/**************************************************************** * * The author of this software is David M. Gay. * * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. * Copyright (C) 2002-2017 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 (dmg at acm dot org, * with " at " changed at "@" and " dot " changed to "."). */ /* On a machine with IEEE extended-precision registers, it is * necessary to specify double-precision (53-bit) rounding precision * before invoking strtod or dtoa. If the machine uses (the equivalent * of) Intel 80x87 arithmetic, the call * _control87(PC_53, MCW_PC); * does this with many compilers. Whether this or another call is * appropriate depends on the compiler; for this to work, it may be * necessary to #include "float.h" or another system-dependent header * file. */ #include "config.h" #include #include #include #include #include #include #if COMPILER(MSVC) #pragma warning(disable: 4244) #pragma warning(disable: 4245) #pragma warning(disable: 4554) #endif #if CPU(PPC64) || CPU(X86_64) || CPU(ARM64) // FIXME: should we enable this on all 64-bit CPUs? // 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 namespace WTF { static Lock s_dtoaP5Mutex; typedef union { double d; uint32_t L[2]; } U; #if CPU(BIG_ENDIAN) || CPU(MIDDLE_ENDIAN) #define word0(x) (x)->L[0] #define word1(x) (x)->L[1] #else #define word0(x) (x)->L[1] #define word1(x) (x)->L[0] #endif #define dval(x) (x)->d #ifndef USE_LONG_LONG /* The following definition of Storeinc is appropriate for MIPS processors. * An alternative that might be better on some machines is * *p++ = high << 16 | low & 0xffff; */ static ALWAYS_INLINE uint32_t* storeInc(uint32_t* p, uint16_t high, uint16_t low) { uint16_t* p16 = reinterpret_cast(p); #if CPU(BIG_ENDIAN) p16[0] = high; p16[1] = low; #else p16[1] = high; p16[0] = low; #endif return p + 1; } #endif // USE_LONG_LONG #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 #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 struct BigInt { BigInt() : sign(0) { } int sign; void clear() { sign = 0; m_words.clear(); } size_t size() const { return m_words.size(); } void resize(size_t s) { m_words.resize(s); } uint32_t* words() { return m_words.data(); } const uint32_t* words() const { return m_words.data(); } void append(uint32_t w) { m_words.append(w); } Vector m_words; }; static void 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.size(); uint32_t* x = b.words(); 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 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); #endif } while (++i < wds); if (carry) b.append((uint32_t)carry); } 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) return 32; } *y = x; return k; } static void i2b(BigInt& b, int i) { b.sign = 0; b.resize(1); b.words()[0] = i; } static void mult(BigInt& aRef, const BigInt& bRef) { const BigInt* a = &aRef; const BigInt* b = &bRef; BigInt c; int wa, wb, wc; const uint32_t* x = 0; const uint32_t* xa; const uint32_t* xb; const uint32_t* xae; const uint32_t* xbe; uint32_t* xc; uint32_t* xc0; uint32_t y; #ifdef USE_LONG_LONG unsigned long long carry, z; #else uint32_t carry, z; #endif if (a->size() < b->size()) { const BigInt* tmp = a; a = b; b = tmp; } wa = a->size(); wb = b->size(); wc = wa + wb; c.resize(wc); for (xc = c.words(), xa = xc + wc; xc < xa; xc++) *xc = 0; xa = a->words(); xae = xa + wa; xb = b->words(); xbe = xb + wb; xc0 = c.words(); #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 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; xc = 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; xc = storeInc(xc, z, z2); z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; carry = z2 >> 16; } while (x < xae); *xc = z2; } } #endif for (xc0 = c.words(), xc = xc0 + wc; wc > 0 && !*--xc; --wc) { } c.resize(wc); aRef = c; } struct P5Node { WTF_MAKE_NONCOPYABLE(P5Node); WTF_MAKE_FAST_ALLOCATED; public: P5Node() { } BigInt val; P5Node* next { nullptr }; }; static P5Node* p5s; static int p5sCount; static ALWAYS_INLINE void pow5mult(BigInt& b, int k) { static const int p05[3] = { 5, 25, 125 }; if (int i = k & 3) multadd(b, p05[i - 1], 0); if (!(k >>= 2)) return; s_dtoaP5Mutex.lock(); P5Node* p5 = p5s; if (!p5) { /* first time */ p5 = new P5Node; i2b(p5->val, 625); p5->next = 0; p5s = p5; p5sCount = 1; } int p5sCountLocal = p5sCount; s_dtoaP5Mutex.unlock(); int p5sUsed = 0; for (;;) { if (k & 1) mult(b, p5->val); if (!