1 //===----- DivisionByConstantInfo.cpp - division by constant -*- C++ -*----===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 /// 9 /// This file implements support for optimizing divisions by a constant 10 /// 11 //===----------------------------------------------------------------------===// 12 13 #include "llvm/Support/DivisionByConstantInfo.h" 14 15 using namespace llvm; 16 17 /// Calculate the magic numbers required to implement a signed integer division 18 /// by a constant as a sequence of multiplies, adds and shifts. Requires that 19 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S. 20 /// Warren, Jr., Chapter 10. 21 SignedDivisionByConstantInfo SignedDivisionByConstantInfo::get(const APInt &D) { 22 assert(!D.isZero() && "Precondition violation."); 23 24 // We'd be endlessly stuck in the loop. 25 assert(D.getBitWidth() >= 3 && "Does not work at smaller bitwidths."); 26 27 APInt Delta; 28 APInt SignedMin = APInt::getSignedMinValue(D.getBitWidth()); 29 struct SignedDivisionByConstantInfo Retval; 30 31 APInt AD = D.abs(); 32 APInt T = SignedMin + (D.lshr(D.getBitWidth() - 1)); 33 APInt ANC = T - 1 - T.urem(AD); // absolute value of NC 34 unsigned P = D.getBitWidth() - 1; // initialize P 35 APInt Q1, R1, Q2, R2; 36 // initialize Q1 = 2P/abs(NC); R1 = rem(2P,abs(NC)) 37 APInt::udivrem(SignedMin, ANC, Q1, R1); 38 // initialize Q2 = 2P/abs(D); R2 = rem(2P,abs(D)) 39 APInt::udivrem(SignedMin, AD, Q2, R2); 40 do { 41 P = P + 1; 42 Q1 <<= 1; // update Q1 = 2P/abs(NC) 43 R1 <<= 1; // update R1 = rem(2P/abs(NC)) 44 if (R1.uge(ANC)) { // must be unsigned comparison 45 ++Q1; 46 R1 -= ANC; 47 } 48 Q2 <<= 1; // update Q2 = 2P/abs(D) 49 R2 <<= 1; // update R2 = rem(2P/abs(D)) 50 if (R2.uge(AD)) { // must be unsigned comparison 51 ++Q2; 52 R2 -= AD; 53 } 54 // Delta = AD - R2 55 Delta = AD; 56 Delta -= R2; 57 } while (Q1.ult(Delta) || (Q1 == Delta && R1.isZero())); 58 59 Retval.Magic = std::move(Q2); 60 ++Retval.Magic; 61 if (D.isNegative()) 62 Retval.Magic.negate(); // resulting magic number 63 Retval.ShiftAmount = P - D.getBitWidth(); // resulting shift 64 return Retval; 65 } 66 67 /// Calculate the magic numbers required to implement an unsigned integer 68 /// division by a constant as a sequence of multiplies, adds and shifts. 69 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry 70 /// S. Warren, Jr., chapter 10. 71 /// LeadingZeros can be used to simplify the calculation if the upper bits 72 /// of the divided value are known zero. 73 UnsignedDivisionByConstantInfo 74 UnsignedDivisionByConstantInfo::get(const APInt &D, unsigned LeadingZeros, 75 bool AllowEvenDivisorOptimization) { 76 assert(!D.isZero() && !D.isOne() && "Precondition violation."); 77 assert(D.getBitWidth() > 1 && "Does not work at smaller bitwidths."); 78 79 APInt Delta; 80 struct UnsignedDivisionByConstantInfo Retval; 81 Retval.IsAdd = false; // initialize "add" indicator 82 APInt AllOnes = APInt::getAllOnes(D.getBitWidth()).lshr(LeadingZeros); 83 APInt SignedMin = APInt::getSignedMinValue(D.getBitWidth()); 84 APInt SignedMax = APInt::getSignedMaxValue(D.getBitWidth()); 85 86 // Calculate NC, the largest dividend such that NC.urem(D) == D-1. 87 APInt NC = AllOnes - (AllOnes + 1 - D).urem(D); 88 assert(NC.urem(D) == D - 1 && "Unexpected NC value"); 89 unsigned P = D.getBitWidth() - 1; // initialize P 90 APInt Q1, R1, Q2, R2; 91 // initialize Q1 = 2P/NC; R1 = rem(2P,NC) 92 APInt::udivrem(SignedMin, NC, Q1, R1); 93 // initialize Q2 = (2P-1)/D; R2 = rem((2P-1),D) 94 APInt::udivrem(SignedMax, D, Q2, R2); 95 do { 96 P = P + 1; 97 if (R1.uge(NC - R1)) { 98 // update Q1 99 Q1 <<= 1; 100 ++Q1; 101 // update R1 102 R1 <<= 1; 103 R1 -= NC; 104 } else { 105 Q1 <<= 1; // update Q1 106 R1 <<= 1; // update R1 107 } 108 if ((R2 + 1).uge(D - R2)) { 109 if (Q2.uge(SignedMax)) 110 Retval.IsAdd = true; 111 // update Q2 112 Q2 <<= 1; 113 ++Q2; 114 // update R2 115 R2 <<= 1; 116 ++R2; 117 R2 -= D; 118 } else { 119 if (Q2.uge(SignedMin)) 120 Retval.IsAdd = true; 121 // update Q2 122 Q2 <<= 1; 123 // update R2 124 R2 <<= 1; 125 ++R2; 126 } 127 // Delta = D - 1 - R2 128 Delta = D; 129 --Delta; 130 Delta -= R2; 131 } while (P < D.getBitWidth() * 2 && 132 (Q1.ult(Delta) || (Q1 == Delta && R1.isZero()))); 133 134 if (Retval.IsAdd && !D[0] && AllowEvenDivisorOptimization) { 135 unsigned PreShift = D.countr_zero(); 136 APInt ShiftedD = D.lshr(PreShift); 137 Retval = 138 UnsignedDivisionByConstantInfo::get(ShiftedD, LeadingZeros + PreShift); 139 assert(Retval.IsAdd == 0 && Retval.PreShift == 0); 140 Retval.PreShift = PreShift; 141 return Retval; 142 } 143 144 Retval.Magic = std::move(Q2); // resulting magic number 145 ++Retval.Magic; 146 Retval.PostShift = P - D.getBitWidth(); // resulting shift 147 // Reduce shift amount for IsAdd. 148 if (Retval.IsAdd) { 149 assert(Retval.PostShift > 0 && "Unexpected shift"); 150 Retval.PostShift -= 1; 151 } 152 Retval.PreShift = 0; 153 return Retval; 154 } 155