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_DIYFP_H_
20 #define RAPIDJSON_DIYFP_H_
21
22 #include "../rapidjson.h"
23
24 #if defined(_MSC_VER) && defined(_M_AMD64)
25 #include <intrin.h>
26 #pragma intrinsic(_BitScanReverse64)
27 #pragma intrinsic(_umul128)
28 #endif
29
30 RAPIDJSON_NAMESPACE_BEGIN
31 namespace internal {
32
33 #ifdef __GNUC__
34 RAPIDJSON_DIAG_PUSH
35 RAPIDJSON_DIAG_OFF(effc++)
36 #endif
37
38 struct DiyFp {
DiyFpDiyFp39 DiyFp() {}
40
DiyFpDiyFp41 DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {}
42
DiyFpDiyFp43 explicit DiyFp(double d) {
44 union {
45 double d;
46 uint64_t u64;
47 } u = { d };
48
49 int biased_e = static_cast<int>((u.u64 & kDpExponentMask) >> kDpSignificandSize);
50 uint64_t significand = (u.u64 & kDpSignificandMask);
51 if (biased_e != 0) {
52 f = significand + kDpHiddenBit;
53 e = biased_e - kDpExponentBias;
54 }
55 else {
56 f = significand;
57 e = kDpMinExponent + 1;
58 }
59 }
60
61 DiyFp operator-(const DiyFp& rhs) const {
62 return DiyFp(f - rhs.f, e);
63 }
64
65 DiyFp operator*(const DiyFp& rhs) const {
66 #if defined(_MSC_VER) && defined(_M_AMD64)
67 uint64_t h;
68 uint64_t l = _umul128(f, rhs.f, &h);
69 if (l & (uint64_t(1) << 63)) // rounding
70 h++;
71 return DiyFp(h, e + rhs.e + 64);
72 #elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
73 __extension__ typedef unsigned __int128 uint128;
74 uint128 p = static_cast<uint128>(f) * static_cast<uint128>(rhs.f);
75 uint64_t h = static_cast<uint64_t>(p >> 64);
76 uint64_t l = static_cast<uint64_t>(p);
77 if (l & (uint64_t(1) << 63)) // rounding
78 h++;
79 return DiyFp(h, e + rhs.e + 64);
80 #else
81 const uint64_t M32 = 0xFFFFFFFF;
82 const uint64_t a = f >> 32;
83 const uint64_t b = f & M32;
84 const uint64_t c = rhs.f >> 32;
85 const uint64_t d = rhs.f & M32;
86 const uint64_t ac = a * c;
87 const uint64_t bc = b * c;
88 const uint64_t ad = a * d;
89 const uint64_t bd = b * d;
90 uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32);
91 tmp += 1U << 31; /// mult_round
92 return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
93 #endif
94 }
95
NormalizeDiyFp96 DiyFp Normalize() const {
97 #if defined(_MSC_VER) && defined(_M_AMD64)
98 unsigned long index;
99 _BitScanReverse64(&index, f);
100 return DiyFp(f << (63 - index), e - (63 - index));
101 #elif defined(__GNUC__) && __GNUC__ >= 4
102 int s = __builtin_clzll(f);
103 return DiyFp(f << s, e - s);
104 #else
105 DiyFp res = *this;
106 while (!(res.f & (static_cast<uint64_t>(1) << 63))) {
107 res.f <<= 1;
108 res.e--;
109 }
110 return res;
111 #endif
112 }
113
NormalizeBoundaryDiyFp114 DiyFp NormalizeBoundary() const {
115 DiyFp res = *this;
116 while (!(res.f & (kDpHiddenBit << 1))) {
117 res.f <<= 1;
118 res.e--;
119 }
120 res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
121 res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
122 return res;
123 }
124
NormalizedBoundariesDiyFp125 void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const {
126 DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
127 DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1);
128 mi.f <<= mi.e - pl.e;
129 mi.e = pl.e;
130 *plus = pl;
131 *minus = mi;
132 }
133
ToDoubleDiyFp134 double ToDouble() const {
135 union {
136 double d;
137 uint64_t u64;
138 }u;
139 const uint64_t be = (e == kDpDenormalExponent && (f & kDpHiddenBit) == 0) ? 0 :
140 static_cast<uint64_t>(e + kDpExponentBias);
141 u.u64 = (f & kDpSignificandMask) | (be << kDpSignificandSize);
142 return u.d;
143 }
144
145 static const int kDiySignificandSize = 64;
146 static const int kDpSignificandSize = 52;
147 static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
148 static const int kDpMaxExponent = 0x7FF - kDpExponentBias;
149 static const int kDpMinExponent = -kDpExponentBias;
150 static const int kDpDenormalExponent = -kDpExponentBias + 1;
151 static const uint64_t kDpExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
152 static const uint64_t kDpSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
153 static const uint64_t kDpHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
154
155 uint64_t f;
156 int e;
157 };
158
GetCachedPowerByIndex(size_t index)159 inline DiyFp GetCachedPowerByIndex(size_t index) {
160 // 10^-348, 10^-340, ..., 10^340
161 static const uint64_t kCachedPowers_F[] = {
162 RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288), RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76),
163 RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76), RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea),
164 RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d), RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df),
165 RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca), RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f),
166 RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c), RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c),
167 RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83), RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5),
168 RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb), RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d),
169 RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57), RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637),
170 RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f), RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7),
171 RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4), RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5),
