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.
get(const APInt & D)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
get(const APInt & D,unsigned LeadingZeros,bool AllowEvenDivisorOptimization)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 =
83 APInt::getLowBitsSet(D.getBitWidth(), D.getBitWidth() - LeadingZeros);
84 APInt SignedMin = APInt::getSignedMinValue(D.getBitWidth());
85 APInt SignedMax = APInt::getSignedMaxValue(D.getBitWidth());
86
87 // Calculate NC, the largest dividend such that NC.urem(D) == D-1.
88 APInt NC = AllOnes - (AllOnes + 1 - D).urem(D);
89 assert(NC.urem(D) == D - 1 && "Unexpected NC value");
90 unsigned P = D.getBitWidth() - 1; // initialize P
91 APInt Q1, R1, Q2, R2;
92 // initialize Q1 = 2P/NC; R1 = rem(2P,NC)
93 APInt::udivrem(SignedMin, NC, Q1, R1);
94 // initialize Q2 = (2P-1)/D; R2 = rem((2P-1),D)
95 APInt::udivrem(SignedMax, D, Q2, R2);
96 do {
97 P = P + 1;
98 if (R1.uge(NC - R1)) {
99 // update Q1
100 Q1 <<= 1;
101 ++Q1;
102 // update R1
103 R1 <<= 1;
104 R1 -= NC;
105 } else {
106 Q1 <<= 1; // update Q1
107 R1 <<= 1; // update R1
108 }
109 if ((R2 + 1).uge(D - R2)) {
110 if (Q2.uge(SignedMax))
111 Retval.IsAdd = true;
112 // update Q2
113 Q2 <<= 1;
114 ++Q2;
115 // update R2
116 R2 <<= 1;
117 ++R2;
118 R2 -= D;
119 } else {
120 if (Q2.uge(SignedMin))
121 Retval.IsAdd = true;
122 // update Q2
123 Q2 <<= 1;
124 // update R2
125 R2 <<= 1;
126 ++R2;
127 }
128 // Delta = D - 1 - R2
129 Delta = D;
130 --Delta;
131 Delta -= R2;
132 } while (P < D.getBitWidth() * 2 &&
133 (Q1.ult(Delta) || (Q1 == Delta && R1.isZero())));
134
135 if (Retval.IsAdd && !D[0] && AllowEvenDivisorOptimization) {
136 unsigned PreShift = D.countr_zero();
137 APInt ShiftedD = D.lshr(PreShift);
138 Retval =
139 UnsignedDivisionByConstantInfo::get(ShiftedD, LeadingZeros + PreShift);
140 assert(Retval.IsAdd == 0 && Retval.PreShift == 0);
141 Retval.PreShift = PreShift;
142 return Retval;
143 }
144
145 Retval.Magic = std::move(Q2); // resulting magic number
146 ++Retval.Magic;
147 Retval.PostShift = P - D.getBitWidth(); // resulting shift
148 // Reduce shift amount for IsAdd.
149 if (Retval.IsAdd) {
150 assert(Retval.PostShift > 0 && "Unexpected shift");
151 Retval.PostShift -= 1;
152 }
153 Retval.PreShift = 0;
154 return Retval;
155 }
156