(k >>= 1)) break; if (++p5sUsed == p5sCountLocal) { s_dtoaP5Mutex.lock(); if (p5sUsed == p5sCount) { ASSERT(!p5->next); p5->next = new P5Node; p5->next->next = 0; p5->next->val = p5->val; mult(p5->next->val, p5->next->val); ++p5sCount; } p5sCountLocal = p5sCount; s_dtoaP5Mutex.unlock(); } p5 = p5->next; } } static ALWAYS_INLINE void lshift(BigInt& b, int k) { int n = k >> 5; int origSize = b.size(); int n1 = n + origSize + 1; if (k &= 0x1f) b.resize(b.size() + n + 1); else b.resize(b.size() + n); const uint32_t* srcStart = b.words(); uint32_t* dstStart = b.words(); const uint32_t* src = srcStart + origSize - 1; uint32_t* dst = dstStart + n1 - 1; if (k) { 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); b.resize(origSize + n + !!b.words()[n1 - 1]); } else { do { *--dst = *src--; } while (src >= srcStart); } for (dst = dstStart + n; dst != dstStart; ) *--dst = 0; ASSERT(b.size() <= 1 || b.words()[b.size() - 1]); } static int cmp(const BigInt& a, const BigInt& b) { const uint32_t *xa, *xa0, *xb, *xb0; int i, j; i = a.size(); j = b.size(); ASSERT(i <= 1 || a.words()[i - 1]); ASSERT(j <= 1 || b.words()[j - 1]); if (i -= j) return i; xa0 = a.words(); xa = xa0 + j; xb0 = b.words(); xb = xb0 + j; for (;;) { if (*--xa != *--xb) return *xa < *xb ? -1 : 1; if (xa <= xa0) break; } return 0; } static ALWAYS_INLINE void diff(BigInt& c, const BigInt& aRef, const BigInt& bRef) { const BigInt* a = &aRef; const BigInt* b = &bRef; int i, wa, wb; uint32_t* xc; i = cmp(*a, *b); if (!i) { c.sign = 0; c.resize(1); c.words()[0] = 0; return; } if (i < 0) { const BigInt* tmp = a; a = b; b = tmp; i = 1; } else i = 0; wa = a->size(); const uint32_t* xa = a->words(); const uint32_t* xae = xa + wa; wb = b->size(); const uint32_t* xb = b->words(); const uint32_t* xbe = xb + wb; c.resize(wa); c.sign = i; xc = c.words(); #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; 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; xc = 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; xc = storeInc(xc, z, y); } #endif while (!*--xc) wa--; c.resize(wa); } static ALWAYS_INLINE void d2b(BigInt& b, U* d, int* e, int* bits) { int de, k; uint32_t* x; uint32_t y, z; int i; #define d0 word0(d) #define d1 word1(d) b.sign = 0; b.resize(1); x = b.words(); z = d0 & Frac_mask; d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ if ((de = (int)(d0 >> Exp_shift))) z |= Exp_msk1; if ((y = d1)) { if ((k = lo0bits(&y))) { x[0] = y | (z << (32 - k)); z >>= k; } else x[0] = y; if (z) { b.resize(2); x[1] = z; } i = b.size(); } else { k = lo0bits(&z); x[0] = z; i = 1; b.resize(1); k += 32; } if (de) { *e = de - Bias - (P - 1) + k; *bits = P - k; } else { *e = 0 - Bias - (P - 1) + 1 + k; *bits = (32 * i) - hi0bits(x[i - 1]); } } #undef d0 #undef d1 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 }; #define Scale_Bit 0x10 #define n_bigtens 5 static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S) { size_t n; uint32_t* bx; uint32_t* bxe; uint32_t q; uint32_t* sx; uint32_t* sxe; #ifdef USE_LONG_LONG unsigned long long borrow, carry, y, ys; #else uint32_t borrow, carry, y, ys; uint32_t si, z, zs; #endif ASSERT(b.size() <= 1 || b.words()[b.size() - 1]); ASSERT(S.size() <= 1 || S.words()[S.size() - 1]); n = S.size(); ASSERT_WITH_MESSAGE(b.size() <= n, "oversize b in quorem"); if (b.size() < n) return 0; sx = S.words(); sxe = sx + --n; bx = b.words(); 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 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; bx = storeInc(bx, z, y); #endif } while (sx <= sxe); if (!*bxe) { bx = b.words(); while (--bxe > bx && !*bxe) --n; b.resize(n); } } if (cmp(b, S) >= 0) { q++; borrow = 0; carry = 0; bx = b.words(); sx = S.words(); 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 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; bx = storeInc(bx, z, y); #endif } while (sx <= sxe); bx = b.words(); bxe = bx + n; if (!*bxe) { while (--bxe > bx && !