This is an archive of the discontinued LLVM Phabricator instance.

Differential D121574

[libc] Implement expm1f function that is correctly rounded for all rounding modes.
ClosedPublic

Authored by lntue on Mar 13 2022, 11:29 PM.

Details

Reviewers
michaelrj
sivachandra
zimmermann6
Commits
rG64af346b185a: [libc] Implement expm1f function that is correctly rounded for all rounding…
Summary

Implement expm1f function that is correctly rounded for all rounding modes. This is based on expf implementation.

From exhaustive testings, using expf implementation, and subtract 1.0 before rounding the final result to single precision
gives correctly rounded results for all |x| > 2^-4 with 1 exception. When |x| < 2^-25, we use x + x^2 (implemented with a
single fma). And for 2^-25 <= |x| <= 2^-4, we use a single degree-8 minimax polynomial generated by Sollya.

Diff Detail

Event Timeline

lntue created this revision.Mar 13 2022, 11:29 PM
Herald added projects: Restricted Project, Restricted Project. · View Herald TranscriptMar 13 2022, 11:29 PM
Herald added subscribers: ecnelises, tschuett, mgorny. · View Herald Transcript
lntue requested review of this revision.Mar 13 2022, 11:29 PM
Harbormaster completed remote builds in B154048: Diff 415011.Mar 13 2022, 11:34 PM
sivachandra accepted this revision.Mar 15 2022, 2:09 AM

OK for structure.

This revision is now accepted and ready to land.Mar 15 2022, 2:09 AM
zimmermann6 accepted this revision.Mar 15 2022, 7:00 AM

ok for me too, I confirm all exhaustive searchs do pass. Great!

Closed by commit rG64af346b185a: [libc] Implement expm1f function that is correctly rounded for all rounding… (authored by lntue). · Explain WhyMar 15 2022, 7:27 AM
This revision was automatically updated to reflect the committed changes.
lntue added a commit: rG64af346b185a: [libc] Implement expm1f function that is correctly rounded for all rounding….

Revision Contents

PathSize
libc/
src/
math/
generic/
7 lines
14 lines
124 lines
128 lines
151 lines
test/
src/
math/
exhaustive/
7 lines
3 lines
6 lines
76 lines
23 lines

Diff 415421

libc/src/math/generic/CMakeLists.txt

Show First 20 Lines • Show All 470 Lines • ▼ Show 20 Lines
add_entrypoint_object( add_entrypoint_object(
expf expf
SRCS SRCS
expf.cpp expf.cpp
HDRS HDRS
../expf.h ../expf.h
DEPENDS DEPENDS
.common_constants
libc.src.__support.FPUtil.fputil libc.src.__support.FPUtil.fputil
libc.include.math libc.include.math
COMPILE_OPTIONS COMPILE_OPTIONS
-O3 -O3
) )
add_entrypoint_object( add_entrypoint_object(
exp2f exp2f
Show All 10 Lines
add_entrypoint_object( add_entrypoint_object(
expm1f expm1f
SRCS SRCS
expm1f.cpp expm1f.cpp
HDRS HDRS
../expm1f.h ../expm1f.h
DEPENDS DEPENDS
.common_constants
libc.src.__support.FPUtil.fputil
libc.include.math libc.include.math
libc.src.math.expf COMPILE_OPTIONS
libc.src.math.fabsf -O3
) )
add_entrypoint_object( add_entrypoint_object(
copysign copysign
SRCS SRCS
copysign.cpp copysign.cpp
HDRS HDRS
../copysign.h ../copysign.h
▲ Show 20 Lines • Show All 561 Lines • Show Last 20 Lines

libc/src/math/generic/common_constants.h

Show All 11 Lines
namespace __llvm_libc { namespace __llvm_libc {
// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127. // Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
extern const double ONE_OVER_F[128]; extern const double ONE_OVER_F[128];
// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127. // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
extern const double LOG_F[128]; extern const double LOG_F[128];
// Lookup table for exp(m) with m = -104, ..., 89.
// -104 = floor(log(single precision's min denormal))
// 89 = ceil(log(single precision's max normal))
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from -104 to 89 do { D(exp(i)); };
extern const double EXP_M1[195];
// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from 0 to 127 do { D(exp(i / 128)); };
extern const double EXP_M2[128];
} // namespace __llvm_libc } // namespace __llvm_libc
#endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H #endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H

