (!*--xc)
|
|
|
|
|
wa--;
|
|
|
|
|
c->wds = wa;
|
|
|
|
|
return c;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
ulp(double x_)
|
|
|
|
|
{
|
|
|
|
|
register Long L;
|
|
|
|
|
double_u x, a;
|
|
|
|
|
dval(x) = x_;
|
|
|
|
|
|
|
|
|
|
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
|
|
|
|
|
#ifndef Avoid_Underflow
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
if (L > 0) {
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
L |= Exp_msk1 >> 4;
|
|
|
|
|
#endif
|
|
|
|
|
word0(a) = L;
|
|
|
|
|
word1(a) = 0;
|
|
|
|
|
#ifndef Avoid_Underflow
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
L = -L >> Exp_shift;
|
|
|
|
|
if (L < Exp_shift) {
|
|
|
|
|
word0(a) = 0x80000 >> L;
|
|
|
|
|
word1(a) = 0;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
word0(a) = 0;
|
|
|
|
|
L -= Exp_shift;
|
|
|
|
|
word1(a) = L >= 31 ? 1 : 1 << 31 - L;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
return dval(a);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
b2d(Bigint *a, int *e)
|
|
|
|
|
{
|
|
|
|
|
ULong *xa, *xa0, w, y, z;
|
|
|
|
|
int k;
|
|
|
|
|
double_u d;
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
ULong d0, d1;
|
|
|
|
|
#else
|
|
|
|
|
#define d0 word0(d)
|
|
|
|
|
#define d1 word1(d)
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
xa0 = a->x;
|
|
|
|
|
xa = xa0 + a->wds;
|
|
|
|
|
y = *--xa;
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
if (!y) Bug("zero y in b2d");
|
|
|
|
|
#endif
|
|
|
|
|
k = hi0bits(y);
|
|
|
|
|
*e = 32 - k;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
if (k < Ebits) {
|
|
|
|
|
d0 = Exp_1 | y >> (Ebits - k);
|
|
|
|
|
w = xa > xa0 ? *--xa : 0;
|
|
|
|
|
d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
|
|
|
|
|
goto ret_d;
|
|
|
|
|
}
|
|
|
|
|
z = xa > xa0 ? *--xa : 0;
|
|
|
|
|
if (k -= Ebits) {
|
|
|
|
|
d0 = Exp_1 | y << k | z >> (32 - k);
|
|
|
|
|
y = xa > xa0 ? *--xa : 0;
|
|
|
|
|
d1 = z << k | y >> (32 - k);
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
d0 = Exp_1 | y;
|
|
|
|
|
d1 = z;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
if (k < Ebits + 16) {
|
|
|
|
|
z = xa > xa0 ? *--xa : 0;
|
|
|
|
|
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
|
|
|
|
|
w = xa > xa0 ? *--xa : 0;
|
|
|
|
|
y = xa > xa0 ? *--xa : 0;
|
|
|
|
|
d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
|
|
|
|
|
goto ret_d;
|
|
|
|
|
}
|
|
|
|
|
z = xa > xa0 ? *--xa : 0;
|
|
|
|
|
w = xa > xa0 ? *--xa : 0;
|
|
|
|
|
k -= Ebits + 16;
|
|
|
|
|
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
|
|
|
|
|
y = xa > xa0 ? *--xa : 0;
|
|
|
|
|
d1 = w << k + 16 | y << k;
|
|
|
|
|
#endif
|
|
|
|
|
ret_d:
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
word0(d) = d0 >> 16 | d0 << 16;
|
|
|
|
|
word1(d) = d1 >> 16 | d1 << 16;
|
|
|
|
|
#else
|
|
|
|
|
#undef d0
|
|
|
|
|
#undef d1
|
|
|
|
|
#endif
|
|
|
|
|
return dval(d);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
|
d2b(double d_, int *e, int *bits)
|
|
|
|
|
{
|
|
|
|
|
double_u d;
|
|
|
|
|
Bigint *b;
|
|
|
|
|
int de, k;
|
|
|
|
|
ULong *x, y, z;
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
int i;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
ULong d0, d1;
|
|
|
|
|
#endif
|
|
|
|
|
dval(d) = d_;
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
d0 = word0(d) >> 16 | word0(d) << 16;
|
|
|
|
|
d1 = word1(d) >> 16 | word1(d) << 16;
|
|
|
|
|
#else
|
|
|
|
|
#define d0 word0(d)
|
|
|
|
|
#define d1 word1(d)
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
b = Balloc(1);
|
|
|
|
|
#else
|
|
|
|
|
b = Balloc(2);
|
|
|
|
|
#endif
|
|
|
|
|
x = b->x;
|
|
|
|
|
|
|
|
|
|
z = d0 & Frac_mask;
|
|
|
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
de = (int)(d0 >> Exp_shift);
|
|
|
|
|
#ifndef IBM
|
|
|
|
|
z |= Exp_msk11;
|
|
|
|
|
#endif
|
|
|
|
|
#else
|
|
|
|
|
if ((de = (int)(d0 >> Exp_shift)) != 0)
|
|
|
|
|
z |= Exp_msk1;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
if ((y = d1) != 0) {
|
|
|
|
|
if ((k = lo0bits(&y)) != 0) {
|
|
|
|
|
x[0] = y | z << (32 - k);
|
|
|
|
|
z >>= k;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
x[0] = y;
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
i =
|
|
|
|
|
#endif
|
|
|
|
|
b->wds = (x[1] = z) ? 2 : 1;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
if (!z)
|
|
|
|
|
Bug("Zero passed to d2b");
|
|
|
|
|
#endif
|
|
|
|
|
k = lo0bits(&z);
|
|
|
|
|
x[0] = z;
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
i =
|
|
|
|
|
#endif
|
|
|
|
|
b->wds = 1;
|
|
|
|
|
k += 32;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
if (y = d1) {
|
|
|
|
|
if (k = lo0bits(&y))
|
|
|
|
|
if (k >= 16) {
|
|
|
|
|
x[0] = y | z << 32 - k & 0xffff;
|
|
|
|
|
x[1] = z >> k - 16 & 0xffff;
|
|
|
|
|
x[2] = z >> k;
|
|
|
|
|
i = 2;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
x[0] = y & 0xffff;
|
|
|
|
|
x[1] = y >> 16 | z << 16 - k & 0xffff;
|
|
|
|
|
x[2] = z >> k & 0xffff;
|
|
|
|
|
x[3] = z >> k+16;
|
|
|
|
|
i = 3;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
x[0] = y & 0xffff;
|
|
|
|
|
x[1] = y >> 16;
|
|
|
|
|
x[2] = z & 0xffff;
|
|
|
|
|
x[3] = z >> 16;
|
|
|
|
|
i = 3;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
if (!z)
|
|
|
|
|
Bug("Zero passed to d2b");
|
|
|
|
|
#endif
|
|
|
|
|
k = lo0bits(&z);
|
|
|
|
|
if (k >= 16) {
|
|
|
|
|
x[0] = z;
|
|
|
|
|
i = 0;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
x[0] = z & 0xffff;
|
|
|
|
|
x[1] = z >> 16;
|
|
|
|
|
i = 1;
|
|
|
|
|
}
|
|
|
|
|
k += 32;
|
|
|
|
|
}
|
|
|
|
|
while (!x[i])
|
|
|
|
|
--i;
|
|
|
|
|
b->wds = i + 1;
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
if (de) {
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
*e = (de - Bias - (P-1) << 2) + k;
|
|
|
|
|
*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
|
|
|
|
|
#else
|
|
|
|
|
*e = de - Bias - (P-1) + k;
|
|
|
|
|
*bits = P - k;
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
*e = de - Bias - (P-1) + 1 + k;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
*bits = 32*i - hi0bits(x[i-1]);
|
|
|
|
|
#else
|
|
|
|
|
*bits = (i+2)*16 - hi0bits(x[i]);
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
return b;
|
|
|
|
|
}
|
|
|
|
|
#undef d0
|
|
|
|
|
#undef d1
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
ratio(Bigint *a, Bigint *b)
|
|
|
|
|
{
|
|
|
|
|
double_u da, db;
|
|
|
|
|
int k, ka, kb;
|
|
|
|
|
|
|
|
|
|
dval(da) = b2d(a, &ka);
|
|
|
|
|
dval(db) = b2d(b, &kb);
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
k = ka - kb + 32*(a->wds - b->wds);
|
|
|
|
|
#else
|
|
|
|
|
k = ka - kb + 16*(a->wds - b->wds);
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
if (k > 0) {
|
|
|
|
|
word0(da) += (k >> 2)*Exp_msk1;
|
|
|
|
|
if (k &= 3)
|
|
|
|
|
dval(da) *= 1 << k;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
k = -k;
|
|
|
|
|
word0(db) += (k >> 2)*Exp_msk1;
|
|
|
|
|
if (k &= 3)
|
|
|
|
|
dval(db) *= 1 << k;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
if (k > 0)
|
|
|
|
|
word0(da) += k*Exp_msk1;
|
|
|
|
|
else {
|
|
|
|
|
k = -k;
|
|
|
|
|
word0(db) += k*Exp_msk1;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
return dval(da) / dval(db);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static const double
|
|
|
|
|
tens[] = {
|
|
|
|
|
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
|
|
|
|
|
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
|
|
|
|
|
1e20, 1e21, 1e22
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
, 1e23, 1e24
|
|
|
|
|
#endif
|
|
|
|
|
};
|
|
|
|
|
|
|
|
|
|
static const double
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
|
|
|
static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
9007199254740992.*9007199254740992.e-256
|
|
|
|
|
/* = 2^106 * 1e-53 */
|
|
|
|
|
#else
|
|
|
|
|
1e-256
|
|
|
|
|
#endif
|
|
|
|
|
};
|
|
|
|
|
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
|
|
|
|
|
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
|
|
|
|
|
#define Scale_Bit 0x10
|
|
|
|
|
#define n_bigtens 5
