llvm-project/llvm/lib/Support/KnownBits.cpp

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//===-- KnownBits.cpp - Stores known zeros/ones ---------------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// This file contains a class for representing known zeros and ones used by
// computeKnownBits.
//
//===----------------------------------------------------------------------===//
#include "llvm/Support/KnownBits.h"
#include <cassert>
using namespace llvm;
static KnownBits computeForAddCarry(
const KnownBits &LHS, const KnownBits &RHS,
bool CarryZero, bool CarryOne) {
assert(!(CarryZero && CarryOne) &&
"Carry can't be zero and one at the same time");
APInt PossibleSumZero = LHS.getMaxValue() + RHS.getMaxValue() + !CarryZero;
APInt PossibleSumOne = LHS.getMinValue() + RHS.getMinValue() + CarryOne;
// Compute known bits of the carry.
APInt CarryKnownZero = ~(PossibleSumZero ^ LHS.Zero ^ RHS.Zero);
APInt CarryKnownOne = PossibleSumOne ^ LHS.One ^ RHS.One;
// Compute set of known bits (where all three relevant bits are known).
APInt LHSKnownUnion = LHS.Zero | LHS.One;
APInt RHSKnownUnion = RHS.Zero | RHS.One;
APInt CarryKnownUnion = std::move(CarryKnownZero) | CarryKnownOne;
APInt Known = std::move(LHSKnownUnion) & RHSKnownUnion & CarryKnownUnion;
assert((PossibleSumZero & Known) == (PossibleSumOne & Known) &&
"known bits of sum differ");
// Compute known bits of the result.
KnownBits KnownOut;
KnownOut.Zero = ~std::move(PossibleSumZero) & Known;
KnownOut.One = std::move(PossibleSumOne) & Known;
return KnownOut;
}
KnownBits KnownBits::computeForAddCarry(
const KnownBits &LHS, const KnownBits &RHS, const KnownBits &Carry) {
assert(Carry.getBitWidth() == 1 && "Carry must be 1-bit");
return ::computeForAddCarry(
LHS, RHS, Carry.Zero.getBoolValue(), Carry.One.getBoolValue());
}
KnownBits KnownBits::computeForAddSub(bool Add, bool NSW,
const KnownBits &LHS, KnownBits RHS) {
KnownBits KnownOut;
if (Add) {
// Sum = LHS + RHS + 0
KnownOut = ::computeForAddCarry(
LHS, RHS, /*CarryZero*/true, /*CarryOne*/false);
} else {
// Sum = LHS + ~RHS + 1
std::swap(RHS.Zero, RHS.One);
KnownOut = ::computeForAddCarry(
LHS, RHS, /*CarryZero*/false, /*CarryOne*/true);
}
// Are we still trying to solve for the sign bit?
if (!KnownOut.isNegative() && !KnownOut.isNonNegative()) {
if (NSW) {
// Adding two non-negative numbers, or subtracting a negative number from
// a non-negative one, can't wrap into negative.
if (LHS.isNonNegative() && RHS.isNonNegative())
KnownOut.makeNonNegative();
// Adding two negative numbers, or subtracting a non-negative number from
// a negative one, can't wrap into non-negative.
else if (LHS.isNegative() && RHS.isNegative())
KnownOut.makeNegative();
}
}
return KnownOut;
}
KnownBits KnownBits::makeGE(const APInt &Val) const {
// Count the number of leading bit positions where our underlying value is
// known to be less than or equal to Val.
unsigned N = (Zero | Val).countLeadingOnes();
// For each of those bit positions, if Val has a 1 in that bit then our
// underlying value must also have a 1.
APInt MaskedVal(Val);
MaskedVal.clearLowBits(getBitWidth() - N);
return KnownBits(Zero, One | MaskedVal);
}
KnownBits KnownBits::umax(const KnownBits &LHS, const KnownBits &RHS) {
// If we can prove that LHS >= RHS then use LHS as the result. Likewise for
// RHS. Ideally our caller would already have spotted these cases and
// optimized away the umax operation, but we handle them here for
// completeness.
if (LHS.getMinValue().uge(RHS.getMaxValue()))
return LHS;
if (RHS.getMinValue().uge(LHS.getMaxValue()))
return RHS;
// If the result of the umax is LHS then it must be greater than or equal to
// the minimum possible value of RHS. Likewise for RHS. Any known bits that
// are common to these two values are also known in the result.
