diff options
Diffstat (limited to 'absl/random/internal/fast_uniform_bits.h')
| -rw-r--r-- | absl/random/internal/fast_uniform_bits.h | 349 |
1 files changed, 164 insertions, 185 deletions
diff --git a/absl/random/internal/fast_uniform_bits.h b/absl/random/internal/fast_uniform_bits.h index 184a2708..e8df92f3 100644 --- a/absl/random/internal/fast_uniform_bits.h +++ b/absl/random/internal/fast_uniform_bits.h @@ -22,11 +22,18 @@ namespace absl { namespace random_internal { +// Returns true if the input value is zero or a power of two. Useful for +// determining if the range of output values in a URBG +template <typename UIntType> +constexpr bool IsPowerOfTwoOrZero(UIntType n) { + return (n == 0) || ((n & (n - 1)) == 0); +} + // 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() { +constexpr typename URBG::result_type RangeSize() { using result_type = typename URBG::result_type; return ((URBG::max)() == (std::numeric_limits<result_type>::max)() && (URBG::min)() == std::numeric_limits<result_type>::lowest()) @@ -34,6 +41,42 @@ constexpr typename URBG::result_type constexpr_range() { : (URBG::max)() - (URBG::min)() + result_type{1}; } +template <typename UIntType> +constexpr UIntType LargestPowerOfTwoLessThanOrEqualTo(UIntType n) { + return n < 2 ? n : 2 * LargestPowerOfTwoLessThanOrEqualTo(n / 2); +} + +// Given a URBG generating values in the closed interval [Lo, Hi], returns the +// largest power of two less than or equal to `Hi - Lo + 1`. +template <typename URBG> +constexpr typename URBG::result_type PowerOfTwoSubRangeSize() { + return LargestPowerOfTwoLessThanOrEqualTo(RangeSize<URBG>()); +} + +// Computes the floor of the log. (i.e., std::floor(std::log2(N)); +template <typename UIntType> +constexpr UIntType IntegerLog2(UIntType n) { + return (n <= 1) ? 0 : 1 + IntegerLog2(n / 2); +} + +// Returns the number of bits of randomness returned through +// `PowerOfTwoVariate(urbg)`. +template <typename URBG> +constexpr size_t NumBits() { + return RangeSize<URBG>() == 0 + ? std::numeric_limits<typename URBG::result_type>::digits + : IntegerLog2(PowerOfTwoSubRangeSize<URBG>()); +} + +// Given a shift value `n`, constructs a mask with exactly the low `n` bits set. +// If `n == 0`, all bits are set. +template <typename UIntType> +constexpr UIntType MaskFromShift(UIntType n) { + return ((n % std::numeric_limits<UIntType>::digits) == 0) + ? ~UIntType{0} + : (UIntType{1} << n) - UIntType{1}; +} + // FastUniformBits implements a fast path to acquire uniform independent bits // from a type which conforms to the [rand.req.urbg] concept. // Parameterized by: @@ -45,14 +88,6 @@ constexpr typename URBG::result_type constexpr_range() { // generator that will outlive the std::independent_bits_engine instance. template <typename UIntType = uint64_t> 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 = std::numeric_limits<UIntType>::digits; - public: using result_type = UIntType; @@ -65,14 +100,47 @@ class FastUniformBits { 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). + static_assert(std::is_unsigned<UIntType>::value, + "Class-template FastUniformBits<> must be parameterized using " + "an unsigned type."); + + // PowerOfTwoVariate() generates a single random variate, always returning a + // value in the half-open interval `[0, PowerOfTwoSubRangeSize<URBG>())`. If + // the URBG already generates values in a power-of-two range, the generator + // itself is used. Otherwise, we use rejection sampling on the largest + // possible power-of-two-sized subrange. + struct PowerOfTwoTag {}; + struct RejectionSamplingTag {}; template <typename URBG> - typename URBG::result_type Variate(URBG& g); // NOLINT(runtime/references) + static typename URBG::result_type PowerOfTwoVariate( + URBG& g) { // NOLINT(runtime/references) + using tag = + typename std::conditional<IsPowerOfTwoOrZero(RangeSize<URBG>()), + PowerOfTwoTag, RejectionSamplingTag>::type; + return PowerOfTwoVariate(g, tag{}); + } + + template <typename URBG> + static typename URBG::result_type PowerOfTwoVariate( + URBG& g, // NOLINT(runtime/references) + PowerOfTwoTag) { + return g() - (URBG::min)(); + } - // generate() generates a random value, dispatched on whether - // the underlying URNG must loop over multiple calls or not. + template <typename URBG> + static typename URBG::result_type PowerOfTwoVariate( + URBG& g, // NOLINT(runtime/references) + RejectionSamplingTag) { + // Use rejection sampling to ensure uniformity across the range. + typename URBG::result_type u; + do { + u = g() - (URBG::min)(); + } while (u >= PowerOfTwoSubRangeSize<URBG>()); + return u; + } + + // Generate() generates a random value, dispatched on whether + // the underlying URBG must loop over multiple calls or not. template <typename URBG> result_type Generate(URBG& g, // NOLINT(runtime/references) std::true_type /* avoid_looping */); @@ -82,196 +150,107 @@ class FastUniformBits { 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 UIntType> 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. +typename FastUniformBits<UIntType>::result_type +FastUniformBits<UIntType>::operator()(URBG& g) { // NOLINT(runtime/references) + // kRangeMask