1 // Tencent is pleased to support the open source community by making RapidJSON available. 2 // 3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. 4 // 5 // Licensed under the MIT License (the "License"); you may not use this file except 6 // in compliance with the License. You may obtain a copy of the License at 7 // 8 // http://opensource.org/licenses/MIT 9 // 10 // Unless required by applicable law or agreed to in writing, software distributed 11 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR 12 // CONDITIONS OF ANY KIND, either express or implied. See the License for the 13 // specific language governing permissions and limitations under the License. 14 15 // This is a C++ header-only implementation of Grisu2 algorithm from the publication: 16 // Loitsch, Florian. "Printing floating-point numbers quickly and accurately with 17 // integers." ACM Sigplan Notices 45.6 (2010): 233-243. 18 19 #ifndef RAPIDJSON_DTOA_ 20 #define RAPIDJSON_DTOA_ 21 22 #include "itoa.h" // GetDigitsLut() 23 #include "diyfp.h" 24 #include "ieee754.h" 25 26 RAPIDJSON_NAMESPACE_BEGIN 27 namespace internal { 28 29 #ifdef __GNUC__ 30 RAPIDJSON_DIAG_PUSH 31 RAPIDJSON_DIAG_OFF(effc++) 32 #endif 33 34 inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) { 35 while (rest < wp_w && delta - rest >= ten_kappa && 36 (rest + ten_kappa < wp_w || /// closer 37 wp_w - rest > rest + ten_kappa - wp_w)) { 38 buffer[len - 1]--; 39 rest += ten_kappa; 40 } 41 } 42 43 inline unsigned CountDecimalDigit32(uint32_t n) { 44 // Simple pure C++ implementation was faster than __builtin_clz version in this situation. 45 if (n < 10) return 1; 46 if (n < 100) return 2; 47 if (n < 1000) return 3; 48 if (n < 10000) return 4; 49 if (n < 100000) return 5; 50 if (n < 1000000) return 6; 51 if (n < 10000000) return 7; 52 if (n < 100000000) return 8; 53 // Will not reach 10 digits in DigitGen() 54 //if (n < 1000000000) return 9; 55 //return 10; 56 return 9; 57 } 58 59 inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) { 60 static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; 61 const DiyFp one(uint64_t(1) << -Mp.e, Mp.e); 62 const DiyFp wp_w = Mp - W; 63 uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e); 64 uint64_t p2 = Mp.f & (one.f - 1); 65 unsigned kappa = CountDecimalDigit32(p1); // kappa in [0, 9] 66 *len = 0; 67 68 while (kappa > 0) { 69 uint32_t d = 0; 70 switch (kappa) { 71 case 9: d = p1 / 100000000; p1 %= 100000000; break; 72 case 8: d = p1 / 10000000; p1 %= 10000000; break; 73 case 7: d = p1 / 1000000; p1 %= 1000000; break; 74 case 6: d = p1 / 100000; p1 %= 100000; break; 75 case 5: d = p1 / 10000; p1 %= 10000; break; 76 case 4: d = p1 / 1000; p1 %= 1000; break; 77 case 3: d = p1 / 100; p1 %= 100; break; 78 case 2: d = p1 / 10; p1 %= 10; break; 79 case 1: d = p1; p1 = 0; break; 80 default:; 81 } 82 if (d || *len) 83 buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d)); 84 kappa--; 85 uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2; 86 if (tmp <= delta) { 87 *K += kappa; 88 GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f); 89 return; 90 } 91 } 92 93 // kappa = 0 94 for (;;) { 95 p2 *= 10; 96 delta *= 10; 97 char d = static_cast<char>(p2 >> -one.e); 98 if (d || *len) 99 buffer[(*len)++] = static_cast<char>('0' + d); 100 p2 &= one.f - 1; 101 kappa--; 102 if (p2 < delta) { 103 *K += kappa; 104 GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * kPow10[-static_cast<int>(kappa)]); 105 return; 106 } 107 } 108 } 109 110 inline void Grisu2(double value, char* buffer, int* length, int* K) { 111 const DiyFp v(value); 112 DiyFp w_m, w_p; 113 v.NormalizedBoundaries(&w_m, &w_p); 114 115 const DiyFp c_mk = GetCachedPower(w_p.e, K); 116 const DiyFp W = v.Normalize() * c_mk; 117 DiyFp Wp = w_p * c_mk; 118 DiyFp Wm = w_m * c_mk; 119 Wm.f++; 120 Wp.f--; 121 DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K); 122 } 123 124 inline char* WriteExponent(int K, char* buffer) { 125 if (K < 0) { 126 *buffer++ = '-'; 127 K = -K; 128 } 129 130 if (K >= 100) { 131 *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100)); 132 K %= 100; 133 const char* d = GetDigitsLut() + K * 2; 134 *buffer++ = d[0]; 135 *buffer++ = d[1]; 136 } 137 else if (K >= 10) { 138 const char* d = GetDigitsLut() + K * 2; 139 *buffer++ = d[0]; 140 *buffer++ = d[1]; 141 } 142 else 143 *buffer++ = static_cast<char>('0' + static_cast<char>(K)); 144 145 return buffer; 146 } 147 148 inline char* Prettify(char* buffer, int length, int k) { 149 const int kk = length + k; // 10^(kk-1) <= v < 10^kk 150 151 if (length <= kk && kk <= 21) { 152 // 1234e7 -> 12340000000 153 for (int i = length; i < kk; i++) 154 buffer[i] = '0'; 155 buffer[kk] = '.'; 156 buffer[kk + 1] = '0'; 157 return &buffer[kk + 2]; 158 } 159 else if (0 < kk && kk <= 21) { 160 // 1234e-2 -> 12.34 161 std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk)); 162 buffer[kk] = '.'; 163 return &buffer[length + 1]; 164 } 165 else if (-6 < kk && kk <= 0) { 166 // 1234e-6 -> 0.001234 167 const int offset = 2 - kk; 168 std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length)); 169 buffer[0] = '0'; 170 buffer[1] = '.'; 171 for (int i = 2; i < offset; i++) 172 buffer[i] = '0'; 173 return &buffer[length + offset]; 174 } 175 else if (length == 1) { 176 // 1e30 177 buffer[1] = 'e'; 178 return WriteExponent(kk - 1, &buffer[2]); 179 } 180 else { 181 // 1234e30 -> 1.234e33 182 std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1)); 183 buffer[1] = '.'; 184 buffer[length + 1] = 'e'; 185 return WriteExponent(kk - 1, &buffer[0 + length + 2]); 186 } 187 } 188 189 inline char* dtoa(double value, char* buffer) { 190 Double d(value); 191 if (d.IsZero()) { 192 if (d.Sign()) 193 *buffer++ = '-'; // -0.0, Issue #289 194 buffer[0] = '0'; 195 buffer[1] = '.'; 196 buffer[2] = '0'; 197 return &buffer[3]; 198 } 199 else { 200 if (value < 0) { 201 *buffer++ = '-'; 202 value = -value; 203 } 204 int length, K; 205 Grisu2(value, buffer, &length, &K); 206 return Prettify(buffer, length, K); 207 } 208 } 209 210 #ifdef __GNUC__ 211 RAPIDJSON_DIAG_POP 212 #endif 213 214 } // namespace internal 215 RAPIDJSON_NAMESPACE_END 216 217 #endif // RAPIDJSON_DTOA_ 218
