| /**************************************************************** |
| * |
| * The author of this software is David M. Gay. |
| * |
| * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. |
| * Copyright (C) 2002, 2005, 2006, 2007, 2008 Apple Inc. All rights reserved. |
| * |
| * 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 |
| Bell Laboratories, Room 2C-463 |
| 600 Mountain Avenue |
| Murray Hill, NJ 07974-0636 |
| U.S.A. |
| [email protected] |
| */ |
| |
| /* 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-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. |
| * 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 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 |
| * and Honor_FLT_ROUNDS is not #defined. |
| * #define Inaccurate_Divide for IEEE-format with correctly rounded |
| * products but inaccurate quotients, e.g., for Intel i860. |
| * #define USE_LONG_LONG on machines that have a "long long" |
| * integer type (of >= 64 bits), and performance testing shows that |
| * it is faster than 32-bit fallback (which is often not the case |
| * on 32-bit machines). On such machines, you can #define Just_16 |
| * to store 16 bits per 32-bit int32_t 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 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 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 NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that |
| * avoids underflows on inputs whose result does not underflow. |
| * If you #define NO_IEEE_Scale on a machine that uses IEEE-format |
| * floating-point numbers and flushes underflows to zero rather |
| * than implementing gradual underflow, then you must also #define |
| * Sudden_Underflow. |
| * #define YES_ALIAS to permit aliasing certain double values with |
| * arrays of ULongs. This leads to slightly better code with |
| * some compilers and was always used prior to 19990916, but it |
| * is not strictly legal and can cause trouble with aggressively |
| * optimizing compilers (e.g., gcc 2.95.1 under -O2). |
| * #define 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. |
| */ |
| |
| #include "config.h" |
| #include "dtoa.h" |
| |
| #include <errno.h> |
| #include <float.h> |
| #include <math.h> |
| #include <stdint.h> |
| #include <stdlib.h> |
| #include <string.h> |
| #include <wtf/AlwaysInline.h> |
| #include <wtf/Assertions.h> |
| #include <wtf/FastMalloc.h> |
| #include <wtf/Threading.h> |
| |
| #if COMPILER(MSVC) |
| #pragma warning(disable: 4244) |
| #pragma warning(disable: 4245) |
| #pragma warning(disable: 4554) |
| #endif |
| |
| // ANDROID : || PLATFORM(MIDDLE_ENDIAN) added in #if statement below |
| // for dtoa, MIDDLE_ENDIAN needs to be same as BIG_ENDIAN according to the following site |
| // http://lists.debian.org/debian-arm/2003/11/msg00008.html |
| #if PLATFORM(BIG_ENDIAN) || PLATFORM(MIDDLE_ENDIAN) |
| #define IEEE_MC68k |
| #elif PLATFORM(MIDDLE_ENDIAN) |
| #define IEEE_ARM |
| #else |
| #define IEEE_8087 |
| #endif |
| |
| #define INFNAN_CHECK |
| |
| #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) != 1 |
| Exactly one of IEEE_8087, IEEE_ARM or IEEE_MC68k should be defined. |
| #endif |
| |
| namespace JSC { |
| |
| #if ENABLE(JSC_MULTIPLE_THREADS) |
| Mutex* s_dtoaP5Mutex; |
| #endif |
| |
| typedef union { double d; uint32_t L[2]; } U; |
| |
| #ifdef YES_ALIAS |
| #define dval(x) x |
| #ifdef IEEE_8087 |
| #define word0(x) ((uint32_t*)&x)[1] |
| #define word1(x) ((uint32_t*)&x)[0] |
| #else |
| #define word0(x) ((uint32_t*)&x)[0] |
| #define word1(x) ((uint32_t*)&x)[1] |
| #endif |
| #else |
| #ifdef IEEE_8087 |
| #define word0(x) ((U*)&x)->L[1] |
