c34026b101
note: done using ```sh git grep -l "2010-2024 Google" | xargs sed -i 's/2010-2024 Google/2010-2025 Google/' ```
60 lines
2.4 KiB
C++
60 lines
2.4 KiB
C++
// Copyright 2010-2025 Google LLC
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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 "ortools/util/rational_approximation.h"
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#include <cmath>
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#include <cstdlib>
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#include <limits>
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#include "ortools/base/logging.h"
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namespace operations_research {
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// Computes a rational approximation numerator/denominator for value x
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// using a continued fraction algorithm. The absolute difference between the
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// output fraction and the input "x" will not exceed "precision".
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Fraction RationalApproximation(const double x, const double precision) {
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DCHECK_LT(x, std::numeric_limits<double>::infinity());
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DCHECK_GT(x, -std::numeric_limits<double>::infinity());
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// All computations are made on long doubles to guarantee the maximum
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// precision for the approximations. This way, the approximations when
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// Fractional is float or double are as accurate as possible.
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long double abs_x = std::abs(x);
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long double y = abs_x;
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int64_t previous_numerator = 0;
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int64_t previous_denominator = 1;
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int64_t numerator = 1;
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int64_t denominator = 0;
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while (true) {
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const int64_t term = static_cast<int64_t>(std::floor(y));
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const int64_t new_numerator = term * numerator + previous_numerator;
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const int64_t new_denominator = term * denominator + previous_denominator;
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// If there was an overflow, we prefer returning a not-so-good approximation
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// rather than something that is completely wrong.
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if (new_numerator < 0 || new_denominator < 0) break;
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previous_numerator = numerator;
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previous_denominator = denominator;
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numerator = new_numerator;
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denominator = new_denominator;
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long double numerator_approximation = abs_x * denominator;
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if (std::abs(numerator_approximation - numerator) <=
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precision * numerator_approximation) {
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break;
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}
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y = 1 / (y - term);
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}
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return Fraction((x < 0) ? -numerator : numerator, denominator);
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}
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} // namespace operations_research
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