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[libc] Implement log10f correctly rounded for all rounding modes. 

Based on RLIBM implementation similar to logf and log2f.  Most of the exceptional inputs are the exact powers of 10.

Reviewed By: sivachandra, zimmermann6, santoshn, jpl169

Differential Revision: https://reviews.llvm.org/D118093
This commit is contained in:
Tue Ly 2022-01-24 21:35:25 -05:00
parent a2505bd063
commit e581841e8c
15 changed files with 415 additions and 0 deletions
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1
libc/config/linux/aarch64/entrypoints.txt
View File

@ -145,6 +145,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.ldexp
libc.src.math.ldexpf
libc.src.math.ldexpl
libc.src.math.log10f
libc.src.math.log2f
libc.src.math.logf
libc.src.math.logb

1
libc/config/linux/x86_64/entrypoints.txt
View File

@ -144,6 +144,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.llround
libc.src.math.llroundf
libc.src.math.llroundl
libc.src.math.log10f
libc.src.math.log2f
libc.src.math.logf
libc.src.math.logb

2
libc/spec/stdc.td
View File

@ -396,6 +396,8 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"ldexpf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<IntType>]>,
FunctionSpec<"ldexpl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<IntType>]>,
FunctionSpec<"log10f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"log2f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"logf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

2
libc/src/math/CMakeLists.txt
View File

@ -116,6 +116,8 @@ add_math_entrypoint_object(ldexp)
add_math_entrypoint_object(ldexpf)
add_math_entrypoint_object(ldexpl)
add_math_entrypoint_object(log10f)
add_math_entrypoint_object(log2f)
add_math_entrypoint_object(logf)

14
libc/src/math/generic/CMakeLists.txt
View File

@ -666,6 +666,20 @@ add_object_library(
-Wno-c++17-extensions
)
add_entrypoint_object(
log10f
SRCS
log10f.cpp
HDRS
../log10f.h
DEPENDS
.common_constants
libc.src.__support.FPUtil.fputil
COMPILE_OPTIONS
-O3
-Wno-c++17-extensions
)
add_entrypoint_object(
log2f
SRCS