| #define word1(x) ((U*)&x)->L[0] |
| #else |
| #define word0(x) ((U*)&x)->L[0] |
| #define word1(x) ((U*)&x)->L[1] |
| #endif |
| #define dval(x) ((U*)&x)->d |
| #endif |
| |
| /* The following definition of Storeinc is appropriate for MIPS processors. |
| * An alternative that might be better on some machines is |
| * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) |
| */ |
| #if defined(IEEE_8087) || defined(IEEE_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 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 |
| |
| #if !defined(NO_IEEE_Scale) |
| #undef Avoid_Underflow |
| #define Avoid_Underflow |
| #endif |
| |
| #if !defined(Flt_Rounds) |
| #if defined(FLT_ROUNDS) |
| #define Flt_Rounds FLT_ROUNDS |
| #else |
| #define Flt_Rounds 1 |
| #endif |
| #endif /*Flt_Rounds*/ |
| |
| |
| #define rounded_product(a,b) a *= b |
| #define rounded_quotient(a,b) a /= b |
| |
| #define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) |
| #define Big1 0xffffffff |
| |
| #ifndef Pack_32 |
| #define Pack_32 |
| #endif |
| |
| #if PLATFORM(PPC64) || PLATFORM(X86_64) |
| // 64-bit emulation provided by the compiler is likely to be slower than dtoa own code on 32-bit hardware. |
| #define USE_LONG_LONG |
| #endif |
| |
| #ifndef USE_LONG_LONG |
| #ifdef Just_16 |
| #undef Pack_32 |
| /* When Pack_32 is not defined, we store 16 bits per 32-bit int32_t. |
| * 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 int32_t. |
| */ |
| #endif |
| #endif |
| |
| #define Kmax 15 |
| |
| struct Bigint { |
| struct Bigint* next; |
| int k, maxwds, sign, wds; |
| uint32_t x[1]; |
| }; |
| |
| static Bigint* Balloc(int k) |
| { |
| int x = 1 << k; |
| Bigint* rv = (Bigint*)fastMalloc(sizeof(Bigint) + (x - 1)*sizeof(uint32_t)); |
| rv->k = k; |
| rv->maxwds = x; |
| rv->next = 0; |
| rv->sign = rv->wds = 0; |
| |
| return rv; |
| } |
| |
| static void Bfree(Bigint* v) |
| { |
| fastFree(v); |
| } |
| |
| #define Bcopy(x, y) memcpy((char*)&x->sign, (char*)&y->sign, y->wds * sizeof(int32_t) + 2 * sizeof(int)) |
| |
| static Bigint* multadd(Bigint* b, int m, int a) /* multiply by m and add a */ |
| { |
| #ifdef USE_LONG_LONG |
| unsigned long long carry; |
| #else |
| uint32_t carry; |
| #endif |
| |
| int wds = b->wds; |
| uint32_t* x = b->x; |
| int i = 0; |
| carry = a; |
| do { |
| #ifdef USE_LONG_LONG |
| unsigned long long y = *x * (unsigned long long)m + carry; |
| carry = y >> 32; |
| *x++ = (uint32_t)y & 0xffffffffUL; |
| #else |
| #ifdef Pack_32 |
| uint32_t xi = *x; |
| uint32_t y = (xi & 0xffff) * m + carry; |
| uint32_t z = (xi >> 16) * m + (y >> 16); |
| carry = z >> 16; |
| *x++ = (z << 16) + (y & 0xffff); |
| #else |
| uint32_t y = *x * m + carry; |
| carry = y >> 16; |
| *x++ = y & 0xffff; |
| #endif |
| #endif |
| } while (++i < wds); |
| |
| if (carry) { |
| if (wds >= b->maxwds) { |
| Bigint* b1 = Balloc(b->k + 1); |
| Bcopy(b1, b); |
| Bfree(b); |
| b = b1; |
| } |
| b->x[wds++] = (uint32_t)carry; |
| b->wds = wds; |
| } |
| return b; |
| } |
| |
| static Bigint* s2b(const char* s, int nd0, int nd, uint32_t y9) |
| { |
| int k; |
| int32_t y; |
| int32_t x = (nd + 8) / 9; |
| |
| for (k = 0, y = 1; x > y; y <<= 1, k++) { } |
| #ifdef Pack_32 |
| Bigint* b = Balloc(k); |
| b->x[0] = y9; |
| b->wds = 1; |
| #else |
| Bigint* b = Balloc(k + 1); |
| b->x[0] = y9 & 0xffff; |
| b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; |
| #endif |
| |
| int 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(uint32_t 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 (uint32_t* y) |
| { |
| int k; |
| uint32_t 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; |
