diff options
Diffstat (limited to 'absl/random/internal/fast_uniform_bits.h')
| -rw-r--r-- | absl/random/internal/fast_uniform_bits.h | 299 |
1 files changed, 299 insertions, 0 deletions
diff --git a/absl/random/internal/fast_uniform_bits.h b/absl/random/internal/fast_uniform_bits.h new file mode 100644 index 00000000..23eabbc8 --- /dev/null +++ b/absl/random/internal/fast_uniform_bits.h @@ -0,0 +1,299 @@ +// 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_FAST_UNIFORM_BITS_H_ +#define ABSL_RANDOM_INTERNAL_FAST_UNIFORM_BITS_H_ + +#include <cstddef> +#include <cstdint> +#include <limits> +#include <type_traits> + +namespace absl { +namespace random_internal { +// Computes the length of the range of values producible by the URBG, or returns +// zero if that would encompass the entire range of representable values in +// URBG::result_type. +template <typename URBG> +constexpr typename URBG::result_type constexpr_range() { + using result_type = typename URBG::result_type; + return ((URBG::max)() == (std::numeric_limits<result_type>::max)() && + (URBG::min)() == std::numeric_limits<result_type>::lowest()) + ? result_type{0} + : (URBG::max)() - (URBG::min)() + result_type{1}; +} + +// FastUniformBits implements a fast path to acquire uniform independent bits +// from a type which conforms to the [rand.req.urbg] concept. +// Parameterized by: +// `UIntType`: the result (output) type +// `Width`: binary output width +// +// The std::independent_bits_engine [rand.adapt.ibits] adaptor can be +// instantiated from an existing generator through a copy or a move. It does +// not, however, facilitate the production of pseudorandom bits from an un-owned +// generator that will outlive the std::independent_bits_engine instance. +template <typename UIntType = uint64_t, + size_t Width = std::numeric_limits<UIntType>::digits> +class FastUniformBits { + static_assert(std::is_unsigned<UIntType>::value, + "Class-template FastUniformBits<> must be parameterized using " + "an unsigned type."); + + // `kWidth` is the width, in binary digits, of the output. By default it is + // the number of binary digits in the `result_type`. + static constexpr size_t kWidth = Width; + static_assert(kWidth > 0, + "Class-template FastUniformBits<> Width argument must be > 0"); + + static_assert(kWidth <= std::numeric_limits<UIntType>::digits, + "Class-template FastUniformBits<> Width argument must be <= " + "width of UIntType."); + + static constexpr bool kIsMaxWidth = + (kWidth >= std::numeric_limits<UIntType>::digits); + + // Computes a mask of `n` bits for the `UIntType`. + static constexpr UIntType constexpr_mask(size_t n) { + return (UIntType(1) << n) - 1; + } + + public: + using result_type = UIntType; + + static constexpr result_type(min)() { return 0; } + static constexpr result_type(max)() { + return kIsMaxWidth ? (std::numeric_limits<result_type>::max)() + : constexpr_mask(kWidth); + } + + template <typename URBG> + result_type operator()(URBG& g); // NOLINT(runtime/references) + + private: + // Variate() generates a single random variate, always returning a value + // in the closed interval [0 ... FastUniformBitsURBGConstants::kRangeMask] + // (kRangeMask+1 is a power of 2). + template <typename URBG> + typename URBG::result_type Variate(URBG& g); // NOLINT(runtime/references) + + // generate() generates a random value, dispatched on whether + // the underlying URNG must loop over multiple calls or not. + template <typename URBG> + result_type Generate(URBG& g, // NOLINT(runtime/references) + std::true_type /* avoid_looping */); + + template <typename URBG> + result_type Generate(URBG& g, // NOLINT(runtime/references) + std::false_type /* avoid_looping */); +}; + +// FastUniformBitsURBGConstants computes the URBG-derived constants used +// by FastUniformBits::Generate and FastUniformBits::Variate. +// Parameterized by the FastUniformBits parameter: +// `URBG`: The underlying UniformRandomNumberGenerator. +// +// The values here indicate the URBG range as well as providing an indicator +// whether the URBG output is a power of 2, and kRangeMask, which allows masking +// the generated output to kRangeBits. +template <typename URBG> +class FastUniformBitsURBGConstants { + // Computes the floor of the log. (i.e., std::floor(std::log2(N)); + static constexpr size_t constexpr_log2(size_t n) { + return (n <= 1) ? 0 : 1 + constexpr_log2(n / 2); + } + + // Computes a mask of n bits for the URBG::result_type. + static constexpr typename URBG::result_type constexpr_mask(size_t n) { + return (typename URBG::result_type(1) << n) - 1; + } + + public: + using result_type = typename URBG::result_type; + + // The range of the URNG, max - min + 1, or zero if that result would cause + // overflow. + static constexpr result_type kRange = constexpr_range<URBG>(); + + static constexpr bool kPowerOfTwo = + (kRange == 0) || ((kRange & (kRange - 1)) == 0); + + // kRangeBits describes the number number of bits suitable to mask off of URNG + // variate, which is: + // kRangeBits = floor(log2(kRange)) + static constexpr size_t kRangeBits = + kRange == 0 ? std::numeric_limits<result_type>::digits + : constexpr_log2(kRange); + + // kRangeMask is the mask used when sampling variates from the URNG when the + // width of the URNG range is not a power of 2. + // Y = (2 ^ kRange) - 1 + static constexpr result_type kRangeMask = + kRange == 0 ? (std::numeric_limits<result_type>::max)() + : constexpr_mask(kRangeBits); + + static_assert((URBG::max)() != (URBG::min)(), + "Class-template FastUniformBitsURBGConstants<> " + "URBG::max