libc/src/math/generic/common_constants.cpp

Show First 20 Lines • Show All 96 Lines • ▼ Show 20 Linesconst double LOG_F[128] = {
0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1, 0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1,
0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1, 0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1,
0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1, 0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1,
0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1, 0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1,
0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1, 0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1,
0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1, 0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1}; 0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
// Lookup table for exp(m) with m = -104, ..., 89.
// -104 = floor(log(single precision's min denormal))
// 89 = ceil(log(single precision's max normal))
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from -104 to 89 do { D(exp(i)); };
const double EXP_M1[195] = {
0x1.f1e6b68529e33p-151, 0x1.525be4e4e601dp-149, 0x1.cbe0a45f75eb1p-148,
0x1.3884e838aea68p-146, 0x1.a8c1f14e2af5dp-145, 0x1.20a717e64a9bdp-143,
0x1.8851d84118908p-142, 0x1.0a9bdfb02d240p-140, 0x1.6a5bea046b42ep-139,
0x1.ec7f3b269efa8p-138, 0x1.4eafb87eab0f2p-136, 0x1.c6e2d05bbc000p-135,
0x1.35208867c2683p-133, 0x1.a425b317eeacdp-132, 0x1.1d8508fa8246ap-130,
0x1.840fbc08fdc8ap-129, 0x1.07b7112bc1ffep-127, 0x1.666d0dad2961dp-126,
0x1.e726c3f64d0fep-125, 0x1.4b0dc07cabf98p-123, 0x1.c1f2daf3b6a46p-122,
0x1.31c5957a47de2p-120, 0x1.9f96445648b9fp-119, 0x1.1a6baeadb4fd1p-117,
0x1.7fd974d372e45p-116, 0x1.04da4d1452919p-114, 0x1.62891f06b3450p-113,
0x1.e1dd273aa8a4ap-112, 0x1.4775e0840bfddp-110, 0x1.bd109d9d94bdap-109,
0x1.2e73f53fba844p-107, 0x1.9b138170d6bfep-106, 0x1.175af0cf60ec5p-104,
0x1.7baee1bffa80bp-103, 0x1.02057d1245cebp-101, 0x1.5eafffb34ba31p-100,
0x1.dca23bae16424p-99, 0x1.43e7fc88b8056p-97, 0x1.b83bf23a9a9ebp-96,
0x1.2b2b8dd05b318p-94, 0x1.969d47321e4ccp-93, 0x1.1452b7723aed2p-91,
0x1.778fe2497184cp-90, 0x1.fe7116182e9ccp-89, 0x1.5ae191a99585ap-87,
0x1.d775d87da854dp-86, 0x1.4063f8cc8bb98p-84, 0x1.b374b315f87c1p-83,
0x1.27ec458c65e3cp-81, 0x1.923372c67a074p-80, 0x1.1152eaeb73c08p-78,
0x1.737c5645114b5p-77, 0x1.f8e6c24b5592ep-76, 0x1.571db733a9d61p-74,
0x1.d257d547e083fp-73, 0x1.3ce9b9de78f85p-71, 0x1.aebabae3a41b5p-70,
0x1.24b6031b49bdap-68, 0x1.8dd5e1bb09d7ep-67, 0x1.0e5b73d1ff53dp-65,
0x1.6f741de1748ecp-64, 0x1.f36bd37f42f3ep-63, 0x1.536452ee2f75cp-61,
0x1.cd480a1b74820p-60, 0x1.39792499b1a24p-58, 0x1.aa0de4bf35b38p-57,
0x1.2188ad6ae3303p-55, 0x1.898471fca6055p-54, 0x1.0b6c3afdde064p-52,
0x1.6b7719a59f0e0p-51, 0x1.ee001eed62aa0p-50, 0x1.4fb547c775da8p-48,
0x1.c8464f7616468p-47, 0x1.36121e24d3bbap-45, 0x1.a56e0c2ac7f75p-44,
0x1.1e642baeb84a0p-42, 0x1.853f01d6d53bap-41, 0x1.0885298767e9ap-39,
0x1.67852a7007e42p-38, 0x1.e8a37a45fc32ep-37, 0x1.4c1078fe9228ap-35,
0x1.c3527e433fab1p-34, 0x1.32b48bf117da2p-32, 0x1.a0db0d0ddb3ecp-31,
0x1.1b48655f37267p-29, 0x1.81056ff2c5772p-28, 0x1.05a628c699fa1p-26,
0x1.639e3175a689dp-25, 0x1.e355bbaee85cbp-24, 0x1.4875ca227ec38p-22,
0x1.be6c6fdb01612p-21, 0x1.2f6053b981d98p-19, 0x1.9c54c3b43bc8bp-18,
0x1.18354238f6764p-16, 0x1.7cd79b5647c9bp-15, 0x1.02cf22526545ap-13,
0x1.5fc21041027adp-12, 0x1.de16b9c24a98fp-11, 0x1.44e51f113d4d6p-9,
0x1.b993fe00d5376p-8, 0x1.2c155b8213cf4p-6, 0x1.97db0ccceb0afp-5,
0x1.152aaa3bf81ccp-3, 0x1.78b56362cef38p-2, 0x1.0000000000000p+0,
0x1.5bf0a8b145769p+1, 0x1.d8e64b8d4ddaep+2, 0x1.415e5bf6fb106p+4,
0x1.b4c902e273a58p+5, 0x1.28d389970338fp+7, 0x1.936dc5690c08fp+8,
0x1.122885aaeddaap+10, 0x1.749ea7d470c6ep+11, 0x1.fa7157c470f82p+12,
0x1.5829dcf950560p+14, 0x1.d3c4488ee4f7fp+15, 0x1.3de1654d37c9ap+17,
0x1.b00b5916ac955p+18, 0x1.259ac48bf05d7p+20, 0x1.8f0ccafad2a87p+21,
0x1.0f2ebd0a80020p+23, 0x1.709348c0ea4f9p+24, 0x1.f4f22091940bdp+25,
0x1.546d8f9ed26e1p+27, 0x1.ceb088b68e804p+28, 0x1.3a6e1fd9eecfdp+30,
0x1.ab5adb9c43600p+31, 0x1.226af33b1fdc1p+33, 0x1.8ab7fb5475fb7p+34,
0x1.0c3d3920962c9p+36, 0x1.6c932696a6b5dp+37, 0x1.ef822f7f6731dp+38,
0x1.50bba3796379ap+40, 0x1.c9aae4631c056p+41, 0x1.370470aec28edp+43,