| uint32_t *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
| uint32_t y; |
| #ifdef USE_LONG_LONG |
| unsigned long long carry, z; |
| #else |
| uint32_t carry, z; |
| #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 USE_LONG_LONG |
| for (; xb < xbe; xc0++) { |
| if ((y = *xb++)) { |
| x = xa; |
| xc = xc0; |
| carry = 0; |
| do { |
| z = *x++ * (unsigned long long)y + *xc + carry; |
| carry = z >> 32; |
| *xc++ = (uint32_t)z & 0xffffffffUL; |
| } while (x < xae); |
| *xc = (uint32_t)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; |
| uint32_t 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; |
| uint32_t 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 int p5s_count; |
| |
| static Bigint* pow5mult(Bigint* b, int k) |
| { |
| static int p05[3] = { 5, 25, 125 }; |
| |
| if (int i = k & 3) |
| b = multadd(b, p05[i - 1], 0); |
| |
| if (!(k >>= 2)) |
| return b; |
| |
| #if ENABLE(JSC_MULTIPLE_THREADS) |
| s_dtoaP5Mutex->lock(); |
| #endif |
| Bigint* p5 = p5s; |
| if (!p5) { |
| /* first time */ |
| p5 = p5s = i2b(625); |
| p5s_count = 1; |
| } |
| int p5s_count_local = p5s_count; |
| #if ENABLE(JSC_MULTIPLE_THREADS) |
| s_dtoaP5Mutex->unlock(); |
| #endif |
| int p5s_used = 0; |
| |
| for (;;) { |
| if (k & 1) { |
| Bigint* b1 = mult(b, p5); |
| Bfree(b); |
| b = b1; |
| } |
| if (!(k >>= 1)) |
| break; |
| |
| if (++p5s_used == p5s_count_local) { |
| #if ENABLE(JSC_MULTIPLE_THREADS) |
| s_dtoaP5Mutex->lock(); |
| #endif |
| if (p5s_used == p5s_count) { |
| ASSERT(!p5->next); |
| p5->next = mult(p5, p5); |
| ++p5s_count; |
| } |
| |
| p5s_count_local = p5s_count; |
| #if ENABLE(JSC_MULTIPLE_THREADS) |
| s_dtoaP5Mutex->unlock(); |
| #endif |
| } |
| p5 = p5->next; |
| } |
| |
| return b; |
| } |
| |
| static Bigint* lshift(Bigint* b, int k) |
| { |
| Bigint* result = b; |
| |
| #ifdef Pack_32 |
| int n = k >> 5; |
| #else |
| int n = k >> 4; |
| #endif |
| |
| int k1 = b->k; |
| int n1 = n + b->wds + 1; |
| for (int i = b->maxwds; n1 > i; i <<= 1) |
| k1++; |
| if (b->k < k1) |
| result = Balloc(k1); |
| |
| const uint32_t* srcStart = b->x; |
| uint32_t* dstStart = result->x; |
| const uint32_t* src = srcStart + b->wds - 1; |
| uint32_t* dst = dstStart + n1 - 1; |
| #ifdef Pack_32 |
| if (k &= 0x1f) { |
| uint32_t hiSubword = 0; |
| int s = 32 - k; |
| for (; src >= srcStart; --src) { |
| *dst-- = hiSubword | *src >> s; |
| hiSubword = *src << k; |
| } |
| *dst = hiSubword; |
| ASSERT(dst == dstStart + n); |
| result->wds = b->wds + n + (result->x[n1 - 1] != 0); |
| } |
| #else |
| if (k &= 0xf) { |
| uint32_t hiSubword = 0; |
| int s = 16 - k; |
| for (; src >= srcStart; --src) { |
| *dst-- = hiSubword | *src >> s; |
| hiSubword = (*src << k) & 0xffff; |
| } |
| *dst = hiSubword; |
| ASSERT(dst == dstStart + n); |
| result->wds = b->wds + n + (result->x[n1 - 1] != 0); |
| } |
| #endif |
| else { |
| do { |
| *--dst = *src--; |
| } while (src >= srcStart); |
| result->wds = b->wds + n; |
| } |
| for (dst = dstStart + n; dst != dstStart; ) |
| *--dst = 0; |
| |
| if (result != b) |
| Bfree(b); |
| return result; |
| } |
| |
| static int cmp(Bigint* a, Bigint* b) |
| { |
| uint32_t *xa, *xa0, *xb, *xb0; |
| int i, j; |
| |
| i = a->wds; |
| j = b->wds; |
| ASSERT(i <= 1 || a->x[i - 1]); |
| ASSERT(j <= 1 || b->x[j - 1]); |
| 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; |
| uint32_t *xa, *xae, *xb, *xbe, *xc; |
| |
| 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; |
| #ifdef USE_LONG_LONG |
| unsigned long long borrow = 0; |
| do { |
| unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow; |
| borrow = y >> 32 & (uint32_t)1; |
