575 lines
20 KiB
C++
575 lines
20 KiB
C++
//===- APFixedPoint.cpp - Fixed point constant handling ---------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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//
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/// \file
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/// Defines the implementation for the fixed point number interface.
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/ADT/APFixedPoint.h"
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#include "llvm/ADT/APFloat.h"
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namespace llvm {
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APFixedPoint APFixedPoint::convert(const FixedPointSemantics &DstSema,
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bool *Overflow) const {
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APSInt NewVal = Val;
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unsigned DstWidth = DstSema.getWidth();
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unsigned DstScale = DstSema.getScale();
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bool Upscaling = DstScale > getScale();
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if (Overflow)
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*Overflow = false;
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if (Upscaling) {
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NewVal = NewVal.extend(NewVal.getBitWidth() + DstScale - getScale());
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NewVal <<= (DstScale - getScale());
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} else {
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NewVal >>= (getScale() - DstScale);
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}
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auto Mask = APInt::getBitsSetFrom(
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NewVal.getBitWidth(),
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std::min(DstScale + DstSema.getIntegralBits(), NewVal.getBitWidth()));
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APInt Masked(NewVal & Mask);
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// Change in the bits above the sign
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if (!(Masked == Mask || Masked == 0)) {
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// Found overflow in the bits above the sign
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if (DstSema.isSaturated())
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NewVal = NewVal.isNegative() ? Mask : ~Mask;
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else if (Overflow)
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*Overflow = true;
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}
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// If the dst semantics are unsigned, but our value is signed and negative, we
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// clamp to zero.
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if (!DstSema.isSigned() && NewVal.isSigned() && NewVal.isNegative()) {
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// Found negative overflow for unsigned result
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if (DstSema.isSaturated())
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NewVal = 0;
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else if (Overflow)
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*Overflow = true;
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}
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NewVal = NewVal.extOrTrunc(DstWidth);
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NewVal.setIsSigned(DstSema.isSigned());
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return APFixedPoint(NewVal, DstSema);
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}
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int APFixedPoint::compare(const APFixedPoint &Other) const {
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APSInt ThisVal = getValue();
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APSInt OtherVal = Other.getValue();
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bool ThisSigned = Val.isSigned();
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bool OtherSigned = OtherVal.isSigned();
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unsigned OtherScale = Other.getScale();
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unsigned OtherWidth = OtherVal.getBitWidth();
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unsigned CommonWidth = std::max(Val.getBitWidth(), OtherWidth);
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// Prevent overflow in the event the widths are the same but the scales differ
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CommonWidth += getScale() >= OtherScale ? getScale() - OtherScale
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: OtherScale - getScale();
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ThisVal = ThisVal.extOrTrunc(CommonWidth);
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OtherVal = OtherVal.extOrTrunc(CommonWidth);
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unsigned CommonScale = std::max(getScale(), OtherScale);
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ThisVal = ThisVal.shl(CommonScale - getScale());
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OtherVal = OtherVal.shl(CommonScale - OtherScale);
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if (ThisSigned && OtherSigned) {
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if (ThisVal.sgt(OtherVal))
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return 1;
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else if (ThisVal.slt(OtherVal))
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return -1;
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} else if (!ThisSigned && !OtherSigned) {
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if (ThisVal.ugt(OtherVal))
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return 1;
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else if (ThisVal.ult(OtherVal))
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return -1;
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} else if (ThisSigned && !OtherSigned) {
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if (ThisVal.isSignBitSet())
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return -1;
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else if (ThisVal.ugt(OtherVal))
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return 1;
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else if (ThisVal.ult(OtherVal))
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return -1;
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} else {
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// !ThisSigned && OtherSigned
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if (OtherVal.isSignBitSet())
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return 1;
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else if (ThisVal.ugt(OtherVal))
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return 1;
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else if (ThisVal.ult(OtherVal))
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return -1;
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}
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return 0;
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}
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APFixedPoint APFixedPoint::getMax(const FixedPointSemantics &Sema) {
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bool IsUnsigned = !Sema.isSigned();
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auto Val = APSInt::getMaxValue(Sema.getWidth(), IsUnsigned);
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if (IsUnsigned && Sema.hasUnsignedPadding())
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Val = Val.lshr(1);
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return APFixedPoint(Val, Sema);
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}
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APFixedPoint APFixedPoint::getMin(const FixedPointSemantics &Sema) {
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auto Val = APSInt::getMinValue(Sema.getWidth(), !Sema.isSigned());
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return APFixedPoint(Val, Sema);
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}
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bool FixedPointSemantics::fitsInFloatSemantics(
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const fltSemantics &FloatSema) const {
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// A fixed point semantic fits in a floating point semantic if the maximum
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// and minimum values as integers of the fixed point semantic can fit in the
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// floating point semantic.
