llvm-for-llvmta/lib/Support/APFixedPoint.cpp

575 lines
20 KiB
C++
Raw Permalink Normal View History

2022-04-25 10:02:23 +02:00
//===- APFixedPoint.cpp - Fixed point constant handling ---------*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
/// \file
/// Defines the implementation for the fixed point number interface.
//
//===----------------------------------------------------------------------===//
#include "llvm/ADT/APFixedPoint.h"
#include "llvm/ADT/APFloat.h"
namespace llvm {
APFixedPoint APFixedPoint::convert(const FixedPointSemantics &DstSema,
bool *Overflow) const {
APSInt NewVal = Val;
unsigned DstWidth = DstSema.getWidth();
unsigned DstScale = DstSema.getScale();
bool Upscaling = DstScale > getScale();
if (Overflow)
*Overflow = false;
if (Upscaling) {
NewVal = NewVal.extend(NewVal.getBitWidth() + DstScale - getScale());
NewVal <<= (DstScale - getScale());
} else {
NewVal >>= (getScale() - DstScale);
}
auto Mask = APInt::getBitsSetFrom(
NewVal.getBitWidth(),
std::min(DstScale + DstSema.getIntegralBits(), NewVal.getBitWidth()));
APInt Masked(NewVal & Mask);
// Change in the bits above the sign
if (!(Masked == Mask || Masked == 0)) {
// Found overflow in the bits above the sign
if (DstSema.isSaturated())
NewVal = NewVal.isNegative() ? Mask : ~Mask;
else if (Overflow)
*Overflow = true;
}
// If the dst semantics are unsigned, but our value is signed and negative, we
// clamp to zero.
if (!DstSema.isSigned() && NewVal.isSigned() && NewVal.isNegative()) {
// Found negative overflow for unsigned result
if (DstSema.isSaturated())
NewVal = 0;
else if (Overflow)
*Overflow = true;
}
NewVal = NewVal.extOrTrunc(DstWidth);
NewVal.setIsSigned(DstSema.isSigned());
return APFixedPoint(NewVal, DstSema);
}
int APFixedPoint::compare(const APFixedPoint &Other) const {
APSInt ThisVal = getValue();
APSInt OtherVal = Other.getValue();
bool ThisSigned = Val.isSigned();
bool OtherSigned = OtherVal.isSigned();
unsigned OtherScale = Other.getScale();
unsigned OtherWidth = OtherVal.getBitWidth();
unsigned CommonWidth = std::max(Val.getBitWidth(), OtherWidth);
// Prevent overflow in the event the widths are the same but the scales differ
CommonWidth += getScale() >= OtherScale ? getScale() - OtherScale
: OtherScale - getScale();
ThisVal = ThisVal.extOrTrunc(CommonWidth);
OtherVal = OtherVal.extOrTrunc(CommonWidth);
unsigned CommonScale = std::max(getScale(), OtherScale);
ThisVal = ThisVal.shl(CommonScale - getScale());
OtherVal = OtherVal.shl(CommonScale - OtherScale);
if (ThisSigned && OtherSigned) {
if (ThisVal.sgt(OtherVal))
return 1;
else if (ThisVal.slt(OtherVal))
return -1;
} else if (!ThisSigned && !OtherSigned) {
if (ThisVal.ugt(OtherVal))
return 1;
else if (ThisVal.ult(OtherVal))
return -1;
} else if (ThisSigned && !OtherSigned) {
if (ThisVal.isSignBitSet())
return -1;
else if (ThisVal.ugt(OtherVal))
return 1;
else if (ThisVal.ult(OtherVal))
return -1;
} else {
// !ThisSigned && OtherSigned
if (OtherVal.isSignBitSet())
return 1;
else if (ThisVal.ugt(OtherVal))
return 1;
else if (ThisVal.ult(OtherVal))
return -1;
}
return 0;
}
APFixedPoint APFixedPoint::getMax(const FixedPointSemantics &Sema) {
bool IsUnsigned = !Sema.isSigned();
auto Val = APSInt::getMaxValue(Sema.getWidth(), IsUnsigned);
if (IsUnsigned && Sema.hasUnsignedPadding())
Val = Val.lshr(1);
return APFixedPoint(Val, Sema);
}
APFixedPoint APFixedPoint::getMin(const FixedPointSemantics &Sema) {
auto Val = APSInt::getMinValue(Sema.getWidth(), !Sema.isSigned());
return APFixedPoint(Val, Sema);
}
bool FixedPointSemantics::fitsInFloatSemantics(
const fltSemantics &FloatSema) const {
// A fixed point semantic fits in a floating point semantic if the maximum
// and minimum values as integers of the fixed point semantic can fit in the
// floating point semantic.