| *xc++ = (uint32_t)y & 0xffffffffUL; |
| } while (xb < xbe); |
| while (xa < xae) { |
| unsigned long long y = *xa++ - borrow; |
| borrow = y >> 32 & (uint32_t)1; |
| *xc++ = (uint32_t)y & 0xffffffffUL; |
| } |
| #else |
| uint32_t borrow = 0; |
| #ifdef Pack_32 |
| do { |
| uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(xc, z, y); |
| } while (xb < xbe); |
| while (xa < xae) { |
| uint32_t y = (*xa & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| uint32_t z = (*xa++ >> 16) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(xc, z, y); |
| } |
| #else |
| do { |
| uint32_t y = *xa++ - *xb++ - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *xc++ = y & 0xffff; |
| } while (xb < xbe); |
| while (xa < xae) { |
| uint32_t y = *xa++ - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *xc++ = y & 0xffff; |
| } |
| #endif |
| #endif |
| while (!*--xc) |
| wa--; |
| c->wds = wa; |
| return c; |
| } |
| |
| static double ulp(double x) |
| { |
| register int32_t L; |
| double a; |
| |
| L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1; |
| #ifndef Avoid_Underflow |
| #ifndef Sudden_Underflow |
| if (L > 0) { |
| #endif |
| #endif |
| word0(a) = L; |
| word1(a) = 0; |
| #ifndef Avoid_Underflow |
| #ifndef Sudden_Underflow |
| } else { |
| L = -L >> Exp_shift; |
| if (L < Exp_shift) { |
| word0(a) = 0x80000 >> L; |
| word1(a) = 0; |
| } else { |
| word0(a) = 0; |
| L -= Exp_shift; |
| word1(a) = L >= 31 ? 1 : 1 << 31 - L; |
| } |
| } |
| #endif |
| #endif |
| return dval(a); |
| } |
| |
| static double b2d(Bigint* a, int* e) |
| { |
| uint32_t* xa; |
| uint32_t* xa0; |
| uint32_t w; |
| uint32_t y; |
| uint32_t z; |
| int k; |
| double d; |
| |
| #define d0 word0(d) |
| #define d1 word1(d) |
| |
| xa0 = a->x; |
| xa = xa0 + a->wds; |
| y = *--xa; |
| ASSERT(y); |
| 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: |
| #undef d0 |
| #undef d1 |
| return dval(d); |
| } |
| |
| static Bigint* d2b(double d, int* e, int* bits) |
| { |
| Bigint* b; |
| int de, k; |
| uint32_t *x, y, z; |
| #ifndef Sudden_Underflow |
| int i; |
| #endif |
| #define d0 word0(d) |
| #define d1 word1(d) |
| |
| #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); |
| #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 { |
| 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 |
| *e = de - Bias - (P - 1) + k; |
| *bits = P - k; |
| #ifndef Sudden_Underflow |
| } else { |
| *e = de - Bias - (P - 1) + 1 + k; |
| #ifdef Pack_32 |
| *bits = (32 * i) - hi0bits(x[i - 1]); |
| #else |
| *bits = (i + 2) * 16 - hi0bits(x[i]); |
| #endif |
| } |
| #endif |
| return b; |
| } |
| #undef d0 |
| #undef d1 |
| |
| static double ratio(Bigint* a, Bigint* b) |
| { |
| double 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 |
| if (k > 0) |
| word0(da) += k * Exp_msk1; |
| else { |
| k = -k; |
| word0(db) += k * Exp_msk1; |
| } |
| 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 |
| }; |
| |
| static const double 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 |
| |
| #if defined(INFNAN_CHECK) |
| |
| #ifndef NAN_WORD0 |
| #define NAN_WORD0 0x7ff80000 |
| #endif |
| |
| #ifndef NAN_WORD1 |
| #define NAN_WORD1 0 |
| #endif |
| |
| static int match(const char** sp, const char* t) |
| { |
| int c, d; |
| const char* s = *sp; |
| |
| while ((d = *t++)) { |
| if ((c = *++s) >= 'A' && c <= 'Z') |
| c += 'a' - 'A'; |
| if (c != d) |
| return 0; |
| } |
| *sp = s + 1; |
| return 1; |
| } |
| |
| #ifndef No_Hex_NaN |
| static void hexnan(double* rvp, const char** sp) |
| { |
| uint32_t 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 */ |
| |
| double strtod(const char* s00, char** se) |
| { |