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// If these values do not fit, then a floating point rescaling of the true
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// maximum/minimum value will not fit either, so the floating point semantic
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// cannot be used to perform such a rescaling.
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APSInt MaxInt = APFixedPoint::getMax(*this).getValue();
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APFloat F(FloatSema);
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APFloat::opStatus Status = F.convertFromAPInt(MaxInt, MaxInt.isSigned(),
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APFloat::rmNearestTiesToAway);
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if ((Status & APFloat::opOverflow) || !isSigned())
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return !(Status & APFloat::opOverflow);
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APSInt MinInt = APFixedPoint::getMin(*this).getValue();
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Status = F.convertFromAPInt(MinInt, MinInt.isSigned(),
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APFloat::rmNearestTiesToAway);
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return !(Status & APFloat::opOverflow);
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}
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FixedPointSemantics FixedPointSemantics::getCommonSemantics(
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const FixedPointSemantics &Other) const {
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unsigned CommonScale = std::max(getScale(), Other.getScale());
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unsigned CommonWidth =
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std::max(getIntegralBits(), Other.getIntegralBits()) + CommonScale;
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bool ResultIsSigned = isSigned() || Other.isSigned();
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bool ResultIsSaturated = isSaturated() || Other.isSaturated();
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bool ResultHasUnsignedPadding = false;
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if (!ResultIsSigned) {
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// Both are unsigned.
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ResultHasUnsignedPadding = hasUnsignedPadding() &&
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Other.hasUnsignedPadding() && !ResultIsSaturated;
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}
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// If the result is signed, add an extra bit for the sign. Otherwise, if it is
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// unsigned and has unsigned padding, we only need to add the extra padding
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// bit back if we are not saturating.
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if (ResultIsSigned || ResultHasUnsignedPadding)
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CommonWidth++;
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return FixedPointSemantics(CommonWidth, CommonScale, ResultIsSigned,
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ResultIsSaturated, ResultHasUnsignedPadding);
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}
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APFixedPoint APFixedPoint::add(const APFixedPoint &Other,
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bool *Overflow) const {
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auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
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APFixedPoint ConvertedThis = convert(CommonFXSema);
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APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
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APSInt ThisVal = ConvertedThis.getValue();
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APSInt OtherVal = ConvertedOther.getValue();
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bool Overflowed = false;
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APSInt Result;
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if (CommonFXSema.isSaturated()) {
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Result = CommonFXSema.isSigned() ? ThisVal.sadd_sat(OtherVal)
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: ThisVal.uadd_sat(OtherVal);
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} else {
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Result = ThisVal.isSigned() ? ThisVal.sadd_ov(OtherVal, Overflowed)
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: ThisVal.uadd_ov(OtherVal, Overflowed);
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}
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if (Overflow)
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*Overflow = Overflowed;
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return APFixedPoint(Result, CommonFXSema);
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}
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APFixedPoint APFixedPoint::sub(const APFixedPoint &Other,
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bool *Overflow) const {
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auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
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APFixedPoint ConvertedThis = convert(CommonFXSema);
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APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
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APSInt ThisVal = ConvertedThis.getValue();
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APSInt OtherVal = ConvertedOther.getValue();
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bool Overflowed = false;
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APSInt Result;
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if (CommonFXSema.isSaturated()) {
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Result = CommonFXSema.isSigned() ? ThisVal.ssub_sat(OtherVal)
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: ThisVal.usub_sat(OtherVal);
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} else {
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Result = ThisVal.isSigned() ? ThisVal.ssub_ov(OtherVal, Overflowed)
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: ThisVal.usub_ov(OtherVal, Overflowed);
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}
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if (Overflow)
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*Overflow = Overflowed;
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return APFixedPoint(Result, CommonFXSema);
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}
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APFixedPoint APFixedPoint::mul(const APFixedPoint &Other,
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bool *Overflow) const {
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auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
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APFixedPoint ConvertedThis = convert(CommonFXSema);
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APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
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APSInt ThisVal = ConvertedThis.getValue();
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APSInt OtherVal = ConvertedOther.getValue();
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bool Overflowed = false;
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// Widen the LHS and RHS so we can perform a full multiplication.