|
|
|
|
|
#else
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
bigtens[] = { 1e16, 1e32, 1e64 };
|
|
|
|
|
static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
|
|
|
|
|
#define n_bigtens 3
|
|
|
|
|
#else
|
|
|
|
|
bigtens[] = { 1e16, 1e32 };
|
|
|
|
|
static const double tinytens[] = { 1e-16, 1e-32 };
|
|
|
|
|
#define n_bigtens 2
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifndef IEEE_Arith
|
|
|
|
|
#undef INFNAN_CHECK
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifdef INFNAN_CHECK
|
|
|
|
|
|
|
|
|
|
#ifndef NAN_WORD0
|
|
|
|
|
#define NAN_WORD0 0x7ff80000
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifndef NAN_WORD1
|
|
|
|
|
#define NAN_WORD1 0
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
static int
|
|
|
|
|
match(const char **sp, char *t)
|
|
|
|
|
{
|
|
|
|
|
int c, d;
|
|
|
|
|
const char *s = *sp;
|
|
|
|
|
|
|
|
|
|
while (d = *t++) {
|
|
|
|
|
if ((c = *++s) >= 'A' && c <= 'Z')
|
|
|
|
|
c += 'a' - 'A';
|
|
|
|
|
if (c != d)
|
|
|
|
|
return 0;
|
|
|
|
|
}
|
|
|
|
|
*sp = s + 1;
|
|
|
|
|
return 1;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#ifndef No_Hex_NaN
|
|
|
|
|
static void
|
|
|
|
|
hexnan(double *rvp, const char **sp)
|
|
|
|
|
{
|
|
|
|
|
ULong c, x[2];
|
|
|
|
|
const char *s;
|
|
|
|
|
int havedig, udx0, xshift;
|
|
|
|
|
|
|
|
|
|
x[0] = x[1] = 0;
|
|
|
|
|
havedig = xshift = 0;
|
|
|
|
|
udx0 = 1;
|
|
|
|
|
s = *sp;
|
|
|
|
|
while (c = *(const unsigned char*)++s) {
|
|
|
|
|
if (c >= '0' && c <= '9')
|
|
|
|
|
c -= '0';
|
|
|
|
|
else if (c >= 'a' && c <= 'f')
|
|
|
|
|
c += 10 - 'a';
|
|
|
|
|
else if (c >= 'A' && c <= 'F')
|
|
|
|
|
c += 10 - 'A';
|
|
|
|
|
else if (c <= ' ') {
|
|
|
|
|
if (udx0 && havedig) {
|
|
|
|
|
udx0 = 0;
|
|
|
|
|
xshift = 1;
|
|
|
|
|
}
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
else if (/*(*/ c == ')' && havedig) {
|
|
|
|
|
*sp = s + 1;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
return; /* invalid form: don't change *sp */
|
|
|
|
|
havedig = 1;
|
|
|
|
|
if (xshift) {
|
|
|
|
|
xshift = 0;
|
|
|
|
|
x[0] = x[1];
|
|
|
|
|
x[1] = 0;
|
|
|
|
|
}
|
|
|
|
|
if (udx0)
|
|
|
|
|
x[0] = (x[0] << 4) | (x[1] >> 28);
|
|
|
|
|
x[1] = (x[1] << 4) | c;
|
|
|
|
|
}
|
|
|
|
|
if ((x[0] &= 0xfffff) || x[1]) {
|
|
|
|
|
word0(*rvp) = Exp_mask | x[0];
|
|
|
|
|
word1(*rvp) = x[1];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif /*No_Hex_NaN*/
|
|
|
|
|
#endif /* INFNAN_CHECK */
|
|
|
|
|
|
|
|
|
|
NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
|
|
|
|
|
double
|
|
|
|
|
strtod(const char *s00, char **se)
|
|
|
|
|
{
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
int scale;
|
|
|
|
|
#endif
|
|
|
|
|
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
|
|
|
|
|
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
|
|
|
|
|
const char *s, *s0, *s1;
|
|
|
|
|
double aadj, adj;
|
|
|
|
|
double_u aadj1, rv, rv0;
|
|
|
|
|
Long L;
|
|
|
|
|
ULong y, z;
|
|
|
|
|
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
int inexact, oldinexact;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
int rounding;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef USE_LOCALE
|
|
|
|
|
const char *s2;
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
errno = 0;
|
|
|
|
|
sign = nz0 = nz = 0;
|
|
|
|
|
dval(rv) = 0.;
|
|
|
|
|
for (s = s00;;s++)
|
|
|
|
|
switch (*s) {
|
|
|
|
|
case '-':
|
|
|
|
|
sign = 1;
|
|
|
|
|
/* no break */
|
|
|
|
|
case '+':
|
|
|
|
|
if (*++s)
|
|
|
|
|
goto break2;
|
|
|
|
|
/* no break */
|
|
|
|
|
case 0:
|
|
|
|
|
goto ret0;
|
|
|
|
|
case '\t':
|
|
|
|
|
case '\n':
|
|
|
|
|
case '\v':
|
|
|
|
|
case '\f':
|
|
|
|
|
case '\r':
|
|
|
|
|
case ' ':
|
|
|
|
|
continue;
|
|
|
|
|
default:
|
|
|
|
|
goto break2;
|
|
|
|
|
}
|
|
|
|
|
break2:
|
|
|
|
|
if (*s == '0') {
|
|
|
|
|
if (s[1] == 'x' || s[1] == 'X') {
|
|
|
|
|
s0 = ++s;
|
|
|
|
|
adj = 0;
|
|
|
|
|
aadj = 1.0;
|
|
|
|
|
nd0 = -4;
|
|
|
|
|
|
|
|
|
|
if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
|
|
|
|
|
if (*s == '0') {
|
|
|
|
|
while (*++s == '0');
|
2021-07-01 00:39:17 +03:00
|
|
|
if (!*s) goto ret;
|
2019-02-07 11:53:11 +03:00
|
|
|
s1 = strchr(hexdigit, *s);
|
|
|
|
|
}
|
|
|
|
|
if (s1 != NULL) {
|
|
|
|
|
do {
|
|
|
|
|
adj += aadj * ((s1 - hexdigit) & 15);
|
|
|
|
|
nd0 += 4;
|
|
|
|
|
aadj /= 16;
|
|
|
|
|
} while (*++s && (s1 = strchr(hexdigit, *s)));
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (*s == '.') {
|
|
|
|
|
dsign = 1;
|
|
|
|
|
if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
|
|
|
|
|
if (nd0 < 0) {
|
|
|
|
|
while (*s == '0') {
|
|
|
|
|
s++;
|
|
|
|
|
nd0 -= 4;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
|
|
|
|
|
adj += aadj * ((s1 - hexdigit) & 15);
|
|
|
|
|
if ((aadj /= 16) == 0.0) {
|
2021-07-01 00:39:17 +03:00
|
|
|
while (*++s && strchr(hexdigit, *s));
|
2019-02-07 11:53:11 +03:00
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
dsign = 0;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (*s == 'P' || *s == 'p') {
|
|
|
|
|
dsign = 0x2C - *++s; /* +: 2B, -: 2D */
|
|
|
|
|
if (abs(dsign) == 1) s++;
|
|
|
|
|
else dsign = 1;
|
|
|
|
|
|
|
|
|
|
nd = 0;
|
|
|
|
|
c = *s;
|
|
|
|
|
if (c < '0' || '9' < c) goto ret0;
|
|
|
|
|
do {
|
|
|
|
|
nd *= 10;
|
|
|
|
|
nd += c;
|
|
|
|
|
nd -= '0';
|
|
|
|
|
c = *++s;
|
|
|
|
|
/* Float("0x0."+("0"*267)+"1fp2095") */
|
|
|
|
|
if (nd + dsign * nd0 > 2095) {
|
|
|
|
|
while ('0' <= c && c <= '9') c = *++s;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
} while ('0' <= c && c <= '9');
|
|
|
|
|
nd0 += nd * dsign;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
if (dsign) goto ret0;
|
|
|
|
|
}
|
|
|
|
|
dval(rv) = ldexp(adj, nd0);
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
nz0 = 1;
|
|
|
|
|
while (*++s == '0') ;
|
|
|
|
|
if (!*s)
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
s0 = s;
|
|
|
|
|
y = z = 0;
|
|
|
|
|
for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
|
|
|
|
|
if (nd < 9)
|
|
|
|
|
y = 10*y + c - '0';
|
|
|
|
|
else if (nd < DBL_DIG + 2)
|
|
|
|
|
z = 10*z + c - '0';
|
|
|
|
|
nd0 = nd;
|
|
|
|
|
#ifdef USE_LOCALE
|
|
|
|
|
s1 = localeconv()->decimal_point;
|
|
|
|
|
if (c == *s1) {
|
|
|
|
|
c = '.';
|
|
|
|
|
if (*++s1) {
|
|
|
|
|
s2 = s;
|
|
|
|
|
for (;;) {
|
|
|
|
|
if (*++s2 != *s1) {
|
|
|
|
|
c = 0;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if (!*++s1) {
|
|
|
|
|
s = s2;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
if (c == '.') {
|
|
|
|
|
if (!ISDIGIT(s[1]))
|
|
|
|
|
goto dig_done;
|
|
|
|
|
c = *++s;
|
|
|
|
|
if (!nd) {
|
|
|
|
|
for (; c == '0'; c = *++s)
|
|
|
|
|
nz++;
|
|
|
|
|
if (c > '0' && c <= '9') {
|
|
|
|
|
s0 = s;
|
|
|
|
|
nf += nz;
|
|
|
|
|
nz = 0;
|
|
|
|
|
goto have_dig;
|
|
|
|
|
}
|
|
|
|
|
goto dig_done;
|
|
|
|
|
}
|
|
|
|
|
for (; c >= '0' && c <= '9'; c = *++s) {
|
|
|
|
|
have_dig:
|
|
|
|
|
nz++;
|
|
|
|
|
if (nd > DBL_DIG * 4) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
if (c -= '0') {
|
|
|
|
|
nf += nz;
|
|
|
|
|
for (i = 1; i < nz; i++)
|
|
|
|
|
if (nd++ < 9)
|
|
|
|
|
y *= 10;
|
|
|
|
|
else if (nd <= DBL_DIG + 2)
|
|
|
|
|
z *= 10;
|
|
|
|
|
if (nd++ < 9)
|
|
|
|
|
y = 10*y + c;
|
|
|
|
|
else if (nd <= DBL_DIG + 2)
|
|
|
|
|
z = 10*z + c;
|
|
|
|
|
nz = 0;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
dig_done:
|
|
|
|
|
e = 0;
|
|
|
|
|
if (c == 'e' || c == 'E') {
|
|
|
|
|
if (!nd && !nz && !nz0) {
|
|
|
|
|
goto ret0;
|
|
|
|
|
}
|
|
|
|
|
s00 = s;
|
|
|
|
|
esign = 0;
|
|
|
|
|
switch (c = *++s) {
|
|
|
|
|
case '-':
|
|
|
|
|
esign = 1;
|
|
|
|
|
case '+':
|
|
|
|
|
c = *++s;
|
|
|
|
|
}
|
|
|
|
|
if (c >= '0' && c <= '9') {
|
|
|
|
|
while (c == '0')
|
|
|
|
|
c = *++s;
|
|
|
|
|
if (c > '0' && c <= '9') {
|
|
|
|
|
L = c - '0';
|
|
|
|
|
s1 = s;
|
|
|
|
|
while ((c = *++s) >= '0' && c <= '9')
|
|
|
|
|
L = 10*L + c - '0';
|
|
|
|
|
if (s - s1 > 8 || L > 19999)
|
|
|
|
|
/* Avoid confusion from exponents
|
|
|
|
|
* so large that e might overflow.
