forked from OSchip/llvm-project
[libc] Implement expm1f function that is correctly rounded for all rounding modes.
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. Reviewed By: sivachandra, zimmermann6 Differential Revision: https://reviews.llvm.org/D121574
This commit is contained in:
Tue Ly
parent
7e4cf582cf
commit
64af346b18
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@ -476,6 +476,7 @@ add_entrypoint_object(
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HDRS
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../expf.h
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DEPENDS
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.common_constants
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libc.src.__support.FPUtil.fputil
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libc.include.math
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COMPILE_OPTIONS
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@ -502,9 +503,11 @@ add_entrypoint_object(
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HDRS
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../expm1f.h
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DEPENDS
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.common_constants
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libc.src.__support.FPUtil.fputil
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libc.include.math
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libc.src.math.expf
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libc.src.math.fabsf
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COMPILE_OPTIONS
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-O3
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)
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add_entrypoint_object(
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@ -102,4 +102,128 @@ const double LOG_F[128] = {
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0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
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0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
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// Lookup table for exp(m) with m = -104, ..., 89.
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// -104 = floor(log(single precision's min denormal))
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// 89 = ceil(log(single precision's max normal))
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// Table is generated with Sollya as follow:
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// > display = hexadecimal;
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// > for i from -104 to 89 do { D(exp(i)); };
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const double EXP_M1[195] = {
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0x1.f1e6b68529e33p-151, 0x1.525be4e4e601dp-149, 0x1.cbe0a45f75eb1p-148,
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0x1.3884e838aea68p-146, 0x1.a8c1f14e2af5dp-145, 0x1.20a717e64a9bdp-143,
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0x1.8851d84118908p-142, 0x1.0a9bdfb02d240p-140, 0x1.6a5bea046b42ep-139,
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0x1.ec7f3b269efa8p-138, 0x1.4eafb87eab0f2p-136, 0x1.c6e2d05bbc000p-135,
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0x1.35208867c2683p-133, 0x1.a425b317eeacdp-132, 0x1.1d8508fa8246ap-130,
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0x1.840fbc08fdc8ap-129, 0x1.07b7112bc1ffep-127, 0x1.666d0dad2961dp-126,
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0x1.e726c3f64d0fep-125, 0x1.4b0dc07cabf98p-123, 0x1.c1f2daf3b6a46p-122,
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0x1.31c5957a47de2p-120, 0x1.9f96445648b9fp-119, 0x1.1a6baeadb4fd1p-117,
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0x1.7fd974d372e45p-116, 0x1.04da4d1452919p-114, 0x1.62891f06b3450p-113,
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0x1.e1dd273aa8a4ap-112, 0x1.4775e0840bfddp-110, 0x1.bd109d9d94bdap-109,
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0x1.2e73f53fba844p-107, 0x1.9b138170d6bfep-106, 0x1.175af0cf60ec5p-104,
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0x1.7baee1bffa80bp-103, 0x1.02057d1245cebp-101, 0x1.5eafffb34ba31p-100,
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0x1.dca23bae16424p-99, 0x1.43e7fc88b8056p-97, 0x1.b83bf23a9a9ebp-96,
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0x1.2b2b8dd05b318p-94, 0x1.969d47321e4ccp-93, 0x1.1452b7723aed2p-91,
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0x1.778fe2497184cp-90, 0x1.fe7116182e9ccp-89, 0x1.5ae191a99585ap-87,
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0x1.d775d87da854dp-86, 0x1.4063f8cc8bb98p-84, 0x1.b374b315f87c1p-83,
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0x1.27ec458c65e3cp-81, 0x1.923372c67a074p-80, 0x1.1152eaeb73c08p-78,
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0x1.737c5645114b5p-77, 0x1.f8e6c24b5592ep-76, 0x1.571db733a9d61p-74,
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0x1.d257d547e083fp-73, 0x1.3ce9b9de78f85p-71, 0x1.aebabae3a41b5p-70,
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0x1.24b6031b49bdap-68, 0x1.8dd5e1bb09d7ep-67, 0x1.0e5b73d1ff53dp-65,
