58 lines
1.9 KiB
C
58 lines
1.9 KiB
C
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// Copyright 2017 The Abseil Authors.
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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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// https://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 ABSL_RANDOM_INTERNAL_FASTMATH_H_
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#define ABSL_RANDOM_INTERNAL_FASTMATH_H_
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// This file contains fast math functions (bitwise ops as well as some others)
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// which are implementation details of various absl random number distributions.
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#include <cassert>
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#include <cmath>
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#include <cstdint>
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#include "absl/numeric/bits.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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namespace random_internal {
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// Compute log2(n) using integer operations.
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// While std::log2 is more accurate than std::log(n) / std::log(2), for
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// very large numbers--those close to std::numeric_limits<uint64_t>::max() - 2,
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// for instance--std::log2 rounds up rather than down, which introduces
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// definite skew in the results.
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inline int IntLog2Floor(uint64_t n) {
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return (n <= 1) ? 0 : (63 - countl_zero(n));
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}
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inline int IntLog2Ceil(uint64_t n) {
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return (n <= 1) ? 0 : (64 - countl_zero(n - 1));
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}
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inline double StirlingLogFactorial(double n) {
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assert(n >= 1);
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// Using Stirling's approximation.
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constexpr double kLog2PI = 1.83787706640934548356;
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const double logn = std::log(n);
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const double ninv = 1.0 / static_cast<double>(n);
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return n * logn - n + 0.5 * (kLog2PI + logn) + (1.0 / 12.0) * ninv -
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(1.0 / 360.0) * ninv * ninv * ninv;
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}
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} // namespace random_internal
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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_RANDOM_INTERNAL_FASTMATH_H_
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