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/base/internal/bits.h"
26
27 namespace absl {
28 ABSL_NAMESPACE_BEGIN
29 namespace random_internal {
30
31 // Returns the position of the first bit set.
LeadingSetBit(uint64_t n)32 inline int LeadingSetBit(uint64_t n) {
33 return 64 - base_internal::CountLeadingZeros64(n);
34 }
35
36 // Compute log2(n) using integer operations.
37 // While std::log2 is more accurate than std::log(n) / std::log(2), for
38 // very large numbers--those close to std::numeric_limits<uint64_t>::max() - 2,
39 // for instance--std::log2 rounds up rather than down, which introduces
40 // definite skew in the results.
IntLog2Floor(uint64_t n)41 inline int IntLog2Floor(uint64_t n) {
42 return (n <= 1) ? 0 : (63 - base_internal::CountLeadingZeros64(n));
43 }
IntLog2Ceil(uint64_t n)44 inline int IntLog2Ceil(uint64_t n) {
45 return (n <= 1) ? 0 : (64 - base_internal::CountLeadingZeros64(n - 1));
46 }
47
StirlingLogFactorial(double n)48 inline double StirlingLogFactorial(double n) {
49 assert(n >= 1);
50 // Using Stirling's approximation.
51 constexpr double kLog2PI = 1.83787706640934548356;
52 const double logn = std::log(n);
53 const double ninv = 1.0 / static_cast<double>(n);
54 return n * logn - n + 0.5 * (kLog2PI + logn) + (1.0 / 12.0) * ninv -
55 (1.0 / 360.0) * ninv * ninv * ninv;
56 }
57
58 // Rotate value right.
59 //
60 // We only implement the uint32_t / uint64_t versions because
61 // 1) those are the only ones we use, and
62 // 2) those are the only ones where clang detects the rotate idiom correctly.
rotr(uint32_t value,uint8_t bits)63 inline constexpr uint32_t rotr(uint32_t value, uint8_t bits) {
64 return (value >> (bits & 31)) | (value << ((-bits) & 31));
65 }
rotr(uint64_t value,uint8_t bits)66 inline constexpr uint64_t rotr(uint64_t value, uint8_t bits) {
67 return (value >> (bits & 63)) | (value << ((-bits) & 63));
68 }
69
70 } // namespace random_internal
71 ABSL_NAMESPACE_END
72 } // namespace absl
73
74 #endif // ABSL_RANDOM_INTERNAL_FASTMATH_H_
75