182
libc/src/math/generic/log10f.cpp Normal file
View File

@ -0,0 +1,182 @@
//===-- Single-precision log10(x) function --------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/log10f.h"
#include "common_constants.h" // Lookup table for (1/f)
#include "src/__support/FPUtil/BasicOperations.h"
#include "src/__support/FPUtil/FEnvUtils.h"
#include "src/__support/FPUtil/FMA.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/common.h"
// This is an algorithm for log10(x) in single precision which is
// correctly rounded for all rounding modes, based on the implementation of
// log10(x) from the RLIBM project at:
// https://people.cs.rutgers.edu/~sn349/rlibm
// Step 1 - Range reduction:
// For x = 2^m * 1.mant, log(x) = m * log10(2) + log10(1.m)
// If x is denormal, we normalize it by multiplying x by 2^23 and subtracting
// m by 23.
// Step 2 - Another range reduction:
// To compute log(1.mant), let f be the highest 8 bits including the hidden
// bit, and d be the difference (1.mant - f), i.e. the remaining 16 bits of the
// mantissa. Then we have the following approximation formula:
// log10(1.mant) = log10(f) + log10(1.mant / f)
// = log10(f) + log10(1 + d/f)
// ~ log10(f) + P(d/f)
// since d/f is sufficiently small.
// log10(f) and 1/f are then stored in two 2^7 = 128 entries look-up tables.
// Step 3 - Polynomial approximation:
// To compute P(d/f), we use a single degree-5 polynomial in double precision
// which provides correct rounding for all but few exception values.
// For more detail about how this polynomial is obtained, please refer to the
// papers:
// Lim, J. and Nagarakatte, S., "One Polynomial Approximation to Produce
// Correctly Rounded Results of an Elementary Function for Multiple
// Representations and Rounding Modes", Proceedings of the 49th ACM SIGPLAN
// Symposium on Principles of Programming Languages (POPL-2022), Philadelphia,
// USA, Jan. 16-22, 2022.
// https://people.cs.rutgers.edu/~sn349/papers/rlibmall-popl-2022.pdf
// Aanjaneya, M., Lim, J., and Nagarakatte, S., "RLibm-Prog: Progressive
// Polynomial Approximations for Fast Correctly Rounded Math Libraries",
// Dept. of Comp. Sci., Rutgets U., Technical Report DCS-TR-758, Nov. 2021.
// https://arxiv.org/pdf/2111.12852.pdf.
namespace __llvm_libc {
// Exact power of 10 in float:
// Lookup table for log10(f) = log10(1 + n*2^(-7)) where n = 0..127.
static constexpr double LOG10_F[128] = {
0x0.0000000000000p+0, 0x1.bafd47221ed26p-9, 0x1.b9476a4fcd10fp-8,
0x1.49b0851443684p-7, 0x1.b5e908eb13790p-7, 0x1.10a83a8446c78p-6,
0x1.45f4f5acb8be0p-6, 0x1.7adc3df3b1ff8p-6, 0x1.af5f92b00e610p-6,
0x1.e3806acbd058fp-6, 0x1.0ba01a8170000p-5, 0x1.25502c0fc314cp-5,
0x1.3ed1199a5e425p-5, 0x1.58238eeb353dap-5, 0x1.71483427d2a99p-5,
0x1.8a3fadeb847f4p-5, 0x1.a30a9d609efeap-5, 0x1.bba9a058dfd84p-5,
0x1.d41d5164facb4p-5, 0x1.ec6647eb58808p-5, 0x1.02428c1f08016p-4,
0x1.0e3d29d81165ep-4, 0x1.1a23445501816p-4, 0x1.25f5215eb594ap-4,
0x1.31b3055c47118p-4, 0x1.3d5d335c53179p-4, 0x1.48f3ed1df48fbp-4,
0x1.5477731973e85p-4, 0x1.5fe80488af4fdp-4, 0x1.6b45df6f3e2c9p-4,
0x1.769140a2526fdp-4, 0x1.81ca63d05a44ap-4, 0x1.8cf183886480dp-4,
0x1.9806d9414a209p-4, 0x1.a30a9d609efeap-4, 0x1.adfd07416be07p-4,
0x1.b8de4d3ab3d98p-4, 0x1.c3aea4a5c6effp-4, 0x1.ce6e41e463da5p-4,
0x1.d91d5866aa99cp-4, 0x1.e3bc1ab0e19fep-4, 0x1.ee4aba610f204p-4,
0x1.f8c9683468191p-4, 0x1.019c2a064b486p-3, 0x1.06cbd67a6c3b6p-3,
0x1.0bf3d0937c41cp-3, 0x1.11142f0811357p-3, 0x1.162d082ac9d10p-3,
0x1.1b3e71ec94f7bp-3, 0x1.204881dee8777p-3, 0x1.254b4d35e7d3cp-3,
0x1.2a46e8ca7ba2ap-3, 0x1.2f3b691c5a001p-3, 0x1.3428e2540096dp-3,
