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
26RAPIDJSON_NAMESPACE_BEGIN
27namespace internal {
28
29#ifdef __GNUC__
30RAPIDJSON_DIAG_PUSH
31RAPIDJSON_DIAG_OFF(effc++)
32#endif
33
34inline 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
43inline 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
59inline 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
110inline 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
124inline 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
148inline 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
189inline 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__
211RAPIDJSON_DIAG_POP
212#endif
213
214} // namespace internal
215RAPIDJSON_NAMESPACE_END
216
217#endif // RAPIDJSON_DTOA_
218