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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_DISTRIBUTION_IMPL_H_
+#define ABSL_RANDOM_INTERNAL_DISTRIBUTION_IMPL_H_
+
+// This file contains some implementation details which are used by one or more
+// of the absl random number distributions.
+
+#include <cfloat>
+#include <cstddef>
+#include <cstdint>
+#include <cstring>
+#include <limits>
+#include <type_traits>
+
+#if (defined(_WIN32) || defined(_WIN64)) && defined(_M_IA64)
+#include <intrin.h>  // NOLINT(build/include_order)
+#pragma intrinsic(_umul128)
+#define ABSL_INTERNAL_USE_UMUL128 1
+#endif
+
+#include "absl/base/config.h"
+#include "absl/base/internal/bits.h"
+#include "absl/numeric/int128.h"
+#include "absl/random/internal/fastmath.h"
+#include "absl/random/internal/traits.h"
+
+namespace absl {
+inline namespace lts_2019_08_08 {
+namespace random_internal {
+
+// Creates a double from `bits`, with the template fields controlling the
+// output.
+//
+// RandU64To is both more efficient and generates more unique values in the
+// result interval than known implementations of std::generate_canonical().
+//
+// The `Signed` parameter controls whether positive, negative, or both are
+// returned (thus affecting the output interval).
+//   When Signed == SignedValueT, range is U(-1, 1)
+//   When Signed == NegativeValueT, range is U(-1, 0)
+//   When Signed == PositiveValueT, range is U(0, 1)
+//
+// When the `IncludeZero` parameter is true, the function may return 0 for some
+// inputs, otherwise it never returns 0.
+//
+// The `ExponentBias` parameter determines the scale of the output range by
+// adjusting the exponent.
+//
+// When a value in U(0,1) is required, use:
+//   RandU64ToDouble<PositiveValueT, true, 0>();
+//
+// When a value in U(-1,1) is required, use:
+//   RandU64ToDouble<SignedValueT, false, 0>() => U(-1, 1)
+// This generates more distinct values than the mathematically equivalent
+// expression `U(0, 1) * 2.0 - 1.0`, and is preferable.
+//
+// Scaling the result by powers of 2 (and avoiding a multiply) is also possible:
+//   RandU64ToDouble<PositiveValueT, false, 1>();  => U(0, 2)
+//   RandU64ToDouble<PositiveValueT, false, -1>();  => U(0, 0.5)
+//
+
+// Tristate types controlling the output.
+struct PositiveValueT {};
+struct NegativeValueT {};
+struct SignedValueT {};
+
+// RandU64ToDouble is the double-result variant of RandU64To, described above.
+template <typename Signed, bool IncludeZero, int ExponentBias = 0>
+inline double RandU64ToDouble(uint64_t bits) {
+  static_assert(std::is_same<Signed, PositiveValueT>::value ||
+                    std::is_same<Signed, NegativeValueT>::value ||
+                    std::is_same<Signed, SignedValueT>::value,
+                "");
+
+  // Maybe use the left-most bit for a sign bit.
+  uint64_t sign = std::is_same<Signed, NegativeValueT>::value
+                      ? 0x8000000000000000ull
+                      : 0;  // Sign bits.
+
+  if (std::is_same<Signed, SignedValueT>::value) {
+    sign = bits & 0x8000000000000000ull;
+    bits = bits & 0x7FFFFFFFFFFFFFFFull;
+  }
+  if (IncludeZero) {
+    if (bits == 0u) return 0;
+  }
+
+  // Number of leading zeros is mapped to the exponent: 2^-clz
+  int clz = base_internal::CountLeadingZeros64(bits);
+  // Shift number left to erase leading zeros.
+  bits <<= IncludeZero ? clz : (clz & 63);
+
+  // Shift number right to remove bits that overflow double mantissa.  The
+  // direction of the shift depends on `clz`.
+  bits >>= (64 - DBL_MANT_DIG);
+
+  // Compute IEEE 754 double exponent.
+  // In the Signed case, bits is a 63-bit number with a 0 msb.  Adjust the
+  // exponent to account for that.
+  const uint64_t exp =
+      (std::is_same<Signed, SignedValueT>::value ? 1023U : 1022U) +
+      static_cast<uint64_t>(ExponentBias - clz);
+  constexpr int kExp = DBL_MANT_DIG - 1;
+  // Construct IEEE 754 double from exponent and mantissa.
+  const uint64_t val = sign | (exp << kExp) | (bits & ((1ULL << kExp) - 1U));
+
+  double res;
+  static_assert(sizeof(res) == sizeof(val), "double is not 64 bit");
+  // Memcpy value from "val" to "res" to avoid aliasing problems.  Assumes that
+  // endian-ness is same for double and uint64_t.
+  std::memcpy(&res, &val, sizeof(res));
+
+  return res;
+}
+
+// RandU64ToFloat is the float-result variant of RandU64To, described above.
+template <typename Signed, bool IncludeZero, int ExponentBias = 0>
+inline float RandU64ToFloat(uint64_t bits) {
+  static_assert(std::is_same<Signed, PositiveValueT>::value ||
+                    std::is_same<Signed, NegativeValueT>::value ||
+                    std::is_same<Signed, SignedValueT>::value,
+                "");
+
+  // Maybe use the left-most bit for a sign bit.