0x1.390f6844a0b83p-3, 0x1.3def0e6dfdf85p-3, 0x1.42c7e7fe3fc02p-3,
0x1.479a07d3b6411p-3, 0x1.4c65807e93338p-3, 0x1.512a644296c3dp-3,
0x1.55e8c518b10f8p-3, 0x1.5aa0b4b0988fap-3, 0x1.5f52447255c92p-3,
0x1.63fd857fc49bbp-3, 0x1.68a288b60b7fcp-3, 0x1.6d415eaf0906bp-3,
0x1.71da17c2b7e80p-3, 0x1.766cc40889e85p-3, 0x1.7af97358b9e04p-3,
0x1.7f80354d952a0p-3, 0x1.84011944bcb75p-3, 0x1.887c2e605e119p-3,
0x1.8cf183886480dp-3, 0x1.9161276ba2978p-3, 0x1.95cb2880f45bap-3,
0x1.9a2f95085a45cp-3, 0x1.9e8e7b0c0d4bep-3, 0x1.a2e7e8618c2d2p-3,
0x1.a73beaaaa22f4p-3, 0x1.ab8a8f56677fcp-3, 0x1.afd3e3a23b680p-3,
0x1.b417f49ab8807p-3, 0x1.b856cf1ca3105p-3, 0x1.bc907fd5d1c40p-3,
0x1.c0c5134610e26p-3, 0x1.c4f495c0002a2p-3, 0x1.c91f1369eb7cap-3,
0x1.cd44983e9e7bdp-3, 0x1.d165300e333f7p-3, 0x1.d580e67edc43dp-3,
0x1.d997c70da9b47p-3, 0x1.dda9dd0f4a329p-3, 0x1.e1b733b0c7381p-3,
0x1.e5bfd5f83d342p-3, 0x1.e9c3cec58f807p-3, 0x1.edc328d3184afp-3,
0x1.f1bdeeb654901p-3, 0x1.f5b42ae08c407p-3, 0x1.f9a5e79f76ac5p-3,
0x1.fd932f1ddb4d6p-3, 0x1.00be05b217844p-2, 0x1.02b0432c96ff0p-2,
0x1.04a054e139004p-2, 0x1.068e3fa282e3dp-2, 0x1.087a0832fa7acp-2,
0x1.0a63b3456c819p-2, 0x1.0c4b457d3193dp-2, 0x1.0e30c36e71a7fp-2,
0x1.1014319e661bdp-2, 0x1.11f594839a5bdp-2, 0x1.13d4f0862b2e1p-2,
0x1.15b24a0004a92p-2, 0x1.178da53d1ee01p-2, 0x1.1967067bb94b8p-2,
0x1.1b3e71ec94f7bp-2, 0x1.1d13ebb32d7f9p-2, 0x1.1ee777e5f0dc3p-2,
0x1.20b91a8e76105p-2, 0x1.2288d7a9b2b64p-2, 0x1.2456b3282f786p-2,
0x1.2622b0ee3b79dp-2, 0x1.27ecd4d41eb67p-2, 0x1.29b522a64b609p-2,
0x1.2b7b9e258e422p-2, 0x1.2d404b073e27ep-2, 0x1.2f032cf56a5bep-2,
0x1.30c4478f0835fp-2, 0x1.32839e681fc62p-2};
INLINE_FMA
LLVM_LIBC_FUNCTION(float, log10f, (float x)) {
constexpr double LOG10_2 = 0x1.34413509f79ffp-2;
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
double m = 0.0;
// Exact powers of 10 and other hard-to-round cases.
switch (xbits.uintval()) {
case 0x4120'0000U: // x = 10
return 1.0f;
case 0x42c8'0000U: // x = 100
return 2.0f;
case 0x447a'0000U: // x = 1,000
return 3.0f;
case 0x461c'4000U: // x = 10,000
return 4.0f;
case 0x47c3'5000U: // x = 100,000
return 5.0f;
case 0x4974'2400U: // x = 1,000,000
return 6.0f;
case 0x4b18'9680U: // x = 10,000,000
return 7.0f;
case 0x4cbe'bc20U: // x = 100,000,000
return 8.0f;
case 0x4e6e'6b28U: // x = 1,000,000,000
return 9.0f;
case 0x5015'02f9U: // x = 10,000,000,000
return 10.0f;
case 0x4f13'4f83U: // x = 2471461632.0
if (fputil::get_round() == FE_UPWARD)
return 0x1.2c9314p+3f;
break;
case 0x7956'ba5eU: { // x = 69683218960000541503257137270226944.0
int round_mode = fputil::get_round();
if (round_mode == FE_DOWNWARD || round_mode == FE_TOWARDZERO)
return 0x1.16bebap+5f;
break;
}
}
if (xbits.uintval() < FPBits::MIN_NORMAL ||
xbits.uintval() > FPBits::MAX_NORMAL) {
if (xbits.is_zero()) {
return static_cast<float>(FPBits::neg_inf());
}
if (xbits.get_sign() && !xbits.is_nan()) {
return FPBits::build_nan(1 << (fputil::MantissaWidth<float>::VALUE - 1));
}
if (xbits.is_inf_or_nan()) {
return x;
}
// Normalize denormal inputs.
xbits.val *= 0x1.0p23f;
m -= 23.0;
}
m += static_cast<double>(xbits.get_exponent());
// Set bits to 1.m
xbits.set_unbiased_exponent(0x7F);
int f_index = xbits.get_mantissa() >> 16;
FPBits f(xbits.val);
f.bits &= ~0x0000'FFFF;
double d = static_cast<float>(xbits) - static_cast<float>(f);
d *= ONE_OVER_F[f_index];
double extra_factor = fputil::fma(m, LOG10_2, LOG10_F[f_index]);
double r = fputil::polyeval(d, extra_factor, 0x1.bcb7b1526e4c5p-2,
-0x1.bcb7b1518a5e9p-3, 0x1.287a72a6f716p-3,
-0x1.bcadb40b85565p-4, 0x1.5e0bc97f97e22p-4);
return static_cast<float>(r);
}
} // namespace __llvm_libc