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unsigned Wide = CommonFXSema.getWidth() * 2;
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if (CommonFXSema.isSigned()) {
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ThisVal = ThisVal.sextOrSelf(Wide);
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OtherVal = OtherVal.sextOrSelf(Wide);
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} else {
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ThisVal = ThisVal.zextOrSelf(Wide);
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OtherVal = OtherVal.zextOrSelf(Wide);
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}
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// Perform the full multiplication and downscale to get the same scale.
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//
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// Note that the right shifts here perform an implicit downwards rounding.
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// This rounding could discard bits that would technically place the result
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// outside the representable range. We interpret the spec as allowing us to
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// perform the rounding step first, avoiding the overflow case that would
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// arise.
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APSInt Result;
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if (CommonFXSema.isSigned())
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Result = ThisVal.smul_ov(OtherVal, Overflowed)
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.ashr(CommonFXSema.getScale());
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else
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Result = ThisVal.umul_ov(OtherVal, Overflowed)
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.lshr(CommonFXSema.getScale());
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assert(!Overflowed && "Full multiplication cannot overflow!");
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Result.setIsSigned(CommonFXSema.isSigned());
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// If our result lies outside of the representative range of the common
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// semantic, we either have overflow or saturation.
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APSInt Max = APFixedPoint::getMax(CommonFXSema).getValue()
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.extOrTrunc(Wide);
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APSInt Min = APFixedPoint::getMin(CommonFXSema).getValue()
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.extOrTrunc(Wide);
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if (CommonFXSema.isSaturated()) {
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if (Result < Min)
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Result = Min;
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else if (Result > Max)
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Result = Max;
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} else
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Overflowed = Result < Min || Result > Max;
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if (Overflow)
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*Overflow = Overflowed;
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return APFixedPoint(Result.sextOrTrunc(CommonFXSema.getWidth()),
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CommonFXSema);
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}
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APFixedPoint APFixedPoint::div(const APFixedPoint &Other,
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bool *Overflow) const {
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auto CommonFXSema = Sema.getCommonSemantics(Other.getSemantics());
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APFixedPoint ConvertedThis = convert(CommonFXSema);
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APFixedPoint ConvertedOther = Other.convert(CommonFXSema);
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APSInt ThisVal = ConvertedThis.getValue();
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APSInt OtherVal = ConvertedOther.getValue();
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bool Overflowed = false;
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// Widen the LHS and RHS so we can perform a full division.
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unsigned Wide = CommonFXSema.getWidth() * 2;
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if (CommonFXSema.isSigned()) {
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ThisVal = ThisVal.sextOrSelf(Wide);
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OtherVal = OtherVal.sextOrSelf(Wide);
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} else {
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ThisVal = ThisVal.zextOrSelf(Wide);
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OtherVal = OtherVal.zextOrSelf(Wide);
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}
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// Upscale to compensate for the loss of precision from division, and
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// perform the full division.
