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/**************************************************************** * * The author of this software is David M. Gay. * * Copyright (c) 1991 by AT&T. * * 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 AT&T 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 AT&T Bell Laboratories, Room 2C-463 600 Mountain Avenue Murray Hill, NJ 07974-2070 U.S.A. dmg@research.att.com or research!dmg */ /* 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_LITTLE_ENDIAN for IEEE-arithmetic machines where the least * significant byte has the lowest address. * #define IEEE_BIG_ENDIAN 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 Sudden_Underflow for IEEE-format machines without gradual * underflow (i.e., that flush to zero on underflow). * #define IBM for IBM mainframe-style floating-point arithmetic. * #define VAX for VAX-style floating-point arithmetic. * #define Unsigned_Shifts if >> does treats its left operand as unsigned. * #define No_leftright to omit left-right logic in fast floating-point * computation of dtoa. * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. * #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 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. * #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. */ /* $Id$ */ #include <zend_operators.h> #include <zend_strtod.h> #ifdef ZTS #include <TSRM.h> #endif #include <stddef.h> #include <stdio.h> #include <ctype.h> #include <stdarg.h> #include <string.h> #include <stdlib.h> #include <math.h> #ifdef HAVE_LOCALE_H #include <locale.h> #endif #ifdef HAVE_SYS_TYPES_H #include <sys/types.h> #endif #if defined(HAVE_INTTYPES_H) #include <inttypes.h> #elif defined(HAVE_STDINT_H) #include <stdint.h> #endif #ifndef HAVE_INT32_T # if SIZEOF_INT == 4 typedef int int32_t; # elif SIZEOF_LONG == 4 typedef long int int32_t; # endif #endif #ifndef HAVE_UINT32_T # if SIZEOF_INT == 4 typedef unsigned int uint32_t; # elif SIZEOF_LONG == 4 typedef unsigned long int uint32_t; # endif #endif #if (defined(__APPLE__) || defined(__APPLE_CC__)) && (defined(__BIG_ENDIAN__) || defined(__LITTLE_ENDIAN__)) # if defined(__LITTLE_ENDIAN__) # undef WORDS_BIGENDIAN # else # if defined(__BIG_ENDIAN__) # define WORDS_BIGENDIAN # endif # endif #endif #ifdef WORDS_BIGENDIAN #define IEEE_BIG_ENDIAN #else #define IEEE_LITTLE_ENDIAN #endif #if defined(__arm__) && !defined(__VFP_FP__) /* * * Although the CPU is little endian the FP has different * * byte and word endianness. The byte order is still little endian * * but the word order is big endian. * */ #define IEEE_BIG_ENDIAN #undef IEEE_LITTLE_ENDIAN #endif #ifdef __vax__ #define VAX #undef IEEE_LITTLE_ENDIAN #endif #if defined(_MSC_VER) #define int32_t __int32 #define uint32_t unsigned __int32 #define IEEE_LITTLE_ENDIAN #endif #define Long int32_t #define ULong uint32_t #ifdef __cplusplus #include "malloc.h" #include "memory.h" #else #ifndef KR_headers #include "stdlib.h" #include "string.h" #include "locale.h" #else #include "malloc.h" #include "memory.h" #endif #endif #ifdef MALLOC #ifdef KR_headers extern char *MALLOC(); #else extern void *MALLOC(size_t); #endif #else #define MALLOC malloc #endif #include "ctype.h" #include "errno.h" #ifdef Bad_float_h #ifdef IEEE_BIG_ENDIAN #define IEEE_ARITHMETIC #endif #ifdef IEEE_LITTLE_ENDIAN #define IEEE_ARITHMETIC #endif #ifdef IEEE_ARITHMETIC #define DBL_DIG 15 #define DBL_MAX_10_EXP 308 #define DBL_MAX_EXP 1024 #define FLT_RADIX 2 #define FLT_ROUNDS 1 #define DBL_MAX 1.7976931348623157e+308 #endif #ifdef IBM #define DBL_DIG 16 #define DBL_MAX_10_EXP 75 #define DBL_MAX_EXP 63 #define FLT_RADIX 16 #define FLT_ROUNDS 0 #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 FLT_ROUNDS 1 #define DBL_MAX 1.7014118346046923e+38 #endif #ifndef LONG_MAX #define LONG_MAX 2147483647 #endif #else #include "float.h" #endif #ifndef __MATH_H__ #include "math.h" #endif BEGIN_EXTERN_C() #ifndef CONST #ifdef KR_headers #define CONST /* blank */ #else #define CONST const #endif #endif #ifdef Unsigned_Shifts #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000; #else #define Sign_Extend(a,b) /*no-op*/ #endif #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \ defined(IBM) != 1 #error "Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or IBM should be defined." #endif typedef union { double d; ULong ul[2]; } _double; #define value(x) ((x).d) #ifdef IEEE_LITTLE_ENDIAN #define word0(x) ((x).ul[1]) #define word1(x) ((x).ul[0]) #else #define word0(x) ((x).ul[0]) #define word1(x) ((x).ul[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_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__) #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ ((unsigned short *)a)[0] = (unsigned short)c, a++) #else #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ ((unsigned short *)a)[1] = (unsigned short)c, a++) #endif /* #define P DBL_MANT_DIG */ /* Ten_pmax = floor(P*log(2)/log(5)) */ /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) #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 IEEE_Arith #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 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */ #else #undef Sudden_Underflow #define Sudden_Underflow #ifdef IBM #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 */ #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 #endif #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 Just_16 /* 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. * */ #ifndef Pack_32 #define Pack_32 #endif #endif #define Kmax 15 struct Bigint { struct Bigint *next; int k, maxwds, sign, wds; ULong x[1]; }; typedef struct Bigint Bigint; /* static variables, multithreading fun! */ static Bigint *freelist[Kmax+1]; static Bigint *p5s; static void destroy_freelist(void); #ifdef ZTS static MUTEX_T dtoa_mutex; static MUTEX_T pow5mult_mutex; #define _THREAD_PRIVATE_MUTEX_LOCK(x) tsrm_mutex_lock(x); #define _THREAD_PRIVATE_MUTEX_UNLOCK(x) tsrm_mutex_unlock(x); #else #define _THREAD_PRIVATE_MUTEX_LOCK(x) #define _THREAD_PRIVATE_MUTEX_UNLOCK(x) #endif /* ZTS */ #ifdef DEBUG static void Bug(const char *message) { fprintf(stderr, "%s\n", message); } #endif ZEND_API int zend_startup_strtod(void) /* {{{ */ { #ifdef ZTS dtoa_mutex = tsrm_mutex_alloc(); pow5mult_mutex = tsrm_mutex_alloc(); #endif return 1; } /* }}} */ ZEND_API int zend_shutdown_strtod(void) /* {{{ */ { destroy_freelist(); #ifdef ZTS tsrm_mutex_free(dtoa_mutex); dtoa_mutex = NULL; tsrm_mutex_free(pow5mult_mutex); pow5mult_mutex = NULL; #endif return 1; } /* }}} */ static Bigint * Balloc(int k) { int x; Bigint *rv; if (k > Kmax) { zend_error(E_ERROR, "Balloc() allocation exceeds list boundary"); } _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex); if ((rv = freelist[k])) { freelist[k] = rv->next; } else { x = 1 << k; rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long)); if (!rv) { _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex); zend_error(E_ERROR, "Balloc() failed to allocate memory"); } rv->k = k; rv->maxwds = x; } _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex); rv->sign = rv->wds = 0; return rv; } static void Bfree(Bigint *v) { if (v) { _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex); v->next = freelist[v->k]; freelist[v->k] = v; _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex); } } #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ y->wds*sizeof(Long) + 2*sizeof(int)) /* return value is only used as a simple string, so mis-aligned parts * inside the Bigint are not at risk on strict align architectures */ static char * rv_alloc(int i) { 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 (char *)(r+1); } static char * nrv_alloc(char *s, char **rve, int n) { char *rv, *t; t = rv = rv_alloc(n); while((*t = *s++) !