0x1.a6b765d8cdf6dp+44, 0x1.1f43fcc4b662cp+46, 0x1.866f34a725782p+47,
0x1.0953e2f3a1ef7p+49, 0x1.689e221bc8d5bp+50, 0x1.ea215a1d20d76p+51,
0x1.4d13fbb1a001ap+53, 0x1.c4b334617cc67p+54, 0x1.33a43d282a519p+56,
0x1.a220d397972ebp+57, 0x1.1c25c88df6862p+59, 0x1.8232558201159p+60,
0x1.0672a3c9eb871p+62, 0x1.64b41c6d37832p+63, 0x1.e4cf766fe49bep+64,
0x1.49767bc0483e3p+66, 0x1.bfc951eb8bb76p+67, 0x1.304d6aeca254bp+69,
0x1.9d97010884251p+70, 0x1.19103e4080b45p+72, 0x1.7e013cd114461p+73,
0x1.03996528e074cp+75, 0x1.60d4f6fdac731p+76, 0x1.df8c5af17ba3bp+77,
0x1.45e3076d61699p+79, 0x1.baed16a6e0da7p+80, 0x1.2cffdfebde1a1p+82,
0x1.9919cabefcb69p+83, 0x1.160345c9953e3p+85, 0x1.79dbc9dc53c66p+86,
0x1.00c810d464097p+88, 0x1.5d009394c5c27p+89, 0x1.da57de8f107a8p+90,
0x1.425982cf597cdp+92, 0x1.b61e5ca3a5e31p+93, 0x1.29bb825dfcf87p+95,
0x1.94a90db0d6fe2p+96, 0x1.12fec759586fdp+98, 0x1.75c1dc469e3afp+99,
0x1.fbfd219c43b04p+100, 0x1.5936d44e1a146p+102, 0x1.d531d8a7ee79cp+103,
0x1.3ed9d24a2d51bp+105, 0x1.b15cfe5b6e17bp+106, 0x1.268038c2c0e00p+108,
0x1.9044a73545d48p+109, 0x1.1002ab6218b38p+111, 0x1.71b3540cbf921p+112,
0x1.f6799ea9c414ap+113, 0x1.55779b984f3ebp+115, 0x1.d01a210c44aa4p+116,
0x1.3b63da8e91210p+118, 0x1.aca8d6b0116b8p+119, 0x1.234de9e0c74e9p+121,
0x1.8bec7503ca477p+122, 0x1.0d0eda9796b90p+124, 0x1.6db0118477245p+125,
0x1.f1056dc7bf22dp+126, 0x1.51c2cc3433801p+128, 0x1.cb108ffbec164p+129,
};
// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from 0 to 127 do { D(exp(i / 128)); };
const double EXP_M2[128] = {
0x1.0000000000000p0, 0x1.0202015600446p0, 0x1.04080ab55de39p0,
0x1.06122436410ddp0, 0x1.08205601127edp0, 0x1.0a32a84e9c1f6p0,
0x1.0c49236829e8cp0, 0x1.0e63cfa7ab09dp0, 0x1.1082b577d34edp0,
0x1.12a5dd543ccc5p0, 0x1.14cd4fc989cd6p0, 0x1.16f9157587069p0,
0x1.192937074e0cdp0, 0x1.1b5dbd3f68122p0, 0x1.1d96b0eff0e79p0,
0x1.1fd41afcba45ep0, 0x1.2216045b6f5cdp0, 0x1.245c7613b8a9bp0,
0x1.26a7793f60164p0, 0x1.28f7170a755fdp0, 0x1.2b4b58b372c79p0,
0x1.2da4478b620c7p0, 0x1.3001ecf601af7p0, 0x1.32645269ea829p0,
0x1.34cb8170b5835p0, 0x1.373783a722012p0, 0x1.39a862bd3c106p0,
0x1.3c1e2876834aap0, 0x1.3e98deaa11dccp0, 0x1.41188f42c3e32p0,
0x1.439d443f5f159p0, 0x1.462707b2bac21p0, 0x1.48b5e3c3e8186p0,
0x1.4b49e2ae5ac67p0, 0x1.4de30ec211e60p0, 0x1.50817263c13cdp0,
0x1.5325180cfacf7p0, 0x1.55ce0a4c58c7cp0, 0x1.587c53c5a7af0p0,
0x1.5b2fff3210fd9p0, 0x1.5de9176045ff5p0, 0x1.60a7a734ab0e8p0,
0x1.636bb9a983258p0, 0x1.663559cf1bc7cp0, 0x1.690492cbf9433p0,
0x1.6bd96fdd034a2p0, 0x1.6eb3fc55b1e76p0, 0x1.719443a03acb9p0,
0x1.747a513dbef6ap0, 0x1.776630c678bc1p0, 0x1.7a57ede9ea23ep0,
0x1.7d4f946f0ba8dp0, 0x1.804d30347b546p0, 0x1.8350cd30ac390p0,
0x1.865a7772164c5p0, 0x1.896a3b1f66a0ep0, 0x1.8c802477b0010p0,
0x1.8f9c3fd29beafp0, 0x1.92be99a09bf00p0, 0x1.95e73e6b1b75ep0,
0x1.99163ad4b1dccp0, 0x1.9c4b9b995509bp0, 0x1.9f876d8e8c566p0,
0x1.a2c9bda3a3e78p0, 0x1.a61298e1e069cp0, 0x1.a9620c6cb3374p0,
0x1.acb82581eee54p0, 0x1.b014f179fc3b8p0, 0x1.b3787dc80f95fp0,
0x1.b6e2d7fa5eb18p0, 0x1.ba540dba56e56p0, 0x1.bdcc2cccd3c85p0,
0x1.c14b431256446p0, 0x1.c4d15e873c193p0, 0x1.c85e8d43f7cd0p0,
0x1.cbf2dd7d490f2p0, 0x1.cf8e5d84758a9p0, 0x1.d3311bc7822b4p0,
0x1.d6db26d16cd67p0, 0x1.da8c8d4a66969p0, 0x1.de455df80e3c0p0,
0x1.e205a7bdab73ep0, 0x1.e5cd799c6a54ep0, 0x1.e99ce2b397649p0,
0x1.ed73f240dc142p0, 0x1.f152b7a07bb76p0, 0x1.f539424d90f5ep0,
0x1.f927a1e24bb76p0, 0x1.fd1de6182f8c9p0, 0x1.008e0f64294abp1,
0x1.02912df5ce72ap1, 0x1.049856cd84339p1, 0x1.06a39207f0a09p1,
0x1.08b2e7d2035cfp1, 0x1.0ac6606916501p1, 0x1.0cde041b0e9aep1,
0x1.0ef9db467dcf8p1, 0x1.1119ee5ac36b6p1, 0x1.133e45d82e952p1,
0x1.1566ea50201d7p1, 0x1.1793e4652cc50p1, 0x1.19c53ccb3fc6bp1,
0x1.1bfafc47bda73p1, 0x1.1e352bb1a74adp1, 0x1.2073d3f1bd518p1,
0x1.22b6fe02a3b9cp1, 0x1.24feb2f105cb8p1, 0x1.274afbdbba4a6p1,
0x1.299be1f3e7f1cp1, 0x1.2bf16e7d2a38cp1, 0x1.2e4baacdb6614p1,
0x1.30aaa04e80d05p1, 0x1.330e587b62b28p1, 0x1.3576dce33feadp1,
0x1.37e437282d4eep1, 0x1.3a5670ff972edp1, 0x1.3ccd9432682b4p1,
0x1.3f49aa9d30590p1, 0x1.41cabe304cb34p1, 0x1.4450d8f00edd4p1,
0x1.46dc04f4e5338p1, 0x1.496c4c6b832dap1, 0x1.4c01b9950a111p1,
0x1.4e9c56c731f5dp1, 0x1.513c2e6c731d7p1, 0x1.53e14b042f9cap1,
0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
};
} // namespace __llvm_libc } // namespace __llvm_libc