// If these values do not fit, then a floating point rescaling of the true
// maximum/minimum value will not fit either, so the floating point semantic
// cannot be used to perform such a rescaling.
APSInt MaxInt = APFixedPoint::getMax(*this).getValue();
APFloat F(FloatSema);
APFloat::opStatus Status = F.convertFromAPInt(MaxInt, MaxInt.isSigned(),
APFloat::rmNearestTiesToAway);
if ((Status & APFloat::opOverflow) || !isSigned())
return !(Status & APFloat::opOverflow);
APSInt MinInt = APFixedPoint::getMin(*this).getValue();
Status = F.convertFromAPInt(MinInt, MinInt.isSigned(),
APFloat::rmNearestTiesToAway);
return !(Status & APFloat::opOverflow);
}
FixedPointSemantics FixedPointSemantics::getCommonSemantics(
const FixedPointSemantics &Other) const {
unsigned CommonScale = std::max(getScale(), Other.getScale());
unsigned CommonWidth =
std::max(getIntegralBits(), Other.getIntegralBits()) + CommonScale;
bool ResultIsSigned = isSigned() || Other.isSigned();
bool ResultIsSaturated = isSaturated() || Other.isSaturated();
bool ResultHasUnsignedPadding = false;
if (!ResultIsSigned) {
// Both are unsigned.
ResultHasUnsignedPadding = hasUnsignedPadding() &&
Other.hasUnsignedPadding() && !ResultIsSaturated;
}
// If the result is signed, add an extra bit for the sign. Otherwise, if it is
// unsigned and has unsigned padding, we only need to add the extra padding
// bit back if we are not saturating.
if (ResultIsSigned || ResultHasUnsignedPadding)
CommonWidth++;
return FixedPointSemantics(CommonWidth, CommonScale, ResultIsSigned,
ResultIsSaturated, ResultHasUnsignedPadding);
}
APFixedPoint APFixedPoint::add(const APFixedPoint &Other,
bool *Overflow) const {
auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
APFixedPoint ConvertedThis = convert(CommonFXSema);
APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
APSInt ThisVal = ConvertedThis.getValue();
APSInt OtherVal = ConvertedOther.getValue();
bool Overflowed = false;
APSInt Result;
if (CommonFXSema.isSaturated()) {
Result = CommonFXSema.isSigned() ? ThisVal.sadd_sat(OtherVal)
: ThisVal.uadd_sat(OtherVal);
} else {
Result = ThisVal.isSigned() ? ThisVal.sadd_ov(OtherVal, Overflowed)
: ThisVal.uadd_ov(OtherVal, Overflowed);
}
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Result, CommonFXSema);
}
APFixedPoint APFixedPoint::sub(const APFixedPoint &Other,
bool *Overflow) const {
auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
APFixedPoint ConvertedThis = convert(CommonFXSema);
APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
APSInt ThisVal = ConvertedThis.getValue();
APSInt OtherVal = ConvertedOther.getValue();
bool Overflowed = false;
APSInt Result;
if (CommonFXSema.isSaturated()) {
Result = CommonFXSema.isSigned() ? ThisVal.ssub_sat(OtherVal)
: ThisVal.usub_sat(OtherVal);
} else {
Result = ThisVal.isSigned() ? ThisVal.ssub_ov(OtherVal, Overflowed)
: ThisVal.usub_ov(OtherVal, Overflowed);
}
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Result, CommonFXSema);
}
APFixedPoint APFixedPoint::mul(const APFixedPoint &Other,
bool *Overflow) const {
auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
APFixedPoint ConvertedThis = convert(CommonFXSema);
APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
APSInt ThisVal = ConvertedThis.getValue();
APSInt OtherVal = ConvertedOther.getValue();
bool Overflowed = false;
// Widen the LHS and RHS so we can perform a full multiplication.
unsigned Wide = CommonFXSema.getWidth() * 2;
if (CommonFXSema.isSigned()) {
ThisVal = ThisVal.sextOrSelf(Wide);
OtherVal = OtherVal.sextOrSelf(Wide);
} else {
ThisVal = ThisVal.zextOrSelf(Wide);
OtherVal = OtherVal.zextOrSelf(Wide);
}
// Perform the full multiplication and downscale to get the same scale.