|
|
|
|
|
*/
|
|
|
|
|
e = 19999; /* safe for 16 bit ints */
|
|
|
|
|
else
|
|
|
|
|
e = (int)L;
|
|
|
|
|
if (esign)
|
|
|
|
|
e = -e;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
e = 0;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
s = s00;
|
|
|
|
|
}
|
|
|
|
|
if (!nd) {
|
|
|
|
|
if (!nz && !nz0) {
|
|
|
|
|
#ifdef INFNAN_CHECK
|
|
|
|
|
/* Check for Nan and Infinity */
|
|
|
|
|
switch (c) {
|
|
|
|
|
case 'i':
|
|
|
|
|
case 'I':
|
|
|
|
|
if (match(&s,"nf")) {
|
|
|
|
|
--s;
|
|
|
|
|
if (!match(&s,"inity"))
|
|
|
|
|
++s;
|
|
|
|
|
word0(rv) = 0x7ff00000;
|
|
|
|
|
word1(rv) = 0;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
case 'n':
|
|
|
|
|
case 'N':
|
|
|
|
|
if (match(&s, "an")) {
|
|
|
|
|
word0(rv) = NAN_WORD0;
|
|
|
|
|
word1(rv) = NAN_WORD1;
|
|
|
|
|
#ifndef No_Hex_NaN
|
|
|
|
|
if (*s == '(') /*)*/
|
|
|
|
|
hexnan(&rv, &s);
|
|
|
|
|
#endif
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif /* INFNAN_CHECK */
|
|
|
|
|
ret0:
|
|
|
|
|
s = s00;
|
|
|
|
|
sign = 0;
|
|
|
|
|
}
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
e1 = e -= nf;
|
|
|
|
|
|
|
|
|
|
/* Now we have nd0 digits, starting at s0, followed by a
|
|
|
|
|
* decimal point, followed by nd-nd0 digits. The number we're
|
|
|
|
|
* after is the integer represented by those digits times
|
|
|
|
|
* 10**e */
|
|
|
|
|
|
|
|
|
|
if (!nd0)
|
|
|
|
|
nd0 = nd;
|
|
|
|
|
k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
|
|
|
|
|
dval(rv) = y;
|
|
|
|
|
if (k > 9) {
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
if (k > DBL_DIG)
|
|
|
|
|
oldinexact = get_inexact();
|
|
|
|
|
#endif
|
|
|
|
|
dval(rv) = tens[k - 9] * dval(rv) + z;
|
|
|
|
|
}
|
|
|
|
|
bd0 = bb = bd = bs = delta = 0;
|
|
|
|
|
if (nd <= DBL_DIG
|
|
|
|
|
#ifndef RND_PRODQUOT
|
|
|
|
|
#ifndef Honor_FLT_ROUNDS
|
|
|
|
|
&& Flt_Rounds == 1
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
) {
|
|
|
|
|
if (!e)
|
|
|
|
|
goto ret;
|
|
|
|
|
if (e > 0) {
|
|
|
|
|
if (e <= Ten_pmax) {
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
goto vax_ovfl_check;
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
|
|
if (sign) {
|
|
|
|
|
dval(rv) = -dval(rv);
|
|
|
|
|
sign = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
/* rv = */ rounded_product(dval(rv), tens[e]);
|
|
|
|
|
goto ret;
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
i = DBL_DIG - nd;
|
|
|
|
|
if (e <= Ten_pmax + i) {
|
|
|
|
|
/* A fancier test would sometimes let us do
|
|
|
|
|
* this for larger i values.
|
|
|
|
|
*/
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
|
|
if (sign) {
|
|
|
|
|
dval(rv) = -dval(rv);
|
|
|
|
|
sign = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
e -= i;
|
|
|
|
|
dval(rv) *= tens[i];
|
|
|
|
|
#ifdef VAX
|
|
|
|
|
/* VAX exponent range is so narrow we must
|
|
|
|
|
* worry about overflow here...
|
|
|
|
|
*/
|
|
|
|
|
vax_ovfl_check:
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
/* rv = */ rounded_product(dval(rv), tens[e]);
|
|
|
|
|
if ((word0(rv) & Exp_mask)
|
|
|
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
|
|
|
|
|
goto ovfl;
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
#else
|
|
|
|
|
/* rv = */ rounded_product(dval(rv), tens[e]);
|
|
|
|
|
#endif
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#ifndef Inaccurate_Divide
|
|
|
|
|
else if (e >= -Ten_pmax) {
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
|
|
|
if (sign) {
|
|
|
|
|
dval(rv) = -dval(rv);
|
|
|
|
|
sign = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
e1 += nd - k;
|
|
|
|
|
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 1;
|
|
|
|
|
if (k <= DBL_DIG)
|
|
|
|
|
oldinexact = get_inexact();
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
scale = 0;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if ((rounding = Flt_Rounds) >= 2) {
|
|
|
|
|
if (sign)
|
|
|
|
|
rounding = rounding == 2 ? 0 : 2;
|
|
|
|
|
else
|
|
|
|
|
if (rounding != 2)
|
|
|
|
|
rounding = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
#endif /*IEEE_Arith*/
|
|
|
|
|
|
|
|
|
|
/* Get starting approximation = rv * 10**e1 */
|
|
|
|
|
|
|
|
|
|
if (e1 > 0) {
|
|
|
|
|
if ((i = e1 & 15) != 0)
|
|
|
|
|
dval(rv) *= tens[i];
|
|
|
|
|
if (e1 &= ~15) {
|
|
|
|
|
if (e1 > DBL_MAX_10_EXP) {
|
|
|
|
|
ovfl:
|
|
|
|
|
#ifndef NO_ERRNO
|
|
|
|
|
errno = ERANGE;
|
|
|
|
|
#endif
|
|
|
|
|
/* Can't trust HUGE_VAL */
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
switch (rounding) {
|
|
|
|
|
case 0: /* toward 0 */
|
|
|
|
|
case 3: /* toward -infinity */
|
|
|
|
|
word0(rv) = Big0;
|
|
|
|
|
word1(rv) = Big1;
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
word0(rv) = Exp_mask;
|
|
|
|
|
word1(rv) = 0;
|
|
|
|
|
}
|
|
|
|
|
#else /*Honor_FLT_ROUNDS*/
|
|
|
|
|
word0(rv) = Exp_mask;
|
|
|
|
|
word1(rv) = 0;
|
|
|
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
/* set overflow bit */
|
|
|
|
|
dval(rv0) = 1e300;
|
|
|
|
|
dval(rv0) *= dval(rv0);
|
|
|
|
|
#endif
|
|
|
|
|
#else /*IEEE_Arith*/
|
|
|
|
|
word0(rv) = Big0;
|
|
|
|
|
word1(rv) = Big1;
|
|
|
|
|
#endif /*IEEE_Arith*/
|
|
|
|
|
if (bd0)
|
|
|
|
|
goto retfree;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
e1 >>= 4;
|
|
|
|
|
for (j = 0; e1 > 1; j++, e1 >>= 1)
|
|
|
|
|
if (e1 & 1)
|
|
|
|
|
dval(rv) *= bigtens[j];
|
|
|
|
|
/* The last multiplication could overflow. */
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
dval(rv) *= bigtens[j];
|
|
|
|
|
if ((z = word0(rv) & Exp_mask)
|
|
|
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
|
|
|
|
|
goto ovfl;
|
|
|
|
|
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
|
|
|
|
|
/* set to largest number */
|
|
|
|
|
/* (Can't trust DBL_MAX) */
|
|
|
|
|
word0(rv) = Big0;
|
|
|
|
|
word1(rv) = Big1;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else if (e1 < 0) {
|
|
|
|
|
e1 = -e1;
|
|
|
|
|
if ((i = e1 & 15) != 0)
|
|
|
|
|
dval(rv) /= tens[i];
|
|
|
|
|
if (e1 >>= 4) {
|
|
|
|
|
if (e1 >= 1 << n_bigtens)
|
|
|
|
|
goto undfl;
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (e1 & Scale_Bit)
|
|
|
|
|
scale = 2*P;
|
|
|
|
|
for (j = 0; e1 > 0; j++, e1 >>= 1)
|
|
|
|
|
if (e1 & 1)
|
|
|
|
|
dval(rv) *= tinytens[j];
|
|
|
|
|
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
|
|
|
|
|
>> Exp_shift)) > 0) {
|
|
|
|
|
/* scaled rv is denormal; zap j low bits */
|
|
|
|
|
if (j >= 32) {
|
|
|
|
|
word1(rv) = 0;
|
|
|
|
|
if (j >= 53)
|
|
|
|
|
word0(rv) = (P+2)*Exp_msk1;
|
|
|
|
|
else
|
|
|
|
|
word0(rv) &= 0xffffffff << (j-32);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
word1(rv) &= 0xffffffff << j;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
for (j = 0; e1 > 1; j++, e1 >>= 1)
|
|
|
|
|
if (e1 & 1)
|
|
|
|
|
dval(rv) *= tinytens[j];
|
|
|
|
|
/* The last multiplication could underflow. */
|
|
|
|
|
dval(rv0) = dval(rv);
|
|
|
|
|
dval(rv) *= tinytens[j];
|
|
|
|
|
if (!dval(rv)) {
|
|
|
|
|
dval(rv) = 2.*dval(rv0);
|
|
|
|
|
dval(rv) *= tinytens[j];
|
|
|
|
|
#endif
|
|
|
|
|
if (!dval(rv)) {
|
|
|
|
|
undfl:
|
|
|
|
|
dval(rv) = 0.;
|
|
|
|
|
#ifndef NO_ERRNO
|
|
|
|
|
errno = ERANGE;
|
|
|
|
|
#endif
|
|
|
|
|
if (bd0)
|
|
|
|
|
goto retfree;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
#ifndef Avoid_Underflow
|
|
|
|
|
word0(rv) = Tiny0;
|
|
|
|
|
word1(rv) = Tiny1;
|
|
|
|
|
/* The refinement below will clean
|
|
|
|
|
* this approximation up.
