1 // Copyright 2011 the V8 project authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style license that can be 3 // found in the LICENSE file. 4 5 #include "src/cached-powers.h" 6 7 #include <limits.h> 8 #include <stdarg.h> 9 #include <stdint.h> 10 #include <cmath> 11 12 #include "src/base/logging.h" 13 #include "src/globals.h" 14 15 namespace v8 { 16 namespace internal { 17 18 struct CachedPower { 19 uint64_t significand; 20 int16_t binary_exponent; 21 int16_t decimal_exponent; 22 }; 23 24 static const CachedPower kCachedPowers[] = { 25 {V8_2PART_UINT64_C(0xfa8fd5a0, 081c0288), -1220, -348}, 26 {V8_2PART_UINT64_C(0xbaaee17f, a23ebf76), -1193, -340}, 27 {V8_2PART_UINT64_C(0x8b16fb20, 3055ac76), -1166, -332}, 28 {V8_2PART_UINT64_C(0xcf42894a, 5dce35ea), -1140, -324}, 29 {V8_2PART_UINT64_C(0x9a6bb0aa, 55653b2d), -1113, -316}, 30 {V8_2PART_UINT64_C(0xe61acf03, 3d1a45df), -1087, -308}, 31 {V8_2PART_UINT64_C(0xab70fe17, c79ac6ca), -1060, -300}, 32 {V8_2PART_UINT64_C(0xff77b1fc, bebcdc4f), -1034, -292}, 33 {V8_2PART_UINT64_C(0xbe5691ef, 416bd60c), -1007, -284}, 34 {V8_2PART_UINT64_C(0x8dd01fad, 907ffc3c), -980, -276}, 35 {V8_2PART_UINT64_C(0xd3515c28, 31559a83), -954, -268}, 36 {V8_2PART_UINT64_C(0x9d71ac8f, ada6c9b5), -927, -260}, 37 {V8_2PART_UINT64_C(0xea9c2277, 23ee8bcb), -901, -252}, 38 {V8_2PART_UINT64_C(0xaecc4991, 4078536d), -874, -244}, 39 {V8_2PART_UINT64_C(0x823c1279, 5db6ce57), -847, -236}, 40 {V8_2PART_UINT64_C(0xc2109436, 4dfb5637), -821, -228}, 41 {V8_2PART_UINT64_C(0x9096ea6f, 3848984f), -794, -220}, 42 {V8_2PART_UINT64_C(0xd77485cb, 25823ac7), -768, -212}, 43 {V8_2PART_UINT64_C(0xa086cfcd, 97bf97f4), -741, -204}, 44 {V8_2PART_UINT64_C(0xef340a98, 172aace5), -715, -196}, 45 {V8_2PART_UINT64_C(0xb23867fb, 2a35b28e), -688, -188}, 46 {V8_2PART_UINT64_C(0x84c8d4df, d2c63f3b), -661, -180}, 47 {V8_2PART_UINT64_C(0xc5dd4427, 1ad3cdba), -635, -172}, 48 {V8_2PART_UINT64_C(0x936b9fce, bb25c996), -608, -164}, 49 {V8_2PART_UINT64_C(0xdbac6c24, 7d62a584), -582, -156}, 50 {V8_2PART_UINT64_C(0xa3ab6658, 0d5fdaf6), -555, -148}, 51 {V8_2PART_UINT64_C(0xf3e2f893, dec3f126), -529, -140}, 52 {V8_2PART_UINT64_C(0xb5b5ada8, aaff80b8), -502, -132}, 53 {V8_2PART_UINT64_C(0x87625f05, 6c7c4a8b), -475, -124}, 54 {V8_2PART_UINT64_C(0xc9bcff60, 34c13053), -449, -116}, 55 {V8_2PART_UINT64_C(0x964e858c, 91ba2655), -422, -108}, 56 {V8_2PART_UINT64_C(0xdff97724, 70297ebd), -396, -100}, 57 {V8_2PART_UINT64_C(0xa6dfbd9f, b8e5b88f), -369, -92}, 58 {V8_2PART_UINT64_C(0xf8a95fcf, 88747d94), -343, -84}, 59 {V8_2PART_UINT64_C(0xb9447093, 8fa89bcf), -316, -76}, 60 {V8_2PART_UINT64_C(0x8a08f0f8, bf0f156b), -289, -68}, 61 {V8_2PART_UINT64_C(0xcdb02555, 653131b6), -263, -60}, 62 {V8_2PART_UINT64_C(0x993fe2c6, d07b7fac), -236, -52}, 63 {V8_2PART_UINT64_C(0xe45c10c4, 2a2b3b06), -210, -44}, 64 {V8_2PART_UINT64_C(0xaa242499, 697392d3), -183, -36}, 65 {V8_2PART_UINT64_C(0xfd87b5f2, 8300ca0e), -157, -28}, 66 {V8_2PART_UINT64_C(0xbce50864, 92111aeb), -130, -20}, 67 {V8_2PART_UINT64_C(0x8cbccc09, 6f5088cc), -103, -12}, 68 {V8_2PART_UINT64_C(0xd1b71758, e219652c), -77, -4}, 69 {V8_2PART_UINT64_C(0x9c400000, 00000000), -50, 4}, 70 {V8_2PART_UINT64_C(0xe8d4a510, 00000000), -24, 12}, 71 {V8_2PART_UINT64_C(0xad78ebc5, ac620000), 3, 20}, 72 {V8_2PART_UINT64_C(0x813f3978, f8940984), 30, 28}, 73 {V8_2PART_UINT64_C(0xc097ce7b, c90715b3), 56, 36}, 74 {V8_2PART_UINT64_C(0x8f7e32ce, 7bea5c70), 83, 44}, 75 {V8_2PART_UINT64_C(0xd5d238a4, abe98068), 109, 52}, 76 {V8_2PART_UINT64_C(0x9f4f2726, 179a2245), 136, 60}, 77 {V8_2PART_UINT64_C(0xed63a231, d4c4fb27), 162, 68}, 78 {V8_2PART_UINT64_C(0xb0de6538, 8cc8ada8), 189, 76}, 79 {V8_2PART_UINT64_C(0x83c7088e, 1aab65db), 216, 84}, 80 {V8_2PART_UINT64_C(0xc45d1df9, 42711d9a), 242, 92}, 81 {V8_2PART_UINT64_C(0x924d692c, a61be758), 