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dtoa.h
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3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
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5 // Licensed under the MIT License (the "License"); you may not use this file except
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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_