=0) { t++; } if (rve) { *rve = t; } return rv; } static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */ { int i, wds; ULong *x, y; #ifdef Pack_32 ULong xi, z; #endif Bigint *b1; wds = b->wds; x = b->x; i = 0; do { #ifdef Pack_32 xi = *x; y = (xi & 0xffff) * m + a; z = (xi >> 16) * m + (y >> 16); a = (int)(z >> 16); *x++ = (z << 16) + (y & 0xffff); #else y = *x * m + a; a = (int)(y >> 16); *x++ = y & 0xffff; #endif } while(++i < wds); if (a) { if (wds >= b->maxwds) { b1 = Balloc(b->k+1); Bcopy(b1, b); Bfree(b); b = b1; } b->x[wds++] = a; b->wds = wds; } return b; } static int hi0bits(ULong x) { 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(ULong *y) { int k; 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 & 1)) { return 32; } } *y = x; return k; } static Bigint * i2b(int i) { Bigint *b; b = Balloc(1); b->x[0] = i; b->wds = 1; return b; } static Bigint * mult(Bigint *a, Bigint *b) { Bigint *c; int k, wa, wb, wc; ULong carry, y, z; ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; #ifdef Pack_32 ULong z2; #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 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 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; c->wds = wc; return c; } static Bigint * s2b (CONST char *s, int nd0, int nd, ULong y9) { 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 Bigint * pow5mult(Bigint *b, int k) { Bigint *b1, *p5, *p51; int i; static int p05[3] = { 5, 25, 125 }; _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex); if ((i = k & 3)) { b = multadd(b, p05[i-1], 0); } if (!(k >>= 2)) { _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex); return b; } if (!(p5 = p5s)) { /* first time */ p5 = p5s = i2b(625); p5->next = 0; } for(;;) { if (k & 1) { b1 = mult(b, p5); Bfree(b); b = b1; } if (!(k >>= 1)) { break; } if (!(p51 = p5->next)) { if (!(p51 = p5->next)) { p51 = p5->next = mult(p5,p5); p51->next = 0; } } p5 = p51; } _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex); return b; } static Bigint *lshift(Bigint *b, int k) { int i, k1, n, n1; Bigint *b1; ULong *x, *x1, *xe, z; #ifdef Pack_32 n = k >> 5; #else n = k >> 4; #endif k1 = b->k; n1 = n + b->wds + 1; for(i = b->maxwds; n1 > i; i <<= 1) { k1++; } b1 = Balloc(k1); x1 = b1->x; for(i = 0; i < n; i++) { *x1++ = 0; } x = b->x; xe = x + b->wds; #ifdef Pack_32 if (k &= 0x1f) { k1 = 32 - k; z = 0; do { *x1++ = *x << k | z; z = *x++ >> k1; } while(x < xe); if ((*x1 = z)) { ++n1; } } #else if (k &= 0xf) { k1 = 16 - k; z = 0; do { *x1++ = *x << k & 0xffff | z; z = *x++ >> k1; } while(x < xe); if (*x1 = z) { ++n1; } } #endif else do *x1++ = *x++; while(x < xe); b1->wds = n1 - 1; Bfree(b); return b1; } static int cmp(Bigint *a, Bigint *b) { ULong *xa, *xa0, *xb, *xb0; int i, j; i = a->wds; j = b->wds; #ifdef DEBUG if (i > 1 && !a->x[i-1]) Bug("cmp called with a->x[a->wds-1] == 0"); if (j > 1 && !b->x[j-1]) Bug("cmp called with b->x[b->wds-1] == 0"); #endif if (i -= j) return i; xa0 = a->x; xa = xa0 + j; xb0 = b->x; xb = xb0 + j; for(;;) { if (*--xa != *--xb) return *xa < *xb ? -1 : 1; if (xa <= xa0) break; } return 0; } static Bigint * diff(Bigint *a, Bigint *b) { Bigint *c; int i, wa, wb; Long borrow, y; /* We need signed shifts here. */ ULong *xa, *xae, *xb, *xbe, *xc; #ifdef Pack_32 Long z; #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 Pack_32 do { y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(xc, z, y); } while(xb < xbe); while(xa < xae) { y = (*xa & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*xa++ >> 16) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(xc, z, y); } #else do { y = *xa++ - *xb++ + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *xc++ = y & 0xffff; } while(xb < xbe); while(xa < xae) { y = *xa++ + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *xc++ = y & 0xffff; } #endif while(!*--xc) { wa--; } c->wds = wa; return c; } static double ulp (double _x) { volatile _double x; register Long L; volatile _double a; value(x) = _x; L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Sudden_Underflow if (L > 0) { #endif #ifdef IBM L |= Exp_msk1 >> 4; #endif word0(a) = L; word1(a) = 0; #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 return value(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; volatile _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 value(d); } static Bigint * d2b(double _d, int *e, int *bits) { Bigint *b; int de, i, k; ULong *x, y, z; volatile _double d; #ifdef VAX ULong d0, d1; #endif value(d) = _d; #ifdef VAX d0 = word0(d) >> 16 | word0(d) << 16; d1 = word1(d) >> 16 | word1(d) << 16; #else #define d0 word0(d) #define d1 word1(d) #endif #ifdef Pack_32 b = Balloc(1); #else b = Balloc(2); #endif x = b->x; z = d0 & Frac_mask; d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ #ifdef Sudden_Underflow de = (int)(d0 >> Exp_shift); #ifndef IBM z |= Exp_msk11; #endif #else if ((de = (int)(d0 >> Exp_shift))) 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; } i = b->wds = (x[1] = z) ? 