libc/src/math/generic/expf.cpp

//===-- Single-precision e^x function -------------------------------------===// //===-- Single-precision e^x function -------------------------------------===//
// //
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information. // See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// //
//===----------------------------------------------------------------------===// //===----------------------------------------------------------------------===//
#include "src/math/expf.h" #include "src/math/expf.h"
#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
#include "src/__support/FPUtil/BasicOperations.h" #include "src/__support/FPUtil/BasicOperations.h"
#include "src/__support/FPUtil/FEnvImpl.h" #include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FMA.h" #include "src/__support/FPUtil/FMA.h"
#include "src/__support/FPUtil/FPBits.h" #include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h" #include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/common.h" #include "src/__support/common.h"
#include <errno.h> #include <errno.h>
namespace __llvm_libc { namespace __llvm_libc {
// Lookup table for exp(m) with m = -104, ..., 89.
// -104 = floor(log(single precision's min denormal))
// 89 = ceil(log(single precision's max normal))
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from -104 to 89 do { D(exp(i)); };
static constexpr double EXP_M1[195] = {
0x1.f1e6b68529e33p-151, 0x1.525be4e4e601dp-149, 0x1.cbe0a45f75eb1p-148,
0x1.3884e838aea68p-146, 0x1.a8c1f14e2af5dp-145, 0x1.20a717e64a9bdp-143,
0x1.8851d84118908p-142, 0x1.0a9bdfb02d240p-140, 0x1.6a5bea046b42ep-139,
0x1.ec7f3b269efa8p-138, 0x1.4eafb87eab0f2p-136, 0x1.c6e2d05bbc000p-135,
0x1.35208867c2683p-133, 0x1.a425b317eeacdp-132, 0x1.1d8508fa8246ap-130,
0x1.840fbc08fdc8ap-129, 0x1.07b7112bc1ffep-127, 0x1.666d0dad2961dp-126,
0x1.e726c3f64d0fep-125, 0x1.4b0dc07cabf98p-123, 0x1.c1f2daf3b6a46p-122,
0x1.31c5957a47de2p-120, 0x1.9f96445648b9fp-119, 0x1.1a6baeadb4fd1p-117,
0x1.7fd974d372e45p-116, 0x1.04da4d1452919p-114, 0x1.62891f06b3450p-113,
0x1.e1dd273aa8a4ap-112, 0x1.4775e0840bfddp-110, 0x1.bd109d9d94bdap-109,
0x1.2e73f53fba844p-107, 0x1.9b138170d6bfep-106, 0x1.175af0cf60ec5p-104,
0x1.7baee1bffa80bp-103, 0x1.02057d1245cebp-101, 0x1.5eafffb34ba31p-100,
0x1.dca23bae16424p-99, 0x1.43e7fc88b8056p-97, 0x1.b83bf23a9a9ebp-96,
0x1.2b2b8dd05b318p-94, 0x1.969d47321e4ccp-93, 0x1.1452b7723aed2p-91,
0x1.778fe2497184cp-90, 0x1.fe7116182e9ccp-89, 0x1.5ae191a99585ap-87,
0x1.d775d87da854dp-86, 0x1.4063f8cc8bb98p-84, 0x1.b374b315f87c1p-83,
0x1.27ec458c65e3cp-81, 0x1.923372c67a074p-80, 0x1.1152eaeb73c08p-78,
0x1.737c5645114b5p-77, 0x1.f8e6c24b5592ep-76, 0x1.571db733a9d61p-74,
0x1.d257d547e083fp-73, 0x1.3ce9b9de78f85p-71, 0x1.aebabae3a41b5p-70,
0x1.24b6031b49bdap-68, 0x1.8dd5e1bb09d7ep-67, 0x1.0e5b73d1ff53dp-65,
0x1.6f741de1748ecp-64, 0x1.f36bd37f42f3ep-63, 0x1.536452ee2f75cp-61,
0x1.cd480a1b74820p-60, 0x1.39792499b1a24p-58, 0x1.aa0de4bf35b38p-57,
0x1.2188ad6ae3303p-55, 0x1.898471fca6055p-54, 0x1.0b6c3afdde064p-52,
0x1.6b7719a59f0e0p-51, 0x1.ee001eed62aa0p-50, 0x1.4fb547c775da8p-48,
0x1.c8464f7616468p-47, 0x1.36121e24d3bbap-45, 0x1.a56e0c2ac7f75p-44,
0x1.1e642baeb84a0p-42, 0x1.853f01d6d53bap-41, 0x1.0885298767e9ap-39,
0x1.67852a7007e42p-38, 0x1.e8a37a45fc32ep-37, 0x1.4c1078fe9228ap-35,
0x1.c3527e433fab1p-34, 0x1.32b48bf117da2p-32, 0x1.a0db0d0ddb3ecp-31,
0x1.1b48655f37267p-29, 0x1.81056ff2c5772p-28, 0x1.05a628c699fa1p-26,
0x1.639e3175a689dp-25, 0x1.e355bbaee85cbp-24, 0x1.4875ca227ec38p-22,
0x1.be6c6fdb01612p-21, 0x1.2f6053b981d98p-19, 0x1.9c54c3b43bc8bp-18,
0x1.18354238f6764p-16, 0x1.7cd79b5647c9bp-15, 0x1.02cf22526545ap-13,
0x1.5fc21041027adp-12, 0x1.de16b9c24a98fp-11, 0x1.44e51f113d4d6p-9,
0x1.b993fe00d5376p-8, 0x1.2c155b8213cf4p-6, 0x1.97db0ccceb0afp-5,
0x1.152aaa3bf81ccp-3, 0x1.78b56362cef38p-2, 0x1.0000000000000p+0,
0x1.5bf0a8b145769p+1, 0x1.d8e64b8d4ddaep+2, 0x1.415e5bf6fb106p+4,
0x1.b4c902e273a58p+5, 0x1.28d389970338fp+7, 0x1.936dc5690c08fp+8,
0x1.122885aaeddaap+10, 0x1.749ea7d470c6ep+11, 0x1.fa7157c470f82p+12,
0x1.5829dcf950560p+14, 0x1.d3c4488ee4f7fp+15, 0x1.3de1654d37c9ap+17,
0x1.b00b5916ac955p+18, 0x1.259ac48bf05d7p+20, 0x1.8f0ccafad2a87p+21,
0x1.0f2ebd0a80020p+23, 0x1.709348c0ea4f9p+24, 0x1.f4f22091940bdp+25,
0x1.546d8f9ed26e1p+27, 0x1.ceb088b68e804p+28, 0x1.3a6e1fd9eecfdp+30,
0x1.ab5adb9c43600p+31, 0x1.226af33b1fdc1p+33, 0x1.8ab7fb5475fb7p+34,
0x1.0c3d3920962c9p+36, 0x1.6c932696a6b5dp+37, 0x1.ef822f7f6731dp+38,
0x1.50bba3796379ap+40, 0x1.c9aae4631c056p+41, 0x1.370470aec28edp+43,
0x1.a6b765d8cdf6dp+44, 0x1.1f43fcc4b662cp+46, 0x1.866f34a725782p+47,
0x1.0953e2f3a1ef7p+49, 0x1.689e221bc8d5bp+50, 0x1.ea215a1d20d76p+51,
0x1.4d13fbb1a001ap+53, 0x1.c4b334617cc67p+54, 0x1.33a43d282a519p+56,
0x1.a220d397972ebp+57, 0x1.1c25c88df6862p+59, 0x1.8232558201159p+60,
0x1.0672a3c9eb871p+62, 0x1.64b41c6d37832p+63, 0x1.e4cf766fe49bep+64,
0x1.49767bc0483e3p+66, 0x1.bfc951eb8bb76p+67, 0x1.304d6aeca254bp+69,
0x1.9d97010884251p+70, 0x1.19103e4080b45p+72, 0x1.7e013cd114461p+73,
0x1.03996528e074cp+75, 0x1.60d4f6fdac731p+76, 0x1.df8c5af17ba3bp+77,