| #ifdef Avoid_Underflow |
| int scale; |
| #endif |
| int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, |
| e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
| const char *s, *s0, *s1; |
| double aadj, aadj1, adj, rv, rv0; |
| int32_t L; |
| uint32_t y, z; |
| Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL; |
| #ifdef SET_INEXACT |
| int inexact, oldinexact; |
| #endif |
| |
| sign = nz0 = nz = 0; |
| dval(rv) = 0.; |
| for (s = s00; ; s++) |
| switch (*s) { |
| case '-': |
| sign = 1; |
| /* no break */ |
| case '+': |
| if (*++s) |
| goto break2; |
| /* no break */ |
| case 0: |
| goto ret0; |
| case '\t': |
| case '\n': |
| case '\v': |
| case '\f': |
| case '\r': |
| case ' ': |
| continue; |
| default: |
| goto break2; |
| } |
| break2: |
| if (*s == '0') { |
| nz0 = 1; |
| while (*++s == '0') { } |
| if (!*s) |
| goto ret; |
| } |
| s0 = s; |
| y = z = 0; |
| for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
| if (nd < 9) |
| y = (10 * y) + c - '0'; |
| else if (nd < 16) |
| z = (10 * z) + c - '0'; |
| nd0 = nd; |
| if (c == '.') { |
| c = *++s; |
| if (!nd) { |
| for (; c == '0'; c = *++s) |
| nz++; |
| if (c > '0' && c <= '9') { |
| s0 = s; |
| nf += nz; |
| nz = 0; |
| goto have_dig; |
| } |
| goto dig_done; |
| } |
| for (; c >= '0' && c <= '9'; c = *++s) { |
| have_dig: |
| nz++; |
| if (c -= '0') { |
| nf += nz; |
| for (i = 1; i < nz; i++) |
| if (nd++ < 9) |
| y *= 10; |
| else if (nd <= DBL_DIG + 1) |
| z *= 10; |
| if (nd++ < 9) |
| y = (10 * y) + c; |
| else if (nd <= DBL_DIG + 1) |
| z = (10 * z) + c; |
| nz = 0; |
| } |
| } |
| } |
| dig_done: |
| e = 0; |
| if (c == 'e' || c == 'E') { |
| if (!nd && !nz && !nz0) { |
| goto ret0; |
| } |
| s00 = s; |
| esign = 0; |
| switch (c = *++s) { |
| case '-': |
| esign = 1; |
| case '+': |
| c = *++s; |
| } |
| if (c >= '0' && c <= '9') { |
| while (c == '0') |
| c = *++s; |
| if (c > '0' && c <= '9') { |
| L = c - '0'; |
| s1 = s; |
| while ((c = *++s) >= '0' && c <= '9') |
| L = (10 * L) + c - '0'; |
| if (s - s1 > 8 || L > 19999) |
| /* Avoid confusion from exponents |
| * so large that e might overflow. |
| */ |
| e = 19999; /* safe for 16 bit ints */ |
| else |
| e = (int)L; |
| if (esign) |
| e = -e; |
| } else |
| e = 0; |
| } else |
| s = s00; |
| } |
| if (!nd) { |
| if (!nz && !nz0) { |
| #ifdef INFNAN_CHECK |
| /* Check for Nan and Infinity */ |
| switch(c) { |
| case 'i': |
| case 'I': |
| if (match(&s,"nf")) { |
| --s; |
| if (!match(&s,"inity")) |
| ++s; |
| word0(rv) = 0x7ff00000; |
| word1(rv) = 0; |
| goto ret; |
| } |
| break; |
| case 'n': |
| case 'N': |
| if (match(&s, "an")) { |
| word0(rv) = NAN_WORD0; |
| word1(rv) = NAN_WORD1; |
| #ifndef No_Hex_NaN |
| if (*s == '(') /*)*/ |
| hexnan(&rv, &s); |
| #endif |
| goto ret; |
| } |
| } |
| #endif /* INFNAN_CHECK */ |
| ret0: |
| s = s00; |
| sign = 0; |
| } |
| goto ret; |
| } |
| e1 = e -= nf; |
| |
| /* Now we have nd0 digits, starting at s0, followed by a |
| * decimal point, followed by nd-nd0 digits. The number we're |
| * after is the integer represented by those digits times |
| * 10**e */ |
| |
| if (!nd0) |
| nd0 = nd; |
| k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
| dval(rv) = y; |
| if (k > 9) { |
| #ifdef SET_INEXACT |
| if (k > DBL_DIG) |
| oldinexact = get_inexact(); |
| #endif |
| dval(rv) = tens[k - 9] * dval(rv) + z; |
| } |
| bd0 = 0; |
| if (nd <= DBL_DIG && Flt_Rounds == 1) { |
| if (!e) |
| goto ret; |
| if (e > 0) { |
| if (e <= Ten_pmax) { |
| /* rv = */ rounded_product(dval(rv), tens[e]); |
| goto ret; |
| } |
| i = DBL_DIG - nd; |
| if (e <= Ten_pmax + i) { |
| /* A fancier test would sometimes let us do |