2 : 1; } else { #ifdef DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); x[0] = z; i = b->wds = 1; k += 32; } #else if (y = d1) { if (k = lo0bits(&y)) { if (k >= 16) { x[0] = y | z << 32 - k & 0xffff; x[1] = z >> k - 16 & 0xffff; x[2] = z >> k; i = 2; } else { x[0] = y & 0xffff; x[1] = y >> 16 | z << 16 - k & 0xffff; x[2] = z >> k & 0xffff; x[3] = z >> k+16; i = 3; } } else { x[0] = y & 0xffff; x[1] = y >> 16; x[2] = z & 0xffff; x[3] = z >> 16; i = 3; } } else { #ifdef DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); if (k >= 16) { x[0] = z; i = 0; } else { x[0] = z & 0xffff; x[1] = z >> 16; i = 1; } k += 32; } while(!x[i]) --i; b->wds = i + 1; #endif #ifndef Sudden_Underflow if (de) { #endif #ifdef IBM *e = (de - Bias - (P-1) << 2) + k; *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); #else *e = de - Bias - (P-1) + k; *bits = P - k; #endif #ifndef Sudden_Underflow } else { *e = de - Bias - (P-1) + 1 + k; #ifdef Pack_32 *bits = 32*i - hi0bits(x[i-1]); #else *bits = (i+2)*16 - hi0bits(x[i]); #endif } #endif return b; } #undef d0 #undef d1 static double ratio (Bigint *a, Bigint *b) { volatile _double da, db; int k, ka, kb; value(da) = b2d(a, &ka); value(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) { da *= 1 << k; } } else { k = -k; word0(db) += (k >> 2)*Exp_msk1; if (k &= 3) db *= 1 << k; } #else if (k > 0) { word0(da) += k*Exp_msk1; } else { k = -k; word0(db) += k*Exp_msk1; } #endif return value(da) / value(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 }; #ifdef IEEE_Arith static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; #define n_bigtens 5 #else #ifdef IBM static CONST double bigtens[] = { 1e16, 1e32, 1e64 }; static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; #define n_bigtens 3 #else static CONST double bigtens[] = { 1e16, 1e32 }; static CONST double tinytens[] = { 1e-16, 1e-32 }; #define n_bigtens 2 #endif #endif static int quorem(Bigint *b, Bigint *S) { int n; Long borrow, y; ULong carry, q, ys; ULong *bx, *bxe, *sx, *sxe; #ifdef Pack_32 Long z; ULong si, zs; #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 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 >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); #else ys = *sx++ * q + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *bx++ = y & 0xffff; #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 Pack_32 si = *sx++; ys = (si & 0xffff) + carry; zs = (si >> 16) + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); #else ys = *sx++ + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *bx++ = y & 0xffff; #endif } while(sx <= sxe); bx = b->x; bxe = bx + n; if (!*bxe) { while(--bxe > bx && !*bxe) --n; b->wds = n; } } return q; } static void destroy_freelist(void) { int i; Bigint *tmp; _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex); for (i = 0; i <= Kmax; i++) { Bigint **listp = &freelist[i]; while ((tmp = *listp) != NULL) { *listp = tmp->next; free(tmp); } freelist[i] = NULL; } _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex); } ZEND_API void zend_freedtoa(char *s) { Bigint *b = (Bigint *)((int *)s - 1); b->maxwds = 1 << (b->k = *(int*)b); Bfree(b); } /* 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. 92-101]. * * 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. */ ZEND_API char * zend_dtoa(double _d, int mode, int ndigits, int *decpt, int *sign, char **rve) { /* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt; trailing zeros are suppressed from the returned string. If not null, *rve is set to point to the end of the return value. If d is +-Infinity or NaN, then *decpt is set to 9999. mode: 0 ==> shortest string that yields d when read in and rounded to nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits. This gives a return value similar to that of ecvt, except that trailing zeros are suppressed. 