1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
|
// Copyright (C) 2011 Milo Yip
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// 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_DIYFP_H_
#define RAPIDJSON_DIYFP_H_
#if defined(_MSC_VER)
#include <intrin.h>
#if defined(_M_AMD64)
#pragma intrinsic(_BitScanReverse64)
#endif
#endif
namespace rapidjson {
namespace internal {
#ifdef __GNUC__
RAPIDJSON_DIAG_PUSH
RAPIDJSON_DIAG_OFF(effc++)
#endif
struct DiyFp {
DiyFp() {}
DiyFp(uint64_t f, int e) : f(f), e(e) {}
DiyFp(double d) {
union {
double d;
uint64_t u64;
} u = { d };
int biased_e = (u.u64 & kDpExponentMask) >> kDpSignificandSize;
uint64_t significand = (u.u64 & kDpSignificandMask);
if (biased_e != 0) {
f = significand + kDpHiddenBit;
e = biased_e - kDpExponentBias;
}
else {
f = significand;
e = kDpMinExponent + 1;
}
}
DiyFp operator-(const DiyFp& rhs) const {
return DiyFp(f - rhs.f, e);
}
DiyFp operator*(const DiyFp& rhs) const {
#if defined(_MSC_VER) && defined(_M_AMD64)
uint64_t h;
uint64_t l = _umul128(f, rhs.f, &h);
if (l & (uint64_t(1) << 63)) // rounding
h++;
return DiyFp(h, e + rhs.e + 64);
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
unsigned __int128 p = static_cast<unsigned __int128>(f) * static_cast<unsigned __int128>(rhs.f);
uint64_t h = p >> 64;
uint64_t l = static_cast<uint64_t>(p);
if (l & (uint64_t(1) << 63)) // rounding
h++;
return DiyFp(h, e + rhs.e + 64);
#else
const uint64_t M32 = 0xFFFFFFFF;
const uint64_t a = f >> 32;
const uint64_t b = f & M32;
const uint64_t c = rhs.f >> 32;
const uint64_t d = rhs.f & M32;
const uint64_t ac = a * c;
const uint64_t bc = b * c;
const uint64_t ad = a * d;
const uint64_t bd = b * d;
uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32);
tmp += 1U << 31; /// mult_round
return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
#endif
}
DiyFp Normalize() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
unsigned long index;
_BitScanReverse64(&index, f);
return DiyFp(f << (63 - index), e - (63 - index));
#elif defined(__GNUC__)
int s = __builtin_clzll(f) + 1;
return DiyFp(f << s, e - s);
#else
DiyFp res = *this;
while (!(res.f & kDpHiddenBit)) {
res.f <<= 1;
res.e--;
}
res.f <<= (kDiySignificandSize - kDpSignificandSize - 1);
res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 1);
return res;
#endif
}
DiyFp NormalizeBoundary() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
unsigned long index;
_BitScanReverse64(&index, f);
return DiyFp (f << (63 - index), e - (63 - index));
#else
DiyFp res = *this;
while (!(res.f & (kDpHiddenBit << 1))) {
res.f <<= 1;
res.e--;
}
res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
return res;
#endif
}
void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const {
DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1);
mi.f <<= mi.e - pl.e;
mi.e = pl.e;
*plus = pl;
*minus = mi;
}
static const int kDiySignificandSize = 64;
static const int kDpSignificandSize = 52;
static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
static const int kDpMinExponent = -kDpExponentBias;
static const uint64_t kDpExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
static const uint64_t kDpSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
static const uint64_t kDpHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
uint64_t f;
int e;
};
inline DiyFp GetCachedPower(int e, int* K) {
// 10^-348, 10^-340, ..., 10^340
static const uint64_t kCachedPowers_F[] = {
RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288), RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76),
RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76), RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea),
RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d), RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df),
RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca), RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f),
RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c), RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c),
RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83), RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5),
RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb), RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d),
RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57), RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637),
RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f), RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7),
RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4), RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5),
RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e), RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b),
RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba), RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996),
RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584), RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126), RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8),
RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b), RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053),
RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655), RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd),
RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94),
RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf), RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b),
RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6), RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac),
RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06), RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3),
RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e), RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb),
RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc), RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c),
RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000),
RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000), RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984),
RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3), RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70),
RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068), RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245),
RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27), RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8),
RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db), RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a),
RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758), RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea),
RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a), RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85),
RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877), RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2),
RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d), RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3),
RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3), RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25),
RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c), RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece),
RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2), RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5),
RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df), RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a),
RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396), RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410), RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a),
RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c), RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129),
RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d), RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429),
RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85), RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d),
RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f), RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841),
RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9), RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9),
RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b)
};
static const int16_t kCachedPowers_E[] = {
-1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980,
-954, -927, -901, -874, -847, -821, -794, -768, -741, -715,
-688, -661, -635, -608, -582, -555, -529, -502, -475, -449,
-422, -396, -369, -343, -316, -289, -263, -236, -210, -183,
-157, -130, -103, -77, -50, -24, 3, 30, 56, 83,
109, 136, 162, 189, 216, 242, 269, 295, 322, 348,
375, 402, 428, 455, 481, 508, 534, 561, 588, 614,
641, 667, 694, 720, 747, 774, 800, 827, 853, 880,
907, 933, 960, 986, 1013, 1039, 1066
};
//int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
double dk = (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive
int k = static_cast<int>(dk);
if (k != dk)
k++;
unsigned index = static_cast<unsigned>((k >> 3) + 1);
*K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table
return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
}
#ifdef __GNUC__
RAPIDJSON_DIAG_POP
#endif
} // namespace internal
} // namespace rapidjson
#endif // RAPIDJSON_DIYFP_H_
|