0x1.45e3076d61699p+79, 0x1.baed16a6e0da7p+80, 0x1.2cffdfebde1a1p+82,
0x1.9919cabefcb69p+83, 0x1.160345c9953e3p+85, 0x1.79dbc9dc53c66p+86,
0x1.00c810d464097p+88, 0x1.5d009394c5c27p+89, 0x1.da57de8f107a8p+90,
0x1.425982cf597cdp+92, 0x1.b61e5ca3a5e31p+93, 0x1.29bb825dfcf87p+95,
0x1.94a90db0d6fe2p+96, 0x1.12fec759586fdp+98, 0x1.75c1dc469e3afp+99,
0x1.fbfd219c43b04p+100, 0x1.5936d44e1a146p+102, 0x1.d531d8a7ee79cp+103,
0x1.3ed9d24a2d51bp+105, 0x1.b15cfe5b6e17bp+106, 0x1.268038c2c0e00p+108,
0x1.9044a73545d48p+109, 0x1.1002ab6218b38p+111, 0x1.71b3540cbf921p+112,
0x1.f6799ea9c414ap+113, 0x1.55779b984f3ebp+115, 0x1.d01a210c44aa4p+116,
0x1.3b63da8e91210p+118, 0x1.aca8d6b0116b8p+119, 0x1.234de9e0c74e9p+121,
0x1.8bec7503ca477p+122, 0x1.0d0eda9796b90p+124, 0x1.6db0118477245p+125,
0x1.f1056dc7bf22dp+126, 0x1.51c2cc3433801p+128, 0x1.cb108ffbec164p+129,
};
// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for i from 0 to 127 do { D(exp(i / 128)); };
static constexpr double EXP_M2[128] = {
0x1.0000000000000p0, 0x1.0202015600446p0, 0x1.04080ab55de39p0,
0x1.06122436410ddp0, 0x1.08205601127edp0, 0x1.0a32a84e9c1f6p0,
0x1.0c49236829e8cp0, 0x1.0e63cfa7ab09dp0, 0x1.1082b577d34edp0,
0x1.12a5dd543ccc5p0, 0x1.14cd4fc989cd6p0, 0x1.16f9157587069p0,
0x1.192937074e0cdp0, 0x1.1b5dbd3f68122p0, 0x1.1d96b0eff0e79p0,
0x1.1fd41afcba45ep0, 0x1.2216045b6f5cdp0, 0x1.245c7613b8a9bp0,
0x1.26a7793f60164p0, 0x1.28f7170a755fdp0, 0x1.2b4b58b372c79p0,
0x1.2da4478b620c7p0, 0x1.3001ecf601af7p0, 0x1.32645269ea829p0,
0x1.34cb8170b5835p0, 0x1.373783a722012p0, 0x1.39a862bd3c106p0,
0x1.3c1e2876834aap0, 0x1.3e98deaa11dccp0, 0x1.41188f42c3e32p0,
0x1.439d443f5f159p0, 0x1.462707b2bac21p0, 0x1.48b5e3c3e8186p0,
0x1.4b49e2ae5ac67p0, 0x1.4de30ec211e60p0, 0x1.50817263c13cdp0,
0x1.5325180cfacf7p0, 0x1.55ce0a4c58c7cp0, 0x1.587c53c5a7af0p0,
0x1.5b2fff3210fd9p0, 0x1.5de9176045ff5p0, 0x1.60a7a734ab0e8p0,
0x1.636bb9a983258p0, 0x1.663559cf1bc7cp0, 0x1.690492cbf9433p0,
0x1.6bd96fdd034a2p0, 0x1.6eb3fc55b1e76p0, 0x1.719443a03acb9p0,
0x1.747a513dbef6ap0, 0x1.776630c678bc1p0, 0x1.7a57ede9ea23ep0,
0x1.7d4f946f0ba8dp0, 0x1.804d30347b546p0, 0x1.8350cd30ac390p0,
0x1.865a7772164c5p0, 0x1.896a3b1f66a0ep0, 0x1.8c802477b0010p0,
0x1.8f9c3fd29beafp0, 0x1.92be99a09bf00p0, 0x1.95e73e6b1b75ep0,
0x1.99163ad4b1dccp0, 0x1.9c4b9b995509bp0, 0x1.9f876d8e8c566p0,
0x1.a2c9bda3a3e78p0, 0x1.a61298e1e069cp0, 0x1.a9620c6cb3374p0,
0x1.acb82581eee54p0, 0x1.b014f179fc3b8p0, 0x1.b3787dc80f95fp0,
0x1.b6e2d7fa5eb18p0, 0x1.ba540dba56e56p0, 0x1.bdcc2cccd3c85p0,
0x1.c14b431256446p0, 0x1.c4d15e873c193p0, 0x1.c85e8d43f7cd0p0,
0x1.cbf2dd7d490f2p0, 0x1.cf8e5d84758a9p0, 0x1.d3311bc7822b4p0,
0x1.d6db26d16cd67p0, 0x1.da8c8d4a66969p0, 0x1.de455df80e3c0p0,
0x1.e205a7bdab73ep0, 0x1.e5cd799c6a54ep0, 0x1.e99ce2b397649p0,
0x1.ed73f240dc142p0, 0x1.f152b7a07bb76p0, 0x1.f539424d90f5ep0,
0x1.f927a1e24bb76p0, 0x1.fd1de6182f8c9p0, 0x1.008e0f64294abp1,
0x1.02912df5ce72ap1, 0x1.049856cd84339p1, 0x1.06a39207f0a09p1,
0x1.08b2e7d2035cfp1, 0x1.0ac6606916501p1, 0x1.0cde041b0e9aep1,
0x1.0ef9db467dcf8p1, 0x1.1119ee5ac36b6p1, 0x1.133e45d82e952p1,
0x1.1566ea50201d7p1, 0x1.1793e4652cc50p1, 0x1.19c53ccb3fc6bp1,
0x1.1bfafc47bda73p1, 0x1.1e352bb1a74adp1, 0x1.2073d3f1bd518p1,
0x1.22b6fe02a3b9cp1, 0x1.24feb2f105cb8p1, 0x1.274afbdbba4a6p1,
0x1.299be1f3e7f1cp1, 0x1.2bf16e7d2a38cp1, 0x1.2e4baacdb6614p1,
0x1.30aaa04e80d05p1, 0x1.330e587b62b28p1, 0x1.3576dce33feadp1,
0x1.37e437282d4eep1, 0x1.3a5670ff972edp1, 0x1.3ccd9432682b4p1,
0x1.3f49aa9d30590p1, 0x1.41cabe304cb34p1, 0x1.4450d8f00edd4p1,
0x1.46dc04f4e5338p1, 0x1.496c4c6b832dap1, 0x1.4c01b9950a111p1,
0x1.4e9c56c731f5dp1, 0x1.513c2e6c731d7p1, 0x1.53e14b042f9cap1,
0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
};
INLINE_FMA INLINE_FMA
LLVM_LIBC_FUNCTION(float, expf, (float x)) { LLVM_LIBC_FUNCTION(float, expf, (float x)) {
using FPBits = typename fputil::FPBits<float>; using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x); FPBits xbits(x);
// When x < log(2^-150) or nan // When x < log(2^-150) or nan
if (unlikely(xbits.uintval() >= 0xc2cf'f1b5U)) { if (unlikely(xbits.uintval() >= 0xc2cf'f1b5U)) {
// exp(-Inf) = 0 // exp(-Inf) = 0
if (xbits.is_inf()) if (xbits.is_inf())
return 0.0f; return 0.0f;
// exp(nan) = nan // exp(nan) = nan
if (xbits.is_nan()) if (xbits.is_nan())
return x; return x;
if (fputil::get_round() == FE_UPWARD) if (fputil::get_round() == FE_UPWARD)
return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL)); return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
if (x != 0.0f)
errno = ERANGE; errno = ERANGE;
return 0.0f; return 0.0f;
} }
// x >= 89 or nan // x >= 89 or nan
if (unlikely(!xbits.get_sign() && (xbits.uintval() >= 0x42b2'0000))) { if (unlikely(!xbits.get_sign() && (xbits.uintval() >= 0x42b2'0000))) {
if (xbits.uintval() < 0x7f80'0000U) { if (xbits.uintval() < 0x7f80'0000U) {
int rounding = fputil::get_round(); int rounding = fputil::get_round();
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
return static_cast<float>(FPBits(FPBits::MAX_NORMAL)); return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
▲ Show 20 Lines • Show All 55 Lines • Show Last 20 Lines

