Mercurial > trustbridge > nss-cmake-static
view nspr/pr/src/misc/prdtoa.c @ 4:b513267f632f tip
Build DBM module
| author | Andre Heinecke <andre.heinecke@intevation.de> |
|---|---|
| date | Tue, 05 Aug 2014 18:58:03 +0200 |
| parents | 1e5118fa0cb1 |
| children |
line wrap: on
line source
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- */ /* This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ /* * This file is based on the third-party code dtoa.c. We minimize our * modifications to third-party code to make it easy to merge new versions. * The author of dtoa.c was not willing to add the parentheses suggested by * GCC, so we suppress these warnings. */ #if (__GNUC__ > 4) || (__GNUC__ == 4 && __GNUC_MINOR__ >= 2) #pragma GCC diagnostic ignored "-Wparentheses" #endif #include "primpl.h" #include "prbit.h" #define MULTIPLE_THREADS #define ACQUIRE_DTOA_LOCK(n) PR_Lock(dtoa_lock[n]) #define FREE_DTOA_LOCK(n) PR_Unlock(dtoa_lock[n]) static PRLock *dtoa_lock[2]; void _PR_InitDtoa(void) { dtoa_lock[0] = PR_NewLock(); dtoa_lock[1] = PR_NewLock(); } void _PR_CleanupDtoa(void) { PR_DestroyLock(dtoa_lock[0]); dtoa_lock[0] = NULL; PR_DestroyLock(dtoa_lock[1]); dtoa_lock[1] = NULL; /* FIXME: deal with freelist and p5s. */ } #if !defined(__ARM_EABI__) \ && (defined(__arm) || defined(__arm__) || defined(__arm26__) \ || defined(__arm32__)) #define IEEE_ARM #elif defined(IS_LITTLE_ENDIAN) #define IEEE_8087 #else #define IEEE_MC68k #endif #define Long PRInt32 #define ULong PRUint32 #define NO_LONG_LONG #define No_Hex_NaN /**************************************************************** * * 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 IEEE_ARM for IEEE-arithmetic machines where the two words * in a double are stored in big endian order but the two shorts * in a word are still stored in little endian order. * #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. * #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. Similarly, if you * want something other than the system's free() to be called to * recycle memory acquired from MALLOC, #define FREE to be the * name of the alternate routine. (FREE or free is only called in * pathological cases, e.g., in a dtoa call after a dtoa return in * mode 3 with thousands of digits requested.) * #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 INFNAN_CHECK on IEEE systems to cause strtod to check 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 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. */ #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_ARM #define IEEE_Arith #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" /* * MacOS 10.2 defines the macro FLT_ROUNDS to an internal function * which does not exist on 10.1. We can safely #define it to 1 here * to allow 10.2 builds to run on 10.1, since we can't use fesetround() * (which does not exist on 10.1 either). */ #if defined(XP_MACOSX) && (!defined(MAC_OS_X_VERSION_10_2) || \ MAC_OS_X_VERSION_MIN_REQUIRED < MAC_OS_X_VERSION_10_2) #undef FLT_ROUNDS #define FLT_ROUNDS 1 #endif /* DT < 10.2 */ #endif /* Bad_float_h */ #ifndef __MATH_H__ #include "math.h" #endif #ifdef __cplusplus extern "C" { #endif #ifndef CONST #ifdef KR_headers #define CONST /* blank */ #else #define CONST const #endif #endif #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) + defined(VAX) + defined(IBM) != 1 Exactly one of IEEE_8087, IEEE_MC68k, IEEE_ARM, VAX, or IBM should be defined. #endif typedef union { double d; ULong L[2]; } U; #define dval(x) (x).d #ifdef IEEE_8087 #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 /* 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(IEEE_ARM) + 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 #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) #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 7 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); /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ /* but this case seems very unlikely. */ if (k <= Kmax && (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 (k <= Kmax && 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) { if (v->k > Kmax) #ifdef FREE FREE((void*)v); #else free((void*)v); #endif else { 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 { #ifdef PR_HAVE_BUILTIN_BITSCAN32 return( (!x) ? 32 : pr_bitscan_clz32(x) ); #else 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; #endif /* PR_HAVE_BUILTIN_BITSCAN32 */ } static int lo0bits #ifdef KR_headers (y) ULong *y; #else (ULong *y) #endif { #ifdef PR_HAVE_BUILTIN_BITSCAN32 int k; ULong x = *y; if (x>1) *y = ( x >> (k = pr_bitscan_ctz32(x)) ); else k = ((x ^ 1) << 5); #else 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; #endif /* PR_HAVE_BUILTIN_BITSCAN32 */ 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 (dx) double dx; #else (double dx) #endif { register Long L; U x, a; dval(x) = dx; 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; 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 #ifdef KR_headers (dd, e, bits) double dd; int *e, *bits; #else (double dd, int *e, int *bits) #endif { 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) = dd; #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)) 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 { 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 { 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 #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; 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 */ PR_IMPLEMENT(double) PR_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; U aadj2, 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 if (!