is the mask used when sampling variates from the URBG when the + // width of the URBG 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<> " + static_assert((URBG::max)() > (URBG::min)(), "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. -// `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, typename URBG> -class FastUniformBitsLoopingConstants { - private: - static constexpr size_t kWidth = std::numeric_limits<UIntType>::digits; 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> -template <typename URBG> -typename FastUniformBits<UIntType>::result_type -FastUniformBits<UIntType>::operator()( - URBG& g) { // NOLINT(runtime/references) - using constants = FastUniformBitsURBGConstants<URBG>; - return Generate( - g, std::integral_constant<bool, constants::kRangeMask >= (max)()>{}); -} - -template <typename UIntType> -template <typename URBG> -typename URBG::result_type FastUniformBits<UIntType>::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; + constexpr urbg_result_type kRangeMask = + RangeSize<URBG>() == 0 + ? (std::numeric_limits<urbg_result_type>::max)() + : static_cast<urbg_result_type>(PowerOfTwoSubRangeSize<URBG>() - 1); + return Generate(g, std::integral_constant<bool, (kRangeMask >= (max)())>{}); } template <typename UIntType> template <typename URBG> typename FastUniformBits<UIntType>::result_type -FastUniformBits<UIntType>::Generate( - URBG& g, // NOLINT(runtime/references) - std::true_type /* avoid_looping */) { +FastUniformBits<UIntType>::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 + // provided by URBG. Thus, generate a single value and then simply mask off // the required bits. - return Variate(g) & (max)(); + + return PowerOfTwoVariate(g) & (max)(); } template <typename UIntType> template <typename URBG> typename FastUniformBits<UIntType>::result_type -FastUniformBits<UIntType>::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, URBG>; +FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references) + std::false_type /* avoid_looping */) { + // See [rand.adapt.ibits] for more details on the constants calculated below. + // + // It is preferable to use roughly the same number of bits from each generator + // call, however this is only possible when the number of bits provided by the + // URBG is a divisor of the number of bits in `result_type`. In all other + // cases, the number of bits used cannot always be the same, but it can be + // guaranteed to be off by at most 1. Thus we run two loops, one with a + // smaller bit-width size (`kSmallWidth`) and one with a larger width size + // (satisfying `kLargeWidth == kSmallWidth + 1`). The loops are run + // `kSmallIters` and `kLargeIters` times respectively such + // that + // + // `kTotalWidth == kSmallIters * kSmallWidth + // + kLargeIters * kLargeWidth` + // + // where `kTotalWidth` is the total number of bits in `result_type`. + // + constexpr size_t kTotalWidth = std::numeric_limits<result_type>::digits; + constexpr size_t kUrbgWidth = NumBits<URBG>(); + constexpr size_t kTotalIters = + kTotalWidth / kUrbgWidth + (kTotalWidth % kUrbgWidth != 0); + constexpr size_t kSmallWidth = kTotalWidth / kTotalIters; + constexpr size_t kLargeWidth = kSmallWidth + 1; + // + // Because `kLargeWidth == kSmallWidth + 1`, it follows that + // + // `kTotalWidth == kTotalIters * kSmallWidth + kLargeIters` + // + // and therefore + // + // `kLargeIters == kTotalWidth % kSmallWidth` + // + // Intuitively, each iteration with the large width accounts for one unit + // of the remainder when `kTotalWidth` is divided by `kSmallWidth`. As + // mentioned above, if the URBG width is a divisor of `kTotalWidth`, then + // there would be no need for any large iterations (i.e., one loop would + // suffice), and indeed, in this case, `kLargeIters` would be zero. + constexpr size_t kLargeIters = kTotalWidth % kSmallWidth; + constexpr size_t kSmallIters = + (kTotalWidth - (kLargeWidth * kLargeIters)) / kSmallWidth; + + static_assert( + kTotalWidth == kSmallIters * kSmallWidth + kLargeIters * kLargeWidth, + "Error in looping constant calculations."); result_type s = 0; - for (size_t n = 0; n < constants::kN0; ++n) { - auto u = Variate(g); - s = (s << constants::kW0) + (u & constants::kM0); + + constexpr size_t kSmallShift = kSmallWidth % kTotalWidth; + constexpr result_type kSmallMask = MaskFromShift(result_type{kSmallShift}); + for (size_t n = 0; n < kSmallIters; ++n) { + s = (s << kSmallShift) + + (static_cast<result_type>(PowerOfTwoVariate(g)) & kSmallMask); } - for (size_t n = constants::kN0; n < constants::kN1; ++n) { - auto u = Variate(g); - s = (s << constants::kW1) + (u & constants::kM1); + + constexpr size_t kLargeShift = kLargeWidth % kTotalWidth; + constexpr result_type kLargeMask = MaskFromShift(result_type{kLargeShift}); + for (size_t n = 0; n < kLargeIters; ++n) { + s = (s << kLargeShift) + + (static_cast<result_type>(PowerOfTwoVariate(g)) & kLargeMask); } + + static_assert( + kLargeShift == kSmallShift + 1 || + (kLargeShift == 0 && + kSmallShift == std::numeric_limits<result_type>::digits - 1), + "Error in looping constant calculations"); + return s; } |