glibc/benchtests/pow-inputs
Wilco Dijkstra c3d466cba1 Remove slow paths from pow
Remove the slow paths from pow.  Like several other double precision math
functions, pow is exactly rounded.  This is not required from math functions
and causes major overheads as it requires multiple fallbacks using higher
precision arithmetic if a result is close to 0.5ULP.  Ridiculous slowdowns
of up to 100000x have been reported when the highest precision path triggers.

All GLIBC math tests pass on AArch64 and x64 (with ULP of pow set to 1).
The worst case error is ~0.506ULP.  A simple test over a few hundred million
values shows pow is 10% faster on average.  This fixes BZ #13932.

	[BZ #13932]
	* sysdeps/ieee754/dbl-64/uexp.h (err_1): Remove.
	* benchtests/pow-inputs: Update comment for slow path cases.
	* manual/probes.texi (slowpow_p10): Delete removed probe.
	(slowpow_p10): Likewise.
	* math/Makefile: Remove halfulp.c and slowpow.c.
	* sysdeps/aarch64/libm-test-ulps: Set ULP of pow to 1.
	* sysdeps/generic/math_private.h (__exp1): Remove error argument.
	(__halfulp): Remove.
	(__slowpow): Remove.
	* sysdeps/i386/fpu/halfulp.c: Delete file.
	* sysdeps/i386/fpu/slowpow.c: Likewise.
	* sysdeps/ia64/fpu/halfulp.c: Likewise.
	* sysdeps/ia64/fpu/slowpow.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_exp.c (__exp1): Remove error argument,
	improve comments and add error analysis.
	* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Add error analysis.
	(power1): Remove function:
	(log1): Remove error argument, add error analysis.
	(my_log2): Remove function.
	* sysdeps/ieee754/dbl-64/halfulp.c: Delete file.
	* sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/halfulp.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/slowpow.c: Likewise.
	* sysdeps/powerpc/power4/fpu/Makefile: Remove CPPFLAGS-slowpow.c.
	* sysdeps/x86_64/fpu/libm-test-ulps: Set ULP of pow to 1.
	* sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowpow-fma.c,
	slowpow-fma4.c, halfulp-fma.c, halfulp-fma4.c.
	* sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__slowpow): Remove define.
	* sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__slowpow): Likewise.
	* sysdeps/x86_64/fpu/multiarch/halfulp-fma.c: Delete file.
	* sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowpow-fma.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c: Likewise.
2018-02-12 10:47:09 +00:00

510 lines
23 KiB
Plaintext

## args: double:double
## ret: double
## includes: math.h
42.0, 42.0
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0x1.c83bb023360a9p879, -0x1.0c6922624c625p97
