diff options
Diffstat (limited to 'absl/random/internal/fast_uniform_bits.h')
| -rw-r--r-- | absl/random/internal/fast_uniform_bits.h | 202 |
1 files changed, 103 insertions, 99 deletions
diff --git a/absl/random/internal/fast_uniform_bits.h b/absl/random/internal/fast_uniform_bits.h index f13c8729..425aaf7d 100644 --- a/absl/random/internal/fast_uniform_bits.h +++ b/absl/random/internal/fast_uniform_bits.h @@ -21,6 +21,7 @@ #include <type_traits> #include "absl/base/config.h" +#include "absl/meta/type_traits.h" namespace absl { ABSL_NAMESPACE_BEGIN @@ -38,28 +39,17 @@ constexpr bool IsPowerOfTwoOrZero(UIntType n) { template <typename URBG> constexpr typename URBG::result_type RangeSize() { using result_type = typename URBG::result_type; + static_assert((URBG::max)() != (URBG::min)(), "URBG range cannot be 0."); 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}; -} - -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>()); + : ((URBG::max)() - (URBG::min)() + result_type{1}); } // 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); + return (n <= 1) ? 0 : 1 + IntegerLog2(n >> 1); } // Returns the number of bits of randomness returned through @@ -68,18 +58,23 @@ template <typename URBG> constexpr size_t NumBits() { return RangeSize<URBG>() == 0 ? std::numeric_limits<typename URBG::result_type>::digits - : IntegerLog2(PowerOfTwoSubRangeSize<URBG>()); + : IntegerLog2(RangeSize<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) { +constexpr UIntType MaskFromShift(size_t n) { return ((n % std::numeric_limits<UIntType>::digits) == 0) ? ~UIntType{0} : (UIntType{1} << n) - UIntType{1}; } +// Tags used to dispatch FastUniformBits::generate to the simple or more complex +// entropy extraction algorithm. +struct SimplifiedLoopTag {}; +struct RejectionLoopTag {}; + // FastUniformBits implements a fast path to acquire uniform independent bits // from a type which conforms to the [rand.req.urbg] concept. // Parameterized by: @@ -107,50 +102,16 @@ class FastUniformBits { "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> - 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)(); - } - - 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. + // the underlying URBG must use rejection sampling to generate a value, + // or whether a simplified loop will suffice. template <typename URBG> result_type Generate(URBG& g, // NOLINT(runtime/references) - std::true_type /* avoid_looping */); + SimplifiedLoopTag); template <typename URBG> result_type Generate(URBG& g, // NOLINT(runtime/references) - std::false_type /* avoid_looping */); + RejectionLoopTag); }; template <typename UIntType> @@ -162,31 +123,47 @@ FastUniformBits<UIntType>::operator()(URBG& g) { // NOLINT(runtime/references) // Y = (2 ^ kRange) - 1 static_assert((URBG::max)() > (URBG::min)(), "URBG::max and URBG::min may not be equal."); - using urbg_result_type = typename URBG::result_type; - 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)())>{}); + + using tag = absl::conditional_t<IsPowerOfTwoOrZero(RangeSize<URBG>()), + SimplifiedLoopTag, RejectionLoopTag>; + return Generate(g, tag{}); } template <typename UIntType> template <typename URBG> typename FastUniformBits<UIntType>::result_type 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 URBG. Thus, generate a single value and then simply mask off - // the required bits. + SimplifiedLoopTag) { + // The simplified version of FastUniformBits works only on URBGs that have + // a range that is a power of 2. In this case we simply loop and shift without + // attempting to balance the bits across calls. + static_assert(IsPowerOfTwoOrZero(RangeSize<URBG>()), + "incorrect Generate tag for URBG instance"); + + static constexpr size_t kResultBits = + std::numeric_limits<result_type>::digits; + static constexpr size_t kUrbgBits = NumBits<URBG>(); + static constexpr size_t kIters = + (kResultBits / kUrbgBits) + (kResultBits % kUrbgBits != 0); + static constexpr size_t kShift = (kIters == 1) ? 