| * this for larger i values. |
| */ |
| e -= i; |
| dval(rv) *= tens[i]; |
| /* rv = */ rounded_product(dval(rv), tens[e]); |
| goto ret; |
| } |
| } |
| #ifndef Inaccurate_Divide |
| else if (e >= -Ten_pmax) { |
| /* rv = */ rounded_quotient(dval(rv), tens[-e]); |
| goto ret; |
| } |
| #endif |
| } |
| e1 += nd - k; |
| |
| #ifdef SET_INEXACT |
| inexact = 1; |
| if (k <= DBL_DIG) |
| oldinexact = get_inexact(); |
| #endif |
| #ifdef Avoid_Underflow |
| scale = 0; |
| #endif |
| |
| /* Get starting approximation = rv * 10**e1 */ |
| |
| if (e1 > 0) { |
| if ((i = e1 & 15)) |
| dval(rv) *= tens[i]; |
| if (e1 &= ~15) { |
| if (e1 > DBL_MAX_10_EXP) { |
| ovfl: |
| #ifndef NO_ERRNO |
| errno = ERANGE; |
| #endif |
| /* Can't trust HUGE_VAL */ |
| word0(rv) = Exp_mask; |
| word1(rv) = 0; |
| #ifdef SET_INEXACT |
| /* set overflow bit */ |
| dval(rv0) = 1e300; |
| dval(rv0) *= dval(rv0); |
| #endif |
| 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 |
| errno = ERANGE; |
| #endif |
| if (bd0) |
| goto retfree; |
| goto ret; |
| } |
| #ifndef Avoid_Underflow |
| word0(rv) = Tiny0; |
| word1(rv) = Tiny1; |
| /* The refinement below will clean |
| * this approximation up. |
| */ |
| } |
| #endif |
| } |
| } |
| |
| /* Now the hard part -- adjusting rv to the correct value.*/ |
| |
| /* Put digits into bd: true value = bd * 10^e */ |
| |
| bd0 = s2b(s0, nd0, nd, y); |
| |
| for (;;) { |
| bd = Balloc(bd0->k); |
| Bcopy(bd, bd0); |
| bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ |
| bs = i2b(1); |
| |
| if (e >= 0) { |
| bb2 = bb5 = 0; |
| bd2 = bd5 = e; |
| } else { |
| bb2 = bb5 = -e; |
| bd2 = bd5 = 0; |
| } |
| if (bbe >= 0) |
| bb2 += bbe; |
| else |
| bd2 -= bbe; |
| bs2 = bb2; |
| #ifdef 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 |
| j = P + 1 - bbbits; |
| #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); |
| |
| 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 Avoid_Underflow |
| || (word0(rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1 |
| #else |
| || (word0(rv) & Exp_mask) <= Exp_msk1 |
| #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; |
| 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 Avoid_Underflow |
| if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1)) |
| #else |
| if (L <= Exp_msk1) |
| #endif /*Avoid_Underflow*/ |
| 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; |
| break; |
| } |
| if (!(word1(rv) & LSB)) |
| break; |
| if (dsign) |
| dval(rv) += ulp(dval(rv)); |
| else { |
| dval(rv) -= ulp(dval(rv)); |
| #ifndef Sudden_Underflow |
| if (!dval(rv)) |
| goto undfl; |
| #endif |
| } |
| #ifdef Avoid_Underflow |
| dsign = 1 - dsign; |
| #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 = (uint32_t)aadj) <= 0) |
| z = 1; |
| aadj = z; |
| aadj1 = dsign ? aadj : -aadj; |
| } |
| word0(aadj1) += (2 * P + 1) * Exp_msk1 - y; |
| } |
| adj = aadj1 * ulp(dval(rv)); |
| dval(rv) += adj; |
| #else |
| #ifdef Sudden_Underflow |
| if ((word0(rv) & Exp_mask) <= P * Exp_msk1) { |
| dval(rv0) = dval(rv); |
| word0(rv) += P * Exp_msk1; |
| adj = aadj1 * ulp(dval(rv)); |
| dval(rv) += adj; |
| if ((word0(rv) & Exp_mask) <= P * Exp_msk1) |
| { |
| 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 = (int32_t)aadj; |
| aadj -= L; |
| /* The tolerances below are conservative. */ |
| if (dsign || word1(rv) || word0(rv) & Bndry_mask) { |
| if (aadj < .4999999 || aadj > .5000001) |
| break; |
| } else if (aadj < .4999999 / FLT_RADIX) |
| break; |
| } |
| #endif |
| cont: |
| Bfree(bb); |
| Bfree(bd); |
| Bfree(bs); |
| Bfree(delta); |
| } |
| #ifdef SET_INEXACT |
| if (inexact) { |