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ThisVal = ThisVal.shl(CommonFXSema.getScale());
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APSInt Result;
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if (CommonFXSema.isSigned()) {
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APInt Rem;
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APInt::sdivrem(ThisVal, OtherVal, Result, Rem);
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// If the quotient is negative and the remainder is nonzero, round
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// towards negative infinity by subtracting epsilon from the result.
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if (ThisVal.isNegative() != OtherVal.isNegative() && !Rem.isNullValue())
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Result = Result - 1;
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} else
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Result = ThisVal.udiv(OtherVal);
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Result.setIsSigned(CommonFXSema.isSigned());
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// If our result lies outside of the representative range of the common
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// semantic, we either have overflow or saturation.
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APSInt Max = APFixedPoint::getMax(CommonFXSema).getValue()
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.extOrTrunc(Wide);
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APSInt Min = APFixedPoint::getMin(CommonFXSema).getValue()
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.extOrTrunc(Wide);
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if (CommonFXSema.isSaturated()) {
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if (Result < Min)
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Result = Min;
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else if (Result > Max)
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Result = Max;
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} else
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Overflowed = Result < Min || Result > Max;
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if (Overflow)
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*Overflow = Overflowed;
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return APFixedPoint(Result.sextOrTrunc(CommonFXSema.getWidth()),
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CommonFXSema);
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}
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APFixedPoint APFixedPoint::shl(unsigned Amt, bool *Overflow) const {
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APSInt ThisVal = Val;
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bool Overflowed = false;
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// Widen the LHS.
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unsigned Wide = Sema.getWidth() * 2;
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if (Sema.isSigned())
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ThisVal = ThisVal.sextOrSelf(Wide);
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else
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ThisVal = ThisVal.zextOrSelf(Wide);
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// Clamp the shift amount at the original width, and perform the shift.
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Amt = std::min(Amt, ThisVal.getBitWidth());
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APSInt Result = ThisVal << Amt;
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Result.setIsSigned(Sema.isSigned());
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// If our result lies outside of the representative range of the
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// semantic, we either have overflow or saturation.
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APSInt Max = APFixedPoint::getMax(Sema).getValue().extOrTrunc(Wide);
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APSInt Min = APFixedPoint::getMin(Sema).getValue().extOrTrunc(Wide);
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if (Sema.isSaturated()) {
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if (Result < Min)
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Result = Min;
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else if (Result > Max)
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Result = Max;
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} else
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Overflowed = Result < Min || Result > Max;
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if (Overflow)
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*Overflow = Overflowed;
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return APFixedPoint(Result.sextOrTrunc(Sema.getWidth()), Sema);
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}
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void APFixedPoint::toString(SmallVectorImpl<char> &Str) const {
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APSInt Val = getValue();
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unsigned Scale = getScale();
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if (Val.isSigned() && Val.isNegative() && Val != -Val) {
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Val = -Val;
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Str.push_back('-');
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}
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APSInt IntPart = Val >> Scale;
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// Add 4 digits to hold the value after multiplying 10 (the radix)
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unsigned Width = Val.getBitWidth() + 4;
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APInt FractPart = Val.zextOrTrunc(Scale).zext(Width);
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APInt FractPartMask = APInt::getAllOnesValue(Scale).zext(Width);
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APInt RadixInt = APInt(Width, 10);
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IntPart.toString(Str, /*Radix=*/10);
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Str.push_back('.');
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do {
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(FractPart * RadixInt)
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.lshr(Scale)
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.toString(Str, /*Radix=*/10, Val.isSigned());
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FractPart = (FractPart * RadixInt) & FractPartMask;
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} while (FractPart != 0);
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}
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APFixedPoint APFixedPoint::negate(bool *Overflow) const {
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if (!isSaturated()) {
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if (Overflow)
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*Overflow =
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(!isSigned() && Val != 0) || (isSigned() && Val.isMinSignedValue());