|
|
|
|
|
*/
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
|
|
|
|
|
|
|
/* Put digits into bd: true value = bd * 10^e */
|
|
|
|
|
|
|
|
|
|
bd0 = s2b(s0, nd0, nd, y);
|
|
|
|
|
|
|
|
|
|
for (;;) {
|
|
|
|
|
bd = Balloc(bd0->k);
|
|
|
|
|
Bcopy(bd, bd0);
|
|
|
|
|
bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
|
|
|
|
|
bs = i2b(1);
|
|
|
|
|
|
|
|
|
|
if (e >= 0) {
|
|
|
|
|
bb2 = bb5 = 0;
|
|
|
|
|
bd2 = bd5 = e;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
bb2 = bb5 = -e;
|
|
|
|
|
bd2 = bd5 = 0;
|
|
|
|
|
}
|
|
|
|
|
if (bbe >= 0)
|
|
|
|
|
bb2 += bbe;
|
|
|
|
|
else
|
|
|
|
|
bd2 -= bbe;
|
|
|
|
|
bs2 = bb2;
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (rounding != 1)
|
|
|
|
|
bs2++;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
j = bbe - scale;
|
|
|
|
|
i = j + bbbits - 1; /* logb(rv) */
|
|
|
|
|
if (i < Emin) /* denormal */
|
|
|
|
|
j += P - Emin;
|
|
|
|
|
else
|
|
|
|
|
j = P + 1 - bbbits;
|
|
|
|
|
#else /*Avoid_Underflow*/
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
|
|
|
|
|
#else
|
|
|
|
|
j = P + 1 - bbbits;
|
|
|
|
|
#endif
|
|
|
|
|
#else /*Sudden_Underflow*/
|
|
|
|
|
j = bbe;
|
|
|
|
|
i = j + bbbits - 1; /* logb(rv) */
|
|
|
|
|
if (i < Emin) /* denormal */
|
|
|
|
|
j += P - Emin;
|
|
|
|
|
else
|
|
|
|
|
j = P + 1 - bbbits;
|
|
|
|
|
#endif /*Sudden_Underflow*/
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
bb2 += j;
|
|
|
|
|
bd2 += j;
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
bd2 += scale;
|
|
|
|
|
#endif
|
|
|
|
|
i = bb2 < bd2 ? bb2 : bd2;
|
|
|
|
|
if (i > bs2)
|
|
|
|
|
i = bs2;
|
|
|
|
|
if (i > 0) {
|
|
|
|
|
bb2 -= i;
|
|
|
|
|
bd2 -= i;
|
|
|
|
|
bs2 -= i;
|
|
|
|
|
}
|
|
|
|
|
if (bb5 > 0) {
|
|
|
|
|
bs = pow5mult(bs, bb5);
|
|
|
|
|
bb1 = mult(bs, bb);
|
|
|
|
|
Bfree(bb);
|
|
|
|
|
bb = bb1;
|
|
|
|
|
}
|
|
|
|
|
if (bb2 > 0)
|
|
|
|
|
bb = lshift(bb, bb2);
|
|
|
|
|
if (bd5 > 0)
|
|
|
|
|
bd = pow5mult(bd, bd5);
|
|
|
|
|
if (bd2 > 0)
|
|
|
|
|
bd = lshift(bd, bd2);
|
|
|
|
|
if (bs2 > 0)
|
|
|
|
|
bs = lshift(bs, bs2);
|
|
|
|
|
delta = diff(bb, bd);
|
|
|
|
|
dsign = delta->sign;
|
|
|
|
|
delta->sign = 0;
|
|
|
|
|
i = cmp(delta, bs);
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (rounding != 1) {
|
|
|
|
|
if (i < 0) {
|
|
|
|
|
/* Error is less than an ulp */
|
|
|
|
|
if (!delta->x[0] && delta->wds <= 1) {
|
|
|
|
|
/* exact */
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if (rounding) {
|
|
|
|
|
if (dsign) {
|
|
|
|
|
adj = 1.;
|
|
|
|
|
goto apply_adj;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else if (!dsign) {
|
|
|
|
|
adj = -1.;
|
|
|
|
|
if (!word1(rv)
|
|
|
|
|
&& !(word0(rv) & Frac_mask)) {
|
|
|
|
|
y = word0(rv) & Exp_mask;
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (!scale || y > 2*P*Exp_msk1)
|
|
|
|
|
#else
|
|
|
|
|
if (y)
|
|
|
|
|
#endif
|
|
|
|
|
{
|
|
|
|
|
delta = lshift(delta,Log2P);
|
|
|
|
|
if (cmp(delta, bs) <= 0)
|
|
|
|
|
adj = -0.5;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
apply_adj:
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (scale && (y = word0(rv) & Exp_mask)
|
|
|
|
|
<= 2*P*Exp_msk1)
|
|
|
|
|
word0(adj) += (2*P+1)*Exp_msk1 - y;
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
if ((word0(rv) & Exp_mask) <=
|
|
|
|
|
P*Exp_msk1) {
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
dval(rv) += adj*ulp(dval(rv));
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
#endif /*Sudden_Underflow*/
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
dval(rv) += adj*ulp(dval(rv));
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
adj = ratio(delta, bs);
|
|
|
|
|
if (adj < 1.)
|
|
|
|
|
adj = 1.;
|
|
|
|
|
if (adj <= 0x7ffffffe) {
|
|
|
|
|
/* adj = rounding ? ceil(adj) : floor(adj); */
|
|
|
|
|
y = adj;
|
|
|
|
|
if (y != adj) {
|
|
|
|
|
if (!((rounding>>1) ^ dsign))
|
|
|
|
|
y++;
|
|
|
|
|
adj = y;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
|
|
|
word0(adj) += (2*P+1)*Exp_msk1 - y;
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
adj *= ulp(dval(rv));
|
|
|
|
|
if (dsign)
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
else
|
|
|
|
|
dval(rv) -= adj;
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
goto cont;
|
|
|
|
|
}
|
|
|
|
|
#endif /*Sudden_Underflow*/
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
adj *= ulp(dval(rv));
|
|
|
|
|
if (dsign)
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
else
|
|
|
|
|
dval(rv) -= adj;
|
|
|
|
|
goto cont;
|
|
|
|
|
}
|
|
|
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
|
|
|
|
|
|
|
|
if (i < 0) {
|
|
|
|
|
/* Error is less than half an ulp -- check for
|
|
|
|
|
* special case of mantissa a power of two.
|
|
|
|
|
*/
|
|
|
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
|
|
|
|
|
#else
|
|
|
|
|
|| (word0(rv) & Exp_mask) <= Exp_msk1
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
) {
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
if (!delta->x[0] && delta->wds <= 1)
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if (!delta->x[0] && delta->wds <= 1) {
|
|
|
|
|
/* exact result */
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
delta = lshift(delta,Log2P);
|
|
|
|
|
if (cmp(delta, bs) > 0)
|
|
|
|
|
goto drop_down;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if (i == 0) {
|
|
|
|
|
/* exactly half-way between */
|
|
|
|
|
if (dsign) {
|
|
|
|
|
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
|
|
|
|
|
&& word1(rv) == (
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
|
|
|
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
|
|
|
|
|
#endif
|
|
|
|
|
0xffffffff)) {
|
|
|
|
|
/*boundary case -- increment exponent*/
|
|
|
|
|
word0(rv) = (word0(rv) & Exp_mask)
|
|
|
|
|
+ Exp_msk1
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
| Exp_msk1 >> 4
|
|
|
|
|
#endif
|
|
|
|
|
;
|
|
|
|
|
word1(rv) = 0;
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
dsign = 0;
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
|
|
|
|
|
drop_down:
|
|
|
|
|
/* boundary case -- decrement exponent */
|
|
|
|
|
#ifdef Sudden_Underflow /*{{*/
|
|
|
|
|
L = word0(rv) & Exp_mask;
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
if (L < Exp_msk1)
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
|
|
|
|
|
#else
|
|
|
|
|
if (L <= Exp_msk1)
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
#endif /*IBM*/
|
|
|
|
|
goto undfl;
|
|
|
|
|
L -= Exp_msk1;
|
|
|
|
|
#else /*Sudden_Underflow}{*/
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (scale) {
|
|
|
|
|
L = word0(rv) & Exp_mask;
|
|
|
|
|
if (L <= (2*P+1)*Exp_msk1) {
|
|
|
|
|
if (L > (P+2)*Exp_msk1)
|
|
|
|
|
/* round even ==> */
|
|
|
|
|
/* accept rv */
|
|
|
|
|
break;
|
|
|
|
|
/* rv = smallest denormal */
|
|
|
|
|
goto undfl;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
L = (word0(rv) & Exp_mask) - Exp_msk1;
|
|
|
|
|
#endif /*Sudden_Underflow}}*/
|
|
|
|
|
word0(rv) = L | Bndry_mask1;
|
|
|
|
|
word1(rv) = 0xffffffff;
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
goto cont;
|
|
|
|
|
#else
|
|
|
|
|
break;
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
#ifndef ROUND_BIASED
|
|
|
|
|
if (!(word1(rv) & LSB))
|
|
|
|
|
break;
|
|
|
|
|
#endif
|
|
|
|
|
if (dsign)
|
|
|
|
|
dval(rv) += ulp(dval(rv));
|
|
|
|
|
#ifndef ROUND_BIASED
|
|
|
|
|
else {
|
|
|
|
|
dval(rv) -= ulp(dval(rv));
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
if (!dval(rv))
|
|
|
|
|
goto undfl;
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
dsign = 1 - dsign;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if ((aadj = ratio(delta, bs)) <= 2.) {
|
|
|
|
|
if (dsign)
|
|
|
|
|
aadj = dval(aadj1) = 1.;
|
|
|
|
|
else if (word1(rv) || word0(rv) & Bndry_mask) {
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
if (word1(rv) == Tiny1 && !word0(rv))
|
|
|
|
|
goto undfl;
|
|
|
|
|
#endif
|
|
|
|
|
aadj = 1.;
|
|
|
|
|
dval(aadj1) = -1.;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
/* special case -- power of FLT_RADIX to be */
|
|
|
|
|
/* rounded down... */
|
|
|
|
|
|
|
|
|
|
if (aadj < 2./FLT_RADIX)
|
|
|
|
|
aadj = 1./FLT_RADIX;
|
|
|
|
|
else
|
|
|
|
|
aadj *= 0.5;
|
|
|
|
|
dval(aadj1) = -aadj;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
aadj *= 0.5;
|
|
|
|
|
dval(aadj1) = dsign ? aadj : -aadj;
|
|
|
|
|
#ifdef Check_FLT_ROUNDS
|
|
|
|
|
switch (Rounding) {
|
|
|
|
|
case 2: /* towards +infinity */
|
|
|
|
|
dval(aadj1) -= 0.5;
|
|
|
|
|
break;
|
|
|
|
|
case 0: /* towards 0 */
|
|
|
|
|
case 3: /* towards -infinity */
|
|
|
|
|
dval(aadj1) += 0.5;
|
|
|
|
|
}
|
|
|
|
|
#else
|
|
|
|
|
if (Flt_Rounds == 0)
|
|
|
|
|
dval(aadj1) += 0.5;
|
|
|
|
|
#endif /*Check_FLT_ROUNDS*/
|
|
|
|
|
}
|
|
|
|
|
y = word0(rv) & Exp_mask;
|
|
|
|
|
|
|
|
|
|
/* Check for overflow */
|
|
|
|
|
|
|
|
|
|
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
|
|
|
|
dval(rv0) = dval(rv);
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
adj = dval(aadj1) * ulp(dval(rv));
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
if ((word0(rv) & Exp_mask) >=
|
|
|
|
|
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
|
|
|
|
if (word0(rv0) == Big0 && word1(rv0) == Big1)
|
|
|
|
|
goto ovfl;
|
|
|
|
|
word0(rv) = Big0;
|
|
|
|
|
word1(rv) = Big1;
|
|
|
|
|
goto cont;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (scale && y <= 2*P*Exp_msk1) {
|
|
|
|
|
if (aadj <= 0x7fffffff) {
|
|
|
|
|
if ((z = (int)aadj) <= 0)
|
|
|
|
|
z = 1;
|
|
|
|
|
aadj = z;
|
|
|
|
|
dval(aadj1) = dsign ? aadj : -aadj;
|
|
|
|
|
}
|
|
|
|
|
word0(aadj1) += (2*P+1)*Exp_msk1 - y;
|
|
|
|
|
}
|
|
|
|
|
adj = dval(aadj1) * ulp(dval(rv));
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
|
|
|
dval(rv0) = dval(rv);
|
|
|
|
|
word0(rv) += P*Exp_msk1;
|
|
|
|
|
adj = dval(aadj1) * ulp(dval(rv));
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
|
|
|
|
|
#else
|
|
|
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
|
|
|
|
|
#endif
|
|
|
|
|
{
|
|
|
|
|
if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
|
|
|
|
|
goto undfl;
|
|
|
|
|
word0(rv) = Tiny0;
|
|
|
|
|
word1(rv) = Tiny1;
|
|
|
|
|
goto cont;
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
word0(rv) -= P*Exp_msk1;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
adj = dval(aadj1) * ulp(dval(rv));
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
}
|
|
|
|
|
#else /*Sudden_Underflow*/
|
|
|
|
|
/* Compute adj so that the IEEE rounding rules will
|
|
|
|
|
* correctly round rv + adj in some half-way cases.
