| // 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. | |
| // This file contains fast math functions (bitwise ops as well as some others) | |
| // which are implementation details of various absl random number distributions. | |
| 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 | |