ed71134af7
Original-commit: flang-compiler/f18@6ec49f6edc Reviewed-on: https://github.com/flang-compiler/f18/pull/101 Tree-same-pre-rewrite: false
691 lines
24 KiB
C++
691 lines
24 KiB
C++
// Copyright (c) 2018, NVIDIA CORPORATION. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef FORTRAN_EVALUATE_REAL_H_
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#define FORTRAN_EVALUATE_REAL_H_
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#include "common.h"
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#include "integer.h"
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#include <cinttypes>
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#include <limits>
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namespace Fortran::evaluate::value {
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// Models IEEE-754 floating-point numbers. The first argument to this
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// class template must be (or look like) an instance of Integer.
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template<typename WORD, int PRECISION, bool IMPLICIT_MSB = true> class Real {
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public:
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using Word = WORD;
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static constexpr int bits{Word::bits};
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static constexpr int precision{PRECISION};
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static constexpr bool implicitMSB{IMPLICIT_MSB};
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static constexpr int significandBits{precision - implicitMSB};
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static constexpr int exponentBits{bits - significandBits - 1 /*sign*/};
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static_assert(precision > 0);
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static_assert(exponentBits > 1);
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static constexpr std::uint64_t maxExponent{(1 << exponentBits) - 1};
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static constexpr std::uint64_t exponentBias{maxExponent / 2};
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constexpr Real() {} // +0.0
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constexpr Real(const Real &) = default;
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constexpr Real(const Word &bits) : word_{bits} {}
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constexpr Real &operator=(const Real &) = default;
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template<typename INT>
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static constexpr ValueWithRealFlags<Real> ConvertSigned(
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const INT &n, Rounding rounding = Rounding::TiesToEven) {
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bool isNegative{n.IsNegative()};
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INT absN{n};
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if (isNegative) {
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absN = n.Negate().value; // overflow is safe to ignore
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}
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int leadz{absN.LEADZ()};
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if (leadz >= absN.bits) {
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return {}; // all bits zero -> +0.0
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}
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ValueWithRealFlags<Real> result;
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std::uint64_t exponent{exponentBias + absN.bits - leadz - 1};
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int bitsNeeded{absN.bits - (leadz + implicitMSB)};
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int bitsLost{bitsNeeded - significandBits};
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if (bitsLost <= 0) {
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Fraction fraction{Fraction::ConvertUnsigned(absN).value};
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result.flags |= result.value.Normalize(
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isNegative, exponent, fraction.SHIFTL(-bitsLost));
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} else {
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Fraction fraction{Fraction::ConvertUnsigned(absN.SHIFTR(bitsLost)).value};
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result.flags |= result.value.Normalize(isNegative, exponent, fraction);
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RoundingBits roundingBits{absN, bitsLost};
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result.flags |= result.value.Round(rounding, roundingBits);
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}
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return result;
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}
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// TODO conversion from (or to?) (other) real types
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// TODO AINT/ANINT, CEILING, FLOOR, DIM, MAX, MIN, DPROD, FRACTION
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// HUGE, INT/NINT, MAXEXPONENT, MINEXPONENT, NEAREST, OUT_OF_RANGE,
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// PRECISION, HUGE, TINY, RRSPACING/SPACING, SCALE, SET_EXPONENT, SIGN
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constexpr Word RawBits() const { return word_; }
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constexpr std::uint64_t Exponent() const {
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return word_.IBITS(significandBits, exponentBits).ToUInt64();
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}
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constexpr bool IsNegative() const {
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return !IsNotANumber() && word_.BTEST(bits - 1);
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}
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constexpr bool IsNotANumber() const {
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return Exponent() == maxExponent && !GetSignificand().IsZero();
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}
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constexpr bool IsQuietNaN() const {
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return Exponent() == maxExponent &&
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GetSignificand().BTEST(significandBits - 1);
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}
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constexpr bool IsSignalingNaN() const {
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return IsNotANumber() && !GetSignificand().BTEST(significandBits - 1);
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}
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constexpr bool IsInfinite() const {
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return Exponent() == maxExponent && GetSignificand().IsZero();
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}
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constexpr bool IsZero() const {
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return Exponent() == 0 && GetSignificand().IsZero();
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}