269, 100}, 82 {V8_2PART_UINT64_C(0xda01ee64, 1a708dea), 295, 108}, 83 {V8_2PART_UINT64_C(0xa26da399, 9aef774a), 322, 116}, 84 {V8_2PART_UINT64_C(0xf209787b, b47d6b85), 348, 124}, 85 {V8_2PART_UINT64_C(0xb454e4a1, 79dd1877), 375, 132}, 86 {V8_2PART_UINT64_C(0x865b8692, 5b9bc5c2), 402, 140}, 87 {V8_2PART_UINT64_C(0xc83553c5, c8965d3d), 428, 148}, 88 {V8_2PART_UINT64_C(0x952ab45c, fa97a0b3), 455, 156}, 89 {V8_2PART_UINT64_C(0xde469fbd, 99a05fe3), 481, 164}, 90 {V8_2PART_UINT64_C(0xa59bc234, db398c25), 508, 172}, 91 {V8_2PART_UINT64_C(0xf6c69a72, a3989f5c), 534, 180}, 92 {V8_2PART_UINT64_C(0xb7dcbf53, 54e9bece), 561, 188}, 93 {V8_2PART_UINT64_C(0x88fcf317, f22241e2), 588, 196}, 94 {V8_2PART_UINT64_C(0xcc20ce9b, d35c78a5), 614, 204}, 95 {V8_2PART_UINT64_C(0x98165af3, 7b2153df), 641, 212}, 96 {V8_2PART_UINT64_C(0xe2a0b5dc, 971f303a), 667, 220}, 97 {V8_2PART_UINT64_C(0xa8d9d153, 5ce3b396), 694, 228}, 98 {V8_2PART_UINT64_C(0xfb9b7cd9, a4a7443c), 720, 236}, 99 {V8_2PART_UINT64_C(0xbb764c4c, a7a44410), 747, 244}, 100 {V8_2PART_UINT64_C(0x8bab8eef, b6409c1a), 774, 252}, 101 {V8_2PART_UINT64_C(0xd01fef10, a657842c), 800, 260}, 102 {V8_2PART_UINT64_C(0x9b10a4e5, e9913129), 827, 268}, 103 {V8_2PART_UINT64_C(0xe7109bfb, a19c0c9d), 853, 276}, 104 {V8_2PART_UINT64_C(0xac2820d9, 623bf429), 880, 284}, 105 {V8_2PART_UINT64_C(0x80444b5e, 7aa7cf85), 907, 292}, 106 {V8_2PART_UINT64_C(0xbf21e440, 03acdd2d), 933, 300}, 107 {V8_2PART_UINT64_C(0x8e679c2f, 5e44ff8f), 960, 308}, 108 {V8_2PART_UINT64_C(0xd433179d, 9c8cb841), 986, 316}, 109 {V8_2PART_UINT64_C(0x9e19db92, b4e31ba9), 1013, 324}, 110 {V8_2PART_UINT64_C(0xeb96bf6e, badf77d9), 1039, 332}, 111 {V8_2PART_UINT64_C(0xaf87023b, 9bf0ee6b), 1066, 340}, 112 }; 113 114 #ifdef DEBUG 115 static const int kCachedPowersLength = arraysize(kCachedPowers); 116 #endif 117 118 static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent. 119 static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10) 120 // Difference between the decimal exponents in the table above. 121 const int PowersOfTenCache::kDecimalExponentDistance = 8; 122 const int PowersOfTenCache::kMinDecimalExponent = -348; 123 const int PowersOfTenCache::kMaxDecimalExponent = 340; 124 125 void PowersOfTenCache::GetCachedPowerForBinaryExponentRange( 126 int min_exponent, 127 int max_exponent, 128 DiyFp* power, 129 int* decimal_exponent) { 130 int kQ = DiyFp::kSignificandSize; 131 // Some platforms return incorrect sign on 0 result. We can ignore that here, 132 // which means we can avoid depending on platform.h. 133 double k = std::ceil((min_exponent + kQ - 1) * kD_1_LOG2_10); 134 int foo = kCachedPowersOffset; 135 int index = 136 (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1; 137 DCHECK(0 <= index && index < kCachedPowersLength); 138 CachedPower cached_power = kCachedPowers[index]; 139 DCHECK(min_exponent <= cached_power.binary_exponent); 140 DCHECK(cached_power.binary_exponent <= max_exponent); 141 *decimal_exponent = cached_power.decimal_exponent; 142 *power = DiyFp(cached_power.significand, cached_power.binary_exponent); 143 } 144 145 146 void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent, 147 DiyFp* power, 148 int* found_exponent) { 149 DCHECK(kMinDecimalExponent <= requested_exponent); 150 DCHECK(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance); 151 int index = 152 (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance; 153 CachedPower cached_power = kCachedPowers[index]; 154 *power = DiyFp(cached_power.significand, cached_power.binary_exponent); 155 *found_exponent = cached_power.decimal_exponent; 156 DCHECK(*found_exponent <= requested_exponent); 157 DCHECK(requested_exponent < *found_exponent + kDecimalExponentDistance); 158 } 159 160 } // namespace internal 161 } // namespace v8 162