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0x1.6f741de1748ecp-64, 0x1.f36bd37f42f3ep-63, 0x1.536452ee2f75cp-61,
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0x1.cd480a1b74820p-60, 0x1.39792499b1a24p-58, 0x1.aa0de4bf35b38p-57,
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0x1.2188ad6ae3303p-55, 0x1.898471fca6055p-54, 0x1.0b6c3afdde064p-52,
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0x1.6b7719a59f0e0p-51, 0x1.ee001eed62aa0p-50, 0x1.4fb547c775da8p-48,
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0x1.c8464f7616468p-47, 0x1.36121e24d3bbap-45, 0x1.a56e0c2ac7f75p-44,
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0x1.1e642baeb84a0p-42, 0x1.853f01d6d53bap-41, 0x1.0885298767e9ap-39,
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0x1.67852a7007e42p-38, 0x1.e8a37a45fc32ep-37, 0x1.4c1078fe9228ap-35,
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0x1.c3527e433fab1p-34, 0x1.32b48bf117da2p-32, 0x1.a0db0d0ddb3ecp-31,
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0x1.1b48655f37267p-29, 0x1.81056ff2c5772p-28, 0x1.05a628c699fa1p-26,
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0x1.639e3175a689dp-25, 0x1.e355bbaee85cbp-24, 0x1.4875ca227ec38p-22,
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0x1.be6c6fdb01612p-21, 0x1.2f6053b981d98p-19, 0x1.9c54c3b43bc8bp-18,
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0x1.18354238f6764p-16, 0x1.7cd79b5647c9bp-15, 0x1.02cf22526545ap-13,
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0x1.5fc21041027adp-12, 0x1.de16b9c24a98fp-11, 0x1.44e51f113d4d6p-9,
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0x1.b993fe00d5376p-8, 0x1.2c155b8213cf4p-6, 0x1.97db0ccceb0afp-5,
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0x1.152aaa3bf81ccp-3, 0x1.78b56362cef38p-2, 0x1.0000000000000p+0,
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0x1.5bf0a8b145769p+1, 0x1.d8e64b8d4ddaep+2, 0x1.415e5bf6fb106p+4,
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0x1.b4c902e273a58p+5, 0x1.28d389970338fp+7, 0x1.936dc5690c08fp+8,
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0x1.122885aaeddaap+10, 0x1.749ea7d470c6ep+11, 0x1.fa7157c470f82p+12,
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0x1.5829dcf950560p+14, 0x1.d3c4488ee4f7fp+15, 0x1.3de1654d37c9ap+17,
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0x1.b00b5916ac955p+18, 0x1.259ac48bf05d7p+20, 0x1.8f0ccafad2a87p+21,
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0x1.0f2ebd0a80020p+23, 0x1.709348c0ea4f9p+24, 0x1.f4f22091940bdp+25,
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0x1.546d8f9ed26e1p+27, 0x1.ceb088b68e804p+28, 0x1.3a6e1fd9eecfdp+30,
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0x1.ab5adb9c43600p+31, 0x1.226af33b1fdc1p+33, 0x1.8ab7fb5475fb7p+34,
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0x1.0c3d3920962c9p+36, 0x1.6c932696a6b5dp+37, 0x1.ef822f7f6731dp+38,
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0x1.50bba3796379ap+40, 0x1.c9aae4631c056p+41, 0x1.370470aec28edp+43,
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0x1.a6b765d8cdf6dp+44, 0x1.1f43fcc4b662cp+46, 0x1.866f34a725782p+47,
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0x1.0953e2f3a1ef7p+49, 0x1.689e221bc8d5bp+50, 0x1.ea215a1d20d76p+51,
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0x1.4d13fbb1a001ap+53, 0x1.c4b334617cc67p+54, 0x1.33a43d282a519p+56,
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0x1.a220d397972ebp+57, 0x1.1c25c88df6862p+59, 0x1.8232558201159p+60,
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0x1.0672a3c9eb871p+62, 0x1.64b41c6d37832p+63, 0x1.e4cf766fe49bep+64,
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0x1.49767bc0483e3p+66, 0x1.bfc951eb8bb76p+67, 0x1.304d6aeca254bp+69,
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0x1.9d97010884251p+70, 0x1.19103e4080b45p+72, 0x1.7e013cd114461p+73,
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0x1.03996528e074cp+75, 0x1.60d4f6fdac731p+76, 0x1.df8c5af17ba3bp+77,
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0x1.45e3076d61699p+79, 0x1.baed16a6e0da7p+80, 0x1.2cffdfebde1a1p+82,
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0x1.9919cabefcb69p+83, 0x1.160345c9953e3p+85, 0x1.79dbc9dc53c66p+86,
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0x1.00c810d464097p+88, 0x1.5d009394c5c27p+89, 0x1.da57de8f107a8p+90,
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0x1.425982cf597cdp+92, 0x1.b61e5ca3a5e31p+93, 0x1.29bb825dfcf87p+95,
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0x1.94a90db0d6fe2p+96, 0x1.12fec759586fdp+98, 0x1.75c1dc469e3afp+99,
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0x1.fbfd219c43b04p+100, 0x1.5936d44e1a146p+102, 0x1.d531d8a7ee79cp+103,
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0x1.3ed9d24a2d51bp+105, 0x1.b15cfe5b6e17bp+106, 0x1.268038c2c0e00p+108,
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0x1.9044a73545d48p+109, 0x1.1002ab6218b38p+111, 0x1.71b3540cbf921p+112,
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0x1.f6799ea9c414ap+113, 0x1.55779b984f3ebp+115, 0x1.d01a210c44aa4p+116,
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0x1.3b63da8e91210p+118, 0x1.aca8d6b0116b8p+119, 0x1.234de9e0c74e9p+121,