|
|
|
|
|
* If rv * ulp(rv) is denormalized (i.e.,
|
|
|
|
|
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
|
|
|
|
* trouble from bits lost to denormalization;
|
|
|
|
|
* example: 1.2e-307 .
|
|
|
|
|
*/
|
|
|
|
|
if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
|
|
|
|
|
dval(aadj1) = (double)(int)(aadj + 0.5);
|
|
|
|
|
if (!dsign)
|
|
|
|
|
dval(aadj1) = -dval(aadj1);
|
|
|
|
|
}
|
|
|
|
|
adj = dval(aadj1) * ulp(dval(rv));
|
|
|
|
|
dval(rv) += adj;
|
|
|
|
|
#endif /*Sudden_Underflow*/
|
|
|
|
|
#endif /*Avoid_Underflow*/
|
|
|
|
|
}
|
|
|
|
|
z = word0(rv) & Exp_mask;
|
|
|
|
|
#ifndef SET_INEXACT
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (!scale)
|
|
|
|
|
#endif
|
|
|
|
|
if (y == z) {
|
|
|
|
|
/* Can we stop now? */
|
|
|
|
|
L = (Long)aadj;
|
|
|
|
|
aadj -= L;
|
|
|
|
|
/* The tolerances below are conservative. */
|
|
|
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
|
|
|
|
|
if (aadj < .4999999 || aadj > .5000001)
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
else if (aadj < .4999999/FLT_RADIX)
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
cont:
|
|
|
|
|
Bfree(bb);
|
|
|
|
|
Bfree(bd);
|
|
|
|
|
Bfree(bs);
|
|
|
|
|
Bfree(delta);
|
|
|
|
|
}
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
if (inexact) {
|
|
|
|
|
if (!oldinexact) {
|
|
|
|
|
word0(rv0) = Exp_1 + (70 << Exp_shift);
|
|
|
|
|
word1(rv0) = 0;
|
|
|
|
|
dval(rv0) += 1.;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else if (!oldinexact)
|
|
|
|
|
clear_inexact();
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Avoid_Underflow
|
|
|
|
|
if (scale) {
|
|
|
|
|
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
|
|
|
|
|
word1(rv0) = 0;
|
|
|
|
|
dval(rv) *= dval(rv0);
|
|
|
|
|
#ifndef NO_ERRNO
|
|
|
|
|
/* try to avoid the bug of testing an 8087 register value */
|
|
|
|
|
if (word0(rv) == 0 && word1(rv) == 0)
|
|
|
|
|
errno = ERANGE;
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
#endif /* Avoid_Underflow */
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
if (inexact && !(word0(rv) & Exp_mask)) {
|
|
|
|
|
/* set underflow bit */
|
|
|
|
|
dval(rv0) = 1e-300;
|
|
|
|
|
dval(rv0) *= dval(rv0);
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
retfree:
|
|
|
|
|
Bfree(bb);
|
|
|
|
|
Bfree(bd);
|
|
|
|
|
Bfree(bs);
|
|
|
|
|
Bfree(bd0);
|
|
|
|
|
Bfree(delta);
|
|
|
|
|
ret:
|
|
|
|
|
if (se)
|
|
|
|
|
*se = (char *)s;
|
|
|
|
|
return sign ? -dval(rv) : dval(rv);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
|
|
|
|
|
static int
|
|
|
|
|
quorem(Bigint *b, Bigint *S)
|
|
|
|
|
{
|
|
|
|
|
int n;
|
|
|
|
|
ULong *bx, *bxe, q, *sx, *sxe;
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
ULLong borrow, carry, y, ys;
|
|
|
|
|
#else
|
|
|
|
|
ULong borrow, carry, y, ys;
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
ULong si, z, zs;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
n = S->wds;
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
/*debug*/ if (b->wds > n)
|
|
|
|
|
/*debug*/ Bug("oversize b in quorem");
|
|
|
|
|
#endif
|
|
|
|
|
if (b->wds < n)
|
|
|
|
|
return 0;
|
|
|
|
|
sx = S->x;
|
|
|
|
|
sxe = sx + --n;
|
|
|
|
|
bx = b->x;
|
|
|
|
|
bxe = bx + n;
|
|
|
|
|
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
|
/*debug*/ if (q > 9)
|
|
|
|
|
/*debug*/ Bug("oversized quotient in quorem");
|
|
|
|
|
#endif
|
|
|
|
|
if (q) {
|
|
|
|
|
borrow = 0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
do {
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
ys = *sx++ * (ULLong)q + carry;
|
|
|
|
|
carry = ys >> 32;
|
|
|
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
|
|
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
si = *sx++;
|
|
|
|
|
ys = (si & 0xffff) * q + carry;
|
|
|
|
|
zs = (si >> 16) * q + (ys >> 16);
|
|
|
|
|
carry = zs >> 16;
|
|
|
|
|
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
|
Storeinc(bx, z, y);
|
|
|
|
|
#else
|
|
|
|
|
ys = *sx++ * q + carry;
|
|
|
|
|
carry = ys >> 16;
|
|
|
|
|
y = *bx - (ys & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
*bx++ = y & 0xffff;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
} while (sx <= sxe);
|
|
|
|
|
if (!*bxe) {
|
|
|
|
|
bx = b->x;
|
|
|
|
|
while (--bxe > bx && !*bxe)
|
|
|
|
|
--n;
|
|
|
|
|
b->wds = n;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
if (cmp(b, S) >= 0) {
|
|
|
|
|
q++;
|
|
|
|
|
borrow = 0;
|
|
|
|
|
carry = 0;
|
|
|
|
|
bx = b->x;
|
|
|
|
|
sx = S->x;
|
|
|
|
|
do {
|
|
|
|
|
#ifdef ULLong
|
|
|
|
|
ys = *sx++ + carry;
|
|
|
|
|
carry = ys >> 32;
|
|
|
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
|
|
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
|
|
|
|
#else
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
si = *sx++;
|
|
|
|
|
ys = (si & 0xffff) + carry;
|
|
|
|
|
zs = (si >> 16) + (ys >> 16);
|
|
|
|
|
carry = zs >> 16;
|
|
|
|
|
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
|
Storeinc(bx, z, y);
|
|
|
|
|
#else
|
|
|
|
|
ys = *sx++ + carry;
|
|
|
|
|
carry = ys >> 16;
|
|
|
|
|
y = *bx - (ys & 0xffff) - borrow;
|
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
|
*bx++ = y & 0xffff;
|
|
|
|
|
#endif
|
|
|
|
|
#endif
|
|
|
|
|
} while (sx <= sxe);
|
|
|
|
|
bx = b->x;
|
|
|
|
|
bxe = bx + n;
|
|
|
|
|
if (!*bxe) {
|
|
|
|
|
while (--bxe > bx && !*bxe)
|
|
|
|
|
--n;
|
|
|
|
|
b->wds = n;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return q;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#ifndef MULTIPLE_THREADS
|
|
|
|
|
static char *dtoa_result;
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#ifndef MULTIPLE_THREADS
|
|
|
|
|
static char *
|
|
|
|
|
rv_alloc(int i)
|
|
|
|
|
{
|
2021-01-10 09:46:23 +03:00
|
|
|
return dtoa_result = MALLOC(i);
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
|
|
|
|
#else
|
2021-01-10 09:46:23 +03:00
|
|
|
#define rv_alloc(i) MALLOC(i)
|
2019-02-07 11:53:11 +03:00
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
static char *
|
|
|
|
|
nrv_alloc(const char *s, char **rve, size_t n)
|
|
|
|
|
{
|
|
|
|
|
char *rv, *t;
|
|
|
|
|
|
|
|
|
|
t = rv = rv_alloc(n);
|
|
|
|
|
while ((*t = *s++) != 0) t++;
|
|
|
|
|
if (rve)
|
|
|
|
|
*rve = t;
|
|
|
|
|
return rv;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
|
|
|
|
|
|
|
|
|
|
#ifndef MULTIPLE_THREADS
|
|
|
|
|
/* freedtoa(s) must be used to free values s returned by dtoa
|
|
|
|
|
* when MULTIPLE_THREADS is #defined. It should be used in all cases,
|
|
|
|
|
* but for consistency with earlier versions of dtoa, it is optional
|
|
|
|
|
* when MULTIPLE_THREADS is not defined.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
static void
|
|
|
|
|
freedtoa(char *s)
|
|
|
|
|
{
|
2021-01-10 09:46:23 +03:00
|
|
|
FREE(s);
|
2019-02-07 11:53:11 +03:00
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
static const char INFSTR[] = "Infinity";
|
|
|
|
|
static const char NANSTR[] = "NaN";
|
|
|
|
|
static const char ZEROSTR[] = "0";
|
|
|
|
|
|
|
|
|
|
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
|
|
|
|
*
|
|
|
|
|
* Inspired by "How to Print Floating-Point Numbers Accurately" by
|
|
|
|
|
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
|
|
|
|
*
|
|
|
|
|
* Modifications:
|
|
|
|
|
* 1. Rather than iterating, we use a simple numeric overestimate
|
|
|
|
|
* to determine k = floor(log10(d)). We scale relevant
|
|
|
|
|
* quantities using O(log2(k)) rather than O(k) multiplications.
|
|
|
|
|
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
|
|
|
|
* try to generate digits strictly left to right. Instead, we
|
|
|
|
|
* compute with fewer bits and propagate the carry if necessary
|
|
|
|
|
* when rounding the final digit up. This is often faster.
|
|
|
|
|
* 3. Under the assumption that input will be rounded nearest,
|
|
|
|
|
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
|
|
|
|
* That is, we allow equality in stopping tests when the
|
|
|
|
|
* round-nearest rule will give the same floating-point value
|
|
|
|
|
* as would satisfaction of the stopping test with strict
|
|
|
|
|
* inequality.
|
|
|
|
|
* 4. We remove common factors of powers of 2 from relevant
|
|
|
|
|
* quantities.