//
// Note that the right shifts here perform an implicit downwards rounding.
// This rounding could discard bits that would technically place the result
// outside the representable range. We interpret the spec as allowing us to
// perform the rounding step first, avoiding the overflow case that would
// arise.
APSInt Result;
if (CommonFXSema.isSigned())
Result = ThisVal.smul_ov(OtherVal, Overflowed)
.ashr(CommonFXSema.getScale());
else
Result = ThisVal.umul_ov(OtherVal, Overflowed)
.lshr(CommonFXSema.getScale());
assert(!Overflowed && "Full multiplication cannot overflow!");
Result.setIsSigned(CommonFXSema.isSigned());
// If our result lies outside of the representative range of the common
// semantic, we either have overflow or saturation.
APSInt Max = APFixedPoint::getMax(CommonFXSema).getValue()
.extOrTrunc(Wide);
APSInt Min = APFixedPoint::getMin(CommonFXSema).getValue()
.extOrTrunc(Wide);
if (CommonFXSema.isSaturated()) {
if (Result < Min)
Result = Min;
else if (Result > Max)
Result = Max;
} else
Overflowed = Result < Min || Result > Max;
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Result.sextOrTrunc(CommonFXSema.getWidth()),
CommonFXSema);
}
APFixedPoint APFixedPoint::div(const APFixedPoint &Other,
bool *Overflow) const {
auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
APFixedPoint ConvertedThis = convert(CommonFXSema);
APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
APSInt ThisVal = ConvertedThis.getValue();
APSInt OtherVal = ConvertedOther.getValue();
bool Overflowed = false;
// Widen the LHS and RHS so we can perform a full division.
unsigned Wide = CommonFXSema.getWidth() * 2;
if (CommonFXSema.isSigned()) {
ThisVal = ThisVal.sextOrSelf(Wide);
OtherVal = OtherVal.sextOrSelf(Wide);
} else {
ThisVal = ThisVal.zextOrSelf(Wide);
OtherVal = OtherVal.zextOrSelf(Wide);
}
// Upscale to compensate for the loss of precision from division, and
// perform the full division.
ThisVal = ThisVal.shl(CommonFXSema.getScale());
APSInt Result;
if (CommonFXSema.isSigned()) {
APInt Rem;
APInt::sdivrem(ThisVal, OtherVal, Result, Rem);
// If the quotient is negative and the remainder is nonzero, round
// towards negative infinity by subtracting epsilon from the result.
if (ThisVal.isNegative() != OtherVal.isNegative() && !Rem.isNullValue())
Result = Result - 1;
} else
Result = ThisVal.udiv(OtherVal);
Result.setIsSigned(CommonFXSema.isSigned());
// If our result lies outside of the representative range of the common
// semantic, we either have overflow or saturation.
APSInt Max = APFixedPoint::getMax(CommonFXSema).getValue()
.extOrTrunc(Wide);
APSInt Min = APFixedPoint::getMin(CommonFXSema).getValue()
.extOrTrunc(Wide);
if (CommonFXSema.isSaturated()) {
if (Result < Min)
Result = Min;
else if (Result > Max)
Result = Max;
} else
Overflowed = Result < Min || Result > Max;
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Result.sextOrTrunc(CommonFXSema.getWidth()),
CommonFXSema);
}
APFixedPoint APFixedPoint::shl(unsigned Amt, bool *Overflow) const {
APSInt ThisVal = Val;
bool Overflowed = false;
// Widen the LHS.
unsigned Wide = Sema.getWidth() * 2;
if (Sema.isSigned())
ThisVal = ThisVal.sextOrSelf(Wide);
else
ThisVal = ThisVal.zextOrSelf(Wide);
// Clamp the shift amount at the original width, and perform the shift.
