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Pods/abseil/absl/random/internal/fast_uniform_bits.h

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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>
+
+#include "absl/base/config.h"
+#include "absl/meta/type_traits.h"
+#include "absl/random/internal/traits.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+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 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});
+}
+
+// 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 >> 1);
+}
+
+// Returns the number of bits of randomness returned through
+// `PowerOfTwoVariate(urbg)`.
+template <typename URBG>
+constexpr size_t NumBits() {
+  return static_cast<size_t>(
+      RangeSize<URBG>() == 0
+          ? std::numeric_limits<typename URBG::result_type>::digits
+          : 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(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:
+//  `UIntType`: the result (output) type
+//
+// 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>
+class FastUniformBits {
+ public:
+  using result_type = UIntType;
+
+  static constexpr result_type(min)() { return 0; }
+  static constexpr result_type(max)() {
+    return (std::numeric_limits<result_type>::max)();
+  }
+
+  template <typename URBG>
+  result_type operator()(URBG& g);  // NOLINT(runtime/references)
+
+ private:
+  static_assert(IsUnsigned<UIntType>::value,
+                "Class-template FastUniformBits<> must be parameterized using "
+                "an unsigned type.");
+
+  // Generate() generates a random value, dispatched on whether
+  // 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)
+                       SimplifiedLoopTag);
+
+  template <typename URBG>
+  result_type Generate(URBG& g,  // NOLINT(runtime/references)
+                       RejectionLoopTag);
+};
+
+template <typename UIntType>
+template <typename URBG>
+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_assert((URBG::max)() > (URBG::min)(),
+                "URBG::max and URBG::min may not be equal.");
+
+  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)
+                                    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)();
+
+  result_type r = static_cast<result_type>(g() - kMin);
+  for (size_t n = 1; n < kIters; ++n) {
+    r = static_cast<result_type>(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)
+                                    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
+  // 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
+  //
+  //    `kResultBits == kSmallIters * kSmallBits
+  //                    + kLargeIters * kLargeBits`
+  //
+  // where `kResultBits` is the total number of bits in `result_type`.
+  //
+  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 `kLargeBits == kSmallBits + 1`, it follows that
+  //
+  //     `kResultBits == kSmallIters * kSmallBits + 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.
+  static_assert(kResultBits == kSmallIters * kSmallBits +
+                                   (kTotalIters - kSmallIters) * kLargeBits,
+                "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);
+
+  static constexpr auto kMin = (URBG::min)();
+
+  result_type s = 0;
+  for (size_t n = 0; n < kSmallIters; ++n) {
+    urbg_result_type v;
+    do {
+      v = g() - kMin;
+    } while (v >= kSmallRejection);
+
+    s = (s << kSmallShift) + static_cast<result_type>(v & kSmallMask);
+  }
+
+  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;
+}
+
+}  // namespace random_internal
+ABSL_NAMESPACE_END
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_INTERNAL_FAST_UNIFORM_BITS_H_