| if (!oldinexact) { |
| word0(rv0) = Exp_1 + (70 << Exp_shift); |
| word1(rv0) = 0; |
| dval(rv0) += 1.; |
| } |
| } else if (!oldinexact) |
| clear_inexact(); |
| #endif |
| #ifdef Avoid_Underflow |
| if (scale) { |
| word0(rv0) = Exp_1 - 2 * P * Exp_msk1; |
| word1(rv0) = 0; |
| dval(rv) *= dval(rv0); |
| #ifndef NO_ERRNO |
| /* try to avoid the bug of testing an 8087 register value */ |
| if (word0(rv) == 0 && word1(rv) == 0) |
| errno = ERANGE; |
| #endif |
| } |
| #endif /* Avoid_Underflow */ |
| #ifdef SET_INEXACT |
| if (inexact && !(word0(rv) & Exp_mask)) { |
| /* set underflow bit */ |
| dval(rv0) = 1e-300; |
| dval(rv0) *= dval(rv0); |
| } |
| #endif |
| retfree: |
| Bfree(bb); |
| Bfree(bd); |
| Bfree(bs); |
| Bfree(bd0); |
| Bfree(delta); |
| ret: |
| if (se) |
| *se = (char*)s; |
| return sign ? -dval(rv) : dval(rv); |
| } |
| |
| static int quorem(Bigint* b, Bigint* S) |
| { |
| int n; |
| uint32_t *bx, *bxe, q, *sx, *sxe; |
| #ifdef USE_LONG_LONG |
| unsigned long long borrow, carry, y, ys; |
| #else |
| uint32_t borrow, carry, y, ys; |
| #ifdef Pack_32 |
| uint32_t si, z, zs; |
| #endif |
| #endif |
| |
| n = S->wds; |
| ASSERT_WITH_MESSAGE(b->wds <= n, "oversize b in quorem"); |
| 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 */ |
| ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem"); |
| if (q) { |
| borrow = 0; |
| carry = 0; |
| do { |
| #ifdef USE_LONG_LONG |
| ys = *sx++ * (unsigned long long)q + carry; |
| carry = ys >> 32; |
| y = *bx - (ys & 0xffffffffUL) - borrow; |
| borrow = y >> 32 & (uint32_t)1; |
| *bx++ = (uint32_t)y & 0xffffffffUL; |
| #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 USE_LONG_LONG |
| ys = *sx++ + carry; |
| carry = ys >> 32; |
| y = *bx - (ys & 0xffffffffUL) - borrow; |
| borrow = y >> 32 & (uint32_t)1; |
| *bx++ = (uint32_t)y & 0xffffffffUL; |
| #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; |
| } |
| |
| #if !ENABLE(JSC_MULTIPLE_THREADS) |
| static char* dtoa_result; |
| #endif |
| |
| static char* rv_alloc(int i) |
| { |
| int k; |
| |
| int j = sizeof(uint32_t); |
| for (k = 0; |
| sizeof(Bigint) - sizeof(uint32_t) - sizeof(int) + j <= (unsigned)i; |
| j <<= 1) |
| k++; |
| int* r = (int*)Balloc(k); |
| *r = k; |
| return |
| #if !ENABLE(JSC_MULTIPLE_THREADS) |
| dtoa_result = |
| #endif |
| (char*)(r + 1); |
| } |
| |
| static char* nrv_alloc(const char* s, char** rve, int n) |
| { |
| char* rv = rv_alloc(n); |
| char* t = rv; |
| |
| while ((*t = *s++)) |
| t++; |
| if (rve) |
| *rve = t; |
| return rv; |
| } |
| |
| /* freedtoa(s) must be used to free values s returned by dtoa |
| * when MULTIPLE_THREADS is #defined. It should be used in all cases, |
| * but for consistency with earlier versions of dtoa, it is optional |
| * when MULTIPLE_THREADS is not defined. |
| */ |
| |
| void freedtoa(char* s) |
| { |
| Bigint* b = (Bigint*)((int*)s - 1); |
| b->maxwds = 1 << (b->k = *(int*)b); |
| Bfree(b); |
| #if !ENABLE(JSC_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. 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 int32_t |
| * calculation. |
| */ |
| |
| char* dtoa(double d, 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. |
| |
| */ |
| |
| int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, |
| j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
| spec_case, try_quick; |
| int32_t L; |
| #ifndef Sudden_Underflow |
| int denorm; |
| uint32_t x; |
| #endif |
| Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S; |
| double d2, ds, eps; |
| char *s, *s0; |
| #ifdef SET_INEXACT |
| int inexact, oldinexact; |
| #endif |
| |
| #if !ENABLE(JSC_MULTIPLE_THREADS) |
| if (dtoa_result) { |