-0x1.e21c0605b5f2bp-634, 0x1.f28232c2ebba3p-74
0x1.e61ed69f4f3e5p558, -0x1.0ee6a03187e13p128
0x1.d32cb4d190af4p-556, -0x1.0000000000000p-64
0x1.97a202fe3d99bp812, -0x1.12eba5e07e17fp131
0x1.5cbf140578025p750, -0x1.0000000000000p-64
0x1.8754d2c071fd1p-796, -0x1.0000000000000p-64
-0x1.c24a21659e391p874, 0x1.8fca31719d26fp-203
0x1.db5587ed33e3dp-392, -0x1.0000000000000p-64
0x1.59b6e3bd2734fp959, -0x1.0000000000000p-64
-0x1.2f68f32a5979ep367, 0x1.d77b92aecf0f8p-414
0x1.73e621f69389dp222, -0x1.1235366e0a84bp216
0x1.076b75274a516p-7, -0x1.0000000000000p-64
0x1.2505e4b701385p-178, -0x1.0000000000000p-64
0x1.ae0c974a70a8fp607, 0x1.0000000000000p-64
0x1.b2c344636c704p595, -0x1.9d1b879d64e7dp213
-0x1.a6f695e9d29eep-629, 0x1.dad8811e62691p422
0x1.e5aca4566a08ap234, -0x1.645ed34f63b48p65
0x1.67faa10de96c9p-929, 0x1.0000000000000p-64
0x1.503a50f3f36c9p-313, 0x1.a1b537c589279p212
-0x1.e62711b5b18aap-336, 0x1.176d22b7c6703p-81
-0x1.78e6d2fb3c6c8p-802, -0x1.4354b70f8d56ap-407
-0x1.a9b890e6a309bp-974, -0x1.fc73521e05c84p446
0x1.605c070891e95p751, -0x1.00e8a0f55071cp255
-0x1.8e249352e8ed4p-690, -0x1.d751a5bb2c420p-254
0x1.67246027c2465p584, 0x1.3aaa16d492946p178
0x1.c53735a56d1edp610, -0x1.630662efaf0c6p60
0x1.d54a131bae182p142, -0x1.a313606a0459dp220
0x1.38afe5f1ed5b4p-779, 0x1.0000000000000p-64
0x1.f2aa76462ad42p-982, 0x1.0000000000000p-64
0x1.e188a166c06b6p45, 0x1.0000000000000p-64
0x1.fbe85766fae96p-463, 0x1.91c903c89b075p85
0x1.3342d36ecf081p28, -0x1.0000000000000p-64
0x1.c2b0a036a1828p719, 0x1.0000000000000p-64
0x1.ba7f308dc60ddp517, -0x1.b38d014638da6p246
-0x1.075aa7ba85f42p624, -0x1.a357d32f45a61p-867
0x1.1fbb4362bf313p995, 0x1.d039c2c0e18bfp-6
-0x1.150426e803137p622, -0x1.9bafe2efa3e89p39
-0x1.3f2456d5cba52p116, 0x1.fa9ec45f18306p-389
0x1.8e58945bd1087p-701, 0x1.0000000000000p-64
-0x1.ab0ef29932d78p111, 0x1.4313d75c1df97p658
0x1.ee3e13dd00d34p1016, 0x1.d6b3d3b9034c1p85
-0x1.7f0bd006c0d62p-324, 0x1.8210646a5ccddp871
-0x1.c004d2256a5b8p402, -0x1.a01df480fdcb7p98
-0x1.3717c2e75f865p-749, -0x1.628ab47e4b9c7p-879
-0x1.dfb414ca1e89fp780, -0x1.b1a6d17b59340p927
0x1.2bb340a5c99b8p772, -0x1.4cb4a208cd38ap49
0x1.983d90ffcdc95p-131, 0x1.294857e7a5d9dp66
0x1.0789a00a3ff0fp-950, -0x1.0000000000000p-64
0x1.6816c6cd93ea9p112, 0x1.985412f1ac3d6p104
0x1.3c0e604f8974bp-226, 0x1.0000000000000p-64
0x1.07acb29e12fc1p687, -0x1.edff80d6b306fp107
0x1.22c1d3b2c0e45p135, -0x1.9a5dc703e46dbp204
0x1.ede956a719d56p248, -0x1.80e8e672e144fp156
-0x1.ff6263662c8fbp-263, 0x1.cf3867b2bac05p652