*bxe) --n; b.resize(n); } } return q; } /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * * Inspired by "How to Print Floating-Point Numbers Accurately" by * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. * * Modifications: * 1. Rather than iterating, we use a simple numeric overestimate * to determine k = floor(log10(d)). We scale relevant * quantities using O(log2(k)) rather than O(k) multiplications. * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't * try to generate digits strictly left to right. Instead, we * compute with fewer bits and propagate the carry if necessary * when rounding the final digit up. This is often faster. * 3. Under the assumption that input will be rounded nearest, * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. * That is, we allow equality in stopping tests when the * round-nearest rule will give the same floating-point value * as would satisfaction of the stopping test with strict * inequality. * 4. We remove common factors of powers of 2 from relevant * quantities. * 5. When converting floating-point integers less than 1e16, * we use floating-point arithmetic rather than resorting * to multiple-precision integers. * 6. When asked to produce fewer than 15 digits, we first try * to get by with floating-point arithmetic; we resort to * multiple-precision integer arithmetic only if we cannot * guarantee that the floating-point calculation has given * the correctly rounded result. For k requested digits and * "uniformly" distributed input, the probability is * something like 10^(k-15) that we must resort to the int32_t * calculation. * * Note: 'leftright' translates to 'generate shortest possible string'. */ template void dtoa(DtoaBuffer result, double dd, int ndigits, bool& signOut, int& exponentOut, unsigned& precisionOut) { // Exactly one rounding mode must be specified. ASSERT(roundingNone + roundingSignificantFigures + roundingDecimalPlaces == 1); // roundingNone only allowed (only sensible?) with leftright set. ASSERT(!roundingNone || leftright); ASSERT(std::isfinite(dd)); int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, j, j1, k, k0, k_check, m2, m5, s2, s5, spec_case; int32_t L; int denorm; uint32_t x; BigInt b, delta, mlo, mhi, S; U d2, eps, u; double ds; char* s; char* s0; u.d = dd; /* Infinity or NaN */ ASSERT((word0(&u) & Exp_mask) != Exp_mask); // JavaScript toString conversion treats -0 as 0. if (!dval(&u)) { signOut = false; exponentOut = 0; precisionOut = 1; result[0] = '0'; result[1] = '\0'; return; } if (word0(&u) & Sign_bit) { signOut = true; word0(&u) &= ~Sign_bit; // clear sign bit } else signOut = false; d2b(b, &u, &be, &bbits); if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) { dval(&d2) = dval(&u); 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; denorm = 0; } else { /* d is denormalized */ i = bbits + be + (Bias + (P - 1) - 1); x = (i > 32) ? (word0(&u) << (64 - i)) | (word1(&u) >> (i - 32)) : word1(&u) << (32 - i); dval(&d2) = x; word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */ i -= (Bias + (P - 1) - 1) + 1; denorm = 1; } 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(&u) < 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 (roundingNone) { ilim = ilim1 = -1; i = 18; ndigits = 0; } if (roundingSignificantFigures) { if (ndigits <= 0) ndigits = 1; ilim = ilim1 = i = ndigits; } if (roundingDecimalPlaces) { i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) i = 1; } s = s0 = result; if (ilim >= 0 && ilim <= Quick_max) { /* Try to get by with floating-point arithmetic. */ i = 0; dval(&d2) = dval(&u); 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(&u) /= bigtens[n_bigtens - 1]; ieps++; } for (; j; j >>= 1, i++) { if (j & 1) { ieps++; ds *= bigtens[i]; } } dval(&u) /= ds; } else if ((j1 = -k)) { dval(&u) *= tens[j1 & 0xf]; for (j = j1 >> 4; j; j >>= 1, i++) { if (j & 1) { ieps++; dval(&u) *= bigtens[i]; } } } if (k_check && dval(&u) < 1. && ilim > 0) { if (ilim1 <= 0) goto fastFailed; ilim = ilim1; k--; dval(&u) *= 10.; ieps++; } dval(&eps) = (ieps * dval(&u)) + 7.; word0(&eps) -= (P - 1) * Exp_msk1; if (!ilim) { S.clear(); mhi.clear(); dval(&u) -= 5.; if (dval(&u) > dval(&eps)) goto oneDigit; if (dval(&u) < -dval(&eps)) goto noDigits; goto fastFailed; } 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(&u); dval(&u) -= L; *s++ = '0' + (int)L; if (dval(&u) < dval(&eps)) goto ret; if (1. - dval(&u) < dval(&eps)) goto bumpUp; if (++i >= ilim) break; dval(&eps) *= 10.; dval(&u) *= 10.; } } else { /* Generate ilim digits, then fix them up. */ dval(&eps) *= tens[ilim - 1]; for (i = 1;; i++, dval(&u) *= 10.) { L = (int32_t)(dval(&u)); if (!