KnownBits L = LHS.makeGE(RHS.getMinValue());
KnownBits R = RHS.makeGE(LHS.getMinValue());
return KnownBits::commonBits(L, R);
}
KnownBits KnownBits::umin(const KnownBits &LHS, const KnownBits &RHS) {
// Flip the range of values: [0, 0xFFFFFFFF] <-> [0xFFFFFFFF, 0]
auto Flip = [](const KnownBits &Val) { return KnownBits(Val.One, Val.Zero); };
return Flip(umax(Flip(LHS), Flip(RHS)));
}
KnownBits KnownBits::smax(const KnownBits &LHS, const KnownBits &RHS) {
// Flip the range of values: [-0x80000000, 0x7FFFFFFF] <-> [0, 0xFFFFFFFF]
auto Flip = [](const KnownBits &Val) {
unsigned SignBitPosition = Val.getBitWidth() - 1;
APInt Zero = Val.Zero;
APInt One = Val.One;
Zero.setBitVal(SignBitPosition, Val.One[SignBitPosition]);
One.setBitVal(SignBitPosition, Val.Zero[SignBitPosition]);
return KnownBits(Zero, One);
};
return Flip(umax(Flip(LHS), Flip(RHS)));
}
KnownBits KnownBits::smin(const KnownBits &LHS, const KnownBits &RHS) {
// Flip the range of values: [-0x80000000, 0x7FFFFFFF] <-> [0xFFFFFFFF, 0]
auto Flip = [](const KnownBits &Val) {
unsigned SignBitPosition = Val.getBitWidth() - 1;
APInt Zero = Val.One;
APInt One = Val.Zero;
Zero.setBitVal(SignBitPosition, Val.Zero[SignBitPosition]);
One.setBitVal(SignBitPosition, Val.One[SignBitPosition]);
return KnownBits(Zero, One);
};
return Flip(umax(Flip(LHS), Flip(RHS)));
}
KnownBits KnownBits::shl(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
KnownBits Known(BitWidth);
// If the shift amount is a valid constant then transform LHS directly.
if (RHS.isConstant() && RHS.getConstant().ult(BitWidth)) {
unsigned Shift = RHS.getConstant().getZExtValue();
Known = LHS;
Known.Zero <<= Shift;
Known.One <<= Shift;
// Low bits are known zero.
Known.Zero.setLowBits(Shift);
return Known;
}
// Minimum shift amount low bits are known zero.
if (RHS.getMinValue().ult(BitWidth))
Known.Zero.setLowBits(RHS.getMinValue().getZExtValue());
// No matter the shift amount, the trailing zeros will stay zero.
Known.Zero.setLowBits(LHS.countMinTrailingZeros());
return Known;
}
KnownBits KnownBits::lshr(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
KnownBits Known(BitWidth);
if (RHS.isConstant() && RHS.getConstant().ult(BitWidth)) {
unsigned Shift = RHS.getConstant().getZExtValue();
Known = LHS;
Known.Zero.lshrInPlace(Shift);
Known.One.lshrInPlace(Shift);
// High bits are known zero.
Known.Zero.setHighBits(Shift);
return Known;
}
// Minimum shift amount high bits are known zero.
if (RHS.getMinValue().ult(BitWidth))
Known.Zero.setHighBits(RHS.getMinValue().getZExtValue());
// No matter the shift amount, the leading zeros will stay zero.