libc/src/math/generic/expm1f.cpp

//===-- Implementation of expm1f function ---------------------------------===// //===-- Single-precision e^x - 1 function ---------------------------------===//
// //
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information. // See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// //
//===----------------------------------------------------------------------===// //===----------------------------------------------------------------------===//
#include "src/math/expm1f.h" #include "src/math/expm1f.h"
#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
#include "src/__support/FPUtil/BasicOperations.h" #include "src/__support/FPUtil/BasicOperations.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FMA.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h" #include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/common.h" #include "src/__support/common.h"
#include "src/math/expf.h"
#include <errno.h>
namespace __llvm_libc { namespace __llvm_libc {
// When |x| > Ln2, catastrophic cancellation does not occur with the
// subtraction expf(x) - 1.0f, so we use it to compute expm1f(x).
//
// We divide [-Ln2; Ln2] into 3 subintervals [-Ln2; -1/8], [-1/8; 1/8],
// [1/8; Ln2]. And we use a degree-6 polynomial to approximate exp(x) - 1 in
// each interval. The coefficients were generated by Sollya's fpminmax.
//
// See libc/utils/mathtools/expm1f.sollya for more detail.
INLINE_FMA INLINE_FMA
LLVM_LIBC_FUNCTION(float, expm1f, (float x)) { LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
const float ln2 = using FPBits = typename fputil::FPBits<float>;
0.69314718055994530941723212145817656807550013436025f; // For C++17: FPBits xbits(x);
// 0x1.62e'42ffp-1
float abs_x = __llvm_libc::fputil::abs(x); // When x < log(2^-25) or nan
if (unlikely(xbits.uintval() >= 0xc18a'a123U)) {
if (abs_x <= ln2) { // exp(-Inf) = 0
if (abs_x <= 0.125f) { if (xbits.is_inf())
return x * __llvm_libc::fputil::polyeval( return -1.0f;
x, 1.0f, 0.5f, 0.16666664183139801025390625f, // exp(nan) = nan
4.1666664183139801025390625e-2f, if (xbits.is_nan())
8.3379410207271575927734375e-3f, return x;
1.3894210569560527801513671875e-3f); int round_mode = fputil::get_round();
} if (round_mode == FE_UPWARD || round_mode == FE_TOWARDZERO)
if (x > 0.125f) { return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
return __llvm_libc::fputil::polyeval( return -1.0f;
x, 1.23142086749794543720781803131103515625e-7f, }
0.9999969005584716796875f, 0.500031292438507080078125f, // x >= 89 or nan
0.16650259494781494140625f, 4.21491153538227081298828125e-2f, if (unlikely(!xbits.get_sign() && (xbits.uintval() >= 0x42b2'0000))) {
7.53940828144550323486328125e-3f, if (xbits.uintval() < 0x7f80'0000U) {
2.05591344274580478668212890625e-3f); int rounding = fputil::get_round();
} if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
return __llvm_libc::fputil::polyeval( return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
x, -6.899231408397099585272371768951416015625e-8f,
0.999998271465301513671875f, 0.4999825656414031982421875f, errno = ERANGE;
0.16657467186450958251953125f, 4.1390590369701385498046875e-2f, }
7.856394164264202117919921875e-3f, return x + static_cast<float>(FPBits::inf());
9.380675037391483783721923828125e-4f); }
int unbiased_exponent = static_cast<int>(xbits.get_unbiased_exponent());
// |x| < 2^-4
if (unbiased_exponent < 123) {
// |x| < 2^-25
if (unbiased_exponent < 102) {
// x = -0.0f
if (unlikely(xbits.uintval() == 0x8000'0000U))
return x;
// When |x| < 2^-25, the relative error:
// |(e^x - 1) - x| / |x| < |x^2| / |x| = |x| < 2^-25 < epsilon(1)/2.
// So the correctly rounded values of expm1(x) are:
// = x + eps(x) if rounding mode = FE_UPWARD,
// or (rounding mode = FE_TOWARDZERO and x is negative),
// = x otherwise.
// To simplify the rounding decision and make it more efficient, we use
// fma(x, x, x) ~ x + x^2 instead.
return fputil::fma(x, x, x);
}
// 2^-25 <= |x| < 2^-4
double xd = static_cast<double>(x);
double xsq = xd * xd;
// Degree-8 minimax polynomial generated by Sollya with:
// > display = hexadecimal;
// > P = fpminimax(expm1(x)/x, 7, [|D...|], [-2^-4, 2^-4]);
double r =
fputil::polyeval(xd, 0x1p-1, 0x1.55555555559abp-3, 0x1.55555555551a7p-5,
0x1.111110f70f2a4p-7, 0x1.6c16c17639e82p-10,
0x1.a02526febbea6p-13, 0x1.a01dc40888fcdp-16);
return static_cast<float>(fputil::fma(r, xsq, xd));
}
// For -18 < x < 89, to compute exp(x), we perform the following range
// reduction: find hi, mid, lo such that:
// x = hi + mid + lo, in which
// hi is an integer,
// mid * 2^7 is an integer
// -2^(-8) <= lo < 2^-8.
// In particular,
// hi + mid = round(x * 2^7) * 2^(-7).
// Then,
// exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
// We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
// respectively. exp(lo) is computed using a degree-7 minimax polynomial
// generated by Sollya.
// Exceptional value
if (xbits.uintval() == 0xbdc1'c6cbU) {
// x = -0x1.838d96p-4f
int round_mode = fputil::get_round();
if (round_mode == FE_TONEAREST || round_mode == FE_DOWNWARD)
return -0x1.71c884p-4f;
return -0x1.71c882p-4f;
}
// x_hi = hi + mid.
int x_hi = static_cast<int>(x * 0x1.0p7f);
// Subtract (hi + mid) from x to get lo.
x -= static_cast<float>(x_hi) * 0x1.0p-7f;
double xd = static_cast<double>(x);
// Make sure that -2^(-8) <= lo < 2^-8.
if (x >= 0x1.0p-8f) {
++x_hi;
xd -= 0x1.0p-7;
}
if (x < -0x1.0p-8f) {
--x_hi;
xd += 0x1.0p-7;
} }
return expf(x) - 1.0f; x_hi += 104 << 7;
// hi = x_hi >> 7
double exp_hi = EXP_M1[x_hi >> 7];
// lo = x_hi & 0x0000'007fU;
double exp_mid = EXP_M2[x_hi & 0x7f];
double exp_hi_mid = exp_hi * exp_mid;
// Degree-7 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
// > Q = fpminimax(expm1(x)/x, 6, [|D...|], [-2^-8, 2^-8]);
// > Q;
double exp_lo = fputil::polyeval(
xd, 0x1p0, 0x1p0, 0x1p-1, 0x1.5555555555555p-3, 0x1.55555555553ap-5,
0x1.1111111204dfcp-7, 0x1.6c16cb2da593ap-10, 0x1.9ff1648996d2ep-13);
return static_cast<float>(fputil::fma(exp_hi_mid, exp_lo, -1.0));
} }
} // namespace __llvm_libc } // namespace __llvm_libc