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constexpr bool IsDenormal() const {
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return Exponent() == 0 && !GetSignificand().IsZero();
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}
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constexpr Real ABS() const { // non-arithmetic, no flags returned
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Real result;
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result.word_ = word_.IBCLR(bits - 1);
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return result;
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}
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constexpr Real Negate() const {
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Real result;
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result.word_ = word_.IEOR(word_.MASKL(1));
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return result;
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}
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template<typename INT> constexpr INT EXPONENT() const {
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std::uint64_t exponent{Exponent()};
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if (exponent == maxExponent) {
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return INT::HUGE();
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} else {
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return {static_cast<std::int64_t>(exponent - exponentBias)};
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}
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}
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static constexpr Real EPSILON() {
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Real epsilon;
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epsilon.Normalize(false, exponentBias - precision, Fraction::MASKL(1));
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return epsilon;
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}
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template<typename INT> constexpr ValueWithRealFlags<INT> ToInteger() const {
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bool isNegative{IsNegative()};
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std::uint64_t exponent{Exponent()};
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Fraction fraction{GetFraction()};
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ValueWithRealFlags<INT> result;
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if (exponent == maxExponent && !fraction.IsZero()) { // NaN
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result.flags.set(RealFlag::InvalidArgument);
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result.value = result.value.HUGE();
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} else if (exponent >= maxExponent || // +/-Inf
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exponent >= exponentBias + result.value.bits) { // too big
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if (isNegative) {
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result.value = result.value.MASKL(1);
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} else {
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result.value = result.value.HUGE();
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}
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result.flags.set(RealFlag::Overflow);
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} else if (exponent < exponentBias) { // |x| < 1.0 -> 0
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if (!fraction.IsZero()) {
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result.flags.set(RealFlag::Underflow);
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result.flags.set(RealFlag::Inexact);
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}
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} else {
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// finite number |x| >= 1.0
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constexpr std::uint64_t noShiftExponent{exponentBias + precision - 1};
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if (exponent < noShiftExponent) {
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int rshift = noShiftExponent - exponent;
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if (!fraction.IBITS(0, rshift).IsZero()) {
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result.flags.set(RealFlag::Inexact);
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}
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auto truncated = result.value.ConvertUnsigned(fraction.SHIFTR(rshift));
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if (truncated.overflow) {
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result.flags.set(RealFlag::Overflow);
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} else {
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result.value = truncated.value;
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}
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} else {
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int lshift = exponent - noShiftExponent;
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if (lshift + precision >= result.value.bits) {
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result.flags.set(RealFlag::Overflow);
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} else {
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result.value =
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result.value.ConvertUnsigned(fraction).value.SHIFTL(lshift);
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}
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}
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if (result.flags.test(RealFlag::Overflow)) {
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result.value = result.value.HUGE();
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} else if (isNegative) {
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auto negated = result.value.Negate();
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if (negated.overflow) {
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result.flags.set(RealFlag::Overflow);
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result.value = result.value.HUGE();
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} else {
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result.value = negated.value;
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}
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}
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}
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return result;
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}
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constexpr Relation Compare(const Real &y) const {
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if (IsNotANumber() || y.IsNotANumber()) { // NaN vs x, x vs NaN
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return Relation::Unordered;
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} else if (IsInfinite()) {
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if (y.IsInfinite()) {
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if (IsNegative()) { // -Inf vs +/-Inf
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return y.IsNegative() ? Relation::Equal : Relation::Less;
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} else { // +Inf vs +/-Inf
