1 // Copyright 2006-2008 the V8 project authors. All rights reserved.
2 // Redistribution and use in source and binary forms, with or without
3 // modification, are permitted provided that the following conditions are
4 // met:
5 //
6 // * Redistributions of source code must retain the above copyright
7 // notice, this list of conditions and the following disclaimer.
8 // * Redistributions in binary form must reproduce the above
9 // copyright notice, this list of conditions and the following
10 // disclaimer in the documentation and/or other materials provided
11 // with the distribution.
12 // * Neither the name of Google Inc. nor the names of its
13 // contributors may be used to endorse or promote products derived
14 // from this software without specific prior written permission.
15 //
16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27
28 #include <stdarg.h>
29 #include <limits.h>
30 #include <math.h>
31
32 #include "utils.h"
33
34 #include "cached-powers.h"
35
36 namespace double_conversion {
37
38 struct CachedPower {
39 uint64_t significand;
40 int16_t binary_exponent;
41 int16_t decimal_exponent;
42 };
43
44 static const CachedPower kCachedPowers[] = {
45 {UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348},
46 {UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340},
47 {UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332},
48 {UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324},
49 {UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316},
50 {UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308},
51 {UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300},
52 {UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292},
53 {UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284},
54 {UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276},
55 {UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268},
56 {UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260},
57 {UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252},
58 {UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244},
59 {UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236},
60 {UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228},
61 {UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220},
62 {UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212},
63 {UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204},
64 {UINT64_2PART_C(0xef340a98, 172aace5), -715, -196},
65 {UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188},
66 {UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180},
67 {UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172},
68 {UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164},
69 {UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156},
70 {UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148},
71 {UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140},
72 {UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132},
73 {UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124},
74 {UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116},
75 {UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108},
76 {UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100},
77 {UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92},
78 {UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84},
79 {UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76},
80 {UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68},
81 {UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60},
82 {UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52},
83 {UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44},
84 {UINT64_2PART_C(0xaa242499, 697392d3), -183, -36},
85 {UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28},
86 {UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20},
87 {UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12},
88 {UINT64_2PART_C(0xd1b71758, e219652c), -77, -4},
89 {UINT64_2PART_C(0x9c400000, 00000000), -50, 4},
90 {UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12},
91 {UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20},
92 {UINT64_2PART_C(0x813f3978, f8940984), 30, 28},
93 {UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36},
94 {UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44},
95 {UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52},
96 {UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60},
97 {UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68},
98 {UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76},
99 {UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84},
100 {UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92},
101 {UINT64_2PART_C(0x924d692c, a61be758), 269, 100},
102 {UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108},
103 {UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116},
104 {UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124},
105 {UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132},
106 {UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140},
107 {UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148},
108 {UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156},
109 {UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164},
110 {UINT64_2PART_C(0xa59bc234, db398c25), 508, 172},
111 {UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180},
112 {UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188},
113 {UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196},
114 {UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204},
115 {UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212},
116 {UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220},
117 {UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228},
118 {UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236},
119 {UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244},
120 {UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252},
121 {UINT64_2PART_C(0xd01fef10, a657842c), 800, 260},
122 {UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268},
123 {UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276},
124 {UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284},
125 {UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292},
126 {UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300},
127 {UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308},
128 {UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316},
129 {UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324},
130 {UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332},
131 {UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340},
132 };
133
134 static const int kCachedPowersLength = ARRAY_SIZE(kCachedPowers);
135 static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent.
136 static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
137 // Difference between the decimal exponents in the table above.
138 const int PowersOfTenCache::kDecimalExponentDistance = 8;
139 const int PowersOfTenCache::kMinDecimalExponent = -348;
140 const int PowersOfTenCache::kMaxDecimalExponent = 340;
141
GetCachedPowerForBinaryExponentRange(int min_exponent,int max_exponent,DiyFp * power,int * decimal_exponent)142 void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
143 int min_exponent,
144 int max_exponent,
145 DiyFp* power,
146 int* decimal_exponent) {
147 int kQ = DiyFp::kSignificandSize;
148 double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
149 int foo = kCachedPowersOffset;
150 int index =
151 (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
152 ASSERT(0 <= index && index < kCachedPowersLength);
153 CachedPower cached_power = kCachedPowers[index];
154 ASSERT(min_exponent <= cached_power.binary_exponent);
155 (void) max_exponent; // Mark variable as used.
156 ASSERT(cached_power.binary_exponent <= max_exponent);
157 *decimal_exponent = cached_power.decimal_exponent;
158 *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
159 }
160
161
GetCachedPowerForDecimalExponent(int requested_exponent,DiyFp * power,int * found_exponent)162 void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
163 DiyFp* power,
164 int* found_exponent) {
165 ASSERT(kMinDecimalExponent <= requested_exponent);
166 ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
167 int index =
168 (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
169 CachedPower cached_power = kCachedPowers[index];
170 *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
171 *found_exponent = cached_power.decimal_exponent;
172 ASSERT(*found_exponent <= requested_exponent);
173 ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
174 }
175
176 } // namespace double_conversion
177