(dval(&u) -= L)) ilim = i; *s++ = '0' + (int)L; if (i == ilim) { if (dval(&u) > 0.5 + dval(&eps)) goto bumpUp; if (dval(&u) < 0.5 - dval(&eps)) { while (*--s == '0') { } s++; goto ret; } break; } } } fastFailed: s = s0; dval(&u) = 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.clear(); mhi.clear(); if (ilim < 0 || dval(&u) <= 5 * ds) goto noDigits; goto oneDigit; } for (i = 1;; i++, dval(&u) *= 10.) { L = (int32_t)(dval(&u) / ds); dval(&u) -= L * ds; *s++ = '0' + (int)L; if (!dval(&u)) { break; } if (i == ilim) { dval(&u) += dval(&u); if (dval(&u) > ds || (dval(&u) == ds && (L & 1))) { bumpUp: while (*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } } goto ret; } m2 = b2; m5 = b5; mhi.clear(); mlo.clear(); if (leftright) { i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits; b2 += i; s2 += i; i2b(mhi, 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) { pow5mult(mhi, m5); mult(b, mhi); } if ((j = b5 - m5)) pow5mult(b, j); } else pow5mult(b, b5); } i2b(S, 1); if (s5 > 0) pow5mult(S, s5); /* Check for special case that d is a normalized power of 2. */ spec_case = 0; if ((roundingNone || leftright) && (!word1(&u) && !(word0(&u) & Bndry_mask) && word0(&u) & (Exp_mask & ~Exp_msk1))) { /* 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. */ if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f)) i = 32 - i; 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) lshift(b, b2); if (s2 > 0) lshift(S, s2); if (k_check) { if (cmp(b, S) < 0) { k--; multadd(b, 10, 0); /* we botched the k estimate */ if (leftright) multadd(mhi, 10, 0); ilim = ilim1; } } if (ilim <= 0 && roundingDecimalPlaces) { if (ilim < 0) goto noDigits; multadd(S, 5, 0); // For IEEE-754 unbiased rounding this check should be <=, such that 0.5 would flush to zero. if (cmp(b, S) < 0) goto noDigits; goto oneDigit; } if (leftright) { if (m2 > 0) lshift(mhi, m2); /* Compute mlo -- check for special case * that d is a normalized power of 2. */ mlo = mhi; if (spec_case) 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); diff(delta, S, mhi); j1 = delta.sign ? 1 : cmp(b, delta); #ifdef DTOA_ROUND_BIASED if (j < 0 || !j) { #else // FIXME: ECMA-262 specifies that equidistant results round away from // zero, which probably means we shouldn't be on the unbiased code path // (the (word1(&u) & 1) clause is looking highly suspicious). I haven't // yet understood this code well enough to make the call, but we should // probably be enabling DTOA_ROUND_BIASED. I think the interesting corner // case to understand is probably "Math.pow(0.5, 24).toString()". // I believe this value is interesting because I think it is precisely // representable in binary floating point, and its decimal representation // has a single digit that Steele & White reduction can remove, with the // value 5 (thus equidistant from the next numbers above and below). // We produce the correct answer using either codepath, and I don't as // yet understand why. :-) if (!j1 && !(word1(&u) & 1)) { if (dig == '9') goto round9up; if (j > 0) dig++; *s++ = dig; goto ret; } if (j < 0 || (!j && !(word1(&u) & 1))) { #endif if ((b.words()[0] || b.size() > 1) && (j1 > 0)) { lshift(b, 1); j1 = cmp(b, S); // For IEEE-754 round-to-even, this check should be (j1 > 0 || (!j1 && (dig & 1))), // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should // be rounded away from zero. if (j1 >= 0) { if (dig == '9') goto round9up; dig++; } } *s++ = dig; goto ret; } if (j1 > 0) { if (dig == '9') { /* possible if i == 1 */ round9up: *s++ = '9'; goto roundoff; } *s++ = dig + 1; goto ret; } *s++ = dig; if (i == ilim) break; multadd(b, 10, 0); multadd(mlo, 10, 0); multadd(mhi, 10, 0); } } else { for (i = 1;; i++) { *s++ = dig = quorem(b, S) + '0'; if (!b.words()[0] && b.size() <= 1) goto ret; if (i >= ilim) break; multadd(b, 10, 0); } } /* Round off last digit */ lshift(b, 1); j = cmp(b, S); // For IEEE-754 round-to-even, this check should be (j > 0 || (!j && (dig & 1))), // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should // be rounded away from zero. if (j >= 0) { roundoff: while (*--s == '9') if (s == s0) { k++; *s++ = '1'; goto ret; } ++*s++; } else { while (*--s == '0') { } s++; } goto ret; noDigits: exponentOut = 0; precisionOut = 1; result[0] = '0'; result[1] = '\0'; return; oneDigit: *s++ = '1'; k++; goto ret; ret: ASSERT(s > result); *s = 0; exponentOut = k; precisionOut = s - result; } void dtoa(DtoaBuffer result, double dd, bool& sign, int& exponent, unsigned& precision) { // flags are roundingNone, leftright. dtoa(result, dd, 0, sign, exponent, precision); } void dtoaRoundSF(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision) { // flag is roundingSignificantFigures. dtoa(result, dd, ndigits, sign, exponent, precision); } void dtoaRoundDP(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision) { // flag is roundingDecimalPlaces. dtoa(result, dd, ndigits, sign, exponent, precision); } const char* numberToString(double d, NumberToStringBuffer buffer) { double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength); auto& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter(); converter.ToShortest(d, &builder); return builder.Finalize(); } static inline const char* formatStringTruncatingTrailingZerosIfNeeded(NumberToStringBuffer buffer, double_conversion::StringBuilder& builder) { size_t length = builder.position(); size_t decimalPointPosition = 0; for (; decimalPointPosition < length; ++decimalPointPosition) { if (buffer[decimalPointPosition] == '.') break; } // No decimal separator found, early exit. if (decimalPointPosition == length) return builder.Finalize(); size_t pastMantissa = decimalPointPosition + 1; for (; pastMantissa < length; ++pastMantissa) { if (buffer[pastMantissa] == 'e') break; } size_t truncatedLength = pastMantissa; for (; truncatedLength > decimalPointPosition + 1; --truncatedLength) { if (buffer[truncatedLength - 1] != '0') break; } // No trailing zeros found to strip. if (truncatedLength == pastMantissa) return builder.Finalize(); // If we removed all trailing zeros, remove the decimal point as well. if (truncatedLength == decimalPointPosition + 1) truncatedLength = decimalPointPosition; // Truncate the mantissa, and return the final result. builder.RemoveCharacters(truncatedLength, pastMantissa); return builder.Finalize(); } const char* numberToFixedPrecisionString(double d, unsigned significantFigures, NumberToStringBuffer buffer, bool truncateTrailingZeros) { // Mimic String::format("%.[precision]g", ...), but use dtoas rounding facilities. // "g": Signed value printed in f or e format, whichever is more compact for the given value and precision. // The e format is used only when the exponent of the value is less than –4 or greater than or equal to the // precision argument. Trailing zeros are truncated, and the decimal point appears only if one or more digits follow it. // "precision": The precision specifies the maximum number of significant digits printed. double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength); auto& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter(); converter.ToPrecision(d, significantFigures, &builder); if (!truncateTrailingZeros) return builder.Finalize(); return formatStringTruncatingTrailingZerosIfNeeded(buffer, builder); } const char* numberToFixedWidthString(double d, unsigned decimalPlaces, NumberToStringBuffer buffer) { // Mimic String::format("%.[precision]f", ...), but use dtoas rounding facilities. // "f": Signed value having the form [ – ]dddd.dddd, where dddd is one or more decimal digits. // The number of digits before the decimal point depends on the magnitude of the number, and // the number of digits after the decimal point depends on the requested precision. // "precision": The precision value specifies the number of digits after the decimal point. // If a decimal point appears, at least one digit appears before it. // The value is rounded to the appropriate number of digits. double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength); auto& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter(); converter.ToFixed(d, decimalPlaces, &builder); return builder.Finalize(); } namespace Internal { double parseDoubleFromLongString(const UChar* string, size_t length, size_t& parsedLength) { Vector conversionBuffer(length); for (size_t i = 0; i < length; ++i) conversionBuffer[i] = isASCII(string[i]) ? string[i] : 0; return parseDouble(conversionBuffer.data(), length, parsedLength); } } // namespace Internal } // namespace WTF