libc/test/src/math/exhaustive/CMakeLists.txt

Show First 20 Lines • Show All 77 Lines • ▼ Show 20 Lines DEPENDS
libc.src.math.exp2f libc.src.math.exp2f
libc.src.__support.FPUtil.fputil libc.src.__support.FPUtil.fputil
LINK_OPTIONS LINK_OPTIONS
-lpthread -lpthread
) )
add_fp_unittest( add_fp_unittest(
expm1f_test expm1f_test
NO_RUN_POSTBUILD
NEED_MPFR NEED_MPFR
SUITE SUITE
libc_math_exhaustive_tests libc_math_exhaustive_tests
SRCS SRCS
expm1f_test.cpp expm1f_test.cpp
DEPENDS DEPENDS
.exhaustive_test
libc.include.math libc.include.math
libc.src.math.expf
libc.src.math.expm1f libc.src.math.expm1f
libc.src.__support.FPUtil.fputil libc.src.__support.FPUtil.fputil
LINK_OPTIONS
-lpthread
) )
add_fp_unittest( add_fp_unittest(
logf_test logf_test
NO_RUN_POSTBUILD NO_RUN_POSTBUILD
NEED_MPFR NEED_MPFR
SUITE SUITE
libc_math_exhaustive_tests libc_math_exhaustive_tests
▲ Show 20 Lines • Show All 80 Lines • Show Last 20 Lines

libc/test/src/math/exhaustive/exhaustive_test.h

Show All 16 Lines
template <typename T> template <typename T>
struct LlvmLibcExhaustiveTest : public __llvm_libc::testing::Test { struct LlvmLibcExhaustiveTest : public __llvm_libc::testing::Test {
// Break [start, stop) into `nthreads` subintervals and apply *check to each // Break [start, stop) into `nthreads` subintervals and apply *check to each
// subinterval in parallel. // subinterval in parallel.
void test_full_range(T start, T stop, int nthreads, void test_full_range(T start, T stop, int nthreads,
mpfr::RoundingMode rounding); mpfr::RoundingMode rounding);
virtual void check(T start, T stop, mpfr::RoundingMode rounding) = 0; virtual void check(T start, T stop, mpfr::RoundingMode rounding,
bool &result) = 0;
}; };

libc/test/src/math/exhaustive/exhaustive_test.cpp

Show All 26 Linesvoid LlvmLibcExhaustiveTest<T>::test_full_range(T start, T stop, int nthreads,
for (int i = 0; i < nthreads; ++i) { for (int i = 0; i < nthreads; ++i) {
thread_list.emplace_back([this, begin, end, rounding]() { thread_list.emplace_back([this, begin, end, rounding]() {
std::stringstream msg; std::stringstream msg;
msg << "-- Testing from " << begin << " to " << end << " [0x" << std::hex msg << "-- Testing from " << begin << " to " << end << " [0x" << std::hex
<< begin << ", 0x" << end << ") ..." << std::endl; << begin << ", 0x" << end << ") ..." << std::endl;
std::cout << msg.str(); std::cout << msg.str();
msg.str(""); msg.str("");
check(begin, end, rounding); bool result;
check(begin, end, rounding, result);
msg << "** Finished testing from " << std::dec << begin << " to " << end msg << "** Finished testing from " << std::dec << begin << " to " << end
<< " [0x" << std::hex << begin << ", 0x" << end << ")" << std::endl; << " [0x" << std::hex << begin << ", 0x" << end
<< ") : " << (result ? "PASSED" : "FAILED") << std::endl;
std::cout << msg.str(); std::cout << msg.str();
}); });
begin += increment; begin += increment;
end += increment; end += increment;
if (end > stop) if (end > stop)
end = stop; end = stop;
} }
for (auto &thread : thread_list) { for (auto &thread : thread_list) {
Show All 12 Lines

