| /**************************************************************** |
| * |
| * The author of this software is David M. Gay. |
| * |
| * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. |
| * Copyright (C) 2002, 2005, 2006, 2007, 2008, 2010, 2012, 2015 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 "dtoa.h" |
| |
| #include <stdio.h> |
| #include <wtf/Lock.h> |
| #include <wtf/MathExtras.h> |
| #include <wtf/Threading.h> |
| #include <wtf/Vector.h> |
| |
| #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 StaticLock 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<uint16_t*>(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<uint32_t, 16> 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; |
| }; |
| |
| 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<bool roundingNone, bool roundingSignificantFigures, bool roundingDecimalPlaces, bool leftright> |
| 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<true, false, false, true>(result, dd, 0, sign, exponent, precision); |
| } |
| |
| void dtoaRoundSF(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision) |
| { |
| // flag is roundingSignificantFigures. |
| dtoa<false, true, false, false>(result, dd, ndigits, sign, exponent, precision); |
| } |
| |
| void dtoaRoundDP(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision) |
| { |
| // flag is roundingDecimalPlaces. |
| dtoa<false, false, true, false>(result, dd, ndigits, sign, exponent, precision); |
| } |
| |
| const char* numberToString(double d, NumberToStringBuffer buffer) |
| { |
| double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength); |
| const double_conversion::DoubleToStringConverter& 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 seperator found, early exit. |
| if (decimalPointPosition == length) |
| return builder.Finalize(); |
| |
| size_t truncatedLength = length - 1; |
| for (; truncatedLength > decimalPointPosition; --truncatedLength) { |
| if (buffer[truncatedLength] != '0') |
| break; |
| } |
| |
| // No trailing zeros found to strip. |
| if (truncatedLength == length - 1) |
| return builder.Finalize(); |
| |
| // If we removed all trailing zeros, remove the decimal point as well. |
| if (truncatedLength == decimalPointPosition) { |
| ASSERT(truncatedLength > 0); |
| --truncatedLength; |
| } |
| |
| // Truncate the StringBuilder, and return the final result. |
| builder.SetPosition(truncatedLength + 1); |
| 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); |
| const double_conversion::DoubleToStringConverter& 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); |
| const double_conversion::DoubleToStringConverter& 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<LChar> 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 |
