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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 #include #include #include #include "absl/meta/type_traits.h" #include "absl/numeric/bits.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: // GenerateRealFromBits; // // When a value in U(-1,1) is required, use: // GenerateRealFromBits; // // 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(..., -1); => U(0, 0.5) // GenerateRealFromBits(..., 1); => U(0, 2) // template inline RealType GenerateRealFromBits(uint64_t bits, int exp_bias = 0) { using real_type = RealType; using uint_type = absl::conditional_t::value, uint32_t, uint64_t>; static_assert( (std::is_same::value || std::is_same::value), "GenerateRealFromBits must be parameterized by either float or double."); static_assert(sizeof(uint_type) == sizeof(real_type), "Mismatched unsigned and real types."); static_assert((std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2), "RealType representation is not IEEE 754 binary."); static_assert((std::is_same::value || std::is_same::value || std::is_same::value), ""); static constexpr int kExp = std::numeric_limits::digits - 1; static constexpr uint_type kMask = (static_cast(1) << kExp) - 1u; static constexpr int kUintBits = sizeof(uint_type) * 8; int exp = exp_bias + int{std::numeric_limits::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::value ? (static_cast(1) << (kUintBits - 1)) : 0; if (std::is_same::value) { if (std::is_same::value) { sign = bits & uint64_t{0x8000000000000000}; } if (std::is_same::value) { const uint64_t tmp = bits & uint64_t{0x8000000000000000}; sign = static_cast(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 = countl_zero(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 = sign | (static_cast(exp) << kExp) | (static_cast(bits) & kMask); // bit_cast to the output-type real_type result; memcpy(static_cast(&result), static_cast(&val), sizeof(result)); return result; } } // namespace random_internal ABSL_NAMESPACE_END } // namespace absl #endif // ABSL_RANDOM_INTERNAL_GENERATE_REAL_H_