libc/test/src/math/exhaustive/expm1f_test.cpp

//===-- Exhaustive test for expm1f-----------------------------------------===// //===-- Exhaustive test for expm1f ----------------------------------------===//
// //
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information. // See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// //
//===----------------------------------------------------------------------===// //===----------------------------------------------------------------------===//
#include "exhaustive_test.h"
#include "src/__support/FPUtil/FPBits.h" #include "src/__support/FPUtil/FPBits.h"
#include "src/math/expm1f.h" #include "src/math/expm1f.h"
#include "utils/MPFRWrapper/MPFRUtils.h" #include "utils/MPFRWrapper/MPFRUtils.h"
#include <math.h> #include "utils/UnitTest/FPMatcher.h"
using FPBits = __llvm_libc::fputil::FPBits<float>; using FPBits = __llvm_libc::fputil::FPBits<float>;
namespace mpfr = __llvm_libc::testing::mpfr; namespace mpfr = __llvm_libc::testing::mpfr;
TEST(LlvmLibcExpm1fExhaustiveTest, AllValues) { struct LlvmLibcExpfExhaustiveTest : public LlvmLibcExhaustiveTest<uint32_t> {
uint32_t bits = 0; void check(uint32_t start, uint32_t stop, mpfr::RoundingMode rounding,
bool &result) override {
mpfr::ForceRoundingMode r(rounding);
uint32_t bits = start;
result = false;
do { do {
FPBits x(bits); FPBits xbits(bits);
if (!x.is_inf_or_nan() && float(x) < 88.70f) { float x = float(xbits);
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, float(x), EXPECT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 0.5,
__llvm_libc::expm1f(float(x)), 1.5); rounding);
} while (bits++ < stop);
result = true;
} }
} while (bits++ < 0xffff'ffffU); };
static constexpr int NUM_THREADS = 16;
// Range: [0, 89];
static constexpr uint32_t POS_START = 0x0000'0000U;
static constexpr uint32_t POS_STOP = 0x42b2'0000U;
TEST_F(LlvmLibcExpfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
test_full_range(POS_START, POS_STOP, NUM_THREADS,
mpfr::RoundingMode::Nearest);
}
TEST_F(LlvmLibcExpfExhaustiveTest, PostiveRangeRoundUp) {
test_full_range(POS_START, POS_STOP, NUM_THREADS, mpfr::RoundingMode::Upward);
}
TEST_F(LlvmLibcExpfExhaustiveTest, PostiveRangeRoundDown) {
test_full_range(POS_START, POS_STOP, NUM_THREADS,
mpfr::RoundingMode::Downward);
}
TEST_F(LlvmLibcExpfExhaustiveTest, PostiveRangeRoundTowardZero) {
test_full_range(POS_START, POS_STOP, NUM_THREADS,
mpfr::RoundingMode::TowardZero);
}
// Range: [-104, 0];
static constexpr uint32_t NEG_START = 0x8000'0000U;
static constexpr uint32_t NEG_STOP = 0xc2d0'0000U;
TEST_F(LlvmLibcExpfExhaustiveTest, NegativeRangeRoundNearestTieToEven) {
test_full_range(NEG_START, NEG_STOP, NUM_THREADS,
mpfr::RoundingMode::Nearest);
}
TEST_F(LlvmLibcExpfExhaustiveTest, NegativeRangeRoundUp) {
test_full_range(NEG_START, NEG_STOP, NUM_THREADS, mpfr::RoundingMode::Upward);
}
TEST_F(LlvmLibcExpfExhaustiveTest, NegativeRangeRoundDown) {
test_full_range(NEG_START, NEG_STOP, NUM_THREADS,
mpfr::RoundingMode::Downward);
}
TEST_F(LlvmLibcExpfExhaustiveTest, NegativeRangeRoundTowardZero) {
test_full_range(NEG_START, NEG_STOP, NUM_THREADS,
mpfr::RoundingMode::TowardZero);
} }

libc/test/src/math/expm1f_test.cpp

Show First 20 Lines • Show All 48 Lines • ▼ Show 20 LinesTEST(LlvmLibcExpm1fTest, Overflow) {
EXPECT_FP_EQ(inf, __llvm_libc::expm1f(float(FPBits(0x42d00008U)))); EXPECT_FP_EQ(inf, __llvm_libc::expm1f(float(FPBits(0x42d00008U))));
EXPECT_MATH_ERRNO(ERANGE); EXPECT_MATH_ERRNO(ERANGE);
} }
TEST(LlvmLibcExpm1fTest, Underflow) { TEST(LlvmLibcExpm1fTest, Underflow) {
errno = 0; errno = 0;
EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(float(FPBits(0xff7fffffU)))); EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(float(FPBits(0xff7fffffU))));
EXPECT_MATH_ERRNO(ERANGE);
float x = float(FPBits(0xc2cffff8U)); float x = float(FPBits(0xc2cffff8U));
EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(x)); EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(x));
EXPECT_MATH_ERRNO(ERANGE);
x = float(FPBits(0xc2d00008U)); x = float(FPBits(0xc2d00008U));
EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(x)); EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(x));
EXPECT_MATH_ERRNO(ERANGE);
} }
// Test with inputs which are the borders of underflow/overflow but still // Test with inputs which are the borders of underflow/overflow but still
// produce valid results without setting errno. // produce valid results without setting errno.
TEST(LlvmLibcExpm1fTest, Borderline) { TEST(LlvmLibcExpm1fTest, Borderline) {
float x; float x;
errno = 0; errno = 0;
x = float(FPBits(0x42affff8U)); x = float(FPBits(0x42affff8U));
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 1.0); ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0); EXPECT_MATH_ERRNO(0);
x = float(FPBits(0x42b00008U)); x = float(FPBits(0x42b00008U));
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 1.0); ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0); EXPECT_MATH_ERRNO(0);
x = float(FPBits(0xc2affff8U)); x = float(FPBits(0xc2affff8U));
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 1.0); ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0); EXPECT_MATH_ERRNO(0);
x = float(FPBits(0xc2b00008U)); x = float(FPBits(0xc2b00008U));
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 1.0); ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0);
x = float(FPBits(0x3dc252ddU));
ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0); EXPECT_MATH_ERRNO(0);
} }
TEST(LlvmLibcExpm1fTest, InFloatRange) { TEST(LlvmLibcExpm1fTest, InFloatRange) {
constexpr uint32_t COUNT = 1000000; constexpr uint32_t COUNT = 1000000;
constexpr uint32_t STEP = UINT32_MAX / COUNT; constexpr uint32_t STEP = UINT32_MAX / COUNT;
for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) { for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
float x = float(FPBits(v)); float x = float(FPBits(v));
if (isnan(x) || isinf(x)) if (isnan(x) || isinf(x))
continue; continue;
errno = 0; errno = 0;
float result = __llvm_libc::expm1f(x); float result = __llvm_libc::expm1f(x);
// If the computation resulted in an error or did not produce valid result // If the computation resulted in an error or did not produce valid result
// in the single-precision floating point range, then ignore comparing with // in the single-precision floating point range, then ignore comparing with
// MPFR result as MPFR can still produce valid results because of its // MPFR result as MPFR can still produce valid results because of its
// wider precision. // wider precision.
if (isnan(result) || isinf(result) || errno != 0) if (isnan(result) || isinf(result) || errno != 0)
continue; continue;
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 2.2); ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
} }
} }