3 ==> through ndigits past the decimal point. This gives a return value similar to that from fcvt, except that trailing zeros are suppressed, and ndigits can be negative. 4-9 should give the same return values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode & 1). These modes are mainly for debugging; often they run slower but sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit generation. 6-9 ==> 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 = 0, ilim0, ilim1, j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case = 0, try_quick; Long L; #ifndef Sudden_Underflow int denorm; ULong x; #endif Bigint *b, *b1, *delta, *mlo, *mhi, *S, *tmp; double ds; char *s, *s0; volatile _double d, d2, eps; value(d) = _d; 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 value(d) += 0; /* normalize */ #endif if (!value(d)) { *decpt = 1; return nrv_alloc("0", rve, 1); } b = d2b(value(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 value(d2) = value(d); word0(d2) &= Frac_mask1; word0(d2) |= Exp_11; #ifdef IBM if (j = 11 - hi0bits(word0(d2) & Frac_mask)) value(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)); value(d2) = x; word0(d2) -= 31*Exp_msk1; /* adjust exponent */ i -= (Bias + (P-1) - 1) + 1; denorm = 1; } #endif ds = (value(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 (value(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; try_quick = 1; 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); if (ilim >= 0 && ilim <= Quick_max && try_quick) { /* Try to get by with floating-point arithmetic. */ i = 0; value(d2) = value(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; value(d) /= bigtens[n_bigtens-1]; ieps++; } for(; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= bigtens[i]; } value(d) /= ds; } else if ((j1 = -k)) { value(d) *= tens[j1 & 0xf]; for(j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; value(d) *= bigtens[i]; } } if (k_check && value(d) < 1. && ilim > 0) { if (ilim1 <= 0) goto fast_failed; ilim = ilim1; k--; value(d) *= 10.; ieps++; } value(eps) = ieps*value(d) + 7.; word0(eps) -= (P-1)*Exp_msk1; if (ilim == 0) { S = mhi = 0; value(d) -= 5.; if (value(d) > value(eps)) goto one_digit; if (value(d) < -value(eps)) goto no_digits; goto fast_failed; } #ifndef No_leftright if (leftright) { /* Use Steele & White method of only * generating digits needed. */ value(eps) = 0.5/tens[ilim-1] - value(eps); for(i = 0;;) { L = value(d); value(d) -= L; *s++ = '0' + (int)L; if (value(d) < value(eps)) goto ret1; if (1. - value(d) < value(eps)) goto bump_up; if (++i >= ilim) break; value(eps) *= 10.; value(d) *= 10.; } } else { #endif /* Generate ilim digits, then fix them up. */ value(eps) *= tens[ilim-1]; for(i = 1;; i++, value(d) *= 10.) { L = value(d); value(d) -= L; *s++ = '0' + (int)L; if (i == ilim) { if (value(d) > 0.5 + value(eps)) goto bump_up; else if (value(d) < 0.5 - value(eps)) { while(*--s == '0'); s++; goto ret1; } break; } } #ifndef No_leftright } #endif fast_failed: s = s0; value(d) = value(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 || value(d) <= 5*ds) goto no_digits; goto one_digit; } for(i = 1;; i++) { L = value(d) / ds; value(d) -= L*ds; #ifdef Check_FLT_ROUNDS /* If FLT_ROUNDS == 2, L will usually be high by 1 */ if (value(d) < 0) { L--; value(d) += ds; } #endif *s++ = '0' + (int)L; if (i == ilim) { value(d) += value(d); if (value(d) > ds || (value(d) == ds && (L & 1))) { bump_up: while(*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } if (!(value(d) *= 10.)) break; } goto ret1; } m2 = b2; m5 = b5; mhi = mlo = 0; if (leftright) { if (mode < 2) { 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 } else { j = ilim - 1; if (m5 >= j) m5 -= j; else { s5 += j -= m5; b5 += j; m5 = 0; } if ((i = ilim) < 0) { m2 -= i; i = 0; } } 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. */ if (mode < 2) { if (!word1(d) && !