1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
|
//===- llvm/unittest/Support/DivisionByConstantTest.cpp -------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "llvm/ADT/APInt.h"
#include "llvm/Support/DivisionByConstantInfo.h"
#include "gtest/gtest.h"
using namespace llvm;
namespace {
template <typename Fn> static void EnumerateAPInts(unsigned Bits, Fn TestFn) {
APInt N(Bits, 0);
do {
TestFn(N);
} while (++N != 0);
}
APInt MULHS(APInt X, APInt Y) {
unsigned Bits = X.getBitWidth();
unsigned WideBits = 2 * Bits;
return (X.sext(WideBits) * Y.sext(WideBits)).lshr(Bits).trunc(Bits);
}
APInt SignedDivideUsingMagic(APInt Numerator, APInt Divisor,
SignedDivisionByConstantInfo Magics) {
unsigned Bits = Numerator.getBitWidth();
APInt Factor(Bits, 0);
APInt ShiftMask(Bits, -1, true);
if (Divisor.isOne() || Divisor.isAllOnes()) {
// If d is +1/-1, we just multiply the numerator by +1/-1.
Factor = Divisor.getSExtValue();
Magics.Magic = 0;
Magics.ShiftAmount = 0;
ShiftMask = 0;
} else if (Divisor.isStrictlyPositive() && Magics.Magic.isNegative()) {
// If d > 0 and m < 0, add the numerator.
Factor = 1;
} else if (Divisor.isNegative() && Magics.Magic.isStrictlyPositive()) {
// If d < 0 and m > 0, subtract the numerator.
Factor = -1;
}
// Multiply the numerator by the magic value.
APInt Q = MULHS(Numerator, Magics.Magic);
// (Optionally) Add/subtract the numerator using Factor.
Factor = Numerator * Factor;
Q = Q + Factor;
// Shift right algebraic by shift value.
Q = Q.ashr(Magics.ShiftAmount);
// Extract the sign bit, mask it and add it to the quotient.
unsigned SignShift = Bits - 1;
APInt T = Q.lshr(SignShift);
T = T & ShiftMask;
return Q + T;
}
TEST(SignedDivisionByConstantTest, Test) {
for (unsigned Bits = 1; Bits <= 32; ++Bits) {
if (Bits < 3)
continue; // Not supported by `SignedDivisionByConstantInfo::get()`.
if (Bits > 12)
continue; // Unreasonably slow.
EnumerateAPInts(Bits, [Bits](const APInt &Divisor) {
if (Divisor.isZero())
return; // Division by zero is undefined behavior.
SignedDivisionByConstantInfo Magics;
if (!(Divisor.isOne() || Divisor.isAllOnes()))
Magics = SignedDivisionByConstantInfo::get(Divisor);
EnumerateAPInts(Bits, [Divisor, Magics, Bits](const APInt &Numerator) {
if (Numerator.isMinSignedValue() && Divisor.isAllOnes())
return; // Overflow is undefined behavior.
APInt NativeResult = Numerator.sdiv(Divisor);
APInt MagicResult = SignedDivideUsingMagic(Numerator, Divisor, Magics);
ASSERT_EQ(MagicResult, NativeResult)
<< " ... given the operation: srem i" << Bits << " " << Numerator
<< ", " << Divisor;
});
});
}
}
APInt MULHU(APInt X, APInt Y) {
unsigned Bits = X.getBitWidth();
unsigned WideBits = 2 * Bits;
return (X.zext(WideBits) * Y.zext(WideBits)).lshr(Bits).trunc(Bits);
}
APInt UnsignedDivideUsingMagic(const APInt &Numerator, const APInt &Divisor,
bool LZOptimization,
bool AllowEvenDivisorOptimization, bool ForceNPQ,
UnsignedDivisionByConstantInfo Magics) {
assert(!Divisor.isOne() && "Division by 1 is not supported using Magic.");
unsigned Bits = Numerator.getBitWidth();
if (LZOptimization) {
unsigned LeadingZeros = Numerator.countl_zero();
// Clip to the number of leading zeros in the divisor.
LeadingZeros = std::min(LeadingZeros, Divisor.countl_zero());
if (LeadingZeros > 0) {
Magics = UnsignedDivisionByConstantInfo::get(
Divisor, LeadingZeros, AllowEvenDivisorOptimization);
assert(!Magics.IsAdd && "Should use cheap fixup now");
}
}
assert(Magics.PreShift < Divisor.getBitWidth() &&
"We shouldn't generate an undefined shift!");
assert(Magics.PostShift < Divisor.getBitWidth() &&
"We shouldn't generate an undefined shift!");
assert((!Magics.IsAdd || Magics.PreShift == 0) && "Unexpected pre-shift");
unsigned PreShift = Magics.PreShift;
unsigned PostShift = Magics.PostShift;
bool UseNPQ = Magics.IsAdd;
APInt NPQFactor =
UseNPQ ? APInt::getSignedMinValue(Bits) : APInt::getZero(Bits);
APInt Q = Numerator.lshr(PreShift);
// Multiply the numerator by the magic value.
Q = MULHU(Q, Magics.Magic);
if (UseNPQ || ForceNPQ) {
APInt NPQ = Numerator - Q;
// For vectors we might have a mix of non-NPQ/NPQ paths, so use
// MULHU to act as a SRL-by-1 for NPQ, else multiply by zero.
APInt NPQ_Scalar = NPQ.lshr(1);
(void)NPQ_Scalar;
NPQ = MULHU(NPQ, NPQFactor);
assert(!UseNPQ || NPQ == NPQ_Scalar);
Q = NPQ + Q;
}
Q = Q.lshr(PostShift);
return Q;
}
TEST(UnsignedDivisionByConstantTest, Test) {
for (unsigned Bits = 1; Bits <= 32; ++Bits) {
if (Bits < 2)
continue; // Not supported by `UnsignedDivisionByConstantInfo::get()`.
if (Bits > 10)
continue; // Unreasonably slow.
EnumerateAPInts(Bits, [Bits](const APInt &Divisor) {
if (Divisor.isZero())
return; // Division by zero is undefined behavior.
if (Divisor.isOne())
return; // Division by one is the numerator.
const UnsignedDivisionByConstantInfo Magics =
UnsignedDivisionByConstantInfo::get(Divisor);
EnumerateAPInts(Bits, [Divisor, Magics, Bits](const APInt &Numerator) {
APInt NativeResult = Numerator.udiv(Divisor);
for (bool LZOptimization : {true, false}) {
for (bool AllowEvenDivisorOptimization : {true, false}) {
for (bool ForceNPQ : {false, true}) {
APInt MagicResult = UnsignedDivideUsingMagic(
Numerator, Divisor, LZOptimization,
AllowEvenDivisorOptimization, ForceNPQ, Magics);
ASSERT_EQ(MagicResult, NativeResult)
<< " ... given the operation: urem i" << Bits << " "
<< Numerator << ", " << Divisor
<< " (allow LZ optimization = "
<< LZOptimization << ", allow even divisior optimization = "
<< AllowEvenDivisorOptimization << ", force NPQ = "
<< ForceNPQ << ")";
}
}
}
});
});
}
}
} // end anonymous namespace
|
