APFixedPoint.cpp

Go to the documentation of this file.

//===- 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"
 
#include <cmath>
 
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.sext(Wide);
    OtherVal = OtherVal.sext(Wide);
  } else {
    ThisVal = ThisVal.zext(Wide);
    OtherVal = OtherVal.zext(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.sext(Wide);
    OtherVal = OtherVal.sext(Wide);
  } else {
    ThisVal = ThisVal.zext(Wide);
    OtherVal = OtherVal.zext(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.isZero())
      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.sext(Wide);
  else
    ThisVal = ThisVal.zext(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::getAllOnes(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