(word0(d) & Bndry_mask) #ifndef Sudden_Underflow && word0(d) & Exp_mask #endif ) { /* The special case */ b2 += Log2P; s2 += Log2P; spec_case = 1; } else { spec_case = 0; } } /* 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 > 2) { 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 && !(word1(d) & 1)) { if (dig == '9') goto round_9_up; if (j > 0) dig++; *s++ = dig; goto ret; } #endif if (j < 0 || (j == 0 && !mode #ifndef ROUND_BIASED && !(word1(d) & 1) #endif )) { if (j1 > 0) { b = lshift(b, 1); j1 = cmp(b, S); if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9') goto round_9_up; } *s++ = dig; goto ret; } if (j1 > 0) { if (dig == '9') { /* possible if i == 1 */ round_9_up: *s++ = '9'; goto roundoff; } *s++ = dig + 1; goto ret; } *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 (i >= ilim) break; b = multadd(b, 10, 0); } /* Round off last digit */ 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 { while(*--s == '0'); s++; } ret: Bfree(S); if (mhi) { if (mlo && mlo != mhi) Bfree(mlo); Bfree(mhi); } ret1: _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex); while (p5s) { tmp = p5s; p5s = p5s->next; free(tmp); } _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex); Bfree(b); if (s == s0) { /* don't return empty string */ *s++ = '0'; k = 0; } *s = 0; *decpt = k + 1; if (rve) *rve = s; return s0; } ZEND_API double zend_strtod (CONST char *s00, CONST char **se) { 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; volatile double aadj, aadj1, adj; volatile _double rv, rv0; Long L; ULong y, z; Bigint *bb, *bb1, *bd, *bd0, *bs, *delta, *tmp; double result; CONST char decimal_point = '.'; sign = nz0 = nz = 0; value(rv) = 0.; for(s = s00; isspace((unsigned char) *s); s++) ; if (*s == '-') { sign = 1; s++; } else if (*s == '+') { s++; } if (*s == '\0') { s = s00; goto ret; } 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; if (c == decimal_point) { 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) { s = s00; goto ret; } 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) s = s00; 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; value(rv) = y; if (k > 9) value(rv) = tens[k - 9] * value(rv) + z; bd0 = 0; if (nd <= DBL_DIG #ifndef RND_PRODQUOT && FLT_ROUNDS == 1 #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else /* value(rv) = */ rounded_product(value(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. */ e -= i; value(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; /* value(rv) = */ rounded_product(value(rv), tens[e]); if ((word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; word0(rv) += P*Exp_msk1; #else /* value(rv) = */ rounded_product(value(rv), tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { /* value(rv) = */ rounded_quotient(value(rv), tens[-e]); goto ret; } #endif } e1 += nd - k; /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if ((i = e1 & 15)) value(rv) *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: errno = ERANGE; #ifndef Bad_float_h value(rv) = HUGE_VAL; #else /* Can't trust HUGE_VAL */ #ifdef IEEE_Arith word0(rv) = Exp_mask; word1(rv) = 0; #else word0(rv) = Big0; word1(rv) = Big1; #endif #endif if (bd0) goto retfree; goto ret; } if (e1 >>= 4) { for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) value(rv) *= bigtens[j]; /* The last multiplication could overflow. */ word0(rv) -= P*Exp_msk1; value(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)) value(rv) /= tens[i]; if (e1 &= ~15) { e1 >>= 4; if (e1 >= 1 << n_bigtens) goto undfl; for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) value(rv) *= tinytens[j]; /* The last multiplication could underflow. */ value(rv0) = value(rv); value(rv) *= tinytens[j]; if (!value(rv)) { value(rv) = 2.