| freedtoa(dtoa_result); |
| dtoa_result = 0; |
| } |
| #endif |
| |
| if (word0(d) & Sign_bit) { |
| /* set sign for everything, including 0's and NaNs */ |
| *sign = 1; |
| word0(d) &= ~Sign_bit; /* clear sign bit */ |
| } else |
| *sign = 0; |
| |
| if ((word0(d) & Exp_mask) == Exp_mask) |
| { |
| /* Infinity or NaN */ |
| *decpt = 9999; |
| if (!word1(d) && !(word0(d) & 0xfffff)) |
| return nrv_alloc("Infinity", rve, 8); |
| return nrv_alloc("NaN", rve, 3); |
| } |
| if (!dval(d)) { |
| *decpt = 1; |
| return nrv_alloc("0", rve, 1); |
| } |
| |
| #ifdef SET_INEXACT |
| try_quick = oldinexact = get_inexact(); |
| inexact = 1; |
| #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; |
| |
| /* 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; |
| #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; |
| } |
| |
| #ifndef SET_INEXACT |
| #ifdef Check_FLT_ROUNDS |
| try_quick = Rounding == 1; |
| #else |
| try_quick = 1; |
| #endif |
| #endif /*SET_INEXACT*/ |
| |
| leftright = 1; |
| ilim = ilim1 = -1; |
| i = 18; |
| ndigits = 0; |
| s = s0 = rv_alloc(i); |
| |
| 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 = (long int)dval(d); |
| dval(d) -= L; |
| *s++ = '0' + (int)L; |
| if (dval(d) < dval(eps)) |
| goto ret1; |
| if (1. - dval(d) < dval(eps)) |
| goto bump_up; |
| if (++i >= ilim) |
| break; |
| dval(eps) *= 10.; |
| dval(d) *= 10.; |
| } |
| } else { |
| #endif |
| /* Generate ilim digits, then fix them up. */ |
| dval(eps) *= tens[ilim - 1]; |
| for (i = 1;; i++, dval(d) *= 10.) { |
| L = (int32_t)(dval(d)); |
| if (!(dval(d) -= L)) |
| ilim = i; |
| *s++ = '0' + (int)L; |
| if (i == ilim) { |
| if (dval(d) > 0.5 + dval(eps)) |
| goto bump_up; |
| else if (dval(d) < 0.5 - dval(eps)) { |
| while (*--s == '0') { } |
| s++; |
| goto ret1; |
| } |
| break; |
| } |
| } |
| #ifndef No_leftright |
| } |
| #endif |
| fast_failed: |
| s = s0; |
| dval(d) = dval(d2); |
| k = k0; |
| ilim = ilim0; |
| } |
| |
| /* Do we have a "small" integer? */ |
| |
| if (be >= 0 && k <= Int_max) { |
| /* Yes. */ |
| ds = tens[k]; |
| if (ndigits < 0 && ilim <= 0) { |
| S = mhi = 0; |
| if (ilim < 0 || dval(d) <= 5 * ds) |
| goto no_digits; |
| goto one_digit; |
| } |
| for (i = 1;; i++, dval(d) *= 10.) { |
| L = (int32_t)(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) { |
| 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 |
| 1 + P - bbits; |
| 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 (!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 (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); |
| if (j1 == 0 && !(word1(d) & 1)) { |
| 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; |
| } |
| if (j < 0 || j == 0 && !(word1(d) & 1)) { |
| if (!b->x[0] && b->wds <= 1) { |
| #ifdef SET_INEXACT |
| inexact = 0; |
| #endif |
| goto accept_dig; |
| } |
| 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) { |
| 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 (!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 */ |
| |
| 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++; |
| } |
| goto ret; |
| no_digits: |
| k = -1 - ndigits; |
| goto ret; |
| one_digit: |
| *s++ = '1'; |
| k++; |
| goto ret; |
| ret: |
| Bfree(S); |
| if (mhi) { |
| if (mlo && mlo != mhi) |
| Bfree(mlo); |
| Bfree(mhi); |
| } |
| ret1: |
| #ifdef SET_INEXACT |
| if (inexact) { |
| if (!oldinexact) { |
| word0(d) = Exp_1 + (70 << Exp_shift); |
| word1(d) = 0; |
| dval(d) += 1.; |
| } |
| } else if (!oldinexact) |
| clear_inexact(); |
| #endif |
| Bfree(b); |
| *s = 0; |
| *decpt = k + 1; |
| if (rve) |
| *rve = s; |
| return s0; |
| } |
| |
| } // namespace JSC |
