Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 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 | bool MagicNumbersForDivision<T>::operator==( |
| 17 | const MagicNumbersForDivision& rhs) const { |
| 18 | return multiplier == rhs.multiplier && shift == rhs.shift && add == rhs.add; |
| 19 | } |
| 20 | |
| 21 | |
| 22 | template <class T> |
| 23 | MagicNumbersForDivision<T> SignedDivisionByConstant(T d) { |
| 24 | STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1)); |
| 25 | DCHECK(d != static_cast<T>(-1) && d != 0 && d != 1); |
| 26 | const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8; |
| 27 | const T min = (static_cast<T>(1) << (bits - 1)); |
| 28 | const bool neg = (min & d) != 0; |
| 29 | const T ad = neg ? (0 - d) : d; |
| 30 | const T t = min + (d >> (bits - 1)); |
| 31 | const T anc = t - 1 - t % ad; // Absolute value of nc |
| 32 | unsigned p = bits - 1; // Init. p. |
| 33 | T q1 = min / anc; // Init. q1 = 2**p/|nc|. |
| 34 | T r1 = min - q1 * anc; // Init. r1 = rem(2**p, |nc|). |
| 35 | T q2 = min / ad; // Init. q2 = 2**p/|d|. |
| 36 | T r2 = min - q2 * ad; // Init. r2 = rem(2**p, |d|). |
| 37 | T delta; |
| 38 | do { |
| 39 | p = p + 1; |
| 40 | q1 = 2 * q1; // Update q1 = 2**p/|nc|. |
| 41 | r1 = 2 * r1; // Update r1 = rem(2**p, |nc|). |
| 42 | if (r1 >= anc) { // Must be an unsigned comparison here. |
| 43 | q1 = q1 + 1; |
| 44 | r1 = r1 - anc; |
| 45 | } |
| 46 | q2 = 2 * q2; // Update q2 = 2**p/|d|. |
| 47 | r2 = 2 * r2; // Update r2 = rem(2**p, |d|). |
| 48 | if (r2 >= ad) { // Must be an unsigned comparison here. |
| 49 | q2 = q2 + 1; |
| 50 | r2 = r2 - ad; |
| 51 | } |
| 52 | delta = ad - r2; |
| 53 | } while (q1 < delta || (q1 == delta && r1 == 0)); |
| 54 | T mul = q2 + 1; |
Emily Bernier | d0a1eb7 | 2015-03-24 16:35:39 -0400 | [diff] [blame] | 55 | return MagicNumbersForDivision<T>(neg ? (0 - mul) : mul, p - bits, false); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 56 | } |
| 57 | |
| 58 | |
| 59 | template <class T> |
| 60 | MagicNumbersForDivision<T> UnsignedDivisionByConstant(T d, |
| 61 | unsigned leading_zeros) { |
| 62 | STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1)); |
| 63 | DCHECK(d != 0); |
| 64 | const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8; |
| 65 | const T ones = ~static_cast<T>(0) >> leading_zeros; |
| 66 | const T min = static_cast<T>(1) << (bits - 1); |
| 67 | const T max = ~static_cast<T>(0) >> 1; |
| 68 | const T nc = ones - (ones - d) % d; |
| 69 | bool a = false; // Init. "add" indicator. |
| 70 | unsigned p = bits - 1; // Init. p. |
| 71 | T q1 = min / nc; // Init. q1 = 2**p/nc |
| 72 | T r1 = min - q1 * nc; // Init. r1 = rem(2**p,nc) |
| 73 | T q2 = max / d; // Init. q2 = (2**p - 1)/d. |
| 74 | T r2 = max - q2 * d; // Init. r2 = rem(2**p - 1, d). |
| 75 | T delta; |
| 76 | do { |
| 77 | p = p + 1; |
| 78 | if (r1 >= nc - r1) { |
| 79 | q1 = 2 * q1 + 1; |
| 80 | r1 = 2 * r1 - nc; |
| 81 | } else { |
| 82 | q1 = 2 * q1; |
| 83 | r1 = 2 * r1; |
| 84 | } |
| 85 | if (r2 + 1 >= d - r2) { |
| 86 | if (q2 >= max) a = true; |
| 87 | q2 = 2 * q2 + 1; |
| 88 | r2 = 2 * r2 + 1 - d; |
| 89 | } else { |
| 90 | if (q2 >= min) a = true; |
| 91 | q2 = 2 * q2; |
| 92 | r2 = 2 * r2 + 1; |
| 93 | } |
| 94 | delta = d - 1 - r2; |
| 95 | } while (p < bits * 2 && (q1 < delta || (q1 == delta && r1 == 0))); |
Emily Bernier | d0a1eb7 | 2015-03-24 16:35:39 -0400 | [diff] [blame] | 96 | return MagicNumbersForDivision<T>(q2 + 1, p - bits, a); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 97 | } |
| 98 | |
| 99 | |
| 100 | // ----------------------------------------------------------------------------- |
| 101 | // Instantiations. |
| 102 | |
| 103 | template struct MagicNumbersForDivision<uint32_t>; |
| 104 | template struct MagicNumbersForDivision<uint64_t>; |
| 105 | |
| 106 | template MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d); |
| 107 | template MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d); |
| 108 | |
| 109 | template MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant( |
| 110 | uint32_t d, unsigned leading_zeros); |
| 111 | template MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant( |
| 112 | uint64_t d, unsigned leading_zeros); |
| 113 | |
| 114 | } // namespace base |
| 115 | } // namespace v8 |