and URBG::min may not be equal."); + + static_assert(std::is_unsigned<result_type>::value, + "Class-template FastUniformBitsURBGConstants<> " + "URBG::result_type must be unsigned."); + + static_assert(kRangeMask > 0, + "Class-template FastUniformBitsURBGConstants<> " + "URBG does not generate sufficient random bits."); + + static_assert(kRange == 0 || + kRangeBits < std::numeric_limits<result_type>::digits, + "Class-template FastUniformBitsURBGConstants<> " + "URBG range computation error."); +}; + +// FastUniformBitsLoopingConstants computes the looping constants used +// by FastUniformBits::Generate. These constants indicate how multiple +// URBG::result_type values are combined into an output_value. +// Parameterized by the FastUniformBits parameters: +// `UIntType`: output type. +// `Width`: binary output width, +// `URNG`: The underlying UniformRandomNumberGenerator. +// +// The looping constants describe the sets of loop counters and mask values +// which control how individual variates are combined the final output. The +// algorithm ensures that the number of bits used by any individual call differs +// by at-most one bit from any other call. This is simplified into constants +// which describe two loops, with the second loop parameters providing one extra +// bit per variate. +// +// See [rand.adapt.ibits] for more details on the use of these constants. +template <typename UIntType, size_t Width, typename URBG> +class FastUniformBitsLoopingConstants { + private: + static constexpr size_t kWidth = Width; + using urbg_result_type = typename URBG::result_type; + using uint_result_type = UIntType; + + public: + using result_type = + typename std::conditional<(sizeof(urbg_result_type) <= + sizeof(uint_result_type)), + uint_result_type, urbg_result_type>::type; + + private: + // Estimate N as ceil(width / urng width), and W0 as (width / N). + static constexpr size_t kRangeBits = + FastUniformBitsURBGConstants<URBG>::kRangeBits; + + // The range of the URNG, max - min + 1, or zero if that result would cause + // overflow. + static constexpr result_type kRange = constexpr_range<URBG>(); + static constexpr size_t kEstimateN = + kWidth / kRangeBits + (kWidth % kRangeBits != 0); + static constexpr size_t kEstimateW0 = kWidth / kEstimateN; + static constexpr result_type kEstimateY0 = (kRange >> kEstimateW0) + << kEstimateW0; + + public: + // Parameters for the two loops: + // kN0, kN1 are the number of underlying calls required for each loop. + // KW0, kW1 are shift widths for each loop. + // + static constexpr size_t kN1 = (kRange - kEstimateY0) > + (kEstimateY0 / kEstimateN) + ? kEstimateN + 1 + : kEstimateN; + static constexpr size_t kN0 = kN1 - (kWidth % kN1); + static constexpr size_t kW0 = kWidth / kN1; + static constexpr size_t kW1 = kW0 + 1; + + static constexpr result_type kM0 = (result_type(1) << kW0) - 1; + static constexpr result_type kM1 = (result_type(1) << kW1) - 1; + + static_assert( + kW0 <= kRangeBits, + "Class-template FastUniformBitsLoopingConstants::kW0 too large."); + + static_assert( + kW0 > 0, + "Class-template FastUniformBitsLoopingConstants::kW0 too small."); +}; + +template <typename UIntType, size_t Width> +template <typename URBG> +typename FastUniformBits<UIntType, Width>::result_type +FastUniformBits<UIntType, Width>::operator()( + URBG& g) { // NOLINT(runtime/references) + using constants = FastUniformBitsURBGConstants<URBG>; + return Generate( + g, std::integral_constant<bool, constants::kRangeMask >= (max)()>{}); +} + +template <typename UIntType, size_t Width> +template <typename URBG> +typename URBG::result_type FastUniformBits<UIntType, Width>::Variate( + URBG& g) { // NOLINT(runtime/references) + using constants = FastUniformBitsURBGConstants<URBG>; + if (constants::kPowerOfTwo) { + return g() - (URBG::min)(); + } + + // Use rejection sampling to ensure uniformity across the range. + typename URBG::result_type u; + do { + u = g() - (URBG::min)(); + } while (u > constants::kRangeMask); + return u; +} + +template <typename UIntType, size_t Width> +template <typename URBG> +typename FastUniformBits<UIntType, Width>::result_type +FastUniformBits<UIntType, Width>::Generate( + URBG& g, // NOLINT(runtime/references) + std::true_type /* avoid_looping */) { + // The width of the result_type is less than than the width of the random bits + // provided by URNG. Thus, generate a single value and then simply mask off + // the required bits. + return Variate(g) & (max)(); +} + +template <typename UIntType, size_t Width> +template <typename URBG> +typename FastUniformBits<UIntType, Width>::result_type +FastUniformBits<UIntType, Width>::Generate( + URBG& g, // NOLINT(runtime/references) + std::false_type /* avoid_looping */) { + // The width of the result_type is wider than the number of random bits + // provided by URNG. Thus we merge several variates of URNG into the result + // using a shift and mask. The constants type generates the parameters used + // ensure that the bits are distributed across all the invocations of the + // underlying URNG. + using constants = FastUniformBitsLoopingConstants<UIntType, Width, URBG>; + + result_type s = 0; + for (size_t n = 0; n < constants::kN0; ++n) { + auto u = Variate(g); + s = (s << constants::kW0) + (u & constants::kM0); + } + for (size_t n = constants::kN0; n < constants::kN1; ++n) { + auto u = Variate(g); + s = (s << constants::kW1) + (u & constants::kM1); + } + return s; +} + +} // namespace random_internal +} // namespace absl + +#endif // ABSL_RANDOM_INTERNAL_FAST_UNIFORM_BITS_H_ |