|
|
|
|
|
* 5. When converting floating-point integers less than 1e16,
|
|
|
|
|
* we use floating-point arithmetic rather than resorting
|
|
|
|
|
* to multiple-precision integers.
|
|
|
|
|
* 6. When asked to produce fewer than 15 digits, we first try
|
|
|
|
|
* to get by with floating-point arithmetic; we resort to
|
|
|
|
|
* multiple-precision integer arithmetic only if we cannot
|
|
|
|
|
* guarantee that the floating-point calculation has given
|
|
|
|
|
* the correctly rounded result. For k requested digits and
|
|
|
|
|
* "uniformly" distributed input, the probability is
|
|
|
|
|
* something like 10^(k-15) that we must resort to the Long
|
|
|
|
|
* calculation.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
char *
|
|
|
|
|
dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
|
|
|
|
{
|
|
|
|
|
/* Arguments ndigits, decpt, sign are similar to those
|
|
|
|
|
of ecvt and fcvt; trailing zeros are suppressed from
|
|
|
|
|
the returned string. If not null, *rve is set to point
|
|
|
|
|
to the end of the return value. If d is +-Infinity or NaN,
|
|
|
|
|
then *decpt is set to 9999.
|
|
|
|
|
|
|
|
|
|
mode:
|
|
|
|
|
0 ==> shortest string that yields d when read in
|
|
|
|
|
and rounded to nearest.
|
|
|
|
|
1 ==> like 0, but with Steele & White stopping rule;
|
|
|
|
|
e.g. with IEEE P754 arithmetic , mode 0 gives
|
|
|
|
|
1e23 whereas mode 1 gives 9.999999999999999e22.
|
|
|
|
|
2 ==> max(1,ndigits) significant digits. This gives a
|
|
|
|
|
return value similar to that of ecvt, except
|
|
|
|
|
that trailing zeros are suppressed.
|
|
|
|
|
3 ==> through ndigits past the decimal point. This
|
|
|
|
|
gives a return value similar to that from fcvt,
|
|
|
|
|
except that trailing zeros are suppressed, and
|
|
|
|
|
ndigits can be negative.
|
|
|
|
|
4,5 ==> similar to 2 and 3, respectively, but (in
|
|
|
|
|
round-nearest mode) with the tests of mode 0 to
|
|
|
|
|
possibly return a shorter string that rounds to d.
|
|
|
|
|
With IEEE arithmetic and compilation with
|
|
|
|
|
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
|
|
|
|
|
as modes 2 and 3 when FLT_ROUNDS != 1.
|
|
|
|
|
6-9 ==> Debugging modes similar to mode - 4: don't try
|
|
|
|
|
fast floating-point estimate (if applicable).
|
|
|
|
|
|
|
|
|
|
Values of mode other than 0-9 are treated as mode 0.
|
|
|
|
|
|
|
|
|
|
Sufficient space is allocated to the return value
|
|
|
|
|
to hold the suppressed trailing zeros.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
|
|
|
|
|
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
|
|
|
|
|
spec_case, try_quick, half = 0;
|
|
|
|
|
Long L;
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
int denorm;
|
|
|
|
|
ULong x;
|
|
|
|
|
#endif
|
|
|
|
|
Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
|
|
|
|
|
double ds;
|
|
|
|
|
double_u d, d2, eps;
|
|
|
|
|
char *s, *s0;
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
int rounding;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
int inexact, oldinexact;
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
dval(d) = d_;
|
|
|
|
|
|
|
|
|
|
#ifndef MULTIPLE_THREADS
|
|
|
|
|
if (dtoa_result) {
|
|
|
|
|
freedtoa(dtoa_result);
|
|
|
|
|
dtoa_result = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
if (word0(d) & Sign_bit) {
|
|
|
|
|
/* set sign for everything, including 0's and NaNs */
|
|
|
|
|
*sign = 1;
|
|
|
|
|
word0(d) &= ~Sign_bit; /* clear sign bit */
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
*sign = 0;
|
|
|
|
|
|
|
|
|
|
#if defined(IEEE_Arith) + defined(VAX)
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
if ((word0(d) & Exp_mask) == Exp_mask)
|
|
|
|
|
#else
|
|
|
|
|
if (word0(d) == 0x8000)
|
|
|
|
|
#endif
|
|
|
|
|
{
|
|
|
|
|
/* Infinity or NaN */
|
|
|
|
|
*decpt = 9999;
|
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
|
if (!word1(d) && !(word0(d) & 0xfffff))
|
|
|
|
|
return rv_strdup(INFSTR, rve);
|
|
|
|
|
#endif
|
|
|
|
|
return rv_strdup(NANSTR, rve);
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
dval(d) += 0; /* normalize */
|
|
|
|
|
#endif
|
|
|
|
|
if (!dval(d)) {
|
|
|
|
|
*decpt = 1;
|
|
|
|
|
return rv_strdup(ZEROSTR, rve);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
try_quick = oldinexact = get_inexact();
|
|
|
|
|
inexact = 1;
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if ((rounding = Flt_Rounds) >= 2) {
|
|
|
|
|
if (*sign)
|
|
|
|
|
rounding = rounding == 2 ? 0 : 2;
|
|
|
|
|
else
|
|
|
|
|
if (rounding != 2)
|
|
|
|
|
rounding = 0;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
b = d2b(dval(d), &be, &bbits);
|
|
|
|
|
#ifdef Sudden_Underflow
|
|
|
|
|
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
|
|
|
|
|
#else
|
|
|
|
|
if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
|
|
|
|
|
#endif
|
|
|
|
|
dval(d2) = dval(d);
|
|
|
|
|
word0(d2) &= Frac_mask1;
|
|
|
|
|
word0(d2) |= Exp_11;
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
if (j = 11 - hi0bits(word0(d2) & Frac_mask))
|
|
|
|
|
dval(d2) /= 1 << j;
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
|
|
|
|
* log10(x) = log(x) / log(10)
|
|
|
|
|
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
|
|
|
|
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
|
|
|
|
*
|
|
|
|
|
* This suggests computing an approximation k to log10(d) by
|
|
|
|
|
*
|
|
|
|
|
* k = (i - Bias)*0.301029995663981
|
|
|
|
|
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
|
|
|
|
*
|
|
|
|
|
* We want k to be too large rather than too small.
|
|
|
|
|
* The error in the first-order Taylor series approximation
|
|
|
|
|
* is in our favor, so we just round up the constant enough
|
|
|
|
|
* to compensate for any error in the multiplication of
|
|
|
|
|
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
|
|
|
|
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
|
|
|
|
* adding 1e-13 to the constant term more than suffices.
|
|
|
|
|
* Hence we adjust the constant term to 0.1760912590558.
|
|
|
|
|
* (We could get a more accurate k by invoking log10,
|
|
|
|
|
* but this is probably not worthwhile.)
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
i -= Bias;
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
i <<= 2;
|
|
|
|
|
i += j;
|
|
|
|
|
#endif
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
denorm = 0;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
/* d is denormalized */
|
|
|
|
|
|
|
|
|
|
i = bbits + be + (Bias + (P-1) - 1);
|
|
|
|
|
x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
|
|
|
|
|
: word1(d) << (32 - i);
|
|
|
|
|
dval(d2) = x;
|
|
|
|
|
word0(d2) -= 31*Exp_msk1; /* adjust exponent */
|
|
|
|
|
i -= (Bias + (P-1) - 1) + 1;
|
|
|
|
|
denorm = 1;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
|
|
|
|
|
k = (int)ds;
|
|
|
|
|
if (ds < 0. && ds != k)
|
|
|
|
|
k--; /* want k = floor(ds) */
|
|
|
|
|
k_check = 1;
|
|
|
|
|
if (k >= 0 && k <= Ten_pmax) {
|
|
|
|
|
if (dval(d) < tens[k])
|
|
|
|
|
k--;
|
|
|
|
|
k_check = 0;
|
|
|
|
|
}
|
|
|
|
|
j = bbits - i - 1;
|
|
|
|
|
if (j >= 0) {
|
|
|
|
|
b2 = 0;
|
|
|
|
|
s2 = j;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
b2 = -j;
|
|
|
|
|
s2 = 0;
|
|
|
|
|
}
|
|
|
|
|
if (k >= 0) {
|
|
|
|
|
b5 = 0;
|
|
|
|
|
s5 = k;
|
|
|
|
|
s2 += k;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
b2 -= k;
|
|
|
|
|
b5 = -k;
|
|
|
|
|
s5 = 0;
|
|
|
|
|
}
|
|
|
|
|
if (mode < 0 || mode > 9)
|
|
|
|
|
mode = 0;
|
|
|
|
|
|
|
|
|
|
#ifndef SET_INEXACT
|
|
|
|
|
#ifdef Check_FLT_ROUNDS
|
|
|
|
|
try_quick = Rounding == 1;
|
|
|
|
|
#else
|
|
|
|
|
try_quick = 1;
|
|
|
|
|
#endif
|
|
|
|
|
#endif /*SET_INEXACT*/
|
|
|
|
|
|
|
|
|
|
if (mode > 5) {
|
|
|
|
|
mode -= 4;
|
|
|
|
|
try_quick = 0;
|
|
|
|
|
}
|
|
|
|
|
leftright = 1;
|
|
|
|
|
ilim = ilim1 = -1;
|
|
|
|
|
switch (mode) {
|
|
|
|
|
case 0:
|
|
|
|
|
case 1:
|
|
|
|
|
i = 18;
|
|
|
|
|
ndigits = 0;
|
|
|
|
|
break;
|
|
|
|
|
case 2:
|
|
|
|
|
leftright = 0;
|
|
|
|
|
/* no break */
|
|
|
|
|
case 4:
|
|
|
|
|
if (ndigits <= 0)
|
|
|
|
|
ndigits = 1;
|
|
|
|
|
ilim = ilim1 = i = ndigits;
|
|
|
|
|
break;
|
|
|
|
|
case 3:
|
|
|
|
|
leftright = 0;
|
|
|
|
|
/* no break */
|
|
|
|
|
case 5:
|
|
|
|
|
i = ndigits + k + 1;
|
|
|
|
|
ilim = i;
|
|
|
|
|
ilim1 = i - 1;
|
|
|
|
|
if (i <= 0)
|
|
|
|
|
i = 1;
|
|
|
|
|
}
|
|
|
|
|
s = s0 = rv_alloc(i+1);
|
|
|
|
|
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (mode > 1 && rounding != 1)
|
|
|
|
|
leftright = 0;
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
|
|
|
|
|
|
|
|
|
/* Try to get by with floating-point arithmetic. */
|
|
|
|
|
|
|
|
|
|
i = 0;
|
|
|
|
|
dval(d2) = dval(d);
|
|
|
|
|
k0 = k;
|
|
|
|
|
ilim0 = ilim;
|
|
|
|
|
ieps = 2; /* conservative */
|
|
|
|
|
if (k > 0) {
|
|
|
|
|
ds = tens[k&0xf];
|
|
|
|
|
j = k >> 4;
|
|
|
|
|
if (j & Bletch) {
|
|
|
|
|
/* prevent overflows */
|
|
|
|
|
j &= Bletch - 1;
|
|
|
|
|
dval(d) /= bigtens[n_bigtens-1];
|
|
|
|
|
ieps++;
|
|
|
|
|
}
|
|
|
|
|
for (; j; j >>= 1, i++)
|
|
|
|
|
if (j & 1) {
|
|
|
|
|
ieps++;
|
|
|
|
|
ds *= bigtens[i];
|
|
|
|
|
}
|
|
|
|
|
dval(d) /= ds;
|
|
|
|
|
}
|
|
|
|
|
else if ((j1 = -k) != 0) {
|
|
|
|
|
dval(d) *= tens[j1 & 0xf];
|
|
|
|
|
for (j = j1 >> 4; j; j >>= 1, i++)
|
|
|
|
|
if (j & 1) {
|
|
|
|
|
ieps++;
|
|
|
|
|
dval(d) *= bigtens[i];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
if (k_check && dval(d) < 1. && ilim > 0) {
|
|
|
|
|
if (ilim1 <= 0)
|
|
|
|
|
goto fast_failed;
|
|
|
|
|
ilim = ilim1;
|
|
|
|
|
k--;
|
|
|
|
|
dval(d) *= 10.;
|
|
|
|
|
ieps++;
|
|
|
|
|
}
|
|
|
|
|
dval(eps) = ieps*dval(d) + 7.;
|
|
|
|
|
word0(eps) -= (P-1)*Exp_msk1;
|
|
|
|
|
if (ilim == 0) {
|
|
|
|
|
S = mhi = 0;
|
|
|
|
|
dval(d) -= 5.;
|
|
|
|
|
if (dval(d) > dval(eps))
|
|
|
|
|
goto one_digit;
|
|
|
|
|
if (dval(d) < -dval(eps))
|
|
|
|
|
goto no_digits;
|
|
|
|
|
goto fast_failed;
|
|
|
|
|
}
|
|
|
|
|
#ifndef No_leftright
|
|
|
|
|
if (leftright) {
|
|
|
|
|
/* Use Steele & White method of only
|
|
|
|
|
* generating digits needed.
|
|
|
|
|
*/
|
|
|
|
|
dval(eps) = 0.5/tens[ilim-1] - dval(eps);
|
|
|
|
|
for (i = 0;;) {
|
|
|
|
|
L = (int)dval(d);
|
|
|
|
|
dval(d) -= L;
|
|
|
|
|
*s++ = '0' + (int)L;
|
|
|
|
|
if (dval(d) < dval(eps))
|
|
|
|
|
goto ret1;
|
|
|
|
|
if (1. - dval(d) < dval(eps))
|
|
|
|
|
goto bump_up;
|
|
|
|
|
if (++i >= ilim)
|
|
|
|
|
break;
|
|
|
|
|
dval(eps) *= 10.;
|
|
|
|
|
dval(d) *= 10.;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
#endif
|
|
|
|
|
/* Generate ilim digits, then fix them up. */
|
|
|
|
|
dval(eps) *= tens[ilim-1];
|
|
|
|
|
for (i = 1;; i++, dval(d) *= 10.) {
|
|
|
|
|
L = (Long)(dval(d));
|
|
|
|
|
if (!(dval(d) -= L))
|
|
|
|
|
ilim = i;
|
|
|
|
|
*s++ = '0' + (int)L;
|
|
|
|
|
if (i == ilim) {
|
|
|
|
|
if (dval(d) > 0.5 + dval(eps))
|
|
|
|
|
goto bump_up;
|
|
|
|
|
else if (dval(d) < 0.5 - dval(eps)) {
|
|
|
|
|
while (*--s == '0') ;
|
|
|
|
|
s++;
|
|
|
|
|
goto ret1;
|
|
|
|
|
}
|
|
|
|
|
half = 1;
|
|
|
|
|
if ((*(s-1) - '0') & 1) {
|
|
|
|
|
goto bump_up;
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
#ifndef No_leftright
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
fast_failed:
|
|
|
|
|
s = s0;
|
|
|
|
|
dval(d) = dval(d2);
|
|
|
|
|
k = k0;
|
|
|
|
|
ilim = ilim0;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Do we have a "small" integer? */
|
|
|
|
|
|
|
|
|
|
if (be >= 0 && k <= Int_max) {
|
|
|
|
|
/* Yes. */
|
|
|
|
|
ds = tens[k];
|
|
|
|
|
if (ndigits < 0 && ilim <= 0) {
|
|
|
|
|
S = mhi = 0;
|
|
|
|
|
if (ilim < 0 || dval(d) <= 5*ds)
|
|
|
|
|
goto no_digits;
|
|
|
|
|
goto one_digit;
|
|
|
|
|
}
|
|
|
|
|
for (i = 1;; i++, dval(d) *= 10.) {
|
|
|
|
|
L = (Long)(dval(d) / ds);
|
|
|
|
|
dval(d) -= L*ds;
|
|
|
|
|
#ifdef Check_FLT_ROUNDS
|
|
|
|
|
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
|
|
|
|
if (dval(d) < 0) {
|
|
|
|
|
L--;
|
|
|
|
|
dval(d) += ds;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
*s++ = '0' + (int)L;
|
|
|
|
|
if (!dval(d)) {
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
if (i == ilim) {
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (mode > 1)
|
|
|
|
|
switch (rounding) {
|
|
|
|
|
case 0: goto ret1;
|
|
|
|
|
case 2: goto bump_up;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
dval(d) += dval(d);
|
|
|
|
|
if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
|
|
|
|
|
bump_up:
|
|
|
|
|
while (*--s == '9')
|
|
|
|
|
if (s == s0) {
|
|
|
|
|
k++;
|
|
|
|
|
*s = '0';
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
++*s++;
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
goto ret1;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
m2 = b2;
|
|
|
|
|
m5 = b5;
|
|
|
|
|
if (leftright) {
|
|
|
|
|
i =
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
denorm ? be + (Bias + (P-1) - 1 + 1) :
|
|
|
|
|
#endif
|
|
|
|
|
#ifdef IBM
|
|
|
|
|
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
|
|
|
|
|
#else
|
|
|
|
|
1 + P - bbits;
|
|
|
|
|
#endif
|
|
|
|
|
b2 += i;
|
|
|
|
|
s2 += i;
|
|
|
|
|
mhi = i2b(1);
|
|
|
|
|
}
|
|
|
|
|
if (m2 > 0 && s2 > 0) {
|
|
|
|
|
i = m2 < s2 ? m2 : s2;
|
|
|
|
|
b2 -= i;
|
|
|
|
|
m2 -= i;
|
|
|
|
|
s2 -= i;
|
|
|
|
|
}
|
|
|
|
|
if (b5 > 0) {
|
|
|
|
|
if (leftright) {
|
|
|
|
|
if (m5 > 0) {
|
|
|
|
|
mhi = pow5mult(mhi, m5);
|
|
|
|
|
b1 = mult(mhi, b);
|
|
|
|
|
Bfree(b);
|
|
|
|
|
b = b1;
|
|
|
|
|
}
|
|
|
|
|
if ((j = b5 - m5) != 0)
|
|
|
|
|
b = pow5mult(b, j);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
b = pow5mult(b, b5);
|
|
|
|
|
}
|
|
|
|
|
S = i2b(1);
|
|
|
|
|
if (s5 > 0)
|
|
|
|
|
S = pow5mult(S, s5);
|
|
|
|
|
|
|
|
|
|
/* Check for special case that d is a normalized power of 2. */
|
|
|
|
|
|
|
|
|
|
spec_case = 0;
|
|
|
|
|
if ((mode < 2 || leftright)
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
&& rounding == 1
|
|
|
|
|
#endif
|
|
|
|
|
) {
|
|
|
|
|
if (!word1(d) && !(word0(d) & Bndry_mask)
|
|
|
|
|
#ifndef Sudden_Underflow
|
|
|
|
|
&& word0(d) & (Exp_mask & ~Exp_msk1)
|
|
|
|
|
#endif
|
|
|
|
|
) {
|
|
|
|
|
/* The special case */
|
|
|
|
|
b2 += Log2P;
|
|
|
|
|
s2 += Log2P;
|
|
|
|
|
spec_case = 1;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Arrange for convenient computation of quotients:
|
|
|
|
|
* shift left if necessary so divisor has 4 leading 0 bits.
|
|
|
|
|
*
|
|
|
|
|
* Perhaps we should just compute leading 28 bits of S once
|
|
|
|
|
* and for all and pass them and a shift to quorem, so it
|
|
|
|
|
* can do shifts and ors to compute the numerator for q.
|
|
|
|
|
*/
|
|
|
|
|
#ifdef Pack_32
|
|
|
|
|
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
|
|
|
|
|
i = 32 - i;
|
|
|
|
|
#else
|
|
|
|
|
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
|
|
|
|
|
i = 16 - i;
|
|
|
|
|
#endif
|
|
|
|
|
if (i > 4) {
|
|
|
|
|
i -= 4;
|
|
|
|
|
b2 += i;
|
|
|
|
|
m2 += i;
|
|
|
|
|
s2 += i;
|
|
|
|
|
}
|
|
|
|
|
else if (i < 4) {
|
|
|
|
|
i += 28;
|
|
|
|
|
b2 += i;
|
|
|
|
|
m2 += i;
|
|
|
|
|
s2 += i;
|
|
|
|
|
}
|
|
|
|
|
if (b2 > 0)
|
|
|
|
|
b = lshift(b, b2);
|
|
|
|
|
if (s2 > 0)
|
|
|
|
|
S = lshift(S, s2);
|
|
|
|
|
if (k_check) {
|
|
|
|
|
if (cmp(b,S) < 0) {
|
|
|
|
|
k--;
|
|
|
|
|
b = multadd(b, 10, 0); /* we botched the k estimate */
|
|
|
|
|
if (leftright)
|
|
|
|
|
mhi = multadd(mhi, 10, 0);
|
|
|
|
|
ilim = ilim1;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
|
|
|
|
if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
|
|
|
|
|
/* no digits, fcvt style */
|
|
|
|
|
no_digits:
|
|
|
|
|
k = -1 - ndigits;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
one_digit:
|
|
|
|
|
*s++ = '1';
|
|
|
|
|
k++;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
if (leftright) {
|
|
|
|
|
if (m2 > 0)
|
|
|
|
|
mhi = lshift(mhi, m2);
|
|
|
|
|
|
|
|
|
|
/* Compute mlo -- check for special case
|
|
|
|
|
* that d is a normalized power of 2.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
mlo = mhi;
|
|
|
|
|
if (spec_case) {
|
|
|
|
|
mhi = Balloc(mhi->k);
|
|
|
|
|
Bcopy(mhi, mlo);
|
|
|
|
|
mhi = lshift(mhi, Log2P);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
for (i = 1;;i++) {
|
|
|
|
|
dig = quorem(b,S) + '0';
|
|
|
|
|
/* Do we yet have the shortest decimal string
|
|
|
|
|
* that will round to d?
|
|
|
|
|
*/
|
|
|
|
|
j = cmp(b, mlo);
|
|
|
|
|
delta = diff(S, mhi);
|
|
|
|
|
j1 = delta->sign ? 1 : cmp(b, delta);
|
|
|
|
|
Bfree(delta);
|
|
|
|
|
#ifndef ROUND_BIASED
|
|
|
|
|
if (j1 == 0 && mode != 1 && !(word1(d) & 1)
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
&& rounding >= 1
|
|
|
|
|
#endif
|
|
|
|
|
) {
|
|
|
|
|
if (dig == '9')
|
|
|
|
|
goto round_9_up;
|
|
|
|
|
if (j > 0)
|
|
|
|
|
dig++;
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
else if (!b->x[0] && b->wds <= 1)
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
*s++ = dig;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
if (j < 0 || (j == 0 && mode != 1
|
|
|
|
|
#ifndef ROUND_BIASED
|
|
|
|
|
&& !(word1(d) & 1)
|
|
|
|
|
#endif
|
|
|
|
|
)) {
|
|
|
|
|
if (!b->x[0] && b->wds <= 1) {
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
goto accept_dig;
|
|
|
|
|
}
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (mode > 1)
|
|
|
|
|
switch (rounding) {
|
|
|
|
|
case 0: goto accept_dig;
|
|
|
|
|
case 2: goto keep_dig;
|
|
|
|
|
}
|
|
|
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
|
|
|
if (j1 > 0) {
|
|
|
|
|
b = lshift(b, 1);
|
|
|
|
|
j1 = cmp(b, S);
|
|
|
|
|
if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
|
|
|
|
|
goto round_9_up;
|
|
|
|
|
}
|
|
|
|
|
accept_dig:
|
|
|
|
|
*s++ = dig;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
if (j1 > 0) {
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
if (!rounding)
|
|
|
|
|
goto accept_dig;
|
|
|
|
|
#endif
|
|
|
|
|
if (dig == '9') { /* possible if i == 1 */
|
|
|
|
|
round_9_up:
|
|
|
|
|
*s++ = '9';
|
|
|
|
|
goto roundoff;
|
|
|
|
|
}
|
|
|
|
|
*s++ = dig + 1;
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
keep_dig:
|
|
|
|
|
#endif
|
|
|
|
|
*s++ = dig;
|
|
|
|
|
if (i == ilim)
|
|
|
|
|
break;
|
|
|
|
|
b = multadd(b, 10, 0);
|
|
|
|
|
if (mlo == mhi)
|
|
|
|
|
mlo = mhi = multadd(mhi, 10, 0);
|
|
|
|
|
else {
|
|
|
|
|
mlo = multadd(mlo, 10, 0);
|
|
|
|
|
mhi = multadd(mhi, 10, 0);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
for (i = 1;; i++) {
|
|
|
|
|
*s++ = dig = quorem(b,S) + '0';
|
|
|
|
|
if (!b->x[0] && b->wds <= 1) {
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
inexact = 0;
|
|
|
|
|
#endif
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
if (i >= ilim)
|
|
|
|
|
break;
|
|
|
|
|
b = multadd(b, 10, 0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Round off last digit */
|
|
|
|
|
|
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
|
|
|
switch (rounding) {
|
|
|
|
|
case 0: goto trimzeros;
|
|
|
|
|
case 2: goto roundoff;
|
|
|
|
|
}
|
|
|
|
|
#endif
|
|
|
|
|
b = lshift(b, 1);
|
|
|
|
|
j = cmp(b, S);
|
|
|
|
|
if (j > 0 || (j == 0 && (dig & 1))) {
|
|
|
|
|
roundoff:
|
|
|
|
|
while (*--s == '9')
|
|
|
|
|
if (s == s0) {
|
|
|
|
|
k++;
|
|
|
|
|
*s++ = '1';
|
|
|
|
|
goto ret;
|
|
|
|
|
}
|
|
|
|
|
if (!half || (*s - '0') & 1)
|
|
|
|
|
++*s;
|
|
|
|
|
}
|
|
|
|
|
else {
|
|
|
|
|
while (*--s == '0') ;
|
|
|
|
|
}
|
|
|
|
|
s++;
|
|
|
|
|
ret:
|
|
|
|
|
Bfree(S);
|
|
|
|
|
if (mhi) {
|
|
|
|
|
if (mlo && mlo != mhi)
|
|
|
|
|
Bfree(mlo);
|
|
|
|
|
Bfree(mhi);
|
|
|
|
|
}
|
|
|
|
|
ret1:
|
|
|
|
|
#ifdef SET_INEXACT
|
|
|
|
|
if (inexact) {
|
|
|
|
|
if (!oldinexact) {
|
|
|
|
|
word0(d) = Exp_1 + (70 << Exp_shift);
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|
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|
word1(d) = 0;
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|
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|
dval(d) += 1.;
|
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|
}
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}
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else if (!oldinexact)
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|
clear_inexact();
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#endif
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|
|
Bfree(b);
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|
*s = 0;
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|
*decpt = k + 1;
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if (rve)
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|
*rve = s;
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|
return s0;
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}
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/*-
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* Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
|
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|
* 1. Redistributions of source code must retain the above copyright
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|
|
* notice, this list of conditions and the following disclaimer.
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|
* 2. Redistributions in binary form must reproduce the above copyright
|
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|
|
* notice, this list of conditions and the following disclaimer in the
|
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|
|
* documentation and/or other materials provided with the distribution.
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*
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|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
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|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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|
* SUCH DAMAGE.
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*/
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#define DBL_MANH_SIZE 20
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#define DBL_MANL_SIZE 32
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#define DBL_ADJ (DBL_MAX_EXP - 2)
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#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
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#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
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#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
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|
|
#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
|
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|
|
#define dmanl_get(u) ((uint32_t)word1(u))
|
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|
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|
|
/*
|
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|
|
* This procedure converts a double-precision number in IEEE format
|
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|
|
* into a string of hexadecimal digits and an exponent of 2. Its
|
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|
|
|
* behavior is bug-for-bug compatible with dtoa() in mode 2, with the
|
|
|
|
|
* following exceptions:
|
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|
|
|
*
|
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|
|
|
* - An ndigits < 0 causes it to use as many digits as necessary to
|
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|
|
* represent the number exactly.
|
|
|
|
|
* - The additional xdigs argument should point to either the string
|
|
|
|
|
* "0123456789ABCDEF" or the string "0123456789abcdef", depending on
|
|
|
|
|
* which case is desired.
|
|
|
|
|
* - This routine does not repeat dtoa's mistake of setting decpt
|
|
|
|
|
* to 9999 in the case of an infinity or NaN. INT_MAX is used
|
|
|
|
|
* for this purpose instead.
|
|
|
|
|
*
|
|
|
|
|
* Note that the C99 standard does not specify what the leading digit
|
|
|
|
|
* should be for non-zero numbers. For instance, 0x1.3p3 is the same
|
|
|
|
|
* as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
|
|
|
|
|
* the leading digit a 1. This ensures that the exponent printed is the
|
|
|
|
|
* actual base-2 exponent, i.e., ilogb(d).
|
|
|
|
|
*
|
|
|
|
|
* Inputs: d, xdigs, ndigits
|
|
|
|
|
* Outputs: decpt, sign, rve
|
|
|
|
|
*/
|
|
|
|
|
char *
|
|
|
|
|
hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
|
|
|
|
|
{
|
|
|
|
|
U u;
|
|
|
|
|
char *s, *s0;
|
|
|
|
|
int bufsize;
|
|
|
|
|
uint32_t manh, manl;
|
|
|
|
|
|
|
|
|
|
u.d = d;
|
|
|
|
|
if (word0(u) & Sign_bit) {
|
|
|
|
|
/* set sign for everything, including 0's and NaNs */
|
|
|
|
|
*sign = 1;
|
|
|
|
|
word0(u) &= ~Sign_bit; /* clear sign bit */
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
*sign = 0;
|
|
|
|
|
|
|
|
|
|
if (isinf(d)) { /* FP_INFINITE */
|
|
|
|
|
*decpt = INT_MAX;
|
|
|
|
|
return rv_strdup(INFSTR, rve);
|
|
|
|
|
}
|
|
|
|
|
else if (isnan(d)) { /* FP_NAN */
|
|
|
|
|
*decpt = INT_MAX;
|
|
|
|
|
return rv_strdup(NANSTR, rve);
|
|
|
|
|
}
|
|
|
|
|
else if (d == 0.0) { /* FP_ZERO */
|
|
|
|
|
*decpt = 1;
|
|
|
|
|
return rv_strdup(ZEROSTR, rve);
|
|
|
|
|
}
|
|
|
|
|
else if (dexp_get(u)) { /* FP_NORMAL */
|
|
|
|
|
*decpt = dexp_get(u) - DBL_ADJ;
|
|
|
|
|
}
|
|
|
|
|
else { /* FP_SUBNORMAL */
|
|
|
|
|
u.d *= 5.363123171977039e+154 /* 0x1p514 */;
|
|
|
|
|
*decpt = dexp_get(u) - (514 + DBL_ADJ);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (ndigits == 0) /* dtoa() compatibility */
|
|
|
|
|
ndigits = 1;
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* If ndigits < 0, we are expected to auto-size, so we allocate
|
|
|
|
|
* enough space for all the digits.
|
|
|
|
|
*/
|
|
|
|
|
bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
|
|
|
|
|
s0 = rv_alloc(bufsize+1);
|
|
|
|
|
|
|
|
|
|
/* Round to the desired number of digits. */
|
|
|
|
|
if (SIGFIGS > ndigits && ndigits > 0) {
|
|
|
|
|
float redux = 1.0f;
|
|
|
|
|
int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
|
|
|
|
|
dexp_set(u, offset);
|
|
|
|
|
u.d += redux;
|
|
|
|
|
u.d -= redux;
|
|
|
|
|
*decpt += dexp_get(u) - offset;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
manh = dmanh_get(u);
|
|
|
|
|
manl = dmanl_get(u);
|
|
|
|
|
*s0 = '1';
|
|
|
|
|
for (s = s0 + 1; s < s0 + bufsize; s++) {
|
|
|
|
|
*s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
|
|
|
|
|
manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
|
|
|
|
|
manl <<= 4;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* If ndigits < 0, we are expected to auto-size the precision. */
|
|
|
|
|
if (ndigits < 0) {
|
|
|
|
|
for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
|
|
|
|
|
;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
s = s0 + ndigits;
|
|
|
|
|
*s = '\0';
|
|
|
|
|
if (rve != NULL)
|
|
|
|
|
*rve = s;
|
|
|
|
|
return (s0);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#ifdef __cplusplus
|
|
|
|
|
#if 0
|
|
|
|
|
{ /* satisfy cc-mode */
|
|
|
|
|
#endif
|
|
|
|
|
}
|
|
|
|
|
#endif
|
