1 // Copyright 2014 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/base/division-by-constant.h" 6 7 #include <stdint.h> 8 9 #include "src/base/logging.h" 10 #include "src/base/macros.h" 11 12 namespace v8 { 13 namespace base { 14 15 template <class T> 16 MagicNumbersForDivision<T> SignedDivisionByConstant(T d) { 17 STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1)); 18 DCHECK(d != static_cast<T>(-1) && d != 0 && d != 1); 19 const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8; 20 const T min = (static_cast<T>(1) << (bits - 1)); 21 const bool neg = (min & d) != 0; 22 const T ad = neg ? (0 - d) : d; 23 const T t = min + (d >> (bits - 1)); 24 const T anc = t - 1 - t % ad; // Absolute value of nc 25 unsigned p = bits - 1; // Init. p. 26 T q1 = min / anc; // Init. q1 = 2**p/|nc|. 27 T r1 = min - q1 * anc; // Init. r1 = rem(2**p, |nc|). 28 T q2 = min / ad; // Init. q2 = 2**p/|d|. 29 T r2 = min - q2 * ad; // Init. r2 = rem(2**p, |d|). 30 T delta; 31 do { 32 p = p + 1; 33 q1 = 2 * q1; // Update q1 = 2**p/|nc|. 34 r1 = 2 * r1; // Update r1 = rem(2**p, |nc|). 35 if (r1 >= anc) { // Must be an unsigned comparison here. 36 q1 = q1 + 1; 37 r1 = r1 - anc; 38 } 39 q2 = 2 * q2; // Update q2 = 2**p/|d|. 40 r2 = 2 * r2; // Update r2 = rem(2**p, |d|). 41 if (r2 >= ad) { // Must be an unsigned comparison here. 42 q2 = q2 + 1; 43 r2 = r2 - ad; 44 } 45 delta = ad - r2; 46 } while (q1 < delta || (q1 == delta && r1 == 0)); 47 T mul = q2 + 1; 48 return MagicNumbersForDivision<T>(neg ? (0 - mul) : mul, p - bits, false); 49 } 50 51 52 template <class T> 53 MagicNumbersForDivision<T> UnsignedDivisionByConstant(T d, 54 unsigned leading_zeros) { 55 STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1)); 56 DCHECK(d != 0); 57 const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8; 58 const T ones = ~static_cast<T>(0) >> leading_zeros; 59 const T min = static_cast<T>(1) << (bits - 1); 60 const T max = ~static_cast<T>(0) >> 1; 61 const T nc = ones - (ones - d) % d; 62 bool a = false; // Init. "add" indicator. 63 unsigned p = bits - 1; // Init. p. 64 T q1 = min / nc; // Init. q1 = 2**p/nc 65 T r1 = min - q1 * nc; // Init. r1 = rem(2**p,nc) 66 T q2 = max / d; // Init. q2 = (2**p - 1)/d. 67 T r2 = max - q2 * d; // Init. r2 = rem(2**p - 1, d). 68 T delta; 69 do { 70 p = p + 1; 71 if (r1 >= nc - r1) { 72 q1 = 2 * q1 + 1; 73 r1 = 2 * r1 - nc; 74 } else { 75 q1 = 2 * q1; 76 r1 = 2 * r1; 77 } 78 if (r2 + 1 >= d - r2) { 79 if (q2 >= max) a = true; 80 q2 = 2 * q2 + 1; 81 r2 = 2 * r2 + 1 - d; 82 } else { 83 if (q2 >= min) a = true; 84 q2 = 2 * q2; 85 r2 = 2 * r2 + 1; 86 } 87 delta = d - 1 - r2; 88 } while (p < bits * 2 && (q1 < delta || (q1 == delta && r1 == 0))); 89 return MagicNumbersForDivision<T>(q2 + 1, p - bits, a); 90 } 91 92 93 // ----------------------------------------------------------------------------- 94 // Instantiations. 95 96 template struct V8_BASE_EXPORT MagicNumbersForDivision<uint32_t>; 97 template struct V8_BASE_EXPORT MagicNumbersForDivision<uint64_t>; 98 99 template MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d); 100 template MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d); 101 102 template MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant( 103 uint32_t d, unsigned leading_zeros); 104 template MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant( 105 uint64_t d, unsigned leading_zeros); 106 107 } // namespace base 108 } // namespace v8 109