Amt = std::min(Amt, ThisVal.getBitWidth());
APSInt Result = ThisVal << Amt;
Result.setIsSigned(Sema.isSigned());
// If our result lies outside of the representative range of the
// semantic, we either have overflow or saturation.
APSInt Max = APFixedPoint::getMax(Sema).getValue().extOrTrunc(Wide);
APSInt Min = APFixedPoint::getMin(Sema).getValue().extOrTrunc(Wide);
if (Sema.isSaturated()) {
if (Result < Min)
Result = Min;
else if (Result > Max)
Result = Max;
} else
Overflowed = Result < Min || Result > Max;
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Result.sextOrTrunc(Sema.getWidth()), Sema);
}
void APFixedPoint::toString(SmallVectorImpl<char> &Str) const {
APSInt Val = getValue();
unsigned Scale = getScale();
if (Val.isSigned() && Val.isNegative() && Val != -Val) {
Val = -Val;
Str.push_back('-');
}
APSInt IntPart = Val >> Scale;
// Add 4 digits to hold the value after multiplying 10 (the radix)
unsigned Width = Val.getBitWidth() + 4;
APInt FractPart = Val.zextOrTrunc(Scale).zext(Width);
APInt FractPartMask = APInt::getAllOnesValue(Scale).zext(Width);
APInt RadixInt = APInt(Width, 10);
IntPart.toString(Str, /*Radix=*/10);
Str.push_back('.');
do {
(FractPart * RadixInt)
.lshr(Scale)
.toString(Str, /*Radix=*/10, Val.isSigned());
FractPart = (FractPart * RadixInt) & FractPartMask;
} while (FractPart != 0);
}
APFixedPoint APFixedPoint::negate(bool *Overflow) const {
if (!isSaturated()) {
if (Overflow)
*Overflow =
(!isSigned() && Val != 0) || (isSigned() && Val.isMinSignedValue());
return APFixedPoint(-Val, Sema);
}
// We never overflow for saturation
if (Overflow)
*Overflow = false;
if (isSigned())
return Val.isMinSignedValue() ? getMax(Sema) : APFixedPoint(-Val, Sema);
else
return APFixedPoint(Sema);
}
APSInt APFixedPoint::convertToInt(unsigned DstWidth, bool DstSign,
bool *Overflow) const {
APSInt Result = getIntPart();
unsigned SrcWidth = getWidth();
APSInt DstMin = APSInt::getMinValue(DstWidth, !DstSign);
APSInt DstMax = APSInt::getMaxValue(DstWidth, !DstSign);
if (SrcWidth < DstWidth) {
Result = Result.extend(DstWidth);
} else if (SrcWidth > DstWidth) {
DstMin = DstMin.extend(SrcWidth);
DstMax = DstMax.extend(SrcWidth);
}
if (Overflow) {
if (Result.isSigned() && !DstSign) {
*Overflow = Result.isNegative() || Result.ugt(DstMax);
} else if (Result.isUnsigned() && DstSign) {
*Overflow = Result.ugt(DstMax);
} else {
*Overflow = Result < DstMin || Result > DstMax;
}
}
Result.setIsSigned(DstSign);
return Result.extOrTrunc(DstWidth);
}
const fltSemantics *APFixedPoint::promoteFloatSemantics(const fltSemantics *S) {
if (S == &APFloat::BFloat())
return &APFloat::IEEEdouble();
else if (S == &APFloat::IEEEhalf())
return &APFloat::IEEEsingle();
else if (S == &APFloat::IEEEsingle())
return &APFloat::IEEEdouble();
else if (S == &APFloat::IEEEdouble())
return &APFloat::IEEEquad();
llvm_unreachable("Could not promote float type!");
}
APFloat APFixedPoint::convertToFloat(const fltSemantics &FloatSema) const {
// For some operations, rounding mode has an effect on the result, while
// other operations are lossless and should never result in rounding.
// To signify which these operations are, we define two rounding modes here.
APFloat::roundingMode RM = APFloat::rmNearestTiesToEven;
APFloat::roundingMode LosslessRM = APFloat::rmTowardZero;
// Make sure that we are operating in a type that works with this fixed-point
// semantic.
const fltSemantics *OpSema = &FloatSema;
while (!Sema.fitsInFloatSemantics(*OpSema))
OpSema = promoteFloatSemantics(OpSema);
// Convert the fixed point value bits as an integer. If the floating point
// value does not have the required precision, we will round according to the
// given mode.
