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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 {
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);
}
};
} // namespace random_internal
} // namespace absl
#endif // ABSL_RANDOM_INTERNAL_DISTRIBUTION_IMPL_H_
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