f7e7cb349b
Original-commit: flang-compiler/f18@aa7f55e15f Reviewed-on: https://github.com/flang-compiler/f18/pull/217
489 lines
17 KiB
C++
489 lines
17 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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#include "real.h"
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#include "int-power.h"
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#include "../common/idioms.h"
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#include "../parser/characters.h"
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#include <limits>
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namespace Fortran::evaluate::value {
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template<typename W, int P, bool IM>
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Relation Real<W, P, IM>::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{evaluate::Compare(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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template<typename W, int P, bool IM>
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ValueWithRealFlags<Real<W, P, IM>> Real<W, P, IM>::Add(
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const Real &y, Rounding rounding) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value = NotANumber(); // 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 = NotANumber(); // +/-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 fraction{GetFraction()};
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Fraction yFraction{y.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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template<typename W, int P, bool IM>
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ValueWithRealFlags<Real<W, P, IM>> Real<W, P, IM>::Multiply(
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const Real &y, Rounding rounding) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value = NotANumber(); // 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 = NotANumber(); // 0 * Inf -> NaN
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result.flags.set(RealFlag::InvalidArgument);
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} else {
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result.value = Infinity(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, true /*multiply*/);
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}
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}
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return result;
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}
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template<typename W, int P, bool IM>
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ValueWithRealFlags<Real<W, P, IM>> Real<W, P, IM>::Divide(
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const Real &y, Rounding rounding) const {
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ValueWithRealFlags<Real> result;
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if (IsNotANumber() || y.IsNotANumber()) {
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result.value = NotANumber(); // 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 = NotANumber(); // 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 = Infinity(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 = NotANumber();
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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 = Infinity(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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template<typename W, int P, bool IM>
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RealFlags Real<W, P, IM>::Normalize(bool negative, std::uint64_t exponent,
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const Fraction &fraction, Rounding rounding, RoundingBits *roundingBits) {
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std::uint64_t lshift = fraction.LEADZ();
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if (lshift == fraction.bits /* fraction is zero */ &&
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(roundingBits == nullptr || roundingBits->empty())) {
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// No fraction, no rounding bits -> +/-0.0
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exponent = lshift = 0;
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} else if (lshift < exponent) {
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exponent -= lshift;
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} else if (exponent > 0) {
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lshift = exponent - 1;
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exponent = 0;
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} else if (lshift == 0) {
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exponent = 1;
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} else {
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lshift = 0;
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}
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if (exponent >= maxExponent) {
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// Infinity or overflow
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if (rounding == Rounding::TiesToEven ||
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rounding == Rounding::TiesAwayFromZero ||
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(rounding == Rounding::Up && !negative) ||
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(rounding == Rounding::Down && negative)) {
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word_ = Word{maxExponent}.SHIFTL(significandBits); // Inf
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} else {
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// directed rounding: round to largest finite value rather than infinity
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// (x86 does this, not sure whether it's standard behavior)
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word_ = Word{word_.MASKR(word_.bits - 1)}.IBCLR(significandBits);
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}
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if (negative) {
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word_ = word_.IBSET(bits - 1);
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}
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RealFlags flags{RealFlag::Overflow};
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if (!fraction.IsZero()) {
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flags.set(RealFlag::Inexact);
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}
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return flags;
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}
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word_ = Word::ConvertUnsigned(fraction).value;
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if (lshift > 0) {
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word_ = word_.SHIFTL(lshift);
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if (roundingBits != nullptr) {
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for (; lshift > 0; --lshift) {
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if (roundingBits->ShiftLeft()) {
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word_ = word_.IBSET(lshift - 1);
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}
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}
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}
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}
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if constexpr (implicitMSB) {
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word_ = word_.IBCLR(significandBits);
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}
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word_ = word_.IOR(Word{exponent}.SHIFTL(significandBits));
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if (negative) {
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word_ = word_.IBSET(bits - 1);
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}
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return {};
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}
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template<typename W, int P, bool IM>
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RealFlags Real<W, P, IM>::Round(
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Rounding rounding, const RoundingBits &bits, bool multiply) {
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std::uint64_t origExponent{Exponent()};
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RealFlags flags;
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bool inexact{!bits.empty()};
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if (inexact) {
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flags.set(RealFlag::Inexact);
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}
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if (origExponent < maxExponent &&
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bits.MustRound(rounding, IsNegative(), word_.BTEST(0) /* is odd */)) {
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typename Fraction::ValueWithCarry sum{
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GetFraction().AddUnsigned(Fraction{}, true)};
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std::uint64_t newExponent{origExponent};
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if (sum.carry) {
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// The fraction was all ones before rounding; sum.value is now zero
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sum.value = sum.value.IBSET(precision - 1);
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if (++newExponent >= maxExponent) {
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flags.set(RealFlag::Overflow); // rounded away to an infinity
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}
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}
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flags |= Normalize(IsNegative(), newExponent, sum.value);
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}
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if (inexact && origExponent == 0) {
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// inexact denormal input
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if (Exponent() == 0) {
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flags.set(RealFlag::Underflow); // output still denormal -> Underflow
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} else {
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// Rounding went up to the smallest normal number.