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return y.IsNegative() ? Relation::Greater : Relation::Equal;
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}
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} else { // +/-Inf vs finite
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return IsNegative() ? Relation::Less : Relation::Greater;
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}
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} else if (y.IsInfinite()) { // finite vs +/-Inf
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return y.IsNegative() ? Relation::Greater : Relation::Less;
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} else { // two finite numbers
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bool isNegative{IsNegative()};
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if (isNegative != y.IsNegative()) {
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if (word_.IOR(y.word_).IBCLR(bits - 1).IsZero()) {
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return Relation::Equal; // +/-0.0 == -/+0.0
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} else {
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return isNegative ? Relation::Less : Relation::Greater;
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}
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} else {
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// same sign
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Ordering order{CompareUnsigned(Exponent(), y.Exponent())};
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if (order == Ordering::Equal) {
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order = GetSignificand().CompareUnsigned(y.GetSignificand());
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}
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if (isNegative) {
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order = Reverse(order);
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}
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return RelationFromOrdering(order);
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}
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}
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}
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constexpr ValueWithRealFlags<Real> Add(
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const Real &y, Rounding rounding = Rounding::TiesToEven) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value.word_ = NaNWord(); // NaN + x -> NaN
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if (IsSignalingNaN() || y.IsSignalingNaN()) {
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result.flags.set(RealFlag::InvalidArgument);
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}
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return result;
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}
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bool isNegative{IsNegative()};
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bool yIsNegative{y.IsNegative()};
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if (IsInfinite()) {
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if (y.IsInfinite()) {
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if (isNegative == yIsNegative) {
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result.value = *this; // +/-Inf + +/-Inf -> +/-Inf
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} else {
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result.value.word_ = NaNWord(); // +/-Inf + -/+Inf -> NaN
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result.flags.set(RealFlag::InvalidArgument);
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}
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} else {
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result.value = *this; // +/-Inf + x -> +/-Inf
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}
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return result;
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}
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if (y.IsInfinite()) {
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result.value = y; // x + +/-Inf -> +/-Inf
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return result;
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}
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std::uint64_t exponent{Exponent()};
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std::uint64_t yExponent{y.Exponent()};
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if (exponent < yExponent) {
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// y is larger in magnitude; simplify by reversing operands
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return y.Add(*this, rounding);
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}
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if (exponent == yExponent && isNegative != yIsNegative) {
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Ordering order{GetSignificand().CompareUnsigned(y.GetSignificand())};
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if (order == Ordering::Less) {
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// Same exponent, opposite signs, and y is larger in magnitude
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return y.Add(*this, rounding);
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}
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if (order == Ordering::Equal) {
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// x + (-x) -> +0.0 unless rounding is directed downwards
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if (rounding == Rounding::Down) {
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result.value.word_ = result.value.word_.IBSET(bits - 1); // -0.0
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}
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return result;
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}
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}
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// Our exponent is greater than y's, or the exponents match and y is not
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// of the opposite sign and greater magnitude. So (x+y) will have the
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// same sign as x.
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Fraction yFraction{y.GetFraction()};
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Fraction fraction{GetFraction()};
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int rshift = exponent - yExponent;
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if (exponent > 0 && yExponent == 0) {
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--rshift; // correct overshift when only y is denormal
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}
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RoundingBits roundingBits{yFraction, rshift};
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yFraction = yFraction.SHIFTR(rshift);
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bool carry{false};
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if (isNegative != yIsNegative) {
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// Opposite signs: subtract via addition of two's complement of y and
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// the rounding bits.
