dtoa.h

00001 // Tencent is pleased to support the open source community by making RapidJSON available.
00002 // 
00003 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
00004 //
00005 // Licensed under the MIT License (the "License"); you may not use this file except
00006 // in compliance with the License. You may obtain a copy of the License at
00007 //
00008 // http://opensource.org/licenses/MIT
00009 //
00010 // Unless required by applicable law or agreed to in writing, software distributed 
00011 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR 
00012 // CONDITIONS OF ANY KIND, either express or implied. See the License for the 
00013 // specific language governing permissions and limitations under the License.
00014 
00015 // This is a C++ header-only implementation of Grisu2 algorithm from the publication:
00016 // Loitsch, Florian. "Printing floating-point numbers quickly and accurately with
00017 // integers." ACM Sigplan Notices 45.6 (2010): 233-243.
00018 
00019 #ifndef RAPIDJSON_DTOA_
00020 #define RAPIDJSON_DTOA_
00021 
00022 #include "itoa.h" // GetDigitsLut()
00023 #include "diyfp.h"
00024 #include "ieee754.h"
00025 
00026 RAPIDJSON_NAMESPACE_BEGIN
00027 namespace internal {
00028 
00029 #ifdef __GNUC__
00030 RAPIDJSON_DIAG_PUSH
00031 RAPIDJSON_DIAG_OFF(effc++)
00032 RAPIDJSON_DIAG_OFF(array-bounds) // some gcc versions generate wrong warnings https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124
00033 #endif
00034 
00035 inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) {
00036     while (rest < wp_w && delta - rest >= ten_kappa &&
00037            (rest + ten_kappa < wp_w ||  /// closer
00038             wp_w - rest > rest + ten_kappa - wp_w)) {
00039         buffer[len - 1]--;
00040         rest += ten_kappa;
00041     }
00042 }
00043 
00044 inline unsigned CountDecimalDigit32(uint32_t n) {
00045     // Simple pure C++ implementation was faster than __builtin_clz version in this situation.
00046     if (n < 10) return 1;
00047     if (n < 100) return 2;
00048     if (n < 1000) return 3;
00049     if (n < 10000) return 4;
00050     if (n < 100000) return 5;
00051     if (n < 1000000) return 6;
00052     if (n < 10000000) return 7;
00053     if (n < 100000000) return 8;
00054     // Will not reach 10 digits in DigitGen()
00055     //if (n < 1000000000) return 9;
00056     //return 10;
00057     return 9;
00058 }
00059 
00060 inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) {
00061     static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
00062     const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
00063     const DiyFp wp_w = Mp - W;
00064     uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
00065     uint64_t p2 = Mp.f & (one.f - 1);
00066     unsigned kappa = CountDecimalDigit32(p1); // kappa in [0, 9]
00067     *len = 0;
00068 
00069     while (kappa > 0) {
00070         uint32_t d = 0;
00071         switch (kappa) {
00072             case  9: d = p1 /  100000000; p1 %=  100000000; break;
00073             case  8: d = p1 /   10000000; p1 %=   10000000; break;
00074             case  7: d = p1 /    1000000; p1 %=    1000000; break;
00075             case  6: d = p1 /     100000; p1 %=     100000; break;
00076             case  5: d = p1 /      10000; p1 %=      10000; break;
00077             case  4: d = p1 /       1000; p1 %=       1000; break;
00078             case  3: d = p1 /        100; p1 %=        100; break;
00079             case  2: d = p1 /         10; p1 %=         10; break;
00080             case  1: d = p1;              p1 =           0; break;
00081             default:;
00082         }
00083         if (d || *len)
00084             buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
00085         kappa--;
00086         uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
00087         if (tmp <= delta) {
00088             *K += kappa;
00089             GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f);
00090             return;
00091         }
00092     }
00093 
00094     // kappa = 0
00095     for (;;) {
00096         p2 *= 10;
00097         delta *= 10;
00098         char d = static_cast<char>(p2 >> -one.e);
00099         if (d || *len)
00100             buffer[(*len)++] = static_cast<char>('0' + d);
00101         p2 &= one.f - 1;
00102         kappa--;
00103         if (p2 < delta) {
00104             *K += kappa;
00105             int index = -static_cast<int>(kappa);
00106             GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 9 ? kPow10[-static_cast<int>(kappa)] : 0));
00107             return;
00108         }
00109     }
00110 }
00111 