APFloat Flt(*OpSema);
APFloat::opStatus S = Flt.convertFromAPInt(Val, Sema.isSigned(), RM);
// If we cared about checking for precision loss, we could look at this
// status.
(void)S;
// Scale down the integer value in the float to match the correct scaling
// factor.
APFloat ScaleFactor(std::pow(2, -(int)Sema.getScale()));
bool Ignored;
ScaleFactor.convert(*OpSema, LosslessRM, &Ignored);
Flt.multiply(ScaleFactor, LosslessRM);
if (OpSema != &FloatSema)
Flt.convert(FloatSema, RM, &Ignored);
return Flt;
}
APFixedPoint APFixedPoint::getFromIntValue(const APSInt &Value,
const FixedPointSemantics &DstFXSema,
bool *Overflow) {
FixedPointSemantics IntFXSema = FixedPointSemantics::GetIntegerSemantics(
Value.getBitWidth(), Value.isSigned());
return APFixedPoint(Value, IntFXSema).convert(DstFXSema, Overflow);
}
APFixedPoint
APFixedPoint::getFromFloatValue(const APFloat &Value,
const FixedPointSemantics &DstFXSema,
bool *Overflow) {
// For some operations, rounding mode has an effect on the result, while
// other operations are lossless and should never result in rounding.
// To signify which these operations are, we define two rounding modes here,
// even though they are the same mode.
APFloat::roundingMode RM = APFloat::rmTowardZero;
APFloat::roundingMode LosslessRM = APFloat::rmTowardZero;
const fltSemantics &FloatSema = Value.getSemantics();
if (Value.isNaN()) {
// Handle NaN immediately.
if (Overflow)
*Overflow = true;
return APFixedPoint(DstFXSema);
}
// Make sure that we are operating in a type that works with this fixed-point
// semantic.
const fltSemantics *OpSema = &FloatSema;
while (!DstFXSema.fitsInFloatSemantics(*OpSema))
OpSema = promoteFloatSemantics(OpSema);
APFloat Val = Value;
bool Ignored;
if (&FloatSema != OpSema)
Val.convert(*OpSema, LosslessRM, &Ignored);
// Scale up the float so that the 'fractional' part of the mantissa ends up in
// the integer range instead. Rounding mode is irrelevant here.
// It is fine if this overflows to infinity even for saturating types,
// since we will use floating point comparisons to check for saturation.
APFloat ScaleFactor(std::pow(2, DstFXSema.getScale()));
ScaleFactor.convert(*OpSema, LosslessRM, &Ignored);
Val.multiply(ScaleFactor, LosslessRM);
// Convert to the integral representation of the value. This rounding mode
// is significant.
APSInt Res(DstFXSema.getWidth(), !DstFXSema.isSigned());
Val.convertToInteger(Res, RM, &Ignored);
// Round the integral value and scale back. This makes the
// overflow calculations below work properly. If we do not round here,
// we risk checking for overflow with a value that is outside the
// representable range of the fixed-point semantic even though no overflow
// would occur had we rounded first.
ScaleFactor = APFloat(std::pow(2, -(int)DstFXSema.getScale()));
ScaleFactor.convert(*OpSema, LosslessRM, &Ignored);
Val.roundToIntegral(RM);
Val.multiply(ScaleFactor, LosslessRM);
// Check for overflow/saturation by checking if the floating point value
// is outside the range representable by the fixed-point value.
APFloat FloatMax = getMax(DstFXSema).convertToFloat(*OpSema);
APFloat FloatMin = getMin(DstFXSema).convertToFloat(*OpSema);
bool Overflowed = false;
if (DstFXSema.isSaturated()) {
if (Val > FloatMax)
Res = getMax(DstFXSema).getValue();
else if (Val < FloatMin)
Res = getMin(DstFXSema).getValue();
} else
Overflowed = Val > FloatMax || Val < FloatMin;
if (Overflow)
*Overflow = Overflowed;
return APFixedPoint(Res, DstFXSema);
}
} // namespace llvm