// Copyright 2017 The Abseil Authors. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // https://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #ifndef ABSL_RANDOM_INTERNAL_FASTMATH_H_ #define ABSL_RANDOM_INTERNAL_FASTMATH_H_ // This file contains fast math functions (bitwise ops as well as some others) // which are implementation details of various absl random number distributions. #include <cassert> #include <cmath> #include <cstdint> #include "absl/numeric/bits.h" namespace absl { ABSL_NAMESPACE_BEGIN namespace random_internal { // Compute log2(n) using integer operations. // While std::log2 is more accurate than std::log(n) / std::log(2), for // very large numbers--those close to std::numeric_limits<uint64_t>::max() - 2, // for instance--std::log2 rounds up rather than down, which introduces // definite skew in the results. inline int IntLog2Floor(uint64_t n) { return (n <= 1) ? 0 : (63 - countl_zero(n)); } inline int IntLog2Ceil(uint64_t n) { return (n <= 1) ? 0 : (64 - countl_zero(n - 1)); } inline double StirlingLogFactorial(double n) { assert(n >= 1); // Using Stirling's approximation. constexpr double kLog2PI = 1.83787706640934548356; const double logn = std::log(n); const double ninv = 1.0 / static_cast<double>(n); return n * logn - n + 0.5 * (kLog2PI + logn) + (1.0 / 12.0) * ninv - (1.0 / 360.0) * ninv * ninv * ninv; } } // namespace random_internal ABSL_NAMESPACE_END } // namespace absl #endif // ABSL_RANDOM_INTERNAL_FASTMATH_H_