00112 inline void Grisu2(double value, char* buffer, int* length, int* K) {
00113     const DiyFp v(value);
00114     DiyFp w_m, w_p;
00115     v.NormalizedBoundaries(&w_m, &w_p);
00116 
00117     const DiyFp c_mk = GetCachedPower(w_p.e, K);
00118     const DiyFp W = v.Normalize() * c_mk;
00119     DiyFp Wp = w_p * c_mk;
00120     DiyFp Wm = w_m * c_mk;
00121     Wm.f++;
00122     Wp.f--;
00123     DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
00124 }
00125 
00126 inline char* WriteExponent(int K, char* buffer) {
00127     if (K < 0) {
00128         *buffer++ = '-';
00129         K = -K;
00130     }
00131 
00132     if (K >= 100) {
00133         *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
00134         K %= 100;
00135         const char* d = GetDigitsLut() + K * 2;
00136         *buffer++ = d[0];
00137         *buffer++ = d[1];
00138     }
00139     else if (K >= 10) {
00140         const char* d = GetDigitsLut() + K * 2;
00141         *buffer++ = d[0];
00142         *buffer++ = d[1];
00143     }
00144     else
00145         *buffer++ = static_cast<char>('0' + static_cast<char>(K));
00146 
00147     return buffer;
00148 }
00149 
00150 inline char* Prettify(char* buffer, int length, int k, int maxDecimalPlaces) {
00151     const int kk = length + k;  // 10^(kk-1) <= v < 10^kk
00152 
00153     if (0 <= k && kk <= 21) {
00154         // 1234e7 -> 12340000000
00155         for (int i = length; i < kk; i++)
00156             buffer[i] = '0';
00157         buffer[kk] = '.';
00158         buffer[kk + 1] = '0';
00159         return &buffer[kk + 2];
00160     }
00161     else if (0 < kk && kk <= 21) {
00162         // 1234e-2 -> 12.34
00163         std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk));
00164         buffer[kk] = '.';
00165         if (0 > k + maxDecimalPlaces) {
00166             // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1
00167             // Remove extra trailing zeros (at least one) after truncation.
00168             for (int i = kk + maxDecimalPlaces; i > kk + 1; i--)
00169                 if (buffer[i] != '0')
00170                     return &buffer[i + 1];
00171             return &buffer[kk + 2]; // Reserve one zero
00172         }
00173         else
00174             return &buffer[length + 1];
00175     }
00176     else if (-6 < kk && kk <= 0) {
00177         // 1234e-6 -> 0.001234
00178         const int offset = 2 - kk;
00179         std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
00180         buffer[0] = '0';
00181         buffer[1] = '.';
00182         for (int i = 2; i < offset; i++)
00183             buffer[i] = '0';
00184         if (length - kk > maxDecimalPlaces) {
00185             // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1
00186             // Remove extra trailing zeros (at least one) after truncation.
00187             for (int i = maxDecimalPlaces + 1; i > 2; i--)
00188                 if (buffer[i] != '0')
00189                     return &buffer[i + 1];
00190             return &buffer[3]; // Reserve one zero
00191         }
00192         else
00193             return &buffer[length + offset];
00194     }
00195     else if (kk < -maxDecimalPlaces) {
00196         // Truncate to zero
00197         buffer[0] = '0';
00198         buffer[1] = '.';
00199         buffer[2] = '0';
00200         return &buffer[3];
00201     }
00202     else if (length == 1) {
00203         // 1e30
00204         buffer[1] = 'e';
00205         return WriteExponent(kk - 1, &buffer[2]);
00206     }
00207     else {
00208         // 1234e30 -> 1.234e33
00209         std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
00210         buffer[1] = '.';
00211         buffer[length + 1] = 'e';
00212         return WriteExponent(kk - 1, &buffer[0 + length + 2]);
00213     }
00214 }
00215 
00216 inline char* dtoa(double value, char* buffer, int maxDecimalPlaces = 324) {
00217     RAPIDJSON_ASSERT(maxDecimalPlaces >= 1);
00218     Double d(value);
00219     if (d.IsZero()) {
00220         if (d.Sign())
00221             *buffer++ = '-';     // -0.0, Issue #289
00222         buffer[0] = '0';
00223         buffer[1] = '.';
00224         buffer[2] = '0';
00225         return &buffer[3];
00226     }
00227     else {
00228         if (value < 0) {
00229             *buffer++ = '-';
00230             value = -value;
00231         }
00232         int length, K;
00233         Grisu2(value, buffer, &length, &K);
00234         return Prettify(buffer, length, K, maxDecimalPlaces);
00235     }
00236 }
00237 
00238 #ifdef __GNUC__
00239 RAPIDJSON_DIAG_POP
00240 #endif
00241 
00242 } // namespace internal
00243 RAPIDJSON_NAMESPACE_END
00244 
00245 #endif // RAPIDJSON_DTOA_