18
libc/src/math/log10f.h Normal file
View File

@ -0,0 +1,18 @@
//===-- Implementation header for log10f ------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_LIBC_SRC_MATH_LOG10F_H
#define LLVM_LIBC_SRC_MATH_LOG10F_H
namespace __llvm_libc {
float log10f(float x);
} // namespace __llvm_libc
#endif // LLVM_LIBC_SRC_MATH_LOG10F_H

13
libc/test/src/math/CMakeLists.txt
View File

@ -1211,6 +1211,19 @@ add_fp_unittest(
libc.src.__support.FPUtil.fputil
)
add_fp_unittest(
log10f_test
NEED_MPFR
SUITE
libc_math_unittests
SRCS
log10f_test.cpp
DEPENDS
libc.include.math
libc.src.math.log10f
libc.src.__support.FPUtil.fputil
)
add_subdirectory(generic)
add_subdirectory(exhaustive)
add_subdirectory(differential_testing)

11
libc/test/src/math/differential_testing/CMakeLists.txt
View File

@ -233,6 +233,17 @@ add_diff_binary(
-fno-builtin
)
add_diff_binary(
log10f_perf
SRCS
log10f_perf.cpp
DEPENDS
.single_input_single_output_diff
libc.src.math.log10f
COMPILE_OPTIONS
-fno-builtin
)
add_diff_binary(
log2f_diff
SRCS

16
libc/test/src/math/differential_testing/log10f_perf.cpp Normal file
View File

@ -0,0 +1,16 @@
//===-- Differential test for log10f --------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "SingleInputSingleOutputDiff.h"
#include "src/math/log10f.h"
#include <math.h>
SINGLE_INPUT_SINGLE_OUTPUT_PERF(float, __llvm_libc::log10f, ::log10f,
"log10f_perf.log")

17
libc/test/src/math/exhaustive/CMakeLists.txt
View File

@ -79,6 +79,23 @@ add_fp_unittest(
-lpthread
)
add_fp_unittest(
log10f_test
NO_RUN_POSTBUILD
NEED_MPFR
SUITE
libc_math_exhaustive_tests
SRCS
log10f_test.cpp
DEPENDS
.exhaustive_test
libc.include.math
libc.src.math.log10f
libc.src.__support.FPUtil.fputil
LINK_OPTIONS
-lpthread
)
add_fp_unittest(
log2f_test
NO_RUN_POSTBUILD

55
libc/test/src/math/exhaustive/log10f_test.cpp Normal file
View File

@ -0,0 +1,55 @@
//===-- Exhaustive test for log10f ----------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "exhaustive_test.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/math/log10f.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
#include "utils/UnitTest/FPMatcher.h"
using FPBits = __llvm_libc::fputil::FPBits<float>;
namespace mpfr = __llvm_libc::testing::mpfr;
struct LlvmLibcLog10fExhaustiveTest : public LlvmLibcExhaustiveTest<uint32_t> {
void check(uint32_t start, uint32_t stop,
mpfr::RoundingMode rounding) override {
mpfr::ForceRoundingMode r(rounding);
uint32_t bits = start;
do {
FPBits xbits(bits);
float x = float(xbits);
EXPECT_MPFR_MATCH(mpfr::Operation::Log10, x, __llvm_libc::log10f(x), 0.5,
rounding);
} while (bits++ < stop);
}
};
// Range: All non-negative;
static constexpr uint32_t START = 0x0000'0000U;
static constexpr uint32_t STOP = 0x7f80'0000U;
// Range: [1, 10];
// static constexpr uint32_t START = 0x3f80'0000U;
// static constexpr uint32_t STOP = 0x41c0'0000U;
static constexpr int NUM_THREADS = 16;
TEST_F(LlvmLibcLog10fExhaustiveTest, RoundNearestTieToEven) {
test_full_range(START, STOP, NUM_THREADS, mpfr::RoundingMode::Nearest);
}
TEST_F(LlvmLibcLog10fExhaustiveTest, RoundUp) {
test_full_range(START, STOP, NUM_THREADS, mpfr::RoundingMode::Upward);
}
TEST_F(LlvmLibcLog10fExhaustiveTest, RoundDown) {
test_full_range(START, STOP, NUM_THREADS, mpfr::RoundingMode::Downward);
}
TEST_F(LlvmLibcLog10fExhaustiveTest, RoundTowardZero) {
test_full_range(START, STOP, NUM_THREADS, mpfr::RoundingMode::TowardZero);
}

