2b5cd3778c
f18 unconditionally uses a scaling algorithm for complex/complex division that avoids needless overflows and underflows when computing the sum of the squares of the components of the denominator -- but testing has shown some 1 ULP differences relative to the naive calculation due to the extra operations and roundings. So use the scaling algorithm only when the naive calculation actually would overflow or underflow. Differential Revision: https://reviews.llvm.org/D132164
126 lines
5.0 KiB
C++
126 lines
5.0 KiB
C++
//===-- lib/Evaluate/complex.cpp ------------------------------------------===//
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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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#include "flang/Evaluate/complex.h"
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#include "llvm/Support/raw_ostream.h"
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namespace Fortran::evaluate::value {
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template <typename R>
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ValueWithRealFlags<Complex<R>> Complex<R>::Add(
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const Complex &that, Rounding rounding) const {
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RealFlags flags;
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Part reSum{re_.Add(that.re_, rounding).AccumulateFlags(flags)};
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Part imSum{im_.Add(that.im_, rounding).AccumulateFlags(flags)};
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return {Complex{reSum, imSum}, flags};
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}
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template <typename R>
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ValueWithRealFlags<Complex<R>> Complex<R>::Subtract(
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const Complex &that, Rounding rounding) const {
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RealFlags flags;
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Part reDiff{re_.Subtract(that.re_, rounding).AccumulateFlags(flags)};
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Part imDiff{im_.Subtract(that.im_, rounding).AccumulateFlags(flags)};
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return {Complex{reDiff, imDiff}, flags};
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}
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template <typename R>
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ValueWithRealFlags<Complex<R>> Complex<R>::Multiply(
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const Complex &that, Rounding rounding) const {
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// (a + ib)*(c + id) -> ac - bd + i(ad + bc)
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RealFlags flags;
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Part ac{re_.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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Part bd{im_.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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Part ad{re_.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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Part bc{im_.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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Part acbd{ac.Subtract(bd, rounding).AccumulateFlags(flags)};
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Part adbc{ad.Add(bc, rounding).AccumulateFlags(flags)};
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return {Complex{acbd, adbc}, flags};
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}
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template <typename R>
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ValueWithRealFlags<Complex<R>> Complex<R>::Divide(
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const Complex &that, Rounding rounding) const {
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// (a + ib)/(c + id) -> [(a+ib)*(c-id)] / [(c+id)*(c-id)]
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// -> [ac+bd+i(bc-ad)] / (cc+dd) -- note (cc+dd) is real
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// -> ((ac+bd)/(cc+dd)) + i((bc-ad)/(cc+dd))
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RealFlags flags;
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Part cc{that.re_.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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Part dd{that.im_.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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Part ccPdd{cc.Add(dd, rounding).AccumulateFlags(flags)};
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if (!flags.test(RealFlag::Overflow) && !flags.test(RealFlag::Underflow)) {
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// den = (cc+dd) did not overflow or underflow; try the naive
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// sequence without scaling to avoid extra roundings.
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Part ac{re_.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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Part ad{re_.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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Part bc{im_.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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Part bd{im_.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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Part acPbd{ac.Add(bd, rounding).AccumulateFlags(flags)};
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Part bcSad{bc.Subtract(ad, rounding).AccumulateFlags(flags)};
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Part re{acPbd.Divide(ccPdd, rounding).AccumulateFlags(flags)};
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Part im{bcSad.Divide(ccPdd, rounding).AccumulateFlags(flags)};
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if (!flags.test(RealFlag::Overflow) && !flags.test(RealFlag::Underflow)) {
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return {Complex{re, im}, flags};
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}
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}
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// Scale numerator and denominator by d/c (if c>=d) or c/d (if c<d)
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flags.clear();
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Part scale; // will be <= 1.0 in magnitude
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bool cGEd{that.re_.ABS().Compare(that.im_.ABS()) != Relation::Less};
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if (cGEd) {
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scale = that.im_.Divide(that.re_, rounding).AccumulateFlags(flags);
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} else {
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scale = that.re_.Divide(that.im_, rounding).AccumulateFlags(flags);
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}
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Part den;
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if (cGEd) {
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Part dS{scale.Multiply(that.im_, rounding).AccumulateFlags(flags)};
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den = dS.Add(that.re_, rounding).AccumulateFlags(flags);
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} else {
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Part cS{scale.Multiply(that.re_, rounding).AccumulateFlags(flags)};
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den = cS.Add(that.im_, rounding).AccumulateFlags(flags);
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}
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Part aS{scale.Multiply(re_, rounding).AccumulateFlags(flags)};
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Part bS{scale.Multiply(im_, rounding).AccumulateFlags(flags)};
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Part re1, im1;
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if (cGEd) {
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re1 = re_.Add(bS, rounding).AccumulateFlags(flags);
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im1 = im_.Subtract(aS, rounding).AccumulateFlags(flags);
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} else {
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re1 = aS.Add(im_, rounding).AccumulateFlags(flags);
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im1 = bS.Subtract(re_, rounding).AccumulateFlags(flags);
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}
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Part re{re1.Divide(den, rounding).AccumulateFlags(flags)};
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Part im{im1.Divide(den, rounding).AccumulateFlags(flags)};
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return {Complex{re, im}, flags};
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}
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template <typename R> std::string Complex<R>::DumpHexadecimal() const {
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std::string result{'('};
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result += re_.DumpHexadecimal();
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result += ',';
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result += im_.DumpHexadecimal();
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result += ')';
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return result;
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}
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template <typename R>
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llvm::raw_ostream &Complex<R>::AsFortran(llvm::raw_ostream &o, int kind) const {
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re_.AsFortran(o << '(', kind);
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im_.AsFortran(o << ',', kind);
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return o << ')';
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}
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template class Complex<Real<Integer<16>, 11>>;
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template class Complex<Real<Integer<16>, 8>>;
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template class Complex<Real<Integer<32>, 24>>;
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template class Complex<Real<Integer<64>, 53>>;
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template class Complex<Real<Integer<80>, 64>>;
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template class Complex<Real<Integer<128>, 113>>;
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} // namespace Fortran::evaluate::value
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