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//===- 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"
#include <array>
#include <optional>
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);
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.countLeadingZeros();
// Clip to the number of leading zeros in the divisor.
LeadingZeros = std::min(LeadingZeros, Divisor.countLeadingZeros());
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
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