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return APFixedPoint(-Val, Sema);
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}
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// We never overflow for saturation
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if (Overflow)
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*Overflow = false;
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if (isSigned())
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return Val.isMinSignedValue() ? getMax(Sema) : APFixedPoint(-Val, Sema);
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else
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return APFixedPoint(Sema);
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}
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APSInt APFixedPoint::convertToInt(unsigned DstWidth, bool DstSign,
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bool *Overflow) const {
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APSInt Result = getIntPart();
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unsigned SrcWidth = getWidth();
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APSInt DstMin = APSInt::getMinValue(DstWidth, !DstSign);
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APSInt DstMax = APSInt::getMaxValue(DstWidth, !DstSign);
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if (SrcWidth < DstWidth) {
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Result = Result.extend(DstWidth);
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} else if (SrcWidth > DstWidth) {
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DstMin = DstMin.extend(SrcWidth);
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DstMax = DstMax.extend(SrcWidth);
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}
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if (Overflow) {
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if (Result.isSigned() && !DstSign) {
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*Overflow = Result.isNegative() || Result.ugt(DstMax);
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} else if (Result.isUnsigned() && DstSign) {
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*Overflow = Result.ugt(DstMax);
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} else {
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*Overflow = Result < DstMin || Result > DstMax;
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}
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}
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Result.setIsSigned(DstSign);
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return Result.extOrTrunc(DstWidth);
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}
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const fltSemantics *APFixedPoint::promoteFloatSemantics(const fltSemantics *S) {
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if (S == &APFloat::BFloat())
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return &APFloat::IEEEdouble();
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else if (S == &APFloat::IEEEhalf())
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return &APFloat::IEEEsingle();
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else if (S == &APFloat::IEEEsingle())
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return &APFloat::IEEEdouble();
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else if (S == &APFloat::IEEEdouble())
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return &APFloat::IEEEquad();
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llvm_unreachable("Could not promote float type!");
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}
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APFloat APFixedPoint::convertToFloat(const fltSemantics &FloatSema) const {
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// For some operations, rounding mode has an effect on the result, while
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// other operations are lossless and should never result in rounding.
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// To signify which these operations are, we define two rounding modes here.
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APFloat::roundingMode RM = APFloat::rmNearestTiesToEven;
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APFloat::roundingMode LosslessRM = APFloat::rmTowardZero;
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// Make sure that we are operating in a type that works with this fixed-point
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// semantic.
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const fltSemantics *OpSema = &FloatSema;
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while (!Sema.fitsInFloatSemantics(*OpSema))
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OpSema = promoteFloatSemantics(OpSema);
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// Convert the fixed point value bits as an integer. If the floating point
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// value does not have the required precision, we will round according to the
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// given mode.
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APFloat Flt(*OpSema);
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APFloat::opStatus S = Flt.convertFromAPInt(Val, Sema.isSigned(), RM);
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// If we cared about checking for precision loss, we could look at this
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// status.
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(void)S;
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// Scale down the integer value in the float to match the correct scaling
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// factor.
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APFloat ScaleFactor(std::pow(2, -(int)Sema.getScale()));
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bool Ignored;
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ScaleFactor.convert(*OpSema, LosslessRM, &Ignored);
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Flt.multiply(ScaleFactor, LosslessRM);
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|
|
|
if (OpSema != &FloatSema)
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|
Flt.convert(FloatSema, RM, &Ignored);
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|
|
|
return Flt;
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|
}
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|
|
|
APFixedPoint APFixedPoint::getFromIntValue(const APSInt &Value,
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|
const FixedPointSemantics &DstFXSema,
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|
bool *Overflow) {
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|
FixedPointSemantics IntFXSema = FixedPointSemantics::GetIntegerSemantics(
|
|
Value.getBitWidth(), Value.isSigned());
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|
return APFixedPoint(Value, IntFXSema).convert(DstFXSema, Overflow);
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|
}
|
|
|
|
APFixedPoint
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|
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
|