// Tencent is pleased to support the open source community by making RapidJSON available. // // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. // // Licensed under the MIT License (the "License"); you may not use this file except // in compliance with the License. You may obtain a copy of the License at // // http://opensource.org/licenses/MIT // // Unless required by applicable law or agreed to in writing, software distributed // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR // CONDITIONS OF ANY KIND, either express or implied. See the License for the // specific language governing permissions and limitations under the License. // This is a C++ header-only implementation of Grisu2 algorithm from the publication: // Loitsch, Florian. "Printing floating-point numbers quickly and accurately with // integers." ACM Sigplan Notices 45.6 (2010): 233-243. #ifndef RAPIDJSON_DTOA_ #define RAPIDJSON_DTOA_ #include "itoa.h" // GetDigitsLut() #include "diyfp.h" #include "ieee754.h" RAPIDJSON_NAMESPACE_BEGIN namespace internal { #ifdef __GNUC__ RAPIDJSON_DIAG_PUSH RAPIDJSON_DIAG_OFF(effc++) RAPIDJSON_DIAG_OFF(array-bounds) // some gcc versions generate wrong warnings https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124 #endif inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) { while (rest < wp_w && delta - rest >= ten_kappa && (rest + ten_kappa < wp_w || /// closer wp_w - rest > rest + ten_kappa - wp_w)) { buffer[len - 1]--; rest += ten_kappa; } } inline unsigned CountDecimalDigit32(uint32_t n) { // Simple pure C++ implementation was faster than __builtin_clz version in this situation. if (n < 10) return 1; if (n < 100) return 2; if (n < 1000) return 3; if (n < 10000) return 4; if (n < 100000) return 5; if (n < 1000000) return 6; if (n < 10000000) return 7; if (n < 100000000) return 8; // Will not reach 10 digits in DigitGen() //if (n < 1000000000) return 9; //return 10; return 9; } inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) { static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; const DiyFp one(uint64_t(1) << -Mp.e, Mp.e); const DiyFp wp_w = Mp - W; uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e); uint64_t p2 = Mp.f & (one.f - 1); unsigned kappa = CountDecimalDigit32(p1); // kappa in [0, 9] *len = 0; while (kappa > 0) { uint32_t d = 0; switch (kappa) { case 9: d = p1 / 100000000; p1 %= 100000000; break; case 8: d = p1 / 10000000; p1 %= 10000000; break; case 7: d = p1 / 1000000; p1 %= 1000000; break; case 6: d = p1 / 100000; p1 %= 100000; break; case 5: d = p1 / 10000; p1 %= 10000; break; case 4: d = p1 / 1000; p1 %= 1000; break; case 3: d = p1 / 100; p1 %= 100; break; case 2: d = p1 / 10; p1 %= 10; break; case 1: d = p1; p1 = 0; break; default:; } if (d || *len) buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d)); kappa--; uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2; if (tmp <= delta) { *K += kappa; GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f); return; } } // kappa = 0 for (;;) { p2 *= 10; delta *= 10; char d = static_cast<char>(p2 >> -one.e); if (d || *len) buffer[(*len)++] = static_cast<char>('0' + d); p2 &= one.f - 1; kappa--; if (p2 < delta) { *K += kappa; int index = -static_cast<int>(kappa); GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 9 ? kPow10[-static_cast<int>(kappa)] : 0)); return; } } } inline void Grisu2(double value, char* buffer, int* length, int* K) { const DiyFp v(value); DiyFp w_m, w_p; v.NormalizedBoundaries(&w_m, &w_p); const DiyFp c_mk = GetCachedPower(w_p.e, K); const DiyFp W = v.Normalize() * c_mk; DiyFp Wp = w_p * c_mk; DiyFp Wm = w_m * c_mk; Wm.f++; Wp.f--; DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K); } inline char* WriteExponent(int K, char* buffer) { if (K < 0) { *buffer++ = '-'; K = -K; } if (K >= 100) { *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100)); K %= 100; const char* d = GetDigitsLut() + K * 2; *buffer++ = d[0]; *buffer++ = d[1]; } else if (K >= 10) { const char* d = GetDigitsLut() + K * 2; *buffer++ = d[0]; *buffer++ = d[1]; } else *buffer++ = static_cast<char>('0' + static_cast<char>(K)); return buffer; } inline char* Prettify(char* buffer, int length, int k, int maxDecimalPlaces) { const int kk = length + k; // 10^(kk-1) <= v < 10^kk if (0 <= k && kk <= 21) { // 1234e7 -> 12340000000 for (int i = length; i < kk; i++) buffer[i] = '0'; buffer[kk] = '.'; buffer[kk + 1] = '0'; return &buffer[kk + 2]; } else if (0 < kk && kk <= 21) { // 1234e-2 -> 12.34 std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk)); buffer[kk] = '.'; if (0 > k + maxDecimalPlaces) { // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1 // Remove extra trailing zeros (at least one) after truncation. for (int i = kk + maxDecimalPlaces; i > kk + 1; i--) if (buffer[i] != '0') return &buffer[i + 1]; return &buffer[kk + 2]; // Reserve one zero } else return &buffer[length + 1]; } else if (-6 < kk && kk <= 0) { // 1234e-6 -> 0.001234 const int offset = 2 - kk; std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length)); buffer[0] = '0'; buffer[1] = '.'; for (int i = 2; i < offset; i++) buffer[i] = '0'; if (length - kk > maxDecimalPlaces) { // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1 // Remove extra trailing zeros (at least one) after truncation. for (int i = maxDecimalPlaces + 1; i > 2; i--) if (buffer[i] != '0') return &buffer[i + 1]; return &buffer[3]; // Reserve one zero } else return &buffer[length + offset]; } else if (kk < -maxDecimalPlaces) { // Truncate to zero buffer[0] = '0'; buffer[1] = '.'; buffer[2] = '0'; return &buffer[3]; } else if (length == 1) { // 1e30 buffer[1] = 'e'; return WriteExponent(kk - 1, &buffer[2]); } else { // 1234e30 -> 1.234e33 std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1)); buffer[1] = '.'; buffer[length + 1] = 'e'; return WriteExponent(kk - 1, &buffer[0 + length + 2]); } } inline char* dtoa(double value, char* buffer, int maxDecimalPlaces = 324) { RAPIDJSON_ASSERT(maxDecimalPlaces >= 1); Double d(value); if (d.IsZero()) { if (d.Sign()) *buffer++ = '-'; // -0.0, Issue #289 buffer[0] = '0'; buffer[1] = '.'; buffer[2] = '0'; return &buffer[3]; } else { if (value < 0) { *buffer++ = '-'; value = -value; } int length, K; Grisu2(value, buffer, &length, &K); return Prettify(buffer, length, K, maxDecimalPlaces); } } #ifdef __GNUC__ RAPIDJSON_DIAG_POP #endif } // namespace internal RAPIDJSON_NAMESPACE_END #endif // RAPIDJSON_DTOA_