74
libc/test/src/math/log10f_test.cpp Normal file
View File

@ -0,0 +1,74 @@
//===-- Unittests for log10f ----------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/__support/FPUtil/FPBits.h"
#include "src/math/log10f.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
#include "utils/UnitTest/FPMatcher.h"
#include "utils/UnitTest/Test.h"
#include <math.h>
#include <errno.h>
#include <stdint.h>
namespace mpfr = __llvm_libc::testing::mpfr;
DECLARE_SPECIAL_CONSTANTS(float)
TEST(LlvmLibcLog10fTest, SpecialNumbers) {
EXPECT_FP_EQ(aNaN, __llvm_libc::log10f(aNaN));
EXPECT_FP_EQ(inf, __llvm_libc::log10f(inf));
EXPECT_TRUE(FPBits(__llvm_libc::log10f(neg_inf)).is_nan());
EXPECT_FP_EQ(neg_inf, __llvm_libc::log10f(0.0f));
EXPECT_FP_EQ(neg_inf, __llvm_libc::log10f(-0.0f));
EXPECT_TRUE(FPBits(__llvm_libc::log10f(-1.0f)).is_nan());
EXPECT_FP_EQ(zero, __llvm_libc::log10f(1.0f));
}
TEST(LlvmLibcLog10fTest, TrickyInputs) {
constexpr int N = 12;
constexpr uint32_t INPUTS[N] = {
0x41200000U /*10.0f*/,
0x42c80000U /*100.0f*/,
0x447a0000U /*1,000.0f*/,
0x461c4000U /*10,000.0f*/,
0x47c35000U /*100,000.0f*/,
0x49742400U /*1,000,000.0f*/,
0x4b189680U /*10,000,000.0f*/,
0x4cbebc20U /*100,000,000.0f*/,
0x4e6e6b28U /*1,000,000,000.0f*/,
0x501502f9U /*10,000,000,000.0f*/,
0x4f134f83U /*2471461632.0f*/,
0x7956ba5eU /*69683218960000541503257137270226944.0f*/};
for (int i = 0; i < N; ++i) {
float x = float(FPBits(INPUTS[i]));
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Log10, x,
__llvm_libc::log10f(x), 0.5);
}
}
TEST(LlvmLibcLog10fTest, InFloatRange) {
constexpr uint32_t COUNT = 1000000;
constexpr uint32_t STEP = UINT32_MAX / COUNT;
for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
float x = float(FPBits(v));
if (isnan(x) || isinf(x))
continue;
errno = 0;
float result = __llvm_libc::log10f(x);
// If the computation resulted in an error or did not produce valid result
// in the single-precision floating point range, then ignore comparing with
// MPFR result as MPFR can still produce valid results because of its
// wider precision.
if (isnan(result) || isinf(result) || errno != 0)
continue;
ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Log10, x,
__llvm_libc::log10f(x), 0.5);
}
}

8
libc/utils/MPFRWrapper/MPFRUtils.cpp
View File

@ -273,6 +273,12 @@ public:
return result;
}
MPFRNumber log10() const {
MPFRNumber result(*this);
mpfr_log10(result.value, value, mpfr_rounding);
return result;
}
MPFRNumber remquo(const MPFRNumber &divisor, int &quotient) {
MPFRNumber remainder(*this);
long q;
@ -502,6 +508,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
return mpfrInput.log();
case Operation::Log2:
return mpfrInput.log2();
case Operation::Log10:
return mpfrInput.log10();
case Operation::Mod2PI:
return mpfrInput.mod_2pi();
case Operation::ModPIOver2:

1
libc/utils/MPFRWrapper/MPFRUtils.h
View File

@ -32,6 +32,7 @@ enum class Operation : int {
Floor,
Log,
Log2,
Log10,
Mod2PI,
ModPIOver2,
ModPIOver4,