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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_GENERATE_REAL_H_
#define ABSL_RANDOM_INTERNAL_GENERATE_REAL_H_
// This file contains some implementation details which are used by one or more
// of the absl random number distributions.
#include <cstdint>
#include <cstring>
#include <limits>
#include <type_traits>
#include "absl/base/internal/bits.h"
#include "absl/meta/type_traits.h"
#include "absl/random/internal/fastmath.h"
#include "absl/random/internal/traits.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
namespace random_internal {
// Tristate tag types controlling the output of GenerateRealFromBits.
struct GeneratePositiveTag {};
struct GenerateNegativeTag {};
struct GenerateSignedTag {};
// GenerateRealFromBits generates a single real value from a single 64-bit
// `bits` with template fields controlling the output.
//
// The `SignedTag` parameter controls whether positive, negative,
// or either signed/unsigned may be returned.
// When SignedTag == GeneratePositiveTag, range is U(0, 1)
// When SignedTag == GenerateNegativeTag, range is U(-1, 0)
// When SignedTag == GenerateSignedTag, range is U(-1, 1)
//
// When the `IncludeZero` parameter is true, the function may return 0 for some
// inputs, otherwise it never returns 0.
//
// When a value in U(0,1) is required, use:
// Uniform64ToReal<double, PositiveValueT, true>;
//
// When a value in U(-1,1) is required, use:
// Uniform64ToReal<double, SignedValueT, false>;
//
// This generates more distinct values than the mathematical equivalent
// `U(0, 1) * 2.0 - 1.0`.
//
// Scaling the result by powers of 2 (and avoiding a multiply) is also possible:
// GenerateRealFromBits<double>(..., -1); => U(0, 0.5)
// GenerateRealFromBits<double>(..., 1); => U(0, 2)
//
template <typename RealType, // Real type, either float or double.
typename SignedTag = GeneratePositiveTag, // Whether a positive,
// negative, or signed
// value is generated.
bool IncludeZero = true>
inline RealType GenerateRealFromBits(uint64_t bits, int exp_bias = 0) {
using real_type = RealType;
using uint_type = absl::conditional_t<std::is_same<real_type, float>::value,
uint32_t, uint64_t>;
static_assert(
(std::is_same<double, real_type>::value ||
std::is_same<float, real_type>::value),
"GenerateRealFromBits must be parameterized by either float or double.");
static_assert(sizeof(uint_type) == sizeof(real_type),
"Mismatched unsinged and real types.");
static_assert((std::numeric_limits<real_type>::is_iec559 &&
std::numeric_limits<real_type>::radix == 2),
"RealType representation is not IEEE 754 binary.");
static_assert((std::is_same<SignedTag, GeneratePositiveTag>::value ||
std::is_same<SignedTag, GenerateNegativeTag>::value ||
std::is_same<SignedTag, GenerateSignedTag>::value),
"");
static constexpr int kExp = std::numeric_limits<real_type>::digits - 1;
static constexpr uint_type kMask = (static_cast<uint_type>(1) << kExp) - 1u;
static constexpr int kUintBits = sizeof(uint_type) * 8;
int exp = exp_bias + int{std::numeric_limits<real_type>::max_exponent - 2};
// Determine the sign bit.
// Depending on the SignedTag, this may use the left-most bit
// or it may be a constant value.
uint_type sign = std::is_same<SignedTag, GenerateNegativeTag>::value
? (static_cast<uint_type>(1) << (kUintBits - 1))
: 0;
if (std::is_same<SignedTag, GenerateSignedTag>::value) {
if (std::is_same<uint_type, uint64_t>::value) {
sign = bits & uint64_t{0x8000000000000000};
}
if (std::is_same<uint_type, uint32_t>::value) {
const uint64_t tmp = bits & uint64_t{0x8000000000000000};
sign = static_cast<uint32_t>(tmp >> 32);
}
// adjust the bits and the exponent to account for removing
// the leading bit.
bits = bits & uint64_t{0x7FFFFFFFFFFFFFFF};
exp++;
}
if (IncludeZero) {
if (bits == 0u) return 0;
}
// Number of leading zeros is mapped to the exponent: 2^-clz
// bits is 0..01xxxxxx. After shifting, we're left with 1xxx...0..0
int clz = base_internal::CountLeadingZeros64(bits);
bits <<= (IncludeZero ? clz : (clz & 63)); // remove 0-bits.
exp -= clz; // set the exponent.
bits >>= (63 - kExp);
// Construct the 32-bit or 64-bit IEEE 754 floating-point value from
// the individual fields: sign, exp, mantissa(bits).
uint_type val =
(std::is_same<SignedTag, GeneratePositiveTag>::value ? 0u : sign) |
(static_cast<uint_type>(exp) << kExp) |
(static_cast<uint_type>(bits) & kMask);
// bit_cast to the output-type
real_type result;
memcpy(static_cast<void*>(&result), static_cast<const void*>(&val),
sizeof(result));
return result;
}
} // namespace random_internal
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_RANDOM_INTERNAL_GENERATE_REAL_H_
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