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+// 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_
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