172 RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e), RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b),
173 RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba), RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996),
174 RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584), RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
175 RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126), RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8),
176 RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b), RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053),
177 RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655), RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd),
178 RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94),
179 RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf), RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b),
180 RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6), RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac),
181 RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06), RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3),
182 RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e), RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb),
183 RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc), RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c),
184 RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000),
185 RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000), RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984),
186 RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3), RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70),
187 RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068), RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245),
188 RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27), RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8),
189 RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db), RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a),
190 RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758), RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea),
191 RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a), RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85),
192 RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877), RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2),
193 RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d), RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3),
194 RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3), RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25),
195 RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c), RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece),
196 RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2), RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5),
197 RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df), RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a),
198 RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396), RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
199 RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410), RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a),
200 RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c), RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129),
201 RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d), RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429),
202 RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85), RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d),
203 RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f), RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841),
204 RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9), RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9),
205 RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b)
206 };
207 static const int16_t kCachedPowers_E[] = {
208 -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980,
209 -954, -927, -901, -874, -847, -821, -794, -768, -741, -715,
210 -688, -661, -635, -608, -582, -555, -529, -502, -475, -449,
211 -422, -396, -369, -343, -316, -289, -263, -236, -210, -183,
212 -157, -130, -103, -77, -50, -24, 3, 30, 56, 83,
213 109, 136, 162, 189, 216, 242, 269, 295, 322, 348,
214 375, 402, 428, 455, 481, 508, 534, 561, 588, 614,
215 641, 667, 694, 720, 747, 774, 800, 827, 853, 880,
216 907, 933, 960, 986, 1013, 1039, 1066
217 };
218 return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
219 }
220
GetCachedPower(int e,int * K)221 inline DiyFp GetCachedPower(int e, int* K) {
222
223 //int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
224 double dk = (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive
225 int k = static_cast<int>(dk);
226 if (dk - k > 0.0)
227 k++;
228
229 unsigned index = static_cast<unsigned>((k >> 3) + 1);
230 *K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table
231
232 return GetCachedPowerByIndex(index);
233 }
234
GetCachedPower10(int exp,int * outExp)235 inline DiyFp GetCachedPower10(int exp, int *outExp) {
236 unsigned index = (static_cast<unsigned>(exp) + 348u) / 8u;
237 *outExp = -348 + static_cast<int>(index) * 8;
238 return GetCachedPowerByIndex(index);
239 }
240
241 #ifdef __GNUC__
242 RAPIDJSON_DIAG_POP
243 #endif
244
245 } // namespace internal
246 RAPIDJSON_NAMESPACE_END
247
248 #endif // RAPIDJSON_DIYFP_H_
249