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0x1.8bec7503ca477p+122, 0x1.0d0eda9796b90p+124, 0x1.6db0118477245p+125,
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0x1.f1056dc7bf22dp+126, 0x1.51c2cc3433801p+128, 0x1.cb108ffbec164p+129,
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};
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// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
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// Table is generated with Sollya as follow:
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// > display = hexadecimal;
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// > for i from 0 to 127 do { D(exp(i / 128)); };
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const double EXP_M2[128] = {
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0x1.0000000000000p0, 0x1.0202015600446p0, 0x1.04080ab55de39p0,
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0x1.06122436410ddp0, 0x1.08205601127edp0, 0x1.0a32a84e9c1f6p0,
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0x1.0c49236829e8cp0, 0x1.0e63cfa7ab09dp0, 0x1.1082b577d34edp0,
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0x1.12a5dd543ccc5p0, 0x1.14cd4fc989cd6p0, 0x1.16f9157587069p0,
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0x1.192937074e0cdp0, 0x1.1b5dbd3f68122p0, 0x1.1d96b0eff0e79p0,
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0x1.1fd41afcba45ep0, 0x1.2216045b6f5cdp0, 0x1.245c7613b8a9bp0,
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0x1.26a7793f60164p0, 0x1.28f7170a755fdp0, 0x1.2b4b58b372c79p0,
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0x1.2da4478b620c7p0, 0x1.3001ecf601af7p0, 0x1.32645269ea829p0,
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0x1.34cb8170b5835p0, 0x1.373783a722012p0, 0x1.39a862bd3c106p0,
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0x1.3c1e2876834aap0, 0x1.3e98deaa11dccp0, 0x1.41188f42c3e32p0,
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0x1.439d443f5f159p0, 0x1.462707b2bac21p0, 0x1.48b5e3c3e8186p0,
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0x1.4b49e2ae5ac67p0, 0x1.4de30ec211e60p0, 0x1.50817263c13cdp0,
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0x1.5325180cfacf7p0, 0x1.55ce0a4c58c7cp0, 0x1.587c53c5a7af0p0,
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0x1.5b2fff3210fd9p0, 0x1.5de9176045ff5p0, 0x1.60a7a734ab0e8p0,
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0x1.636bb9a983258p0, 0x1.663559cf1bc7cp0, 0x1.690492cbf9433p0,
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0x1.6bd96fdd034a2p0, 0x1.6eb3fc55b1e76p0, 0x1.719443a03acb9p0,
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0x1.747a513dbef6ap0, 0x1.776630c678bc1p0, 0x1.7a57ede9ea23ep0,
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0x1.7d4f946f0ba8dp0, 0x1.804d30347b546p0, 0x1.8350cd30ac390p0,
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0x1.865a7772164c5p0, 0x1.896a3b1f66a0ep0, 0x1.8c802477b0010p0,
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0x1.8f9c3fd29beafp0, 0x1.92be99a09bf00p0, 0x1.95e73e6b1b75ep0,
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0x1.99163ad4b1dccp0, 0x1.9c4b9b995509bp0, 0x1.9f876d8e8c566p0,
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0x1.a2c9bda3a3e78p0, 0x1.a61298e1e069cp0, 0x1.a9620c6cb3374p0,
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0x1.acb82581eee54p0, 0x1.b014f179fc3b8p0, 0x1.b3787dc80f95fp0,
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0x1.b6e2d7fa5eb18p0, 0x1.ba540dba56e56p0, 0x1.bdcc2cccd3c85p0,
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0x1.c14b431256446p0, 0x1.c4d15e873c193p0, 0x1.c85e8d43f7cd0p0,
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0x1.cbf2dd7d490f2p0, 0x1.cf8e5d84758a9p0, 0x1.d3311bc7822b4p0,
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0x1.d6db26d16cd67p0, 0x1.da8c8d4a66969p0, 0x1.de455df80e3c0p0,
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0x1.e205a7bdab73ep0, 0x1.e5cd799c6a54ep0, 0x1.e99ce2b397649p0,
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0x1.ed73f240dc142p0, 0x1.f152b7a07bb76p0, 0x1.f539424d90f5ep0,
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0x1.f927a1e24bb76p0, 0x1.fd1de6182f8c9p0, 0x1.008e0f64294abp1,
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0x1.02912df5ce72ap1, 0x1.049856cd84339p1, 0x1.06a39207f0a09p1,
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0x1.08b2e7d2035cfp1, 0x1.0ac6606916501p1, 0x1.0cde041b0e9aep1,
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0x1.0ef9db467dcf8p1, 0x1.1119ee5ac36b6p1, 0x1.133e45d82e952p1,
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0x1.1566ea50201d7p1, 0x1.1793e4652cc50p1, 0x1.19c53ccb3fc6bp1,
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0x1.1bfafc47bda73p1, 0x1.1e352bb1a74adp1, 0x1.2073d3f1bd518p1,
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0x1.22b6fe02a3b9cp1, 0x1.24feb2f105cb8p1, 0x1.274afbdbba4a6p1,
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0x1.299be1f3e7f1cp1, 0x1.2bf16e7d2a38cp1, 0x1.2e4baacdb6614p1,
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0x1.30aaa04e80d05p1, 0x1.330e587b62b28p1, 0x1.3576dce33feadp1,
