| // 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_ |