*value(rv0); value(rv) *= tinytens[j]; if (!value(rv)) { undfl: value(rv) = 0.; errno = ERANGE; if (bd0) goto retfree; goto ret; } word0(rv) = Tiny0; word1(rv) = Tiny1; /* The refinement below will clean * this approximation up. */ } } } /* 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(value(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 Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else j = P + 1 - bbbits; #endif #else i = bbe + bbbits - 1; /* logb(rv) */ if (i < Emin) /* denormal */ j = bbe + (P-Emin); else j = P + 1 - bbbits; #endif bb2 += j; bd2 += j; 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); 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) 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) == 0xffffffff) { /*boundary case -- increment exponent*/ word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; word1(rv) = 0; 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 if (L <= Exp_msk1) #endif goto undfl; L -= Exp_msk1; #else L = (word0(rv) & Exp_mask) - Exp_msk1; #endif 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) value(rv) += ulp(value(rv)); #ifndef ROUND_BIASED else { value(rv) -= ulp(value(rv)); #ifndef Sudden_Underflow if (!value(rv)) goto undfl; #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(FLT_ROUNDS) { 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 } y = word0(rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { value(rv0) = value(rv); word0(rv) -= P*Exp_msk1; adj = aadj1 * ulp(value(rv)); value(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 Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { value(rv0) = value(rv); word0(rv) += P*Exp_msk1; adj = aadj1 * ulp(value(rv)); value(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(value(rv)); value(rv) += adj; } #else /* 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(value(rv)); value(rv) += adj; #endif } z = word0(rv) & Exp_mask; if (y == z) { /* Can we stop now? */ L = 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; } cont: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(delta); } retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = s; result = sign ? -value(rv) : value(rv); _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex); while (p5s) { tmp = p5s; p5s = p5s->next; free(tmp); } _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex); return result; } ZEND_API double zend_hex_strtod(const char *str, const char **endptr) { const char *s = str; char c; int any = 0; double value = 0; if (s[0] == '\0' || s[1] == '\0') { *endptr = str; return 0.0; } if (*s == '0' && (s[1] == 'x' || s[1] == 'X')) { s += 2; } while ((c = *s++)) { if (c >= '0' && c <= '9') { c -= '0'; } else if (c >= 'A' && c <= 'F') { c -= 'A' - 10; } else if (c >= 'a' && c <= 'f') { c -= 'a' - 10; } else { break; } any = 1; value = value * 16 + c; } if (endptr != NULL) { *endptr = any ? s - 1 : str; } return value; } ZEND_API double zend_oct_strtod(const char *str, const char **endptr) { const char *s = str; char c; double value = 0; int any = 0; if (strlen(str) < 1) { *endptr = str; return 0.0; } /* skip leading zero */ s++; while ((c = *s++)) { if (c < '0' || c > '7') { /* break and return the current value if the number is not well-formed * that's what Linux strtol() does */ break; } value = value * 8 + c - '0'; any = 1; } if (endptr != NULL) { *endptr = any ? s - 1 : str; } return value; } ZEND_API double zend_bin_strtod(const char *str, const char **endptr) { const char *s = str; char c; double value = 0; int any = 0; if (strlen(str) < 2) { *endptr = str; return 0.0; } if ('0' == *s && ('b' == s[1] || 'B' == s[1])) { s += 2; } while ((c = *s++)) { /* * Verify the validity of the current character as a base-2 digit. In * the event that an invalid digit is found, halt the conversion and * return the portion which has been converted thus far. */ if ('0' == c || '1' == c) value = value * 2 + c - '0'; else break; any = 1; } /* * As with many strtoX implementations, should the subject sequence be * empty or not well-formed, no conversion is performed and the original * value of str is stored in *endptr, provided that endptr is not a null * pointer. */ if (NULL != endptr) { *endptr = (char *)(any ? s - 1 : str); } return value; } /* * Local variables: * tab-width: 4 * c-basic-offset: 4 * End: * vim600: sw=4 ts=4 fdm=marker * vim<600: sw=4 ts=4 */
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