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0x1.37e437282d4eep1, 0x1.3a5670ff972edp1, 0x1.3ccd9432682b4p1,
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0x1.3f49aa9d30590p1, 0x1.41cabe304cb34p1, 0x1.4450d8f00edd4p1,
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0x1.46dc04f4e5338p1, 0x1.496c4c6b832dap1, 0x1.4c01b9950a111p1,
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0x1.4e9c56c731f5dp1, 0x1.513c2e6c731d7p1, 0x1.53e14b042f9cap1,
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0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
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};
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} // namespace __llvm_libc
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@ -17,6 +17,20 @@ extern const double ONE_OVER_F[128];
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// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
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extern const double LOG_F[128];
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// Lookup table for exp(m) with m = -104, ..., 89.
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// -104 = floor(log(single precision's min denormal))
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// 89 = ceil(log(single precision's max normal))
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// Table is generated with Sollya as follow:
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// > display = hexadecimal;
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// > for i from -104 to 89 do { D(exp(i)); };
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extern const double EXP_M1[195];
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// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
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// Table is generated with Sollya as follow:
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// > display = hexadecimal;
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// > for i from 0 to 127 do { D(exp(i / 128)); };
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extern const double EXP_M2[128];
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} // namespace __llvm_libc
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#endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
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@ -7,6 +7,7 @@
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//===----------------------------------------------------------------------===//
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#include "src/math/expf.h"
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#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
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#include "src/__support/FPUtil/BasicOperations.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FMA.h"
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@ -18,130 +19,6 @@
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namespace __llvm_libc {
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// Lookup table for exp(m) with m = -104, ..., 89.
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// -104 = floor(log(single precision's min denormal))
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// 89 = ceil(log(single precision's max normal))
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// Table is generated with Sollya as follow:
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// > display = hexadecimal;
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// > for i from -104 to 89 do { D(exp(i)); };
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static constexpr double EXP_M1[195] = {
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0x1.f1e6b68529e33p-151, 0x1.525be4e4e601dp-149, 0x1.cbe0a45f75eb1p-148,
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0x1.3884e838aea68p-146, 0x1.a8c1f14e2af5dp-145, 0x1.20a717e64a9bdp-143,
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0x1.8851d84118908p-142, 0x1.0a9bdfb02d240p-140, 0x1.6a5bea046b42ep-139,
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0x1.ec7f3b269efa8p-138, 0x1.4eafb87eab0f2p-136, 0x1.c6e2d05bbc000p-135,
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0x1.35208867c2683p-133, 0x1.a425b317eeacdp-132, 0x1.1d8508fa8246ap-130,
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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
|
||||
LLVM_LIBC_FUNCTION(float, expf, (float x)) {
|
||||
using FPBits = typename fputil::FPBits<float>;
|
||||
|
|
@ -157,8 +34,7 @@ LLVM_LIBC_FUNCTION(float, expf, (float x)) {
|
|||
return x;
|
||||
if (fputil::get_round() == FE_UPWARD)
|
||||
return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
|
||||
if (x != 0.0f)
|
||||
errno = ERANGE;
|
||||
errno = ERANGE;
|
||||
return 0.0f;
|
||||
}
|
||||
// x >= 89 or nan
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
//===-- Implementation of expm1f function ---------------------------------===//
|
||||
//===-- Single-precision e^x - 1 function ---------------------------------===//
|
||||
//
|
||||
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
|
||||
// See https://llvm.org/LICENSE.txt for license information.