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// Still signal Underflow unless we're in a weird x86 edge case with
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// multiplication: if the sticky bit is set (i.e., the lower half of
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// the full product had bits below the top 2), Underflow gets set in
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// a directed rounding mode only if the guard bit was also set.
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if (multiply && bits.sticky() &&
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(bits.guard() ||
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!(rounding == Rounding::Up || rounding == Rounding::Down))) {
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} else {
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flags.set(RealFlag::Underflow);
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}
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}
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}
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return flags;
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}
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template<typename W, int P, bool IM>
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void Real<W, P, IM>::NormalizeAndRound(ValueWithRealFlags<Real> &result,
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bool isNegative, std::uint64_t exponent, const Fraction &fraction,
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Rounding rounding, RoundingBits roundingBits, bool multiply) {
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result.flags |= result.value.Normalize(
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isNegative, exponent, fraction, rounding, &roundingBits);
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result.flags |= result.value.Round(rounding, roundingBits, multiply);
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}
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template<typename W, int P, bool IM>
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ValueWithRealFlags<Real<W, P, IM>> Real<W, P, IM>::Read(
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const char *&p, Rounding rounding) {
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ValueWithRealFlags<Real> result;
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Real ten{FromInteger(Integer<32>{10}).value};
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for (; parser::IsDecimalDigit(*p); ++p) {
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result.value =
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result.value.Multiply(ten, rounding).AccumulateFlags(result.flags);
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result.value =
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result.value.Add(FromInteger(Integer<32>{*p - '0'}).value, rounding)
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.AccumulateFlags(result.flags);
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}
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std::int64_t exponent{0};
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if (*p == '.') {
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for (++p; parser::IsDecimalDigit(*p); ++p) {
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--exponent;
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result.value =
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result.value.Multiply(ten, rounding).AccumulateFlags(result.flags);
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result.value =
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result.value.Add(FromInteger(Integer<32>{*p - '0'}).value, rounding)
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.AccumulateFlags(result.flags);
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}
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}
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if (parser::IsLetter(*p)) {
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bool negExpo{false};
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if (*++p == '-') {
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negExpo = true;
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++p;
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} else if (*p == '+') {
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++p;
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}
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auto expo{Integer<32>::ReadUnsigned(p)};
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std::int64_t expoVal{expo.value.ToInt64()};
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if (expo.overflow) {
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expoVal = std::numeric_limits<std::int32_t>::max();
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} else if (negExpo) {
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expoVal *= -1;
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}
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exponent += expoVal;
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}
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if (exponent == 0) {
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return result;
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}
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Real tenPower{IntPower(ten, Integer<64>{std::abs(exponent)}, rounding)
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.AccumulateFlags(result.flags)};
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if (exponent > 0) {
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result.value =
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result.value.Multiply(tenPower, rounding).AccumulateFlags(result.flags);
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} else {
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result.value =
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result.value.Divide(tenPower, rounding).AccumulateFlags(result.flags);
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}
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return result;
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}
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template<typename W, int P, bool IM>
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std::string Real<W, P, IM>::DumpHexadecimal() const {
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if (IsNotANumber()) {
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return "NaN 0x"s + word_.Hexadecimal();
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} else if (IsNegative()) {
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return "-"s + Negate().DumpHexadecimal();
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} else if (IsInfinite()) {
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return "Inf"s;
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} else if (IsZero()) {
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return "0.0"s;
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} else {
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Fraction frac{GetFraction()};
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std::string result{"0x"};
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char intPart = '0' + frac.BTEST(frac.bits - 1);
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result += intPart;
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result += '.';
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int trailz{frac.TRAILZ()};
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if (trailz >= frac.bits - 1) {
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result += '0';
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} else {
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int remainingBits{frac.bits - 1 - trailz};
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int wholeNybbles{remainingBits / 4};
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int lostBits{remainingBits - 4 * wholeNybbles};
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if (wholeNybbles > 0) {
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std::string fracHex{frac.SHIFTR(trailz + lostBits)
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.IAND(frac.MASKR(4 * wholeNybbles))
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.Hexadecimal()};
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std::size_t field = wholeNybbles;
|
|
if (fracHex.size() < field) {
|
|
result += std::string(field - fracHex.size(), '0');
|
|
}
|
|
result += fracHex;
|
|
}
|
|
if (lostBits > 0) {
|
|
result += frac.SHIFTR(trailz)
|
|
.IAND(frac.MASKR(lostBits))
|
|
.SHIFTL(4 - lostBits)
|
|
.Hexadecimal();
|
|
}
|
|
}
|
|
result += 'p';
|
|
int exponent = Exponent() - exponentBias;
|
|
result += Integer<32>{exponent}.SignedDecimal();
|
|
return result;
|
|
}
|
|
}
|
|
|
|
template class Real<Integer<16>, 11>;
|
|
template class Real<Integer<32>, 24>;
|
|
template class Real<Integer<64>, 53>;
|
|
template class Real<Integer<80>, 64, false>;
|
|
template class Real<Integer<128>, 112>;
|
|
}
|