Known.Zero.setHighBits(LHS.countMinLeadingZeros());
return Known;
}
KnownBits KnownBits::ashr(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
KnownBits Known(BitWidth);
if (RHS.isConstant() && RHS.getConstant().ult(BitWidth)) {
unsigned Shift = RHS.getConstant().getZExtValue();
Known = LHS;
Known.Zero.ashrInPlace(Shift);
Known.One.ashrInPlace(Shift);
return Known;
}
// TODO: Minimum shift amount high bits are known sign bits.
// TODO: No matter the shift amount, the leading sign bits will stay.
return Known;
}
KnownBits KnownBits::abs() const {
// If the source's MSB is zero then we know the rest of the bits already.
if (isNonNegative())
return *this;
// Assume we know nothing.
KnownBits KnownAbs(getBitWidth());
// We only know that the absolute values's MSB will be zero iff there is
// a set bit that isn't the sign bit (otherwise it could be INT_MIN).
APInt Val = One;
Val.clearSignBit();
if (!Val.isNullValue())
KnownAbs.Zero.setSignBit();
return KnownAbs;
}
KnownBits KnownBits::computeForMul(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
assert(!LHS.hasConflict() && !RHS.hasConflict());
// Compute a conservative estimate for high known-0 bits.
unsigned LeadZ =
std::max(LHS.countMinLeadingZeros() + RHS.countMinLeadingZeros(),
BitWidth) -
BitWidth;
LeadZ = std::min(LeadZ, BitWidth);
// The result of the bottom bits of an integer multiply can be
// inferred by looking at the bottom bits of both operands and
// multiplying them together.
// We can infer at least the minimum number of known trailing bits
// of both operands. Depending on number of trailing zeros, we can
// infer more bits, because (a*b) <=> ((a/m) * (b/n)) * (m*n) assuming
// a and b are divisible by m and n respectively.
// We then calculate how many of those bits are inferrable and set
// the output. For example, the i8 mul:
// a = XXXX1100 (12)
// b = XXXX1110 (14)
// We know the bottom 3 bits are zero since the first can be divided by
// 4 and the second by 2, thus having ((12/4) * (14/2)) * (2*4).
// Applying the multiplication to the trimmed arguments gets:
// XX11 (3)
// X111 (7)
// -------
// XX11
// XX11
// XX11
// XX11
// -------
// XXXXX01
// Which allows us to infer the 2 LSBs. Since we're multiplying the result
// by 8, the bottom 3 bits will be 0, so we can infer a total of 5 bits.
// The proof for this can be described as:
// Pre: (C1 >= 0) && (C1 < (1 << C5)) && (C2 >= 0) && (C2 < (1 << C6)) &&
// (C7 == (1 << (umin(countTrailingZeros(C1), C5) +
// umin(countTrailingZeros(C2), C6) +
// umin(C5 - umin(countTrailingZeros(C1), C5),
// C6 - umin(countTrailingZeros(C2), C6)))) - 1)
// %aa = shl i8 %a, C5
// %bb = shl i8 %b, C6
// %aaa = or i8 %aa, C1
// %bbb = or i8 %bb, C2
// %mul = mul i8 %aaa, %bbb
// %mask = and i8 %mul, C7
// =>
// %mask = i8 ((C1*C2)&C7)
// Where C5, C6 describe the known bits of %a, %b
// C1, C2 describe the known bottom bits of %a, %b.
// C7 describes the mask of the known bits of the result.
const APInt &Bottom0 = LHS.One;
const APInt &Bottom1 = RHS.One;
// How many times we'd be able to divide each argument by 2 (shr by 1).
// This gives us the number of trailing zeros on the multiplication result.
unsigned TrailBitsKnown0 = (LHS.Zero | LHS.One).countTrailingOnes();
unsigned TrailBitsKnown1 = (RHS.Zero | RHS.One).countTrailingOnes();
unsigned TrailZero0 = LHS.countMinTrailingZeros();
unsigned TrailZero1 = RHS.countMinTrailingZeros();
unsigned TrailZ = TrailZero0 + TrailZero1;
// Figure out the fewest known-bits operand.
unsigned SmallestOperand =
std::min(TrailBitsKnown0 - TrailZero0, TrailBitsKnown1 - TrailZero1);
unsigned ResultBitsKnown = std::min(SmallestOperand + TrailZ, BitWidth);
APInt BottomKnown =
Bottom0.getLoBits(TrailBitsKnown0) * Bottom1.getLoBits(TrailBitsKnown1);
KnownBits Res(BitWidth);
Res.Zero.setHighBits(LeadZ);
Res.Zero |= (~BottomKnown).getLoBits(ResultBitsKnown);
Res.One = BottomKnown.getLoBits(ResultBitsKnown);
return Res;
}
KnownBits KnownBits::udiv(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
assert(!LHS.hasConflict() && !RHS.hasConflict());
KnownBits Known(BitWidth);
// For the purposes of computing leading zeros we can conservatively
// treat a udiv as a logical right shift by the power of 2 known to
// be less than the denominator.
unsigned LeadZ = LHS.countMinLeadingZeros();
unsigned RHSMaxLeadingZeros = RHS.countMaxLeadingZeros();
if (RHSMaxLeadingZeros != BitWidth)
LeadZ = std::min(BitWidth, LeadZ + BitWidth - RHSMaxLeadingZeros - 1);
Known.Zero.setHighBits(LeadZ);
return Known;
}
KnownBits KnownBits::urem(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
assert(!LHS.hasConflict() && !RHS.hasConflict());
KnownBits Known(BitWidth);
if (RHS.isConstant() && RHS.getConstant().isPowerOf2()) {
// The upper bits are all zero, the lower ones are unchanged.
APInt LowBits = RHS.getConstant() - 1;
Known.Zero = LHS.Zero | ~LowBits;
Known.One = LHS.One & LowBits;
return Known;
}
// Since the result is less than or equal to either operand, any leading
// zero bits in either operand must also exist in the result.
uint32_t Leaders =
std::max(LHS.countMinLeadingZeros(), RHS.countMinLeadingZeros());
Known.Zero.setHighBits(Leaders);
return Known;
}
KnownBits KnownBits::srem(const KnownBits &LHS, const KnownBits &RHS) {
unsigned BitWidth = LHS.getBitWidth();
assert(!LHS.hasConflict() && !RHS.hasConflict());
KnownBits Known(BitWidth);
if (RHS.isConstant() && RHS.getConstant().isPowerOf2()) {
// The low bits of the first operand are unchanged by the srem.
APInt LowBits = RHS.getConstant() - 1;
Known.Zero = LHS.Zero & LowBits;
Known.One = LHS.One & LowBits;
// If the first operand is non-negative or has all low bits zero, then
// the upper bits are all zero.
if (LHS.isNonNegative() || LowBits.isSubsetOf(LHS.Zero))
Known.Zero |= ~LowBits;
// If the first operand is negative and not all low bits are zero, then
// the upper bits are all one.
if (LHS.isNegative() && LowBits.intersects(LHS.One))
Known.One |= ~LowBits;
return Known;
}
// The sign bit is the LHS's sign bit, except when the result of the
// remainder is zero. If it's known zero, our sign bit is also zero.
if (LHS.isNonNegative())
Known.makeNonNegative();
return Known;
}
KnownBits &KnownBits::operator&=(const KnownBits &RHS) {
// Result bit is 0 if either operand bit is 0.
Zero |= RHS.Zero;
// Result bit is 1 if both operand bits are 1.
One &= RHS.One;
return *this;
}
KnownBits &KnownBits::operator|=(const KnownBits &RHS) {
// Result bit is 0 if both operand bits are 0.
Zero &= RHS.Zero;
// Result bit is 1 if either operand bit is 1.
One |= RHS.One;
return *this;
}
KnownBits &KnownBits::operator^=(const KnownBits &RHS) {
// Result bit is 0 if both operand bits are 0 or both are 1.
APInt Z = (Zero & RHS.Zero) | (One & RHS.One);
// Result bit is 1 if one operand bit is 0 and the other is 1.
One = (Zero & RHS.One) | (One & RHS.Zero);
Zero = std::move(Z);
return *this;
}