|
||||
|
|
@ -7,52 +7,131 @@
|
|||
//===----------------------------------------------------------------------===//
|
||||
|
||||
#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/FEnvImpl.h"
|
||||
#include "src/__support/FPUtil/FMA.h"
|
||||
#include "src/__support/FPUtil/FPBits.h"
|
||||
#include "src/__support/FPUtil/PolyEval.h"
|
||||
#include "src/__support/common.h"
|
||||
#include "src/math/expf.h"
|
||||
|
||||
#include <errno.h>
|
||||
|
||||
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
|
||||
LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
|
||||
const float ln2 =
|
||||
0.69314718055994530941723212145817656807550013436025f; // For C++17:
|
||||
// 0x1.62e'42ffp-1
|
||||
float abs_x = __llvm_libc::fputil::abs(x);
|
||||
using FPBits = typename fputil::FPBits<float>;
|
||||
FPBits xbits(x);
|
||||
|
||||
if (abs_x <= ln2) {
|
||||
if (abs_x <= 0.125f) {
|
||||
return x * __llvm_libc::fputil::polyeval(
|
||||
x, 1.0f, 0.5f, 0.16666664183139801025390625f,
|
||||
4.1666664183139801025390625e-2f,
|
||||
8.3379410207271575927734375e-3f,
|
||||
1.3894210569560527801513671875e-3f);
|
||||
}
|
||||
if (x > 0.125f) {
|
||||
return __llvm_libc::fputil::polyeval(
|
||||
x, 1.23142086749794543720781803131103515625e-7f,
|
||||
0.9999969005584716796875f, 0.500031292438507080078125f,
|
||||
0.16650259494781494140625f, 4.21491153538227081298828125e-2f,
|
||||
7.53940828144550323486328125e-3f,
|
||||
2.05591344274580478668212890625e-3f);
|
||||
}
|
||||
return __llvm_libc::fputil::polyeval(
|
||||
x, -6.899231408397099585272371768951416015625e-8f,
|
||||
0.999998271465301513671875f, 0.4999825656414031982421875f,
|
||||
0.16657467186450958251953125f, 4.1390590369701385498046875e-2f,
|
||||
7.856394164264202117919921875e-3f,
|
||||
9.380675037391483783721923828125e-4f);
|
||||
// When x < log(2^-25) or nan
|
||||
if (unlikely(xbits.uintval() >= 0xc18a'a123U)) {
|
||||
// exp(-Inf) = 0
|
||||
if (xbits.is_inf())
|
||||
return -1.0f;
|
||||
// exp(nan) = nan
|
||||
if (xbits.is_nan())
|
||||
return x;
|
||||
int round_mode = fputil::get_round();
|
||||
if (round_mode == FE_UPWARD || round_mode == FE_TOWARDZERO)
|
||||
return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
|
||||
return -1.0f;
|
||||
}
|
||||
return expf(x) - 1.0f;
|
||||
// x >= 89 or nan
|
||||
if (unlikely(!xbits.get_sign() && (xbits.uintval() >= 0x42b2'0000))) {
|
||||
if (xbits.uintval() < 0x7f80'0000U) {
|
||||
int rounding = fputil::get_round();
|
||||
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
|
||||
return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
|
||||
|
||||
errno = ERANGE;
|
||||
}
|
||||
return x + static_cast<float>(FPBits::inf());
|
||||
}
|
||||
|
||||
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;
|
||||
}
|
||||
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
|
||||
|
|
|
|||
|
|
@ -83,15 +83,20 @@ add_fp_unittest(
|
|||
|
||||
add_fp_unittest(
|
||||
expm1f_test
|
||||
NO_RUN_POSTBUILD
|
||||
NEED_MPFR
|
||||
SUITE
|
||||
libc_math_exhaustive_tests
|
||||
SRCS
|
||||
expm1f_test.cpp
|
||||
expm1f_test.cpp
|
||||
DEPENDS
|
||||
.exhaustive_test
|
||||
libc.include.math
|
||||
libc.src.math.expf
|
||||
libc.src.math.expm1f
|
||||
libc.src.__support.FPUtil.fputil
|
||||
LINK_OPTIONS
|
||||
-lpthread
|
||||
)
|
||||
|
||||
add_fp_unittest(
|
||||
|
|
|
|||
|
|
