fastmath.h (1956B)
1 // Copyright 2017 The Abseil Authors. 2 // 3 // Licensed under the Apache License, Version 2.0 (the "License"); 4 // you may not use this file except in compliance with the License. 5 // You may obtain a copy of the License at 6 // 7 // https://www.apache.org/licenses/LICENSE-2.0 8 // 9 // Unless required by applicable law or agreed to in writing, software 10 // distributed under the License is distributed on an "AS IS" BASIS, 11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 // See the License for the specific language governing permissions and 13 // limitations under the License. 14 15 #ifndef ABSL_RANDOM_INTERNAL_FASTMATH_H_ 16 #define ABSL_RANDOM_INTERNAL_FASTMATH_H_ 17 18 // This file contains fast math functions (bitwise ops as well as some others) 19 // which are implementation details of various absl random number distributions. 20 21 #include <cassert> 22 #include <cmath> 23 #include <cstdint> 24 25 #include "absl/numeric/bits.h" 26 27 namespace absl { 28 ABSL_NAMESPACE_BEGIN 29 namespace random_internal { 30 31 // Compute log2(n) using integer operations. 32 // While std::log2 is more accurate than std::log(n) / std::log(2), for 33 // very large numbers--those close to std::numeric_limits<uint64_t>::max() - 2, 34 // for instance--std::log2 rounds up rather than down, which introduces 35 // definite skew in the results. 36 inline int IntLog2Floor(uint64_t n) { 37 return (n <= 1) ? 0 : (63 - countl_zero(n)); 38 } 39 inline int IntLog2Ceil(uint64_t n) { 40 return (n <= 1) ? 0 : (64 - countl_zero(n - 1)); 41 } 42 43 inline double StirlingLogFactorial(double n) { 44 assert(n >= 1); 45 // Using Stirling's approximation. 46 constexpr double kLog2PI = 1.83787706640934548356; 47 const double logn = std::log(n); 48 const double ninv = 1.0 / static_cast<double>(n); 49 return n * logn - n + 0.5 * (kLog2PI + logn) + (1.0 / 12.0) * ninv - 50 (1.0 / 360.0) * ninv * ninv * ninv; 51 } 52 53 } // namespace random_internal 54 ABSL_NAMESPACE_END 55 } // namespace absl 56 57 #endif // ABSL_RANDOM_INTERNAL_FASTMATH_H_