_pr_initialized) _PR_ImplicitInitialization(); 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: if (nd > 64 * 1024) goto ret0; 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 = 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) dval(rv) *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: #ifndef NO_ERRNO PR_SetError(PR_RANGE_ERROR, 0); #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; 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 PR_SetError(PR_RANGE_ERROR, 0); #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 = 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; } dval(aadj2) = aadj1; word0(aadj2) += (2*P+1)*Exp_msk1 - y; aadj1 = dval(aadj2); } 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 */ if (word0(rv) == 0 && word1(rv) == 0) PR_SetError(PR_RANGE_ERROR, 0); #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. */ static 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. */ static char * dtoa #ifdef KR_headers (dd, mode, ndigits, decpt, sign, rve) double dd; int mode, ndigits, *decpt, *sign; char **rve; #else (double dd, 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; U d, d2, eps; double ds; char *s, *s0; #ifdef Honor_FLT_ROUNDS int rounding; #endif #ifdef SET_INEXACT int inexact, oldinexact; #endif #ifndef MULTIPLE_THREADS if (dtoa_result) { freedtoa(dtoa_result); dtoa_result = 0; } #endif dval(d) = dd; 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 = 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))) { #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 <= k+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 { #ifdef Honor_FLT_ROUNDS trimzeros: #endif 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; } #ifdef __cplusplus } #endif PR_IMPLEMENT(PRStatus) PR_dtoa(PRFloat64 d, PRIntn mode, PRIntn ndigits, PRIntn *decpt, PRIntn *sign, char **rve, char *buf, PRSize bufsize) { char *result; PRSize resultlen; PRStatus rv = PR_FAILURE; if (!_pr_initialized) _PR_ImplicitInitialization(); if (mode < 0 || mode > 3) { PR_SetError(PR_INVALID_ARGUMENT_ERROR, 0); return rv; } result = dtoa(d, mode, ndigits, decpt, sign, rve); if (!result) { PR_SetError(PR_OUT_OF_MEMORY_ERROR, 0); return rv; } resultlen = strlen(result)+1; if (bufsize < resultlen) { PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0); } else { memcpy(buf, result, resultlen); if (rve) { *rve = buf + (*rve - result); } rv = PR_SUCCESS; } freedtoa(result); return rv; } /* ** conversion routines for floating point ** prcsn - number of digits of precision to generate floating ** point value. ** This should be reparameterized so that you can send in a ** prcn for the positive and negative ranges. For now, ** conform to the ECMA JavaScript spec which says numbers ** less than 1e-6 are in scientific notation. ** Also, the ECMA spec says that there should always be a ** '+' or '-' after the 'e' in scientific notation */ PR_IMPLEMENT(void) PR_cnvtf(char *buf, int bufsz, int prcsn, double dfval) { PRIntn decpt, sign, numdigits; char *num, *nump; char *bufp = buf; char *endnum; U fval; dval(fval) = dfval; /* If anything fails, we store an empty string in 'buf' */ num = (char*)PR_MALLOC(bufsz); if (num == NULL) { buf[0] = '\0'; return; } /* XXX Why use mode 1? */ if (PR_dtoa(dval(fval),1,prcsn,&decpt,&sign,&endnum,num,bufsz) == PR_FAILURE) { buf[0] = '\0'; goto done; } numdigits = endnum - num; nump = num; if (sign && !(word0(fval) == Sign_bit && word1(fval) == 0) && !((word0(fval) & Exp_mask) == Exp_mask && (word1(fval) || (word0(fval) & 0xfffff)))) { *bufp++ = '-'; } if (decpt == 9999) { while ((*bufp++ = *nump++) != 0) {} /* nothing to execute */ goto done; } if (decpt > (prcsn+1) || decpt < -(prcsn-1) || decpt < -5) { *bufp++ = *nump++; if (numdigits != 1) { *bufp++ = '.'; } while (*nump != '\0') { *bufp++ = *nump++; } *bufp++ = 'e'; PR_snprintf(bufp, bufsz - (bufp - buf), "%+d", decpt-1); } else if (decpt >= 0) { if (decpt == 0) { *bufp++ = '0'; } else { while (decpt--) { if (*nump != '\0') { *bufp++ = *nump++; } else { *bufp++ = '0'; } } } if (*nump != '\0') { *bufp++ = '.'; while (*nump != '\0') { *bufp++ = *nump++; } } *bufp++ = '\0'; } else if (decpt < 0) { *bufp++ = '0'; *bufp++ = '.'; while (decpt++) { *bufp++ = '0'; } while (*nump != '\0') { *bufp++ = *nump++; } *bufp++ = '\0'; } done: PR_DELETE(num); }