@ -32,10 +32,12 @@ void LlvmLibcExhaustiveTest<T>::test_full_range(T start, T stop, int nthreads,
|
|||
std::cout << msg.str();
|
||||
msg.str("");
|
||||
|
||||
check(begin, end, rounding);
|
||||
bool result;
|
||||
check(begin, end, rounding, result);
|
||||
|
||||
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();
|
||||
});
|
||||
begin += increment;
|
||||
|
|
|
|||
|
|
@ -22,5 +22,6 @@ struct LlvmLibcExhaustiveTest : public __llvm_libc::testing::Test {
|
|||
void test_full_range(T start, T stop, int nthreads,
|
||||
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;
|
||||
};
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
//===-- Exhaustive test for expm1f-----------------------------------------===//
|
||||
//===-- Exhaustive test for expm1f ----------------------------------------===//
|
||||
//
|
||||
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
|
||||
// See https://llvm.org/LICENSE.txt for license information.
|
||||
|
|
@ -6,22 +6,76 @@
|
|||
//
|
||||
//===----------------------------------------------------------------------===//
|
||||
|
||||
#include "exhaustive_test.h"
|
||||
#include "src/__support/FPUtil/FPBits.h"
|
||||
#include "src/math/expm1f.h"
|
||||
#include "utils/MPFRWrapper/MPFRUtils.h"
|
||||
#include <math.h>
|
||||
#include "utils/UnitTest/FPMatcher.h"
|
||||
|
||||
using FPBits = __llvm_libc::fputil::FPBits<float>;
|
||||
|
||||
namespace mpfr = __llvm_libc::testing::mpfr;
|
||||
|
||||
TEST(LlvmLibcExpm1fExhaustiveTest, AllValues) {
|
||||
uint32_t bits = 0;
|
||||
do {
|
||||
FPBits x(bits);
|
||||
if (!x.is_inf_or_nan() && float(x) < 88.70f) {
|
||||
ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, float(x),
|
||||
__llvm_libc::expm1f(float(x)), 1.5);
|
||||
}
|
||||
} while (bits++ < 0xffff'ffffU);
|
||||
struct LlvmLibcExpfExhaustiveTest : public LlvmLibcExhaustiveTest<uint32_t> {
|
||||
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 {
|
||||
FPBits xbits(bits);
|
||||
float x = float(xbits);
|
||||
EXPECT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 0.5,
|
||||
rounding);
|
||||
} while (bits++ < stop);
|
||||
result = true;
|
||||
}
|
||||
};
|
||||
|
||||
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);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -54,15 +54,12 @@ TEST(LlvmLibcExpm1fTest, Overflow) {
|
|||
TEST(LlvmLibcExpm1fTest, Underflow) {
|
||||
errno = 0;
|
||||
EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(float(FPBits(0xff7fffffU))));
|
||||
EXPECT_MATH_ERRNO(ERANGE);
|
||||
|
||||
float x = float(FPBits(0xc2cffff8U));
|
||||
EXPECT_FP_EQ(-1.0f, __llvm_libc::expm1f(x));
|
||||
EXPECT_MATH_ERRNO(ERANGE);
|
||||
|
||||
x = float(FPBits(0xc2d00008U));
|
||||
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
|
||||
|
|
@ -72,19 +69,28 @@ TEST(LlvmLibcExpm1fTest, Borderline) {
|
|||
|
||||
errno = 0;
|
||||
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);
|
||||
|
||||
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);
|
||||
|
||||
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);
|
||||
|
||||
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);
|
||||
}
|
||||
|
||||
|
|
@ -104,6 +110,7 @@ TEST(LlvmLibcExpm1fTest, InFloatRange) {
|
|||
// wider precision.
|
||||
if (isnan(result) || isinf(result) || errno != 0)
|
||||
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);
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue