From 078b89b3c046d230ef3ad39494e5852184eb528b Mon Sep 17 00:00:00 2001 From: Abseil Team Date: Wed, 23 Oct 2019 19:35:39 -0700 Subject: Export of internal Abseil changes -- e54b9c7bbb0c58475676c268e2e19c69f4bce48a by Jorg Brown : Tweak ABSL_PREDICT_TRUE slightly, for better code on some platforms and/or optimization levels. "false || (x)" is more verbose than "!!(x)", but ultimately more efficient. For example, given this code: void InitIfNecessary() { if (ABSL_PREDICT_TRUE(NeedsInit())) { SlowInitIfNecessary(); } } Clang with default optimization level will produce: Before this CL After this CL InitIfNecessary: InitIfNecessary: push rbp push rbp mov rbp, rsp mov rbp, rsp call NeedsInit call NeedsInit xor al, -1 xor al, -1 test al, 1 test al, 1 jne .LBB2_1 jne .LBB3_1 jmp .LBB2_2 jmp .LBB3_2 .LBB2_1: .LBB3_1: call SlowInitIfNecessary call SlowInitIfNecessary .LBB2_2: .LBB3_2: pop rbp pop rbp ret ret PiperOrigin-RevId: 276401386 -- 0a3c4dfd8342bf2b1b11a87f1c662c883f73cab7 by Abseil Team : Fix comment nit: sem_open => sem_init. The code calls sem_init, not sem_open, to initialize an unnamed semaphore. (sem_open creates or opens a named semaphore.) PiperOrigin-RevId: 276344072 -- b36a664e9459057509a90e83d3482e1d3a4c44c7 by Abseil Team : Fix typo in flat_hash_map.h: exchaged -> exchanged PiperOrigin-RevId: 276295792 -- 7bbd8d18276eb110c8335743e35fceb662ddf3d6 by Samuel Benzaquen : Add assertions to verify use of iterators. PiperOrigin-RevId: 276283300 -- 677398a8ffcb1f59182cffe57a4fe7ff147a0404 by Laramie Leavitt : Migrate distribution_impl.h/cc to generate_real.h/cc. Combine the methods RandU64To into a single method: GenerateRealFromBits(). Remove rejection sampling from absl::uniform_real_distribution. PiperOrigin-RevId: 276158675 -- c60c9d11d24b0c546329d998e78e15a84b3153f5 by Abseil Team : Internal change PiperOrigin-RevId: 276126962 -- 4c840cab6a8d86efa29b397cafaf7520eece68cc by Andy Soffer : Update CMakeLists.txt to address https://github.com/abseil/abseil-cpp/issues/365. This does not cover every platform, but it does at least address the first-order issue of assuming gcc implies x86. PiperOrigin-RevId: 276116253 -- 98da366e6b5d51afe5d7ac6722126aca23d85ee6 by Abseil Team : Internal change PiperOrigin-RevId: 276097452 GitOrigin-RevId: e54b9c7bbb0c58475676c268e2e19c69f4bce48a Change-Id: I02d84454bb71ab21ad3d39650acf6cc6e36f58d7 --- absl/random/BUILD.bazel | 2 +- absl/random/CMakeLists.txt | 17 +- absl/random/beta_distribution.h | 31 +- absl/random/beta_distribution_test.cc | 2 +- absl/random/exponential_distribution.h | 14 +- absl/random/gaussian_distribution.h | 22 +- absl/random/internal/BUILD.bazel | 16 +- absl/random/internal/distribution_impl.h | 194 ---------- absl/random/internal/distribution_impl_test.cc | 464 ----------------------- absl/random/internal/generate_real.h | 144 +++++++ absl/random/internal/generate_real_test.cc | 497 +++++++++++++++++++++++++ absl/random/log_uniform_int_distribution.h | 2 +- absl/random/poisson_distribution.h | 20 +- absl/random/uniform_int_distribution.h | 1 - absl/random/uniform_real_distribution.h | 15 +- 15 files changed, 729 insertions(+), 712 deletions(-) delete mode 100644 absl/random/internal/distribution_impl.h delete mode 100644 absl/random/internal/distribution_impl_test.cc create mode 100644 absl/random/internal/generate_real.h create mode 100644 absl/random/internal/generate_real_test.cc (limited to 'absl/random') diff --git a/absl/random/BUILD.bazel b/absl/random/BUILD.bazel index 828f1348..c3520df8 100644 --- a/absl/random/BUILD.bazel +++ b/absl/random/BUILD.bazel @@ -69,10 +69,10 @@ cc_library( "//absl/base:base_internal", "//absl/base:core_headers", "//absl/meta:type_traits", - "//absl/random/internal:distribution_impl", "//absl/random/internal:distributions", "//absl/random/internal:fast_uniform_bits", "//absl/random/internal:fastmath", + "//absl/random/internal:generate_real", "//absl/random/internal:iostream_state_saver", "//absl/random/internal:traits", "//absl/random/internal:uniform_helper", diff --git a/absl/random/CMakeLists.txt b/absl/random/CMakeLists.txt index 19dd2cab..289854ff 100644 --- a/absl/random/CMakeLists.txt +++ b/absl/random/CMakeLists.txt @@ -58,7 +58,7 @@ absl_cc_library( DEPS absl::base_internal absl::core_headers - absl::random_internal_distribution_impl + absl::random_internal_generate_real absl::random_internal_distributions absl::random_internal_fast_uniform_bits absl::random_internal_fastmath @@ -543,19 +543,18 @@ absl_cc_library( # Internal-only target, do not depend on directly. absl_cc_library( NAME - random_internal_distribution_impl + random_internal_generate_real HDRS - "internal/distribution_impl.h" + "internal/generate_real.h" COPTS ${ABSL_DEFAULT_COPTS} LINKOPTS ${ABSL_DEFAULT_LINKOPTS} DEPS absl::bits - absl::config - absl::int128 absl::random_internal_fastmath absl::random_internal_traits + absl::type_traits ) # Internal-only target, do not depend on directly. @@ -767,9 +766,9 @@ absl_cc_test( # Internal-only target, do not depend on directly. absl_cc_test( NAME - random_internal_distribution_impl_test + random_internal_generate_real_test SRCS - "internal/distribution_impl_test.cc" + "internal/generate_real_test.cc" COPTS ${ABSL_TEST_COPTS} LINKOPTS @@ -777,8 +776,7 @@ absl_cc_test( DEPS absl::bits absl::flags - absl::int128 - absl::random_internal_distribution_impl + absl::random_internal_generate_real gtest_main ) @@ -1029,7 +1027,6 @@ absl_cc_library( ${ABSL_DEFAULT_LINKOPTS} DEPS absl::core_headers - absl::random_internal_distribution_impl absl::random_internal_fast_uniform_bits absl::random_internal_iostream_state_saver absl::random_internal_traits diff --git a/absl/random/beta_distribution.h b/absl/random/beta_distribution.h index e29894f2..b09b02f0 100644 --- a/absl/random/beta_distribution.h +++ b/absl/random/beta_distribution.h @@ -22,9 +22,10 @@ #include #include -#include "absl/random/internal/distribution_impl.h" +#include "absl/meta/type_traits.h" #include "absl/random/internal/fast_uniform_bits.h" #include "absl/random/internal/fastmath.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" namespace absl { @@ -275,15 +276,21 @@ typename beta_distribution::result_type beta_distribution::AlgorithmJoehnk( URBG& g, // NOLINT(runtime/references) const param_type& p) { + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + using real_type = + absl::conditional_t::value, float, double>; + // Based on Joehnk, M. D. Erzeugung von betaverteilten und gammaverteilten // Zufallszahlen. Metrika 8.1 (1964): 5-15. // This method is described in Knuth, Vol 2 (Third Edition), pp 134. - using RandU64ToReal = typename random_internal::RandU64ToReal; - using random_internal::PositiveValueT; + result_type u, v, x, y, z; for (;;) { - u = RandU64ToReal::template Value(fast_u64_(g)); - v = RandU64ToReal::template Value(fast_u64_(g)); + u = GenerateRealFromBits( + fast_u64_(g)); + v = GenerateRealFromBits( + fast_u64_(g)); // Direct method. std::pow is slow for float, so rely on the optimizer to // remove the std::pow() path for that case. @@ -327,12 +334,14 @@ typename beta_distribution::result_type beta_distribution::AlgorithmCheng( URBG& g, // NOLINT(runtime/references) const param_type& p) { + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + using real_type = + absl::conditional_t::value, float, double>; + // Based on Cheng, Russell CH. Generating beta variates with nonintegral // shape parameters. Communications of the ACM 21.4 (1978): 317-322. // (https://dl.acm.org/citation.cfm?id=359482). - using RandU64ToReal = typename random_internal::RandU64ToReal; - using random_internal::PositiveValueT; - static constexpr result_type kLogFour = result_type(1.3862943611198906188344642429163531361); // log(4) static constexpr result_type kS = @@ -341,8 +350,10 @@ beta_distribution::AlgorithmCheng( const bool use_algorithm_ba = (p.method_ == param_type::CHENG_BA); result_type u1, u2, v, w, z, r, s, t, bw_inv, lhs; for (;;) { - u1 = RandU64ToReal::template Value(fast_u64_(g)); - u2 = RandU64ToReal::template Value(fast_u64_(g)); + u1 = GenerateRealFromBits( + fast_u64_(g)); + u2 = GenerateRealFromBits( + fast_u64_(g)); v = p.y_ * std::log(u1 / (1 - u1)); w = p.a_ * std::exp(v); bw_inv = result_type(1) / (p.b_ + w); diff --git a/absl/random/beta_distribution_test.cc b/absl/random/beta_distribution_test.cc index 966ad08b..d0111b3e 100644 --- a/absl/random/beta_distribution_test.cc +++ b/absl/random/beta_distribution_test.cc @@ -92,7 +92,7 @@ TYPED_TEST(BetaDistributionInterfaceTest, SerializeTest) { for (TypeParam alpha : kValues) { for (TypeParam beta : kValues) { ABSL_INTERNAL_LOG( - INFO, absl::StrFormat("Smoke test for Beta(%f, %f)", alpha, beta)); + INFO, absl::StrFormat("Smoke test for Beta(%a, %a)", alpha, beta)); param_type param(alpha, beta); absl::beta_distribution before(alpha, beta); diff --git a/absl/random/exponential_distribution.h b/absl/random/exponential_distribution.h index c8af1975..24abf57e 100644 --- a/absl/random/exponential_distribution.h +++ b/absl/random/exponential_distribution.h @@ -21,8 +21,9 @@ #include #include -#include "absl/random/internal/distribution_impl.h" +#include "absl/meta/type_traits.h" #include "absl/random/internal/fast_uniform_bits.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" namespace absl { @@ -118,9 +119,14 @@ typename exponential_distribution::result_type exponential_distribution::operator()( URBG& g, // NOLINT(runtime/references) const param_type& p) { - using random_internal::NegativeValueT; - const result_type u = random_internal::RandU64ToReal< - result_type>::template Value(fast_u64_(g)); + using random_internal::GenerateNegativeTag; + using random_internal::GenerateRealFromBits; + using real_type = + absl::conditional_t::value, float, double>; + + const result_type u = GenerateRealFromBits(fast_u64_(g)); // U(-1, 0) + // log1p(-x) is mathematically equivalent to log(1 - x) but has more // accuracy for x near zero. return p.neg_inv_lambda_ * std::log1p(u); diff --git a/absl/random/gaussian_distribution.h b/absl/random/gaussian_distribution.h index 1d1347bc..c299e944 100644 --- a/absl/random/gaussian_distribution.h +++ b/absl/random/gaussian_distribution.h @@ -28,8 +28,8 @@ #include #include -#include "absl/random/internal/distribution_impl.h" #include "absl/random/internal/fast_uniform_bits.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" namespace absl { @@ -207,12 +207,18 @@ namespace random_internal { template inline double gaussian_distribution_base::zignor_fallback(URBG& g, bool neg) { + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + // This fallback path happens approximately 0.05% of the time. double x, y; do { // kRInv = 1/r, U(0, 1) - x = kRInv * std::log(RandU64ToDouble(fast_u64_(g))); - y = -std::log(RandU64ToDouble(fast_u64_(g))); + x = kRInv * + std::log(GenerateRealFromBits( + fast_u64_(g))); + y = -std::log( + GenerateRealFromBits(fast_u64_(g))); } while ((y + y) < (x * x)); return neg ? (x - kR) : (kR - x); } @@ -220,6 +226,10 @@ inline double gaussian_distribution_base::zignor_fallback(URBG& g, bool neg) { template inline double gaussian_distribution_base::zignor( URBG& g) { // NOLINT(runtime/references) + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + using random_internal::GenerateSignedTag; + while (true) { // We use a single uint64_t to generate both a double and a strip. // These bits are unused when the generated double is > 1/2^5. @@ -227,7 +237,8 @@ inline double gaussian_distribution_base::zignor( // values (those smaller than 1/2^5, which all end up on the left tail). uint64_t bits = fast_u64_(g); int i = static_cast(bits & kMask); // pick a random strip - double j = RandU64ToDouble(bits); // U(-1, 1) + double j = GenerateRealFromBits( + bits); // U(-1, 1) const double x = j * zg_.x[i]; // Retangular box. Handles >97% of all cases. @@ -244,7 +255,8 @@ inline double gaussian_distribution_base::zignor( } // i > 0: Wedge samples using precomputed values. - double v = RandU64ToDouble(fast_u64_(g)); // U(0, 1) + double v = GenerateRealFromBits( + fast_u64_(g)); // U(0, 1) if ((zg_.f[i + 1] + v * (zg_.f[i] - zg_.f[i + 1])) < std::exp(-0.5 * x * x)) { return x; diff --git a/absl/random/internal/BUILD.bazel b/absl/random/internal/BUILD.bazel index ec58cecd..91388d19 100644 --- a/absl/random/internal/BUILD.bazel +++ b/absl/random/internal/BUILD.bazel @@ -175,9 +175,9 @@ cc_library( ) cc_library( - name = "distribution_impl", + name = "generate_real", hdrs = [ - "distribution_impl.h", + "generate_real.h", ], copts = ABSL_DEFAULT_COPTS, linkopts = ABSL_DEFAULT_LINKOPTS, @@ -185,8 +185,7 @@ cc_library( ":fastmath", ":traits", "//absl/base:bits", - "//absl/base:config", - "//absl/numeric:int128", + "//absl/meta:type_traits", ], ) @@ -398,16 +397,17 @@ cc_test( ) cc_test( - name = "distribution_impl_test", + name = "generate_real_test", size = "small", - srcs = ["distribution_impl_test.cc"], + srcs = [ + "generate_real_test.cc", + ], copts = ABSL_TEST_COPTS, linkopts = ABSL_DEFAULT_LINKOPTS, deps = [ - ":distribution_impl", + ":generate_real", "//absl/base:bits", "//absl/flags:flag", - "//absl/numeric:int128", "@com_google_googletest//:gtest_main", ], ) diff --git a/absl/random/internal/distribution_impl.h b/absl/random/internal/distribution_impl.h deleted file mode 100644 index 49b3e1a6..00000000 --- a/absl/random/internal/distribution_impl.h +++ /dev/null @@ -1,194 +0,0 @@ -// 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 -#include -#include -#include -#include -#include - -#if (defined(_WIN32) || defined(_WIN64)) && defined(_M_IA64) -#include // 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(); -// -// When a value in U(-1,1) is required, use: -// RandU64ToDouble() => 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(); => U(0, 2) -// RandU64ToDouble(); => 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 -inline double RandU64ToDouble(uint64_t bits) { - static_assert(std::is_same::value || - std::is_same::value || - std::is_same::value, - ""); - - // Maybe use the left-most bit for a sign bit. - uint64_t sign = std::is_same::value - ? 0x8000000000000000ull - : 0; // Sign bits. - - if (std::is_same::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::value ? 1023U : 1022U) + - static_cast(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 -inline float RandU64ToFloat(uint64_t bits) { - static_assert(std::is_same::value || - std::is_same::value || - std::is_same::value, - ""); - - // Maybe use the left-most bit for a sign bit. - uint64_t sign = std::is_same::value - ? 0x80000000ul - : 0; // Sign bits. - - if (std::is_same::value) { - uint64_t a = bits & 0x8000000000000000ull; - sign = static_cast(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::value ? 127U : 126U) + - static_cast(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 -struct RandU64ToReal { - template - static inline Result Value(uint64_t bits) { - return RandU64ToDouble(bits); - } -}; - -template <> -struct RandU64ToReal { - template - static inline float Value(uint64_t bits) { - return RandU64ToFloat(bits); - } -}; - -} // namespace random_internal -} // namespace absl - -#endif // ABSL_RANDOM_INTERNAL_DISTRIBUTION_IMPL_H_ diff --git a/absl/random/internal/distribution_impl_test.cc b/absl/random/internal/distribution_impl_test.cc deleted file mode 100644 index fcc16904..00000000 --- a/absl/random/internal/distribution_impl_test.cc +++ /dev/null @@ -1,464 +0,0 @@ -// 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. - -#include "absl/random/internal/distribution_impl.h" - -#include "gtest/gtest.h" -#include "absl/base/internal/bits.h" -#include "absl/flags/flag.h" -#include "absl/numeric/int128.h" - -ABSL_FLAG(int64_t, absl_random_test_trials, 50000, - "Number of trials for the probability tests."); - -using absl::random_internal::NegativeValueT; -using absl::random_internal::PositiveValueT; -using absl::random_internal::RandU64ToDouble; -using absl::random_internal::RandU64ToFloat; -using absl::random_internal::SignedValueT; - -namespace { - -TEST(DistributionImplTest, U64ToFloat_Positive_NoZero_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), 2.710505431e-20f); - EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); - EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloat_Positive_Zero_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), 0.0); - EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); - EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloat_Negative_NoZero_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), -2.710505431e-20f); - EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f); - EXPECT_EQ(ToFloat(0x8000000000000000), -0.5); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloat_Signed_NoZero_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), 5.421010862e-20f); - EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); - EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); - EXPECT_EQ(ToFloat(0x8000000000000000), -5.421010862e-20f); - EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloat_Signed_Zero_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), 0); - EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); - EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); - EXPECT_EQ(ToFloat(0x8000000000000000), 0); - EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloat_Signed_Bias_Test) { - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - EXPECT_EQ(ToFloat(0x0000000000000000), 0); - EXPECT_EQ(ToFloat(0x0000000000000001), 2 * 1.084202172e-19f); - EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 2 * 0.9999999404f); - EXPECT_EQ(ToFloat(0x8000000000000000), 0); - EXPECT_EQ(ToFloat(0x8000000000000001), 2 * -1.084202172e-19f); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 2 * -0.9999999404f); -} - -TEST(DistributionImplTest, U64ToFloatTest) { - auto ToFloat = [](uint64_t a) -> float { - return RandU64ToFloat(a); - }; - - EXPECT_EQ(ToFloat(0x0000000000000000), 0.0f); - - EXPECT_EQ(ToFloat(0x8000000000000000), 0.5f); - EXPECT_EQ(ToFloat(0x8000000000000001), 0.5f); - EXPECT_EQ(ToFloat(0x800000FFFFFFFFFF), 0.5f); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); - - EXPECT_GT(ToFloat(0x0000000000000001), 0.0f); - - EXPECT_NE(ToFloat(0x7FFFFF0000000000), ToFloat(0x7FFFFEFFFFFFFFFF)); - - EXPECT_LT(ToFloat(0xFFFFFFFFFFFFFFFF), 1.0f); - int32_t two_to_24 = 1 << 24; - EXPECT_EQ(static_cast(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24), - two_to_24 - 1); - EXPECT_NE(static_cast(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24 * 2), - two_to_24 * 2 - 1); - EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFF0000000000)); - EXPECT_NE(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFEFFFFFFFFFF)); - EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF8000000000)); - EXPECT_NE(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF7FFFFFFFFF)); - EXPECT_EQ(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFC000000000)); - EXPECT_NE(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFBFFFFFFFFF)); - - // For values where every bit counts, the values scale as multiples of the - // input. - for (int i = 0; i < 100; ++i) { - EXPECT_EQ(i * ToFloat(0x0000000000000001), ToFloat(i)); - } - - // For each i: value generated from (1 << i). - float exp_values[64]; - exp_values[63] = 0.5f; - for (int i = 62; i >= 0; --i) exp_values[i] = 0.5f * exp_values[i + 1]; - constexpr uint64_t one = 1; - for (int i = 0; i < 64; ++i) { - EXPECT_EQ(ToFloat(one << i), exp_values[i]); - for (int j = 1; j < FLT_MANT_DIG && i - j >= 0; ++j) { - EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); - EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), - exp_values[i] + exp_values[i - j]); - } - for (int j = FLT_MANT_DIG; i - j >= 0; ++j) { - EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); - EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), exp_values[i]); - } - } -} - -TEST(DistributionImplTest, U64ToDouble_Positive_NoZero_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), 2.710505431213761085e-20); - EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x0000000000000002), 1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); -} - -TEST(DistributionImplTest, U64ToDouble_Positive_Zero_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); - EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); -} - -TEST(DistributionImplTest, U64ToDouble_Negative_NoZero_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), -2.710505431213761085e-20); - EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0x8000000000000000), -0.5); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); -} - -TEST(DistributionImplTest, U64ToDouble_Signed_NoZero_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); - EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); -} - -TEST(DistributionImplTest, U64ToDouble_Signed_Zero_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - EXPECT_EQ(ToDouble(0x0000000000000000), 0); - EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); - EXPECT_EQ(ToDouble(0x8000000000000000), 0); - EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); -} - -TEST(DistributionImplTest, U64ToDouble_Signed_Bias_Test) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - EXPECT_EQ(ToDouble(0x0000000000000000), 0); - EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19 / 2); - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978 / 2); - EXPECT_EQ(ToDouble(0x8000000000000000), 0); - EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19 / 2); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978 / 2); -} - -TEST(DistributionImplTest, U64ToDoubleTest) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); - EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); - - EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x7fffffffffffffef), 0.499999999999999944489); - EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); - - // For values > 0.5, RandU64ToDouble discards up to 11 bits. (64-53). - EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); - EXPECT_EQ(ToDouble(0x80000000000007FF), 0.5); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); - EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); - - EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFF), 1.0); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF800)); - EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF7FF)); - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); - EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFBFF)); - EXPECT_EQ(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFE00)); - EXPECT_NE(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFDFF)); - - EXPECT_EQ(ToDouble(0x1000000000000001), 0.0625); - EXPECT_EQ(ToDouble(0x2000000000000001), 0.125); - EXPECT_EQ(ToDouble(0x3000000000000001), 0.1875); - EXPECT_EQ(ToDouble(0x4000000000000001), 0.25); - EXPECT_EQ(ToDouble(0x5000000000000001), 0.3125); - EXPECT_EQ(ToDouble(0x6000000000000001), 0.375); - EXPECT_EQ(ToDouble(0x7000000000000001), 0.4375); - EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); - EXPECT_EQ(ToDouble(0x9000000000000001), 0.5625); - EXPECT_EQ(ToDouble(0xa000000000000001), 0.625); - EXPECT_EQ(ToDouble(0xb000000000000001), 0.6875); - EXPECT_EQ(ToDouble(0xc000000000000001), 0.75); - EXPECT_EQ(ToDouble(0xd000000000000001), 0.8125); - EXPECT_EQ(ToDouble(0xe000000000000001), 0.875); - EXPECT_EQ(ToDouble(0xf000000000000001), 0.9375); - - // Large powers of 2. - int64_t two_to_53 = int64_t{1} << 53; - EXPECT_EQ(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), - two_to_53 - 1); - EXPECT_NE(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53 * 2), - two_to_53 * 2 - 1); - - // For values where every bit counts, the values scale as multiples of the - // input. - for (int i = 0; i < 100; ++i) { - EXPECT_EQ(i * ToDouble(0x0000000000000001), ToDouble(i)); - } - - // For each i: value generated from (1 << i). - double exp_values[64]; - exp_values[63] = 0.5; - for (int i = 62; i >= 0; --i) exp_values[i] = 0.5 * exp_values[i + 1]; - constexpr uint64_t one = 1; - for (int i = 0; i < 64; ++i) { - EXPECT_EQ(ToDouble(one << i), exp_values[i]); - for (int j = 1; j < DBL_MANT_DIG && i - j >= 0; ++j) { - EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); - EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), - exp_values[i] + exp_values[i - j]); - } - for (int j = DBL_MANT_DIG; i - j >= 0; ++j) { - EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); - EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), exp_values[i]); - } - } -} - -TEST(DistributionImplTest, U64ToDoubleSignedTest) { - auto ToDouble = [](uint64_t a) { - return RandU64ToDouble(a); - }; - - EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); - - EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); - EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); - - const double e_plus = ToDouble(0x0000000000000001); - const double e_minus = ToDouble(0x8000000000000001); - EXPECT_EQ(e_plus, 1.084202172485504434e-19); - EXPECT_EQ(e_minus, -1.084202172485504434e-19); - - EXPECT_EQ(ToDouble(0x3fffffffffffffef), 0.499999999999999944489); - EXPECT_EQ(ToDouble(0xbfffffffffffffef), -0.499999999999999944489); - - // For values > 0.5, RandU64ToDouble discards up to 10 bits. (63-53). - EXPECT_EQ(ToDouble(0x4000000000000000), 0.5); - EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); - EXPECT_EQ(ToDouble(0x40000000000003FF), 0.5); - - EXPECT_EQ(ToDouble(0xC000000000000000), -0.5); - EXPECT_EQ(ToDouble(0xC000000000000001), -0.5); - EXPECT_EQ(ToDouble(0xC0000000000003FF), -0.5); - - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFe), 0.999999999999999888978); - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999999999888978); - - EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); - - EXPECT_LT(ToDouble(0x7FFFFFFFFFFFFFFF), 1.0); - EXPECT_GT(ToDouble(0x7FFFFFFFFFFFFFFF), 0.9999999999); - - EXPECT_GT(ToDouble(0xFFFFFFFFFFFFFFFe), -1.0); - EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999); - - EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFFC00)); - EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); - EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFF3FF)); - EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFF3FF)); - - EXPECT_EQ(ToDouble(0x1000000000000001), 0.125); - EXPECT_EQ(ToDouble(0x2000000000000001), 0.25); - EXPECT_EQ(ToDouble(0x3000000000000001), 0.375); - EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); - EXPECT_EQ(ToDouble(0x5000000000000001), 0.625); - EXPECT_EQ(ToDouble(0x6000000000000001), 0.75); - EXPECT_EQ(ToDouble(0x7000000000000001), 0.875); - EXPECT_EQ(ToDouble(0x7800000000000001), 0.9375); - EXPECT_EQ(ToDouble(0x7c00000000000001), 0.96875); - EXPECT_EQ(ToDouble(0x7e00000000000001), 0.984375); - EXPECT_EQ(ToDouble(0x7f00000000000001), 0.9921875); - - // 0x8000000000000000 ~= 0 - EXPECT_EQ(ToDouble(0x9000000000000001), -0.125); - EXPECT_EQ(ToDouble(0xa000000000000001), -0.25); - EXPECT_EQ(ToDouble(0xb000000000000001), -0.375); - EXPECT_EQ(ToDouble(0xc000000000000001), -0.5); - EXPECT_EQ(ToDouble(0xd000000000000001), -0.625); - EXPECT_EQ(ToDouble(0xe000000000000001), -0.75); - EXPECT_EQ(ToDouble(0xf000000000000001), -0.875); - - // Large powers of 2. - int64_t two_to_53 = int64_t{1} << 53; - EXPECT_EQ(static_cast(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53), - two_to_53 - 1); - EXPECT_EQ(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), - -(two_to_53 - 1)); - - EXPECT_NE(static_cast(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53 * 2), - two_to_53 * 2 - 1); - - // For values where every bit counts, the values scale as multiples of the - // input. - for (int i = 1; i < 100; ++i) { - EXPECT_EQ(i * e_plus, ToDouble(i)) << i; - EXPECT_EQ(i * e_minus, ToDouble(0x8000000000000000 | i)) << i; - } -} - -TEST(DistributionImplTest, ExhaustiveFloat) { - using absl::base_internal::CountLeadingZeros64; - auto ToFloat = [](uint64_t a) { - return RandU64ToFloat(a); - }; - - // Rely on RandU64ToFloat generating values from greatest to least when - // supplied with uint64_t values from greatest (0xfff...) to least (0x0). Thus, - // this algorithm stores the previous value, and if the new value is at - // greater than or equal to the previous value, then there is a collision in - // the generation algorithm. - // - // Use the computation below to convert the random value into a result: - // double res = a() * (1.0f - sample) + b() * sample; - float last_f = 1.0, last_g = 2.0; - uint64_t f_collisions = 0, g_collisions = 0; - uint64_t f_unique = 0, g_unique = 0; - uint64_t total = 0; - auto count = [&](const float r) { - total++; - // `f` is mapped to the range [0, 1) (default) - const float f = 0.0f * (1.0f - r) + 1.0f * r; - if (f >= last_f) { - f_collisions++; - } else { - f_unique++; - last_f = f; - } - // `g` is mapped to the range [1, 2) - const float g = 1.0f * (1.0f - r) + 2.0f * r; - if (g >= last_g) { - g_collisions++; - } else { - g_unique++; - last_g = g; - } - }; - - size_t limit = absl::GetFlag(FLAGS_absl_random_test_trials); - - // Generate all uint64_t which have unique floating point values. - // Counting down from 0xFFFFFFFFFFFFFFFFu ... 0x0u - uint64_t x = ~uint64_t(0); - for (; x != 0 && limit > 0;) { - constexpr int kDig = (64 - FLT_MANT_DIG); - // Set a decrement value & the next point at which to change - // the decrement value. By default these are 1, 0. - uint64_t dec = 1; - uint64_t chk = 0; - - // Adjust decrement and check value based on how many leading 0 - // bits are set in the current value. - const int clz = CountLeadingZeros64(x); - if (clz < kDig) { - dec <<= (kDig - clz); - chk = (~uint64_t(0)) >> (clz + 1); - } - for (; x > chk && limit > 0; x -= dec) { - count(ToFloat(x)); - --limit; - } - } - - static_assert(FLT_MANT_DIG == 24, - "The float type is expected to have a 24 bit mantissa."); - - if (limit != 0) { - // There are between 2^28 and 2^29 unique values in the range [0, 1). For - // the low values of x, there are 2^24 -1 unique values. Once x > 2^24, - // there are 40 * 2^24 unique values. Thus: - // (2 + 4 + 8 ... + 2^23) + 40 * 2^23 - EXPECT_LT(1 << 28, f_unique); - EXPECT_EQ((1 << 24) + 40 * (1 << 23) - 1, f_unique); - EXPECT_EQ(total, f_unique); - EXPECT_EQ(0, f_collisions); - - // Expect at least 2^23 unique values for the range [1, 2) - EXPECT_LE(1 << 23, g_unique); - EXPECT_EQ(total - g_unique, g_collisions); - } -} - -} // namespace diff --git a/absl/random/internal/generate_real.h b/absl/random/internal/generate_real.h new file mode 100644 index 00000000..246d863e --- /dev/null +++ b/absl/random/internal/generate_real.h @@ -0,0 +1,144 @@ +// 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/base/internal/bits.h" +#include "absl/meta/type_traits.h" +#include "absl/random/internal/fastmath.h" +#include "absl/random/internal/traits.h" + +namespace absl { +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; +// +// When a value in U(-1,1) is required, use: +// Uniform64ToReal; +// +// 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 unsinged 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 = 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::value ? 0u : 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 +} // namespace absl + +#endif // ABSL_RANDOM_INTERNAL_GENERATE_REAL_H_ diff --git a/absl/random/internal/generate_real_test.cc b/absl/random/internal/generate_real_test.cc new file mode 100644 index 00000000..aa02f0c2 --- /dev/null +++ b/absl/random/internal/generate_real_test.cc @@ -0,0 +1,497 @@ +// 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. + +#include "absl/random/internal/generate_real.h" + +#include +#include +#include +#include + +#include "gtest/gtest.h" +#include "absl/base/internal/bits.h" +#include "absl/flags/flag.h" + +ABSL_FLAG(int64_t, absl_random_test_trials, 50000, + "Number of trials for the probability tests."); + +using absl::random_internal::GenerateNegativeTag; +using absl::random_internal::GeneratePositiveTag; +using absl::random_internal::GenerateRealFromBits; +using absl::random_internal::GenerateSignedTag; + +namespace { + +TEST(GenerateRealTest, U64ToFloat_Positive_NoZero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 2.710505431e-20f); + EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); + EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); + EXPECT_EQ(ToFloat(0x8000000000000001), 0.5); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Positive_Zero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 0.0); + EXPECT_EQ(ToFloat(0x0000000000000001), 5.421010862e-20f); + EXPECT_EQ(ToFloat(0x8000000000000000), 0.5); + EXPECT_EQ(ToFloat(0x8000000000000001), 0.5); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Negative_NoZero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), -2.710505431e-20f); + EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f); + EXPECT_EQ(ToFloat(0x8000000000000000), -0.5); + EXPECT_EQ(ToFloat(0x8000000000000001), -0.5); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Negative_Zero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 0.0); + EXPECT_EQ(ToFloat(0x0000000000000001), -5.421010862e-20f); + EXPECT_EQ(ToFloat(0x8000000000000000), -0.5); + EXPECT_EQ(ToFloat(0x8000000000000001), -0.5); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Signed_NoZero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 5.421010862e-20f); + EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); + EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); + EXPECT_EQ(ToFloat(0x8000000000000000), -5.421010862e-20f); + EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Signed_Zero_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 0); + EXPECT_EQ(ToFloat(0x0000000000000001), 1.084202172e-19f); + EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 0.9999999404f); + EXPECT_EQ(ToFloat(0x8000000000000000), 0); + EXPECT_EQ(ToFloat(0x8000000000000001), -1.084202172e-19f); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), -0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloat_Signed_Bias_Test) { + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a, 1); + }; + EXPECT_EQ(ToFloat(0x0000000000000000), 0); + EXPECT_EQ(ToFloat(0x0000000000000001), 2 * 1.084202172e-19f); + EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), 2 * 0.9999999404f); + EXPECT_EQ(ToFloat(0x8000000000000000), 0); + EXPECT_EQ(ToFloat(0x8000000000000001), 2 * -1.084202172e-19f); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 2 * -0.9999999404f); +} + +TEST(GenerateRealTest, U64ToFloatTest) { + auto ToFloat = [](uint64_t a) -> float { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToFloat(0x0000000000000000), 0.0f); + + EXPECT_EQ(ToFloat(0x8000000000000000), 0.5f); + EXPECT_EQ(ToFloat(0x8000000000000001), 0.5f); + EXPECT_EQ(ToFloat(0x800000FFFFFFFFFF), 0.5f); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), 0.9999999404f); + + EXPECT_GT(ToFloat(0x0000000000000001), 0.0f); + + EXPECT_NE(ToFloat(0x7FFFFF0000000000), ToFloat(0x7FFFFEFFFFFFFFFF)); + + EXPECT_LT(ToFloat(0xFFFFFFFFFFFFFFFF), 1.0f); + int32_t two_to_24 = 1 << 24; + EXPECT_EQ(static_cast(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24), + two_to_24 - 1); + EXPECT_NE(static_cast(ToFloat(0xFFFFFFFFFFFFFFFF) * two_to_24 * 2), + two_to_24 * 2 - 1); + EXPECT_EQ(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFF0000000000)); + EXPECT_NE(ToFloat(0xFFFFFFFFFFFFFFFF), ToFloat(0xFFFFFEFFFFFFFFFF)); + EXPECT_EQ(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF8000000000)); + EXPECT_NE(ToFloat(0x7FFFFFFFFFFFFFFF), ToFloat(0x7FFFFF7FFFFFFFFF)); + EXPECT_EQ(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFC000000000)); + EXPECT_NE(ToFloat(0x3FFFFFFFFFFFFFFF), ToFloat(0x3FFFFFBFFFFFFFFF)); + + // For values where every bit counts, the values scale as multiples of the + // input. + for (int i = 0; i < 100; ++i) { + EXPECT_EQ(i * ToFloat(0x0000000000000001), ToFloat(i)); + } + + // For each i: value generated from (1 << i). + float exp_values[64]; + exp_values[63] = 0.5f; + for (int i = 62; i >= 0; --i) exp_values[i] = 0.5f * exp_values[i + 1]; + constexpr uint64_t one = 1; + for (int i = 0; i < 64; ++i) { + EXPECT_EQ(ToFloat(one << i), exp_values[i]); + for (int j = 1; j < FLT_MANT_DIG && i - j >= 0; ++j) { + EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); + EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), + exp_values[i] + exp_values[i - j]); + } + for (int j = FLT_MANT_DIG; i - j >= 0; ++j) { + EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); + EXPECT_EQ(ToFloat((one << i) + (one << (i - j))), exp_values[i]); + } + } +} + +TEST(GenerateRealTest, U64ToDouble_Positive_NoZero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 2.710505431213761085e-20); + EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x0000000000000002), 1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); + EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_Positive_Zero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); + EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); + EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_Negative_NoZero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), -2.710505431213761085e-20); + EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0x8000000000000000), -0.5); + EXPECT_EQ(ToDouble(0x8000000000000001), -0.5); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_Negative_Zero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); + EXPECT_EQ(ToDouble(0x0000000000000001), -5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x0000000000000002), -1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0x8000000000000000), -0.5); + EXPECT_EQ(ToDouble(0x8000000000000001), -0.5); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_Signed_NoZero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); + EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_Signed_Zero_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + EXPECT_EQ(ToDouble(0x0000000000000000), 0); + EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978); + EXPECT_EQ(ToDouble(0x8000000000000000), 0); + EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978); +} + +TEST(GenerateRealTest, U64ToDouble_GenerateSignedTag_Bias_Test) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a, -1); + }; + EXPECT_EQ(ToDouble(0x0000000000000000), 0); + EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19 / 2); + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), 0.999999999999999888978 / 2); + EXPECT_EQ(ToDouble(0x8000000000000000), 0); + EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19 / 2); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), -0.999999999999999888978 / 2); +} + +TEST(GenerateRealTest, U64ToDoubleTest) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); + EXPECT_EQ(ToDouble(0x0000000000000000), 0.0); + + EXPECT_EQ(ToDouble(0x0000000000000001), 5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x7fffffffffffffef), 0.499999999999999944489); + EXPECT_EQ(ToDouble(0x8000000000000000), 0.5); + + // For values > 0.5, RandU64ToDouble discards up to 11 bits. (64-53). + EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); + EXPECT_EQ(ToDouble(0x80000000000007FF), 0.5); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), 0.999999999999999888978); + EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); + + EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFF), 1.0); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF800)); + EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFF), ToDouble(0xFFFFFFFFFFFFF7FF)); + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); + EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFBFF)); + EXPECT_EQ(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFE00)); + EXPECT_NE(ToDouble(0x3FFFFFFFFFFFFFFF), ToDouble(0x3FFFFFFFFFFFFDFF)); + + EXPECT_EQ(ToDouble(0x1000000000000001), 0.0625); + EXPECT_EQ(ToDouble(0x2000000000000001), 0.125); + EXPECT_EQ(ToDouble(0x3000000000000001), 0.1875); + EXPECT_EQ(ToDouble(0x4000000000000001), 0.25); + EXPECT_EQ(ToDouble(0x5000000000000001), 0.3125); + EXPECT_EQ(ToDouble(0x6000000000000001), 0.375); + EXPECT_EQ(ToDouble(0x7000000000000001), 0.4375); + EXPECT_EQ(ToDouble(0x8000000000000001), 0.5); + EXPECT_EQ(ToDouble(0x9000000000000001), 0.5625); + EXPECT_EQ(ToDouble(0xa000000000000001), 0.625); + EXPECT_EQ(ToDouble(0xb000000000000001), 0.6875); + EXPECT_EQ(ToDouble(0xc000000000000001), 0.75); + EXPECT_EQ(ToDouble(0xd000000000000001), 0.8125); + EXPECT_EQ(ToDouble(0xe000000000000001), 0.875); + EXPECT_EQ(ToDouble(0xf000000000000001), 0.9375); + + // Large powers of 2. + int64_t two_to_53 = int64_t{1} << 53; + EXPECT_EQ(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), + two_to_53 - 1); + EXPECT_NE(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53 * 2), + two_to_53 * 2 - 1); + + // For values where every bit counts, the values scale as multiples of the + // input. + for (int i = 0; i < 100; ++i) { + EXPECT_EQ(i * ToDouble(0x0000000000000001), ToDouble(i)); + } + + // For each i: value generated from (1 << i). + double exp_values[64]; + exp_values[63] = 0.5; + for (int i = 62; i >= 0; --i) exp_values[i] = 0.5 * exp_values[i + 1]; + constexpr uint64_t one = 1; + for (int i = 0; i < 64; ++i) { + EXPECT_EQ(ToDouble(one << i), exp_values[i]); + for (int j = 1; j < DBL_MANT_DIG && i - j >= 0; ++j) { + EXPECT_NE(exp_values[i] + exp_values[i - j], exp_values[i]); + EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), + exp_values[i] + exp_values[i - j]); + } + for (int j = DBL_MANT_DIG; i - j >= 0; ++j) { + EXPECT_EQ(exp_values[i] + exp_values[i - j], exp_values[i]); + EXPECT_EQ(ToDouble((one << i) + (one << (i - j))), exp_values[i]); + } + } +} + +TEST(GenerateRealTest, U64ToDoubleSignedTest) { + auto ToDouble = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + EXPECT_EQ(ToDouble(0x0000000000000000), 5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x0000000000000001), 1.084202172485504434e-19); + + EXPECT_EQ(ToDouble(0x8000000000000000), -5.42101086242752217004e-20); + EXPECT_EQ(ToDouble(0x8000000000000001), -1.084202172485504434e-19); + + const double e_plus = ToDouble(0x0000000000000001); + const double e_minus = ToDouble(0x8000000000000001); + EXPECT_EQ(e_plus, 1.084202172485504434e-19); + EXPECT_EQ(e_minus, -1.084202172485504434e-19); + + EXPECT_EQ(ToDouble(0x3fffffffffffffef), 0.499999999999999944489); + EXPECT_EQ(ToDouble(0xbfffffffffffffef), -0.499999999999999944489); + + // For values > 0.5, RandU64ToDouble discards up to 10 bits. (63-53). + EXPECT_EQ(ToDouble(0x4000000000000000), 0.5); + EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); + EXPECT_EQ(ToDouble(0x40000000000003FF), 0.5); + + EXPECT_EQ(ToDouble(0xC000000000000000), -0.5); + EXPECT_EQ(ToDouble(0xC000000000000001), -0.5); + EXPECT_EQ(ToDouble(0xC0000000000003FF), -0.5); + + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFe), 0.999999999999999888978); + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999999999888978); + + EXPECT_NE(ToDouble(0x7FFFFFFFFFFFF800), ToDouble(0x7FFFFFFFFFFFF7FF)); + + EXPECT_LT(ToDouble(0x7FFFFFFFFFFFFFFF), 1.0); + EXPECT_GT(ToDouble(0x7FFFFFFFFFFFFFFF), 0.9999999999); + + EXPECT_GT(ToDouble(0xFFFFFFFFFFFFFFFe), -1.0); + EXPECT_LT(ToDouble(0xFFFFFFFFFFFFFFFe), -0.999999999); + + EXPECT_EQ(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFFC00)); + EXPECT_EQ(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFFC00)); + EXPECT_NE(ToDouble(0xFFFFFFFFFFFFFFFe), ToDouble(0xFFFFFFFFFFFFF3FF)); + EXPECT_NE(ToDouble(0x7FFFFFFFFFFFFFFF), ToDouble(0x7FFFFFFFFFFFF3FF)); + + EXPECT_EQ(ToDouble(0x1000000000000001), 0.125); + EXPECT_EQ(ToDouble(0x2000000000000001), 0.25); + EXPECT_EQ(ToDouble(0x3000000000000001), 0.375); + EXPECT_EQ(ToDouble(0x4000000000000001), 0.5); + EXPECT_EQ(ToDouble(0x5000000000000001), 0.625); + EXPECT_EQ(ToDouble(0x6000000000000001), 0.75); + EXPECT_EQ(ToDouble(0x7000000000000001), 0.875); + EXPECT_EQ(ToDouble(0x7800000000000001), 0.9375); + EXPECT_EQ(ToDouble(0x7c00000000000001), 0.96875); + EXPECT_EQ(ToDouble(0x7e00000000000001), 0.984375); + EXPECT_EQ(ToDouble(0x7f00000000000001), 0.9921875); + + // 0x8000000000000000 ~= 0 + EXPECT_EQ(ToDouble(0x9000000000000001), -0.125); + EXPECT_EQ(ToDouble(0xa000000000000001), -0.25); + EXPECT_EQ(ToDouble(0xb000000000000001), -0.375); + EXPECT_EQ(ToDouble(0xc000000000000001), -0.5); + EXPECT_EQ(ToDouble(0xd000000000000001), -0.625); + EXPECT_EQ(ToDouble(0xe000000000000001), -0.75); + EXPECT_EQ(ToDouble(0xf000000000000001), -0.875); + + // Large powers of 2. + int64_t two_to_53 = int64_t{1} << 53; + EXPECT_EQ(static_cast(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53), + two_to_53 - 1); + EXPECT_EQ(static_cast(ToDouble(0xFFFFFFFFFFFFFFFF) * two_to_53), + -(two_to_53 - 1)); + + EXPECT_NE(static_cast(ToDouble(0x7FFFFFFFFFFFFFFF) * two_to_53 * 2), + two_to_53 * 2 - 1); + + // For values where every bit counts, the values scale as multiples of the + // input. + for (int i = 1; i < 100; ++i) { + EXPECT_EQ(i * e_plus, ToDouble(i)) << i; + EXPECT_EQ(i * e_minus, ToDouble(0x8000000000000000 | i)) << i; + } +} + +TEST(GenerateRealTest, ExhaustiveFloat) { + using absl::base_internal::CountLeadingZeros64; + auto ToFloat = [](uint64_t a) { + return GenerateRealFromBits(a); + }; + + // Rely on RandU64ToFloat generating values from greatest to least when + // supplied with uint64_t values from greatest (0xfff...) to least (0x0). Thus, + // this algorithm stores the previous value, and if the new value is at + // greater than or equal to the previous value, then there is a collision in + // the generation algorithm. + // + // Use the computation below to convert the random value into a result: + // double res = a() * (1.0f - sample) + b() * sample; + float last_f = 1.0, last_g = 2.0; + uint64_t f_collisions = 0, g_collisions = 0; + uint64_t f_unique = 0, g_unique = 0; + uint64_t total = 0; + auto count = [&](const float r) { + total++; + // `f` is mapped to the range [0, 1) (default) + const float f = 0.0f * (1.0f - r) + 1.0f * r; + if (f >= last_f) { + f_collisions++; + } else { + f_unique++; + last_f = f; + } + // `g` is mapped to the range [1, 2) + const float g = 1.0f * (1.0f - r) + 2.0f * r; + if (g >= last_g) { + g_collisions++; + } else { + g_unique++; + last_g = g; + } + }; + + size_t limit = absl::GetFlag(FLAGS_absl_random_test_trials); + + // Generate all uint64_t which have unique floating point values. + // Counting down from 0xFFFFFFFFFFFFFFFFu ... 0x0u + uint64_t x = ~uint64_t(0); + for (; x != 0 && limit > 0;) { + constexpr int kDig = (64 - FLT_MANT_DIG); + // Set a decrement value & the next point at which to change + // the decrement value. By default these are 1, 0. + uint64_t dec = 1; + uint64_t chk = 0; + + // Adjust decrement and check value based on how many leading 0 + // bits are set in the current value. + const int clz = CountLeadingZeros64(x); + if (clz < kDig) { + dec <<= (kDig - clz); + chk = (~uint64_t(0)) >> (clz + 1); + } + for (; x > chk && limit > 0; x -= dec) { + count(ToFloat(x)); + --limit; + } + } + + static_assert(FLT_MANT_DIG == 24, + "The float type is expected to have a 24 bit mantissa."); + + if (limit != 0) { + // There are between 2^28 and 2^29 unique values in the range [0, 1). For + // the low values of x, there are 2^24 -1 unique values. Once x > 2^24, + // there are 40 * 2^24 unique values. Thus: + // (2 + 4 + 8 ... + 2^23) + 40 * 2^23 + EXPECT_LT(1 << 28, f_unique); + EXPECT_EQ((1 << 24) + 40 * (1 << 23) - 1, f_unique); + EXPECT_EQ(total, f_unique); + EXPECT_EQ(0, f_collisions); + + // Expect at least 2^23 unique values for the range [1, 2) + EXPECT_LE(1 << 23, g_unique); + EXPECT_EQ(total - g_unique, g_collisions); + } +} + +} // namespace diff --git a/absl/random/log_uniform_int_distribution.h b/absl/random/log_uniform_int_distribution.h index ac43416e..956a6907 100644 --- a/absl/random/log_uniform_int_distribution.h +++ b/absl/random/log_uniform_int_distribution.h @@ -23,8 +23,8 @@ #include #include -#include "absl/random/internal/distribution_impl.h" #include "absl/random/internal/fastmath.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" #include "absl/random/internal/traits.h" #include "absl/random/uniform_int_distribution.h" diff --git a/absl/random/poisson_distribution.h b/absl/random/poisson_distribution.h index 7750b1c9..23a953ff 100644 --- a/absl/random/poisson_distribution.h +++ b/absl/random/poisson_distribution.h @@ -22,9 +22,9 @@ #include #include -#include "absl/random/internal/distribution_impl.h" #include "absl/random/internal/fast_uniform_bits.h" #include "absl/random/internal/fastmath.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" namespace absl { @@ -164,9 +164,9 @@ typename poisson_distribution::result_type poisson_distribution::operator()( URBG& g, // NOLINT(runtime/references) const param_type& p) { - using random_internal::PositiveValueT; - using random_internal::RandU64ToDouble; - using random_internal::SignedValueT; + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + using random_internal::GenerateSignedTag; if (p.split_ != 0) { // Use Knuth's algorithm with range splitting to avoid floating-point @@ -186,7 +186,8 @@ poisson_distribution::operator()( for (int split = p.split_; split > 0; --split) { double r = 1.0; do { - r *= RandU64ToDouble(fast_u64_(g)); + r *= GenerateRealFromBits( + fast_u64_(g)); // U(-1, 0) ++n; } while (r > p.emu_); --n; @@ -205,10 +206,11 @@ poisson_distribution::operator()( // and k = max(f). const double a = p.mean_ + 0.5; for (;;) { - const double u = - RandU64ToDouble(fast_u64_(g)); // (0, 1) - const double v = - RandU64ToDouble(fast_u64_(g)); // (-1, 1) + const double u = GenerateRealFromBits( + fast_u64_(g)); // U(0, 1) + const double v = GenerateRealFromBits( + fast_u64_(g)); // U(-1, 1) + const double x = std::floor(p.s_ * v / u + a); if (x < 0) continue; // f(negative) = 0 const double rhs = x * p.lmu_; diff --git a/absl/random/uniform_int_distribution.h b/absl/random/uniform_int_distribution.h index 02aa3765..dc8ba8c1 100644 --- a/absl/random/uniform_int_distribution.h +++ b/absl/random/uniform_int_distribution.h @@ -34,7 +34,6 @@ #include #include "absl/base/optimization.h" -#include "absl/random/internal/distribution_impl.h" #include "absl/random/internal/fast_uniform_bits.h" #include "absl/random/internal/iostream_state_saver.h" #include "absl/random/internal/traits.h" diff --git a/absl/random/uniform_real_distribution.h b/absl/random/uniform_real_distribution.h index 336abb39..bf2ed2c5 100644 --- a/absl/random/uniform_real_distribution.h +++ b/absl/random/uniform_real_distribution.h @@ -39,8 +39,9 @@ #include #include -#include "absl/random/internal/distribution_impl.h" +#include "absl/meta/type_traits.h" #include "absl/random/internal/fast_uniform_bits.h" +#include "absl/random/internal/generate_real.h" #include "absl/random/internal/iostream_state_saver.h" namespace absl { @@ -76,6 +77,7 @@ class uniform_real_distribution { // is not possible, so value generation cannot use the full range of the // real type. assert(range_ <= (std::numeric_limits::max)()); + assert(std::isfinite(range_)); } result_type a() const { return lo_; } @@ -151,10 +153,15 @@ template typename uniform_real_distribution::result_type uniform_real_distribution::operator()( URBG& gen, const param_type& p) { // NOLINT(runtime/references) - using random_internal::PositiveValueT; + using random_internal::GeneratePositiveTag; + using random_internal::GenerateRealFromBits; + using real_type = + absl::conditional_t::value, float, double>; + while (true) { - const result_type sample = random_internal::RandU64ToReal< - result_type>::template Value(fast_u64_(gen)); + const result_type sample = + GenerateRealFromBits( + fast_u64_(gen)); const result_type res = p.a() + (sample * p.range_); if (res < p.b() || p.range_ <= 0 || !std::isfinite(p.range_)) { return res; -- cgit v1.2.3