| Index: base/third_party/dmg_fp/dtoa.cc
|
| diff --git a/base/third_party/dmg_fp/dtoa.cc b/base/third_party/dmg_fp/dtoa.cc
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..4f9f4fe2b89fc97cf0cfffd1575a9e0c3d89bdae
|
| --- /dev/null
|
| +++ b/base/third_party/dmg_fp/dtoa.cc
|
| @@ -0,0 +1,3356 @@
|
| +/****************************************************************
|
| + *
|
| + * The author of this software is David M. Gay.
|
| + *
|
| + * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
|
| + *
|
| + * Permission to use, copy, modify, and distribute this software for any
|
| + * purpose without fee is hereby granted, provided that this entire notice
|
| + * is included in all copies of any software which is or includes a copy
|
| + * or modification of this software and in all copies of the supporting
|
| + * documentation for such software.
|
| + *
|
| + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
|
| + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
|
| + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
|
| + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
|
| + *
|
| + ***************************************************************/
|
| +
|
| +/* Please send bug reports to David M. Gay (dmg at acm dot org,
|
| + * with " at " changed at "@" and " dot " changed to "."). */
|
| +
|
| +/* On a machine with IEEE extended-precision registers, it is
|
| + * necessary to specify double-precision (53-bit) rounding precision
|
| + * before invoking strtod or dtoa. If the machine uses (the equivalent
|
| + * of) Intel 80x87 arithmetic, the call
|
| + * _control87(PC_53, MCW_PC);
|
| + * does this with many compilers. Whether this or another call is
|
| + * appropriate depends on the compiler; for this to work, it may be
|
| + * necessary to #include "float.h" or another system-dependent header
|
| + * file.
|
| + */
|
| +
|
| +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
|
| + *
|
| + * This strtod returns a nearest machine number to the input decimal
|
| + * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
|
| + * broken by the IEEE round-even rule. Otherwise ties are broken by
|
| + * biased rounding (add half and chop).
|
| + *
|
| + * Inspired loosely by William D. Clinger's paper "How to Read Floating
|
| + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
|
| + *
|
| + * Modifications:
|
| + *
|
| + * 1. We only require IEEE, IBM, or VAX double-precision
|
| + * arithmetic (not IEEE double-extended).
|
| + * 2. We get by with floating-point arithmetic in a case that
|
| + * Clinger missed -- when we're computing d * 10^n
|
| + * for a small integer d and the integer n is not too
|
| + * much larger than 22 (the maximum integer k for which
|
| + * we can represent 10^k exactly), we may be able to
|
| + * compute (d*10^k) * 10^(e-k) with just one roundoff.
|
| + * 3. Rather than a bit-at-a-time adjustment of the binary
|
| + * result in the hard case, we use floating-point
|
| + * arithmetic to determine the adjustment to within
|
| + * one bit; only in really hard cases do we need to
|
| + * compute a second residual.
|
| + * 4. Because of 3., we don't need a large table of powers of 10
|
| + * for ten-to-e (just some small tables, e.g. of 10^k
|
| + * for 0 <= k <= 22).
|
| + */
|
| +
|
| +/*
|
| + * #define IEEE_8087 for IEEE-arithmetic machines where the least
|
| + * significant byte has the lowest address.
|
| + * #define IEEE_MC68k for IEEE-arithmetic machines where the most
|
| + * significant byte has the lowest address.
|
| + * #define Long int on machines with 32-bit ints and 64-bit longs.
|
| + * #define IBM for IBM mainframe-style floating-point arithmetic.
|
| + * #define VAX for VAX-style floating-point arithmetic (D_floating).
|
| + * #define No_leftright to omit left-right logic in fast floating-point
|
| + * computation of dtoa.
|
| + * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
|
| + * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS
|
| + * is also #defined, fegetround() will be queried for the rounding mode.
|
| + * Note that both FLT_ROUNDS and fegetround() are specified by the C99
|
| + * standard (and are specified to be consistent, with fesetround()
|
| + * affecting the value of FLT_ROUNDS), but that some (Linux) systems
|
| + * do not work correctly in this regard, so using fegetround() is more
|
| + * portable than using FLT_FOUNDS directly.
|
| + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
|
| + * and Honor_FLT_ROUNDS is not #defined.
|
| + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
|
| + * that use extended-precision instructions to compute rounded
|
| + * products and quotients) with IBM.
|
| + * #define ROUND_BIASED for IEEE-format with biased rounding.
|
| + * #define Inaccurate_Divide for IEEE-format with correctly rounded
|
| + * products but inaccurate quotients, e.g., for Intel i860.
|
| + * #define NO_LONG_LONG on machines that do not have a "long long"
|
| + * integer type (of >= 64 bits). On such machines, you can
|
| + * #define Just_16 to store 16 bits per 32-bit Long when doing
|
| + * high-precision integer arithmetic. Whether this speeds things
|
| + * up or slows things down depends on the machine and the number
|
| + * being converted. If long long is available and the name is
|
| + * something other than "long long", #define Llong to be the name,
|
| + * and if "unsigned Llong" does not work as an unsigned version of
|
| + * Llong, #define #ULLong to be the corresponding unsigned type.
|
| + * #define KR_headers for old-style C function headers.
|
| + * #define Bad_float_h if your system lacks a float.h or if it does not
|
| + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
|
| + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
|
| + * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
|
| + * if memory is available and otherwise does something you deem
|
| + * appropriate. If MALLOC is undefined, malloc will be invoked
|
| + * directly -- and assumed always to succeed.
|
| + * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
|
| + * memory allocations from a private pool of memory when possible.
|
| + * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
|
| + * unless #defined to be a different length. This default length
|
| + * suffices to get rid of MALLOC calls except for unusual cases,
|
| + * such as decimal-to-binary conversion of a very long string of
|
| + * digits. The longest string dtoa can return is about 751 bytes
|
| + * long. For conversions by strtod of strings of 800 digits and
|
| + * all dtoa conversions in single-threaded executions with 8-byte
|
| + * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
|
| + * pointers, PRIVATE_MEM >= 7112 appears adequate.
|
| + * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
|
| + * #defined automatically on IEEE systems. On such systems,
|
| + * when INFNAN_CHECK is #defined, strtod checks
|
| + * for Infinity and NaN (case insensitively). On some systems
|
| + * (e.g., some HP systems), it may be necessary to #define NAN_WORD0
|
| + * appropriately -- to the most significant word of a quiet NaN.
|
| + * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
|
| + * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
|
| + * strtod also accepts (case insensitively) strings of the form
|
| + * NaN(x), where x is a string of hexadecimal digits and spaces;
|
| + * if there is only one string of hexadecimal digits, it is taken
|
| + * for the 52 fraction bits of the resulting NaN; if there are two
|
| + * or more strings of hex digits, the first is for the high 20 bits,
|
| + * the second and subsequent for the low 32 bits, with intervening
|
| + * white space ignored; but if this results in none of the 52
|
| + * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
|
| + * and NAN_WORD1 are used instead.
|
| + * #define MULTIPLE_THREADS if the system offers preemptively scheduled
|
| + * multiple threads. In this case, you must provide (or suitably
|
| + * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
|
| + * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
|
| + * in pow5mult, ensures lazy evaluation of only one copy of high
|
| + * powers of 5; omitting this lock would introduce a small
|
| + * probability of wasting memory, but would otherwise be harmless.)
|
| + * You must also invoke freedtoa(s) to free the value s returned by
|
| + * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
|
| + * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
|
| + * avoids underflows on inputs whose result does not underflow.
|
| + * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
|
| + * floating-point numbers and flushes underflows to zero rather
|
| + * than implementing gradual underflow, then you must also #define
|
| + * Sudden_Underflow.
|
| + * #define YES_ALIAS to permit aliasing certain double values with
|
| + * arrays of ULongs. This leads to slightly better code with
|
| + * some compilers and was always used prior to 19990916, but it
|
| + * is not strictly legal and can cause trouble with aggressively
|
| + * optimizing compilers (e.g., gcc 2.95.1 under -O2).
|
| + * #define USE_LOCALE to use the current locale's decimal_point value.
|
| + * #define SET_INEXACT if IEEE arithmetic is being used and extra
|
| + * computation should be done to set the inexact flag when the
|
| + * result is inexact and avoid setting inexact when the result
|
| + * is exact. In this case, dtoa.c must be compiled in
|
| + * an environment, perhaps provided by #include "dtoa.c" in a
|
| + * suitable wrapper, that defines two functions,
|
| + * int get_inexact(void);
|
| + * void clear_inexact(void);
|
| + * such that get_inexact() returns a nonzero value if the
|
| + * inexact bit is already set, and clear_inexact() sets the
|
| + * inexact bit to 0. When SET_INEXACT is #defined, strtod
|
| + * also does extra computations to set the underflow and overflow
|
| + * flags when appropriate (i.e., when the result is tiny and
|
| + * inexact or when it is a numeric value rounded to +-infinity).
|
| + * #define NO_ERRNO if strtod should not assign errno = ERANGE when
|
| + * the result overflows to +-Infinity or underflows to 0.
|
| + */
|
| +
|
| +#define IEEE_8087
|
| +
|
| +#ifndef Long
|
| +#define Long long
|
| +#endif
|
| +#ifndef ULong
|
| +typedef unsigned Long ULong;
|
| +#endif
|
| +
|
| +#ifdef DEBUG
|
| +#include "stdio.h"
|
| +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
|
| +#endif
|
| +
|
| +#include "stdlib.h"
|
| +#include "string.h"
|
| +
|
| +#ifdef USE_LOCALE
|
| +#include "locale.h"
|
| +#endif
|
| +
|
| +#ifdef MALLOC
|
| +#ifdef KR_headers
|
| +extern char *MALLOC();
|
| +#else
|
| +extern void *MALLOC(size_t);
|
| +#endif
|
| +#else
|
| +#define MALLOC malloc
|
| +#endif
|
| +
|
| +#ifndef Omit_Private_Memory
|
| +#ifndef PRIVATE_MEM
|
| +#define PRIVATE_MEM 2304
|
| +#endif
|
| +#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
|
| +static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
|
| +#endif
|
| +
|
| +#undef IEEE_Arith
|
| +#undef Avoid_Underflow
|
| +#ifdef IEEE_MC68k
|
| +#define IEEE_Arith
|
| +#endif
|
| +#ifdef IEEE_8087
|
| +#define IEEE_Arith
|
| +#endif
|
| +
|
| +#ifdef IEEE_Arith
|
| +#ifndef NO_INFNAN_CHECK
|
| +#undef INFNAN_CHECK
|
| +#define INFNAN_CHECK
|
| +#endif
|
| +#else
|
| +#undef INFNAN_CHECK
|
| +#endif
|
| +
|
| +#include "errno.h"
|
| +
|
| +#ifdef Bad_float_h
|
| +
|
| +#ifdef IEEE_Arith
|
| +#define DBL_DIG 15
|
| +#define DBL_MAX_10_EXP 308
|
| +#define DBL_MAX_EXP 1024
|
| +#define FLT_RADIX 2
|
| +#endif /*IEEE_Arith*/
|
| +
|
| +#ifdef IBM
|
| +#define DBL_DIG 16
|
| +#define DBL_MAX_10_EXP 75
|
| +#define DBL_MAX_EXP 63
|
| +#define FLT_RADIX 16
|
| +#define DBL_MAX 7.2370055773322621e+75
|
| +#endif
|
| +
|
| +#ifdef VAX
|
| +#define DBL_DIG 16
|
| +#define DBL_MAX_10_EXP 38
|
| +#define DBL_MAX_EXP 127
|
| +#define FLT_RADIX 2
|
| +#define DBL_MAX 1.7014118346046923e+38
|
| +#endif
|
| +
|
| +#ifndef LONG_MAX
|
| +#define LONG_MAX 2147483647
|
| +#endif
|
| +
|
| +#else /* ifndef Bad_float_h */
|
| +#include "float.h"
|
| +#endif /* Bad_float_h */
|
| +
|
| +#ifndef __MATH_H__
|
| +#include "math.h"
|
| +#endif
|
| +
|
| +namespace dmg_fp {
|
| +
|
| +#ifndef CONST
|
| +#ifdef KR_headers
|
| +#define CONST /* blank */
|
| +#else
|
| +#define CONST const
|
| +#endif
|
| +#endif
|
| +
|
| +#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
|
| +Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
|
| +#endif
|
| +
|
| +typedef union { double d; ULong L[2]; } U;
|
| +
|
| +#ifdef YES_ALIAS
|
| +#define dval(x) x
|
| +#ifdef IEEE_8087
|
| +#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
|
| +#ifdef IEEE_8087
|
| +#define word0(x) ((U*)&x)->L[1]
|
| +#define word1(x) ((U*)&x)->L[0]
|
| +#else
|
| +#define word0(x) ((U*)&x)->L[0]
|
| +#define word1(x) ((U*)&x)->L[1]
|
| +#endif
|
| +#define dval(x) ((U*)&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_8087) + defined(VAX)
|
| +#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
|
| +#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)
|
| +#ifdef KR_headers
|
| +extern double rnd_prod(), rnd_quot();
|
| +#else
|
| +extern double rnd_prod(double, double), rnd_quot(double, double);
|
| +#endif
|
| +#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
|
| +
|
| +#ifdef KR_headers
|
| +#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
|
| +#else
|
| +#define FFFFFFFF 0xffffffffUL
|
| +#endif
|
| +
|
| +#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 */
|
| +
|
| +#ifndef MULTIPLE_THREADS
|
| +#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
|
| +#define FREE_DTOA_LOCK(n) /*nothing*/
|
| +#endif
|
| +
|
| +#define Kmax 15
|
| +
|
| +double strtod(const char *s00, char **se);
|
| +char *dtoa(double d, int mode, int ndigits,
|
| + int *decpt, int *sign, char **rve);
|
| +
|
| + struct
|
| +Bigint {
|
| + struct Bigint *next;
|
| + int k, maxwds, sign, wds;
|
| + ULong x[1];
|
| + };
|
| +
|
| + typedef struct Bigint Bigint;
|
| +
|
| + static Bigint *freelist[Kmax+1];
|
| +
|
| + static Bigint *
|
| +Balloc
|
| +#ifdef KR_headers
|
| + (k) int k;
|
| +#else
|
| + (int k)
|
| +#endif
|
| +{
|
| + int x;
|
| + Bigint *rv;
|
| +#ifndef Omit_Private_Memory
|
| + unsigned int len;
|
| +#endif
|
| +
|
| + ACQUIRE_DTOA_LOCK(0);
|
| + if (rv = freelist[k]) {
|
| + freelist[k] = rv->next;
|
| + }
|
| + else {
|
| + 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);
|
| + if (pmem_next - private_mem + len <= PRIVATE_mem) {
|
| + rv = (Bigint*)pmem_next;
|
| + pmem_next += len;
|
| + }
|
| + else
|
| + 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
|
| +#ifdef KR_headers
|
| + (v) Bigint *v;
|
| +#else
|
| + (Bigint *v)
|
| +#endif
|
| +{
|
| + if (v) {
|
| + ACQUIRE_DTOA_LOCK(0);
|
| + v->next = freelist[v->k];
|
| + freelist[v->k] = v;
|
| + FREE_DTOA_LOCK(0);
|
| + }
|
| + }
|
| +
|
| +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
|
| +y->wds*sizeof(Long) + 2*sizeof(int))
|
| +
|
| + static Bigint *
|
| +multadd
|
| +#ifdef KR_headers
|
| + (b, m, a) Bigint *b; int m, a;
|
| +#else
|
| + (Bigint *b, int m, int a) /* multiply by m and add a */
|
| +#endif
|
| +{
|
| + int i, wds;
|
| +#ifdef ULLong
|
| + ULong *x;
|
| + ULLong carry, y;
|
| +#else
|
| + ULong carry, *x, y;
|
| +#ifdef Pack_32
|
| + ULong xi, z;
|
| +#endif
|
| +#endif
|
| + Bigint *b1;
|
| +
|
| + wds = b->wds;
|
| + x = b->x;
|
| + i = 0;
|
| + carry = a;
|
| + do {
|
| +#ifdef ULLong
|
| + y = *x * (ULLong)m + carry;
|
| + carry = y >> 32;
|
| + *x++ = y & FFFFFFFF;
|
| +#else
|
| +#ifdef Pack_32
|
| + xi = *x;
|
| + y = (xi & 0xffff) * m + carry;
|
| + z = (xi >> 16) * m + (y >> 16);
|
| + carry = z >> 16;
|
| + *x++ = (z << 16) + (y & 0xffff);
|
| +#else
|
| + y = *x * m + carry;
|
| + carry = y >> 16;
|
| + *x++ = y & 0xffff;
|
| +#endif
|
| +#endif
|
| + }
|
| + while(++i < wds);
|
| + if (carry) {
|
| + if (wds >= b->maxwds) {
|
| + b1 = Balloc(b->k+1);
|
| + Bcopy(b1, b);
|
| + Bfree(b);
|
| + b = b1;
|
| + }
|
| + b->x[wds++] = carry;
|
| + b->wds = wds;
|
| + }
|
| + return b;
|
| + }
|
| +
|
| + static Bigint *
|
| +s2b
|
| +#ifdef KR_headers
|
| + (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
|
| +#else
|
| + (CONST char *s, int nd0, int nd, ULong y9)
|
| +#endif
|
| +{
|
| + Bigint *b;
|
| + int i, k;
|
| + Long x, y;
|
| +
|
| + x = (nd + 8) / 9;
|
| + for(k = 0, y = 1; x > y; y <<= 1, k++) ;
|
| +#ifdef Pack_32
|
| + b = Balloc(k);
|
| + b->x[0] = y9;
|
| + b->wds = 1;
|
| +#else
|
| + b = Balloc(k+1);
|
| + b->x[0] = y9 & 0xffff;
|
| + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
|
| +#endif
|
| +
|
| + i = 9;
|
| + if (9 < nd0) {
|
| + s += 9;
|
| + do b = multadd(b, 10, *s++ - '0');
|
| + while(++i < nd0);
|
| + s++;
|
| + }
|
| + else
|
| + s += 10;
|
| + for(; i < nd; i++)
|
| + b = multadd(b, 10, *s++ - '0');
|
| + return b;
|
| + }
|
| +
|
| + static int
|
| +hi0bits
|
| +#ifdef KR_headers
|
| + (x) register ULong x;
|
| +#else
|
| + (register ULong x)
|
| +#endif
|
| +{
|
| + register int k = 0;
|
| +
|
| + if (!(x & 0xffff0000)) {
|
| + k = 16;
|
| + x <<= 16;
|
| + }
|
| + if (!(x & 0xff000000)) {
|
| + k += 8;
|
| + x <<= 8;
|
| + }
|
| + 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
|
| +#ifdef KR_headers
|
| + (y) ULong *y;
|
| +#else
|
| + (ULong *y)
|
| +#endif
|
| +{
|
| + 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
|
| +#ifdef KR_headers
|
| + (i) int i;
|
| +#else
|
| + (int i)
|
| +#endif
|
| +{
|
| + Bigint *b;
|
| +
|
| + b = Balloc(1);
|
| + b->x[0] = i;
|
| + b->wds = 1;
|
| + return b;
|
| + }
|
| +
|
| + static Bigint *
|
| +mult
|
| +#ifdef KR_headers
|
| + (a, b) Bigint *a, *b;
|
| +#else
|
| + (Bigint *a, Bigint *b)
|
| +#endif
|
| +{
|
| + 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++) {
|
| + x = xa;
|
| + xc = xc0;
|
| + carry = 0;
|
| + do {
|
| + z = *x++ * (ULLong)y + *xc + carry;
|
| + carry = z >> 32;
|
| + *xc++ = z & FFFFFFFF;
|
| + }
|
| + while(x < xae);
|
| + *xc = carry;
|
| + }
|
| + }
|
| +#else
|
| +#ifdef Pack_32
|
| + for(; xb < xbe; xb++, xc0++) {
|
| + if (y = *xb & 0xffff) {
|
| + 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 = carry;
|
| + }
|
| + if (y = *xb >> 16) {
|
| + 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 = 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
|
| +#ifdef KR_headers
|
| + (b, k) Bigint *b; int k;
|
| +#else
|
| + (Bigint *b, int k)
|
| +#endif
|
| +{
|
| + Bigint *b1, *p5, *p51;
|
| + int i;
|
| + static int p05[3] = { 5, 25, 125 };
|
| +
|
| + if (i = k & 3)
|
| + b = multadd(b, p05[i-1], 0);
|
| +
|
| + if (!(k >>= 2))
|
| + return b;
|
| + if (!(p5 = p5s)) {
|
| + /* first time */
|
| +#ifdef MULTIPLE_THREADS
|
| + ACQUIRE_DTOA_LOCK(1);
|
| + if (!(p5 = p5s)) {
|
| + p5 = p5s = i2b(625);
|
| + p5->next = 0;
|
| + }
|
| + FREE_DTOA_LOCK(1);
|
| +#else
|
| + p5 = p5s = i2b(625);
|
| + p5->next = 0;
|
| +#endif
|
| + }
|
| + for(;;) {
|
| + if (k & 1) {
|
| + b1 = mult(b, p5);
|
| + Bfree(b);
|
| + b = b1;
|
| + }
|
| + if (!(k >>= 1))
|
| + break;
|
| + if (!(p51 = p5->next)) {
|
| +#ifdef MULTIPLE_THREADS
|
| + ACQUIRE_DTOA_LOCK(1);
|
| + if (!(p51 = p5->next)) {
|
| + p51 = p5->next = mult(p5,p5);
|
| + p51->next = 0;
|
| + }
|
| + FREE_DTOA_LOCK(1);
|
| +#else
|
| + p51 = p5->next = mult(p5,p5);
|
| + p51->next = 0;
|
| +#endif
|
| + }
|
| + p5 = p51;
|
| + }
|
| + return b;
|
| + }
|
| +
|
| + static Bigint *
|
| +lshift
|
| +#ifdef KR_headers
|
| + (b, k) Bigint *b; int k;
|
| +#else
|
| + (Bigint *b, int k)
|
| +#endif
|
| +{
|
| + 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)
|
| + ++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
|
| +#ifdef KR_headers
|
| + (a, b) Bigint *a, *b;
|
| +#else
|
| + (Bigint *a, Bigint *b)
|
| +#endif
|
| +{
|
| + 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;
|
| + }
|
| +
|
| + static Bigint *
|
| +diff
|
| +#ifdef KR_headers
|
| + (a, b) Bigint *a, *b;
|
| +#else
|
| + (Bigint *a, Bigint *b)
|
| +#endif
|
| +{
|
| + 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++ = y & FFFFFFFF;
|
| + }
|
| + while(xb < xbe);
|
| + while(xa < xae) {
|
| + y = *xa++ - borrow;
|
| + borrow = y >> 32 & (ULong)1;
|
| + *xc++ = 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
|
| +#ifdef KR_headers
|
| + (x) double x;
|
| +#else
|
| + (double x)
|
| +#endif
|
| +{
|
| + register Long L;
|
| + double a;
|
| +
|
| + 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
|
| +#ifdef KR_headers
|
| + (a, e) Bigint *a; int *e;
|
| +#else
|
| + (Bigint *a, int *e)
|
| +#endif
|
| +{
|
| + ULong *xa, *xa0, w, y, z;
|
| + int k;
|
| + double 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
|
| +#ifdef KR_headers
|
| + (d, e, bits) double d; int *e, *bits;
|
| +#else
|
| + (double d, int *e, int *bits)
|
| +#endif
|
| +{
|
| + Bigint *b;
|
| + int de, k;
|
| + ULong *x, y, z;
|
| +#ifndef Sudden_Underflow
|
| + int i;
|
| +#endif
|
| +#ifdef VAX
|
| + ULong d0, d1;
|
| + 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))
|
| + z |= Exp_msk1;
|
| +#endif
|
| +#ifdef Pack_32
|
| + if (y = d1) {
|
| + if (k = lo0bits(&y)) {
|
| + 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
|
| +#ifdef KR_headers
|
| + (a, b) Bigint *a, *b;
|
| +#else
|
| + (Bigint *a, Bigint *b)
|
| +#endif
|
| +{
|
| + double 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-256 */
|
| +#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
|
| +
|
| +#ifdef INFNAN_CHECK
|
| +
|
| +#ifndef NAN_WORD0
|
| +#define NAN_WORD0 0x7ff80000
|
| +#endif
|
| +
|
| +#ifndef NAN_WORD1
|
| +#define NAN_WORD1 0
|
| +#endif
|
| +
|
| + static int
|
| +match
|
| +#ifdef KR_headers
|
| + (sp, t) char **sp, *t;
|
| +#else
|
| + (CONST char **sp, char *t)
|
| +#endif
|
| +{
|
| + 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
|
| +#ifdef KR_headers
|
| + (rvp, sp) double *rvp; CONST char **sp;
|
| +#else
|
| + (double *rvp, CONST char **sp)
|
| +#endif
|
| +{
|
| + ULong c, x[2];
|
| + CONST char *s;
|
| + int havedig, udx0, xshift;
|
| +
|
| + x[0] = x[1] = 0;
|
| + havedig = xshift = 0;
|
| + udx0 = 1;
|
| + s = *sp;
|
| + /* allow optional initial 0x or 0X */
|
| + while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
|
| + ++s;
|
| + if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
|
| + s += 2;
|
| + 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;
|
| + }
|
| +#ifdef GDTOA_NON_PEDANTIC_NANCHECK
|
| + else if (/*(*/ c == ')' && havedig) {
|
| + *sp = s + 1;
|
| + break;
|
| + }
|
| + else
|
| + return; /* invalid form: don't change *sp */
|
| +#else
|
| + else {
|
| + do {
|
| + if (/*(*/ c == ')') {
|
| + *sp = s + 1;
|
| + break;
|
| + }
|
| + } while(c = *++s);
|
| + break;
|
| + }
|
| +#endif
|
| + 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 */
|
| +
|
| + double
|
| +strtod
|
| +#ifdef KR_headers
|
| + (s00, se) CONST char *s00; char **se;
|
| +#else
|
| + (CONST char *s00, char **se)
|
| +#endif
|
| +{
|
| +#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, aadj1, adj, 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;
|
| +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
|
| + Rounding = Flt_Rounds;
|
| +#else /*}{*/
|
| + Rounding = 1;
|
| + switch(fegetround()) {
|
| + case FE_TOWARDZERO: Rounding = 0; break;
|
| + case FE_UPWARD: Rounding = 2; break;
|
| + case FE_DOWNWARD: Rounding = 3;
|
| + }
|
| +#endif /*}}*/
|
| +#endif /*}*/
|
| +#ifdef USE_LOCALE
|
| + CONST char *s2;
|
| +#endif
|
| +
|
| + 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') {
|
| + 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 < 16)
|
| + 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 == '.') {
|
| + 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 (c -= '0') {
|
| + nf += nz;
|
| + for(i = 1; i < nz; i++)
|
| + if (nd++ < 9)
|
| + y *= 10;
|
| + else if (nd <= DBL_DIG + 1)
|
| + z *= 10;
|
| + if (nd++ < 9)
|
| + y = 10*y + c;
|
| + else if (nd <= DBL_DIG + 1)
|
| + 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 + 1 ? nd : DBL_DIG + 1;
|
| + 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 = 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) {
|
| + rv = -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) {
|
| + rv = -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) {
|
| + rv = -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 >= 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)
|
| + 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)
|
| + 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; clear 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) {
|
| + if (word0(rv) == Big0 && word1(rv) == Big1)
|
| + goto ovfl;
|
| + 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 = aadj1 = 1.;
|
| + else if (word1(rv) || word0(rv) & Bndry_mask) {
|
| +#ifndef Sudden_Underflow
|
| + if (word1(rv) == Tiny1 && !word0(rv))
|
| + goto undfl;
|
| +#endif
|
| + aadj = 1.;
|
| + 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;
|
| + aadj1 = -aadj;
|
| + }
|
| + }
|
| + else {
|
| + aadj *= 0.5;
|
| + aadj1 = dsign ? aadj : -aadj;
|
| +#ifdef Check_FLT_ROUNDS
|
| + switch(Rounding) {
|
| + case 2: /* towards +infinity */
|
| + aadj1 -= 0.5;
|
| + break;
|
| + case 0: /* towards 0 */
|
| + case 3: /* towards -infinity */
|
| + aadj1 += 0.5;
|
| + }
|
| +#else
|
| + if (Flt_Rounds == 0)
|
| + 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 = 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 = aadj) <= 0)
|
| + z = 1;
|
| + aadj = z;
|
| + aadj1 = dsign ? aadj : -aadj;
|
| + }
|
| + word0(aadj1) += (2*P+1)*Exp_msk1 - y;
|
| + }
|
| + adj = 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 = 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 = 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.) {
|
| + aadj1 = (double)(int)(aadj + 0.5);
|
| + if (!dsign)
|
| + aadj1 = -aadj1;
|
| + }
|
| + adj = 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 */
|
| +#ifdef IEEE_Arith
|
| + if (!(word0(rv) & Exp_mask))
|
| +#else
|
| + if (word0(rv) == 0 && word1(rv) == 0)
|
| +#endif
|
| + 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);
|
| + }
|
| +
|
| + static int
|
| +quorem
|
| +#ifdef KR_headers
|
| + (b, S) Bigint *b, *S;
|
| +#else
|
| + (Bigint *b, Bigint *S)
|
| +#endif
|
| +{
|
| + 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++ = 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++ = 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
|
| +
|
| + static char *
|
| +#ifdef KR_headers
|
| +rv_alloc(i) int i;
|
| +#else
|
| +rv_alloc(int i)
|
| +#endif
|
| +{
|
| + int j, k, *r;
|
| +
|
| + j = sizeof(ULong);
|
| + for(k = 0;
|
| + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
|
| + j <<= 1)
|
| + k++;
|
| + r = (int*)Balloc(k);
|
| + *r = k;
|
| + return
|
| +#ifndef MULTIPLE_THREADS
|
| + dtoa_result =
|
| +#endif
|
| + (char *)(r+1);
|
| + }
|
| +
|
| + static char *
|
| +#ifdef KR_headers
|
| +nrv_alloc(s, rve, n) char *s, **rve; int n;
|
| +#else
|
| +nrv_alloc(char *s, char **rve, int n)
|
| +#endif
|
| +{
|
| + char *rv, *t;
|
| +
|
| + t = rv = rv_alloc(n);
|
| + while(*t = *s++) t++;
|
| + if (rve)
|
| + *rve = t;
|
| + return rv;
|
| + }
|
| +
|
| +/* 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.
|
| + */
|
| +
|
| + void
|
| +#ifdef KR_headers
|
| +freedtoa(s) char *s;
|
| +#else
|
| +freedtoa(char *s)
|
| +#endif
|
| +{
|
| + Bigint *b = (Bigint *)((int *)s - 1);
|
| + b->maxwds = 1 << (b->k = *(int*)b);
|
| + Bfree(b);
|
| +#ifndef MULTIPLE_THREADS
|
| + if (s == dtoa_result)
|
| + dtoa_result = 0;
|
| +#endif
|
| + }
|
| +
|
| +/* 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
|
| +#ifdef KR_headers
|
| + (d, mode, ndigits, decpt, sign, rve)
|
| + double d; int mode, ndigits, *decpt, *sign; char **rve;
|
| +#else
|
| + (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
| +#endif
|
| +{
|
| + /* 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;
|
| + Long L;
|
| +#ifndef Sudden_Underflow
|
| + int denorm;
|
| + ULong x;
|
| +#endif
|
| + Bigint *b, *b1, *delta, *mlo, *mhi, *S;
|
| + double d2, ds, eps;
|
| + char *s, *s0;
|
| +#ifdef SET_INEXACT
|
| + int inexact, oldinexact;
|
| +#endif
|
| +#ifdef Honor_FLT_ROUNDS /*{*/
|
| + int Rounding;
|
| +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
|
| + Rounding = Flt_Rounds;
|
| +#else /*}{*/
|
| + Rounding = 1;
|
| + switch(fegetround()) {
|
| + case FE_TOWARDZERO: Rounding = 0; break;
|
| + case FE_UPWARD: Rounding = 2; break;
|
| + case FE_DOWNWARD: Rounding = 3;
|
| + }
|
| +#endif /*}}*/
|
| +#endif /*}*/
|
| +
|
| +#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 nrv_alloc("Infinity", rve, 8);
|
| +#endif
|
| + return nrv_alloc("NaN", rve, 3);
|
| + }
|
| +#endif
|
| +#ifdef IBM
|
| + dval(d) += 0; /* normalize */
|
| +#endif
|
| + if (!dval(d)) {
|
| + *decpt = 1;
|
| + return nrv_alloc("0", rve, 1);
|
| + }
|
| +
|
| +#ifdef SET_INEXACT
|
| + try_quick = oldinexact = get_inexact();
|
| + inexact = 1;
|
| +#endif
|
| +#ifdef Honor_FLT_ROUNDS
|
| + if (Rounding >= 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))) {
|
| +#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;
|
| + switch(mode) {
|
| + case 0:
|
| + case 1:
|
| + ilim = ilim1 = -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);
|
| +
|
| +#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) {
|
| + 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 = 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;
|
| + }
|
| + 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;
|
| + mhi = mlo = 0;
|
| + 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)
|
| + 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)
|
| + i = 32 - i;
|
| +#else
|
| + if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
|
| + 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;
|
| + }
|
| + ++*s++;
|
| + }
|
| + else {
|
| + trimzeros:
|
| + 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);
|
| + word1(d) = 0;
|
| + dval(d) += 1.;
|
| + }
|
| + }
|
| + else if (!oldinexact)
|
| + clear_inexact();
|
| +#endif
|
| + Bfree(b);
|
| + *s = 0;
|
| + *decpt = k + 1;
|
| + if (rve)
|
| + *rve = s;
|
| + return s0;
|
| + }
|
| +
|
| +} // namespace dmg_fp
|
|
|
Chromium Code Reviews
Issue 10716:
Move dmg_fp to base/third_party/dmg_fp and include the (Closed)