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yFraction = yFraction.NOT();
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carry = roundingBits.Negate();
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}
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auto sum = fraction.AddUnsigned(yFraction, carry);
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fraction = sum.value;
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if (isNegative == yIsNegative && sum.carry) {
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roundingBits.ShiftRight(sum.value.BTEST(0));
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fraction = fraction.SHIFTR(1).IBSET(fraction.bits - 1);
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++exponent;
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}
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NormalizeAndRound(
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result, isNegative, exponent, fraction, rounding, roundingBits);
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return result;
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}
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constexpr ValueWithRealFlags<Real> Subtract(
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const Real &y, Rounding rounding = Rounding::TiesToEven) const {
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return Add(y.Negate(), rounding);
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}
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constexpr ValueWithRealFlags<Real> Multiply(
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const Real &y, Rounding rounding = Rounding::TiesToEven) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value.word_ = NaNWord(); // NaN * x -> NaN
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if (IsSignalingNaN() || y.IsSignalingNaN()) {
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result.flags.set(RealFlag::InvalidArgument);
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}
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} else {
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bool isNegative{IsNegative() != y.IsNegative()};
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if (IsInfinite() || y.IsInfinite()) {
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if (IsZero() || y.IsZero()) {
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result.value.word_ = NaNWord(); // 0 * Inf -> NaN
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result.flags.set(RealFlag::InvalidArgument);
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} else {
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result.value.word_ = InfinityWord(isNegative);
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}
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} else {
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auto product = GetFraction().MultiplyUnsigned(y.GetFraction());
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std::int64_t exponent{CombineExponents(y, false)};
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if (exponent < 1) {
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int rshift = 1 - exponent;
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exponent = 1;
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bool sticky{false};
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if (rshift >= product.upper.bits + product.lower.bits) {
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sticky = !product.lower.IsZero() || !product.upper.IsZero();
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} else if (rshift >= product.lower.bits) {
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sticky = !product.lower.IsZero() ||
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!product.upper
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.IAND(product.upper.MASKR(rshift - product.lower.bits))
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.IsZero();
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} else {
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sticky = !product.lower.IAND(product.lower.MASKR(rshift)).IsZero();
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}
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product.lower = product.lower.DSHIFTR(product.upper, rshift);
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product.upper = product.upper.SHIFTR(rshift);
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if (sticky) {
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product.lower = product.lower.IBSET(0);
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}
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}
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int leadz{product.upper.LEADZ()};
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if (leadz >= product.upper.bits) {
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leadz += product.lower.LEADZ();
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}
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int lshift{leadz};
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if (lshift > exponent - 1) {
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lshift = exponent - 1;
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}
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exponent -= lshift;
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product.upper = product.upper.DSHIFTL(product.lower, lshift);
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product.lower = product.lower.SHIFTL(lshift);
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RoundingBits roundingBits{product.lower, product.lower.bits};
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NormalizeAndRound(result, isNegative, exponent, product.upper, rounding,
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roundingBits);
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}
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}
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return result;
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}
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constexpr ValueWithRealFlags<Real> Divide(
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const Real &y, Rounding rounding = Rounding::TiesToEven) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value.word_ = NaNWord(); // NaN / x -> NaN, x / NaN -> NaN
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if (IsSignalingNaN() || y.IsSignalingNaN()) {
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result.flags.set(RealFlag::InvalidArgument);
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}
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} else {
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bool isNegative{IsNegative() != y.IsNegative()};
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if (IsInfinite()) {
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if (y.IsInfinite()) {
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result.value.word_ = NaNWord(); // Inf/Inf -> NaN
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result.flags.set(RealFlag::InvalidArgument);
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} else { // Inf/x -> Inf, Inf/0 -> Inf
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result.value.word_ = InfinityWord(isNegative);
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}
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} else if (y.IsZero()) {
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if (IsZero()) { // 0/0 -> NaN
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result.value.word_ = NaNWord();
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result.flags.set(RealFlag::InvalidArgument);
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} else { // x/0 -> Inf, Inf/0 -> Inf
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result.value.word_ = InfinityWord(isNegative);
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result.flags.set(RealFlag::DivideByZero);
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}
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} else if (IsZero() || y.IsInfinite()) { // 0/x, x/Inf -> 0
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if (isNegative) {
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result.value.word_ = result.value.word_.IBSET(bits - 1);
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}
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} else {
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// dividend and divisor are both finite and nonzero numbers
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Fraction top{GetFraction()}, divisor{y.GetFraction()};
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std::int64_t exponent{CombineExponents(y, true)};
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Fraction quotient;
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bool msb{false};
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if (!top.BTEST(top.bits - 1) || !divisor.BTEST(divisor.bits - 1)) {
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// One or two denormals
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int topLshift{top.LEADZ()};
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top = top.SHIFTL(topLshift);
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int divisorLshift{divisor.LEADZ()};
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divisor = divisor.SHIFTL(divisorLshift);
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exponent += divisorLshift - topLshift;
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}
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for (int j{1}; j <= quotient.bits; ++j) {
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if (NextQuotientBit(top, msb, divisor)) {
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quotient = quotient.IBSET(quotient.bits - j);
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}
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}
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bool guard{NextQuotientBit(top, msb, divisor)};
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bool round{NextQuotientBit(top, msb, divisor)};
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bool sticky{msb | !top.IsZero()};
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RoundingBits roundingBits{guard, round, sticky};
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if (exponent < 1) {
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std::int64_t rshift{1 - exponent};
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for (; rshift > 0; --rshift) {
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roundingBits.ShiftRight(quotient.BTEST(0));
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quotient = quotient.SHIFTR(1);
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}
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exponent = 1;
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}
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NormalizeAndRound(
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result, isNegative, exponent, quotient, rounding, roundingBits);
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}
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}
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return result;
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}
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private:
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using Fraction = Integer<precision>; // all bits made explicit
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using Significand = Integer<significandBits>; // no implicit bit
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class RoundingBits {
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public:
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constexpr RoundingBits(
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bool guard = false, bool round = false, bool sticky = false)
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: guard_{guard}, round_{round}, sticky_{sticky} {}
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template<typename FRACTION>
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constexpr RoundingBits(const FRACTION &fraction, int rshift) {
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if (rshift > 0 && rshift < fraction.bits + 1) {
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guard_ = fraction.BTEST(rshift - 1);
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}
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if (rshift > 1 && rshift < fraction.bits + 2) {
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round_ = fraction.BTEST(rshift - 2);
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}
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if (rshift > 2) {
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if (rshift >= fraction.bits + 2) {
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sticky_ = !fraction.IsZero();
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} else {
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auto mask = fraction.MASKR(rshift - 2);
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sticky_ = !fraction.IAND(mask).IsZero();
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}
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}
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}
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constexpr bool Zero() const { return !(guard_ | round_ | sticky_); }
|
|
|
|
constexpr bool Negate() {
|
|
bool carry{!sticky_};
|
|
if (carry) {
|
|
carry = !round_;
|
|
} else {
|
|
round_ = !round_;
|
|
}
|
|
if (carry) {
|
|
carry = !guard_;
|
|
} else {
|
|
guard_ = !guard_;
|
|
}
|
|
return carry;
|
|
}
|
|
|
|
constexpr bool ShiftLeft() {
|
|
bool oldGuard{guard_};
|
|
guard_ = round_;
|
|
round_ = sticky_;
|
|
return oldGuard;
|
|
}
|
|
|
|
constexpr void ShiftRight(bool newGuard) {
|
|
sticky_ |= round_;
|
|
round_ = guard_;
|
|
guard_ = newGuard;
|
|
}
|
|
|
|
// Determines whether a value should be rounded by increasing its
|
|
// fraction, given a rounding mode and a summary of the lost bits.
|
|
constexpr bool MustRound(Rounding rounding, const Real &real) const {
|
|
bool round{false}; // to dodge bogus g++ warning about missing return
|
|
switch (rounding) {
|
|
case Rounding::TiesToEven:
|
|
round = guard_ && (round_ | sticky_ | real.RawBits().BTEST(0));
|
|
break;
|
|
case Rounding::ToZero: break;
|
|
case Rounding::Down: round = real.IsNegative() && !Zero(); break;
|
|
case Rounding::Up: round = !real.IsNegative() && !Zero(); break;
|
|
case Rounding::TiesAwayFromZero: round = guard_; break;
|
|
}
|
|
return round;
|
|
}
|
|
|
|
private:
|
|
bool guard_{false};
|
|
bool round_{false};
|
|
bool sticky_{false};
|
|
};
|
|
|
|
constexpr Significand GetSignificand() const {
|
|
return Significand::ConvertUnsigned(word_).value;
|
|
}
|
|
|
|
constexpr Fraction GetFraction() const {
|
|
Fraction result{Fraction::ConvertUnsigned(word_).value};
|
|
if constexpr (!implicitMSB) {
|
|
return result;
|
|
} else {
|
|
std::uint64_t exponent{Exponent()};
|
|
if (exponent > 0 && exponent < maxExponent) {
|
|
return result.IBSET(significandBits);
|
|
} else {
|
|
return result.IBCLR(significandBits);
|
|
}
|
|
}
|
|
}
|
|
|
|
constexpr std::int64_t CombineExponents(const Real &y, bool forDivide) const {
|
|
std::int64_t exponent = Exponent(), yExponent = y.Exponent();
|
|
// A zero exponent field value has the same weight as 1.
|
|
exponent += !exponent;
|
|
yExponent += !yExponent;
|
|
if (forDivide) {
|
|
exponent += exponentBias - yExponent;
|
|
} else {
|
|
exponent += yExponent - exponentBias + 1;
|
|
}
|
|
return exponent;
|
|
}
|
|
|
|
static constexpr bool NextQuotientBit(
|
|
Fraction &top, bool &msb, const Fraction &divisor) {
|
|
bool greaterOrEqual{msb || top.CompareUnsigned(divisor) != Ordering::Less};
|
|
if (greaterOrEqual) {
|
|
top = top.SubtractSigned(divisor).value;
|
|
}
|
|
auto doubled{top.AddUnsigned(top)};
|
|
top = doubled.value;
|
|
msb = doubled.carry;
|
|
return greaterOrEqual;
|
|
}
|
|
|
|
// TODO: Configurable NaN representations
|
|
static constexpr Word NaNWord() {
|
|
return Word{maxExponent}
|
|
.SHIFTL(significandBits)
|
|
.IBSET(significandBits - 1)
|
|
.IBSET(significandBits - 2);
|
|
}
|
|
|
|
static constexpr Word InfinityWord(bool negative) {
|
|
Word infinity{maxExponent};
|
|
infinity = infinity.SHIFTL(significandBits);
|
|
if (negative) {
|
|
infinity = infinity.IBSET(infinity.bits - 1);
|
|
}
|
|
return infinity;
|
|
}
|
|
|
|
constexpr RealFlags Normalize(bool negative, std::uint64_t exponent,
|
|
const Fraction &fraction, Rounding rounding = Rounding::TiesToEven,
|
|
RoundingBits *roundingBits = nullptr) {
|
|
std::uint64_t lshift = fraction.LEADZ();
|
|
if (lshift < fraction.bits) {
|
|
if (lshift < exponent) {
|
|
exponent -= lshift;
|
|
} else if (exponent > 0) {
|
|
lshift = exponent - 1;
|
|
exponent = 0;
|
|
} else if (lshift == 0) {
|
|
exponent = 1;
|
|
} else {
|
|
lshift = 0;
|
|
}
|
|
}
|
|
if (exponent >= maxExponent) {
|
|
if (rounding == Rounding::TiesToEven ||
|
|
rounding == Rounding::TiesAwayFromZero ||
|
|
(rounding == Rounding::Up && !negative) ||
|
|
(rounding == Rounding::Down && negative)) {
|
|
word_ = Word{maxExponent}.SHIFTL(significandBits); // Inf
|
|
} else {
|
|
// directed rounding: round to largest finite value rather than infinity
|
|
// (x86 does this, not sure whether it's standard or not)
|
|
word_ = Word{word_.MASKR(word_.bits - 1)}.IBCLR(significandBits);
|
|
}
|
|
if (negative) {
|
|
word_ = word_.IBSET(bits - 1);
|
|
}
|
|
RealFlags flags{RealFlag::Overflow};
|
|
if (!fraction.IsZero()) {
|
|
flags.set(RealFlag::Inexact);
|
|
}
|
|
return flags;
|
|
}
|
|
if (lshift >= fraction.bits) {
|
|
// +/-0.0
|
|
word_ = Word{};
|
|
exponent = 0;
|
|
} else {
|
|
word_ = Word::ConvertUnsigned(fraction).value;
|
|
if (lshift > 0) {
|
|
word_ = word_.SHIFTL(lshift);
|
|
if (roundingBits != nullptr) {
|
|
for (; lshift > 0; --lshift) {
|
|
if (roundingBits->ShiftLeft()) {
|
|
word_ = word_.IBSET(lshift - 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (implicitMSB) {
|
|
word_ = word_.IBCLR(significandBits);
|
|
}
|
|
word_ = word_.IOR(Word{exponent}.SHIFTL(significandBits));
|
|
if (negative) {
|
|
word_ = word_.IBSET(bits - 1);
|
|
}
|
|
return {};
|
|
}
|
|
|
|
// Rounds a result, if necessary.
|
|
constexpr RealFlags Round(Rounding rounding, const RoundingBits &bits) {
|
|
std::uint64_t exponent{Exponent()};
|
|
RealFlags flags;
|
|
if (!bits.Zero()) {
|
|
flags.set(RealFlag::Inexact);
|
|
}
|
|
if (exponent < maxExponent && bits.MustRound(rounding, *this)) {
|
|
typename Fraction::ValueWithCarry sum{
|
|
GetFraction().AddUnsigned(Fraction{}, true)};
|
|
if (sum.carry) {
|
|
// The fraction was all ones before rounding; sum.value is now zero
|
|
if (++exponent < maxExponent) {
|
|
sum.value = sum.value.IBSET(precision - 1);
|
|
} else {
|
|
// rounded away to an infinity
|
|
flags.set(RealFlag::Overflow);
|
|
}
|
|
}
|
|
flags |= Normalize(IsNegative(), exponent, sum.value);
|
|
}
|
|
return flags;
|
|
}
|
|
|
|
// Common code for multiplication and divison, isolated here so that any
|
|
// future maintenance will apply to both operations.
|
|
static constexpr void NormalizeAndRound(ValueWithRealFlags<Real> &result,
|
|
bool isNegative, std::uint64_t exponent, const Fraction &fraction,
|
|
Rounding rounding, RoundingBits &roundingBits) {
|
|
result.flags |= result.value.Normalize(
|
|
isNegative, exponent, fraction, rounding, &roundingBits);
|
|
std::uint64_t normalizedExponent{result.value.Exponent()};
|
|
result.flags |= result.value.Round(rounding, roundingBits);
|
|
if (result.flags.test(RealFlag::Inexact) && normalizedExponent == 0) {
|
|
result.flags.set(RealFlag::Underflow);
|
|
}
|
|
}
|
|
|
|
Word word_{}; // an Integer<>
|
|
};
|
|
|
|
extern template class Real<Integer<16>, 11>;
|
|
extern template class Real<Integer<32>, 24>;
|
|
extern template class Real<Integer<64>, 53>;
|
|
extern template class Real<Integer<80>, 64, false>; // 80387 extended precision
|
|
extern template class Real<Integer<128>, 112>;
|
|
// N.B. No "double-double" support.
|
|
|
|
} // namespace Fortran::evaluate::value
|
|
#endif // FORTRAN_EVALUATE_REAL_H_
|