0 : kUrbgBits; + static constexpr auto kMin = (URBG::min)(); - return PowerOfTwoVariate(g) & (max)(); + result_type r = static_cast<result_type>(g() - kMin); + for (size_t n = 1; n < kIters; ++n) { + r = (r << kShift) + static_cast<result_type>(g() - kMin); + } + return r; } template <typename UIntType> template <typename URBG> typename FastUniformBits<UIntType>::result_type FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references) - std::false_type /* avoid_looping */) { + RejectionLoopTag) { + static_assert(!IsPowerOfTwoOrZero(RangeSize<URBG>()), + "incorrect Generate tag for URBG instance"); + using urbg_result_type = typename URBG::result_type; + // 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 @@ -199,21 +176,44 @@ FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references) // `kSmallIters` and `kLargeIters` times respectively such // that // - // `kTotalWidth == kSmallIters * kSmallWidth - // + kLargeIters * kLargeWidth` + // `kResultBits == kSmallIters * kSmallBits + // + kLargeIters * kLargeBits` // - // where `kTotalWidth` is the total number of bits in `result_type`. + // where `kResultBits` 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; + static constexpr size_t kResultBits = + std::numeric_limits<result_type>::digits; // w + static constexpr urbg_result_type kUrbgRange = RangeSize<URBG>(); // R + static constexpr size_t kUrbgBits = NumBits<URBG>(); // m + + // compute the initial estimate of the bits used. + // [rand.adapt.ibits] 2 (c) + static constexpr size_t kA = // ceil(w/m) + (kResultBits / kUrbgBits) + ((kResultBits % kUrbgBits) != 0); // n' + + static constexpr size_t kABits = kResultBits / kA; // w0' + static constexpr urbg_result_type kARejection = + ((kUrbgRange >> kABits) << kABits); // y0' + + // refine the selection to reduce the rejection frequency. + static constexpr size_t kTotalIters = + ((kUrbgRange - kARejection) <= (kARejection / kA)) ? kA : (kA + 1); // n + + // [rand.adapt.ibits] 2 (b) + static constexpr size_t kSmallIters = + kTotalIters - (kResultBits % kTotalIters); // n0 + static constexpr size_t kSmallBits = kResultBits / kTotalIters; // w0 + static constexpr urbg_result_type kSmallRejection = + ((kUrbgRange >> kSmallBits) << kSmallBits); // y0 + + static constexpr size_t kLargeBits = kSmallBits + 1; // w0+1 + static constexpr urbg_result_type kLargeRejection = + ((kUrbgRange >> kLargeBits) << kLargeBits); // y1 + // - // Because `kLargeWidth == kSmallWidth + 1`, it follows that + // Because `kLargeBits == kSmallBits + 1`, it follows that // - // `kTotalWidth == kTotalIters * kSmallWidth + kLargeIters` + // `kResultBits == kSmallIters * kSmallBits + kLargeIters` // // and therefore // @@ -224,36 +224,40 @@ FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references) // 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(kResultBits == kSmallIters * kSmallBits + + (kTotalIters - kSmallIters) * kLargeBits, + "Error in looping constant calculations."); - static_assert( - kTotalWidth == kSmallIters * kSmallWidth + kLargeIters * kLargeWidth, - "Error in looping constant calculations."); + // The small shift is essentially small bits, but due to the potential + // of generating a smaller result_type from a larger urbg type, the actual + // shift might be 0. + static constexpr size_t kSmallShift = kSmallBits % kResultBits; + static constexpr auto kSmallMask = + MaskFromShift<urbg_result_type>(kSmallShift); + static constexpr size_t kLargeShift = kLargeBits % kResultBits; + static constexpr auto kLargeMask = + MaskFromShift<urbg_result_type>(kLargeShift); - result_type s = 0; + static constexpr auto kMin = (URBG::min)(); - constexpr size_t kSmallShift = kSmallWidth % kTotalWidth; - constexpr result_type kSmallMask = MaskFromShift(result_type{kSmallShift}); + result_type s = 0; for (size_t n = 0; n < kSmallIters; ++n) { - s = (s << kSmallShift) + - (static_cast<result_type>(PowerOfTwoVariate(g)) & kSmallMask); - } + urbg_result_type v; + do { + v = g() - kMin; + } while (v >= kSmallRejection); - 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); + s = (s << kSmallShift) + static_cast<result_type>(v & kSmallMask); } - static_assert( - kLargeShift == kSmallShift + 1 || - (kLargeShift == 0 && - kSmallShift == std::numeric_limits<result_type>::digits - 1), - "Error in looping constant calculations"); + for (size_t n = kSmallIters; n < kTotalIters; ++n) { + urbg_result_type v; + do { + v = g() - kMin; + } while (v >= kLargeRejection); + s = (s << kLargeShift) + static_cast<result_type>(v & kLargeMask); + } return s; } |