+  uint64_t sign = std::is_same<Signed, NegativeValueT>::value
+                      ? 0x80000000ul
+                      : 0;  // Sign bits.
+
+  if (std::is_same<Signed, SignedValueT>::value) {
+    uint64_t a = bits & 0x8000000000000000ull;
+    sign = static_cast<uint32_t>(a >> 32);
+    bits = bits & 0x7FFFFFFFFFFFFFFFull;
+  }
+  if (IncludeZero) {
+    if (bits == 0u) return 0;
+  }
+
+  // Number of leading zeros is mapped to the exponent: 2^-clz
+  int clz = base_internal::CountLeadingZeros64(bits);
+  // Shift number left to erase leading zeros.
+  bits <<= IncludeZero ? clz : (clz & 63);
+  // Shift number right to remove bits that overflow double mantissa.  The
+  // direction of the shift depends on `clz`.
+  bits >>= (64 - FLT_MANT_DIG);
+
+  // Construct IEEE 754 float exponent.
+  // In the Signed case, bits is a 63-bit number with a 0 msb.  Adjust the
+  // exponent to account for that.
+  const uint32_t exp =
+      (std::is_same<Signed, SignedValueT>::value ? 127U : 126U) +
+      static_cast<uint32_t>(ExponentBias - clz);
+  constexpr int kExp = FLT_MANT_DIG - 1;
+  const uint32_t val = sign | (exp << kExp) | (bits & ((1U << kExp) - 1U));
+
+  float res;
+  static_assert(sizeof(res) == sizeof(val), "float is not 32 bit");
+  // Assumes that endian-ness is same for float and uint32_t.
+  std::memcpy(&res, &val, sizeof(res));
+
+  return res;
+}
+
+template <typename Result>
+struct RandU64ToReal {
+  template <typename Signed, bool IncludeZero, int ExponentBias = 0>
+  static inline Result Value(uint64_t bits) {
+    return RandU64ToDouble<Signed, IncludeZero, ExponentBias>(bits);
+  }
+};
+
+template <>
+struct RandU64ToReal<float> {
+  template <typename Signed, bool IncludeZero, int ExponentBias = 0>
+  static inline float Value(uint64_t bits) {
+    return RandU64ToFloat<Signed, IncludeZero, ExponentBias>(bits);
+  }
+};
+
+inline uint128 MultiplyU64ToU128(uint64_t a, uint64_t b) {
+#if defined(ABSL_HAVE_INTRINSIC_INT128)
+  return uint128(static_cast<__uint128_t>(a) * b);
+#elif defined(ABSL_INTERNAL_USE_UMUL128)
+  // uint64_t * uint64_t => uint128 multiply using imul intrinsic on MSVC.
+  uint64_t high = 0;
+  const uint64_t low = _umul128(a, b, &high);
+  return absl::MakeUint128(high, low);
+#else
+  // uint128(a) * uint128(b) in emulated mode computes a full 128-bit x 128-bit
+  // multiply.  However there are many cases where that is not necessary, and it
+  // is only necessary to support a 64-bit x 64-bit = 128-bit multiply.  This is
+  // for those cases.
+  const uint64_t a00 = static_cast<uint32_t>(a);
+  const uint64_t a32 = a >> 32;
+  const uint64_t b00 = static_cast<uint32_t>(b);
+  const uint64_t b32 = b >> 32;
+
+  const uint64_t c00 = a00 * b00;
+  const uint64_t c32a = a00 * b32;
+  const uint64_t c32b = a32 * b00;
+  const uint64_t c64 = a32 * b32;
+
+  const uint32_t carry =
+      static_cast<uint32_t>(((c00 >> 32) + static_cast<uint32_t>(c32a) +
+                             static_cast<uint32_t>(c32b)) >>
+                            32);
+
+  return absl::MakeUint128(c64 + (c32a >> 32) + (c32b >> 32) + carry,
+                           c00 + (c32a << 32) + (c32b << 32));
+#endif
+}
+
+// wide_multiply<T> multiplies two N-bit values to a 2N-bit result.
+template <typename UIntType>
+struct wide_multiply {
+  static constexpr size_t kN = std::numeric_limits<UIntType>::digits;
+  using input_type = UIntType;
+  using result_type = typename random_internal::unsigned_bits<kN * 2>::type;
+
+  static result_type multiply(input_type a, input_type b) {
+    return static_cast<result_type>(a) * b;
+  }
+
+  static input_type hi(result_type r) { return r >> kN; }
+  static input_type lo(result_type r) { return r; }
+
+  static_assert(std::is_unsigned<UIntType>::value,
+                "Class-template wide_multiply<> argument must be unsigned.");
+};
+
+#ifndef ABSL_HAVE_INTRINSIC_INT128
+template <>
+struct wide_multiply<uint64_t> {
+  using input_type = uint64_t;
+  using result_type = uint128;
+
+  static result_type multiply(uint64_t a, uint64_t b) {
+    return MultiplyU64ToU128(a, b);
+  }
+
+  static uint64_t hi(result_type r) { return Uint128High64(r); }
+  static uint64_t lo(result_type r) { return Uint128Low64(r); }
+};
+#endif
+
+}  // namespace random_internal
+}  // inline namespace lts_2019_08_08
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_INTERNAL_DISTRIBUTION_IMPL_H_