0x1.f01e46c129d76p-5, 0x1.00d113cf96023p137
0x1.45cf928146851p636, 0x1.26b1c5666d711p131
-0x1.768376c2f7584p563, 0x1.017143ae97b27p545
-0x1.1f72a3d4f7881p-764, 0x1.4617565381163p177
0x1.dd9431675dbb5p-114, 0x1.0000000000000p-64
-0x1.64cc1762105b7p-569, -0x1.2d69b27570067p840
0x1.bd1077dadd530p235, 0x1.0000000000000p-64
0x1.0aa166c2b93bdp488, -0x1.48d03430453b8p213
-0x1.b513845f09747p-331, -0x1.d04e154527b26p685
0x1.5c97b3a12df62p696, -0x1.e160e008f7d3ap89
0x1.8eec91bde3d69p-376, -0x1.0000000000000p-64
0x1.7d29f253d3e79p636, -0x1.8e30a1ba55f7fp77
0x1.c004d2256a5b8p402, -0x1.a01df480fdcb7p98
0x1.52b9d41aaa1e9p-589, -0x1.292cb15f1459dp46
-0x1.ea9ca6fa0919ep-279, -0x1.601e44b6a588cp40
# old pow slow path at 240 bits
## name: 240bits
0x1.01fcd33493ea3p596, -0x1.724bd4e887783p-14
0x1.032ff59ab34fdp-540, -0x1.61e3632080b87p-24
0x1.045c337b80f53p304, 0x1.dc3404c30fa69p-56
0x1.0681338469475p-294, -0x1.3562210f27dfap-51
0x1.0b55c01eab2a6p-447, -0x1.cd7162fecd483p-48
0x1.0b74d4b709002p-811, -0x1.0af1478682e96p-50
0x1.0e4d10f3aabc8p664, 0x1.e2bde3471eaa1p-55
0x1.110607de11aa5p120, 0x1.dcec269cfd865p-47
0x1.132aa4cc6f38bp-751, 0x1.366ca7979d9bbp-8
0x1.138ae6f5a6dadp-680, 0x1.890a0755fce7ap-40
0x1.1b7b95bdc6400p467, 0x1.ec36f5f75ce4cp-8
0x1.1c20e7f14086cp-788, 0x1.f22967f8b5d7cp-48
0x1.278262637b59cp446, -0x1.1aab83169f61cp-10
0x1.2936f2eb01500p-234, -0x1.aa25c56c7a42ap-51
0x1.2991068d7df8dp-895, -0x1.e22e0335a6813p-19
0x1.2a4320a5a4e06p342, 0x1.a60de202d0f39p0
0x1.2baa57016f98bp445, -0x1.19b39156d7af6p-42
0x1.3003b731560f2p189, -0x1.d03a35d7809bbp-6
0x1.3098f631b79b3p322, 0x1.936cf77d12901p-58
0x1.329f9083895d6p-470, 0x1.c4e0407eac9e1p-60
0x1.32e62120a48dep-373, 0x1.8c03970ea6143p-15
0x1.3b69741c89827p-951, 0x1.d7e2d50ab916bp-13
0x1.46d346d411a30p-451, -0x1.5bed1300261dcp-37
0x1.48d0870fc99a7p-691, -0x1.4f6541a43b8cdp-5
0x1.49ae5141ea416p-825, 0x1.cfc4b51dbe592p-24
0x1.4d1fb5a2a4d73p738, -0x1.d2a54658b1df9p-50
0x1.4ddb12f9500cbp962, 0x1.48bc1158eb70ap-15
0x1.4f51d32b02376p758, 0x1.11d1409aaea9fp-27
0x1.54f723dd63e3bp605, 0x1.6c02f2514de2ap-23
0x1.5529070b8d631p-489, 0x1.1c3dd76010b92p-37
0x1.569bf17eb40dfp217, -0x1.8cb97627ae884p-31
0x1.5e2892c719a5ap817, 0x1.f0e3d4b66e9c0p-11
0x1.619a049c49284p329, -0x1.0bc7b3735d182p-12
0x1.62e6745b17235p344, 0x1.86dcb0cd4e584p-39
0x1.6532120398cb6p374, -0x1.dd57d385dde4ap-56
0x1.6ab9873394341p712, 0x1.6cec233df7f19p-59
0x1.6d7c56b0ec1f9p723, -0x1.864ae3aa72d4ap-11
0x1.6decf38117b3ap-629, 0x1.e1c8b1eaebfbbp-27
0x1.6f57771705979p518, -0x1.44fbe6fcf4182p-24
0x1.6f57b14f5f248p880, 0x1.e2554493e7f0cp-2
0x1.6fee9735004b7p-71, 0x1.8eaf1527d88bep-48
0x1.7190e00c6cae0p-495, 0x1.705594f79ee43p-33
0x1.7238a1904c29cp40, 0x1.d454673e675eep-30
0x1.76aa529cae2a7p-457, -0x1.0652207d202acp-45
0x1.78e630a117b59p-105, 0x1.ecb1a67d5b9dcp-32
0x1.7d0976b552b5bp-316, -0x1.9c52a2a02f146p1
0x1.80a10162f3c9ep-462, 0x1.af6ef1f1d004ep-54
0x1.8794943d6e34bp-745, -0x1.0c7df064d51e9p-10
0x1.8a3d749288cbcp-469, 0x1.a9bf9202d914fp-46
0x1.8da421e64749bp-540, -0x1.494a81df89b6bp-26
0x1.8e05154795810p247, 0x1.3c04802f44ddcp-47
0x1.91b9d616c0878p-313, 0x1.a3c9263d26b2ap-30
0x1.95e973a94d414p-229, 0x1.d83d8244e6566p-28
0x1.9a3217b4fb0e5p-990, 0x1.82853149b1e30p-42
0x1.9e2556775fc02p-377, -0x1.a6ec93193a127p-38
0x1.9e83d7b0c831fp-906, 0x1.6a3485e3e4fe8p-21
0x1.a51cf0f0f49f7p751, 0x1.07b941a3af664p-12
0x1.a883c2cef7802p-432, 0x1.b5ee3711a8260p-34
0x1.aca70602f90f3p205, -0x1.a40d85c2b0ddap-55
0x1.b118069c4e0f8p133, 0x1.85ed946b41169p0
0x1.b1ada0a8ca383p-699, 0x1.ddfec76f67c1fp-37
0x1.b236b6872f638p419, 0x1.fa8f6525758b6p-5
0x1.b2413258b83b1p892, -0x1.bcea65c80772bp-12
0x1.b51563dac9885p-571, 0x1.7a1e16e485fdcp-30
0x1.b5e4833e40f76p-445, 0x1.44e23325bcc3fp-22
0x1.b6a2168ec3212p-674, -0x1.35bda0265f18bp-30
0x1.b8dd676727fa1p124, 0x1.3605e6ec76006p-29
0x1.b95437f961192p-500, 0x1.9276767f94721p-10
0x1.bb6647f65218ap741, -0x1.b9dd250927a8ap-6
0x1.bffdf0efb5c4ep-703, 0x1.85fac77188c01p-9
0x1.c0345583020c9p236, 0x1.de31b044cb918p-37
0x1.c4b9163604b90p548, 0x1.0a51f116977d3p-17
0x1.c66ec323be811p-726, -0x1.8829c716f5ddbp-24
0x1.c69da72348031p-390, 0x1.109f77bb4a2a2p-37
0x1.c712558c00177p-883, -0x1.9cf047e60fa38p-8
0x1.c74df6d64da29p-154, -0x1.bdba55e26ef07p2
0x1.c75fa2c065d1dp731, 0x1.fa827749d723cp-21
0x1.c8f5b7f54aa5fp-998, 0x1.59fa40e2d7a95p-10
0x1.c957e3768f0c2p-102, 0x1.0047f59669535p-5
0x1.ce0615637c099p-737, 0x1.b1795333136d6p-59
0x1.d1a7872210098p245, -0x1.afd8c410a1918p-16
0x1.d39ee7b8cae5ep722, 0x1.639a1575eb95cp-56
0x1.d4b4276a02096p-5, -0x1.7ff8354a6ba9cp-21
0x1.d500d1daf1bfcp-352, 0x1.e4c7243104fa7p-34
0x1.d684c68e86321p-661, -0x1.11305765580a9p-13
0x1.db08f6fcae9f5p-637, -0x1.a8cba163bd1dep-21
0x1.db09e6535414dp809, -0x1.0b10e70ed8d88p-48
0x1.e50573d07ecc0p41, 0x1.19ec44b6d99e6p-58
0x1.e59505ef043e0p926, -0x1.3201c7a1e8882p-62
0x1.e6b9b28e678a4p546, 0x1.70e042daa89e7p-30
0x1.e9a4e6bbbf235p-851, -0x1.1d70f7b787412p-21
0x1.ea68a16e4b7c9p-733, -0x1.ee7f337779825p-34
0x1.f0e76025ece1cp642, -0x1.bdc0d0d7020d5p-57
0x1.f1bcb1d70f84bp-568, 0x1.98c5d3b11e934p-21
0x1.f568146a8c658p240, 0x1.4def9749a6a7ep-44
0x1.f75bd43867225p-454, 0x1.34b1e5cb0df40p-16
0x1.fae7a09d10f34p955, -0x1.f7f8439082552p-31
0x1.fae913d4f952ep-809, -0x1.4b649402fce63p-6
0x1.fe6d725408f24p484, -0x1.25f4f6441d2e4p-12
0x1.ff6393f9150ccp-718, 0x1.a0cb50a9bf2f3p-31
# old pow slowest path at 768 bits
## name: 768bits
1.0000000000000020, 1.5
0x1.006777b4b61dep843, -0x1.67e3145491872p-1
0x1.0477a5cfb1972p-402, 0x1.8742e7a1ce99dp-1
0x1.0827a160ab475p-239, 0x1.fcae51d2d997dp-1
0x1.083723672b1a4p-204, 0x1.baddc57f1404cp-2
0x1.0b39f4b2f5c4fp-546, 0x1.7d02a31183f36p-1
0x1.0e2d62ea9d078p-68, 0x1.8afb43919ece2p3
0x1.0fedd1fd9bdc5p-1011, 0x1.c0ce64b178832p-6
0x1.10b984764821ep724, -0x1.36e872083e630p-4
0x1.12424342d99bbp686, -0x1.f8d4e18b1b309p-5
0x1.1335f40a059c7p1014, -0x1.5818e19224448p-2
0x1.14185484cbdb2p-780, 0x1.23f8d7d596280p-4
0x1.14f5b49e12b8fp-751, 0x1.522c717bca3eap0
0x1.15fe345b21e2bp399, -0x1.0a09061cd1de9p-1
0x1.17c3e75436530p104, -0x1.ef30d09c541e9p0
0x1.1e5296bbfeea7p747, -0x1.f68df5996bfedp-1
0x1.1efdd081a8d35p-90, 0x1.7c7d10d98a3c9p-1
0x1.203101f62452ap317, -0x1.3be834bfd34fap-1
0x1.29cb8617add92p968, -0x1.9cbe73f892a16p-6
0x1.2d75353d5df74p719, -0x1.e2f317d7b2c01p-1
0x1.2f08247664913p592, -0x1.35ab9793384a5p-2
0x1.2ff58217e86d7p725, -0x1.2c98b6be067ccp-2
0x1.3113614c8b9e1p159, -0x1.fc2f4279c8cbep-1
0x1.3115402118c24p134, -0x1.d435f65f0eefcp1
0x1.32e5a1ba96cdap52, -0x1.f7d8248930c17p-1
0x1.346f712d4c234p78, -0x1.830235fa4eb2cp3
0x1.35ea84ad8b4fap742, -0x1.728dd1bc7d70cp-3
0x1.36b91497c147ep579, -0x1.b7e7b0d1ad44dp-2
0x1.3752c6b5da9e6p351, -0x1.2a00f003acdd1p-1
0x1.3bccb31761b21p-193, 0x1.bdd7b5da189c8p1
0x1.42c0b561c10bep-850, 0x1.dcdee5de63ebcp-3
0x1.4520f56ca1422p-471, 0x1.348c312c9f319p-1
0x1.46e7406c8e11ep546, -0x1.876f67bed28c4p0
0x1.4ba3f35d2f4afp-333, 0x1.6e39f0895a072p-3
0x1.4cb3303ab8786p-838, 0x1.fe88a032de46ap-1
0x1.4d61505a36a60p234, -0x1.45c3e271db1fep1
0x1.4fcff0e946b1ep909, -0x1.90fa07de4eea5p-1
0x1.5172c6b32f2aep293, -0x1.fb0fa58fc74abp-2
0x1.51e4b4afeb58ap-2, 0x1.f184d702a5f4bp3
0x1.5212b31c06068p306, -0x1.e8e5c1b09f30dp-2
0x1.55c7413fbdd0cp-168, 0x1.68687102fa0b8p-3
0x1.5975f5580b29cp361, -0x1.cda627a0b0899p-3
0x1.5b3d77ff20607p-694, 0x1.95877099718f5p-4
0x1.5b85e6f45d26fp763, -0x1.b727a35d92656p-4
0x1.5c83b2d038766p-984, 0x1.4232c330c81b9p-1
0x1.5ec6e7e275af2p773, -0x1.8da470ca7dd62p-1
0x1.60b0e6123149bp-743, 0x1.25a696ab5fc09p-4
0x1.6567f1ab52caap-769, 0x1.ff57c1e78cc81p-3
0x1.689cb423d7ec7p95, -0x1.71d3f5a46c36fp-2
0x1.69e2a022e3db6p-672, 0x1.209f77b27f146p-1
0x1.6a6bb05202fd0p-621, 0x1.bc1f316194126p-5
0x1.72b181bf25fd7p303, -0x1.629be448db4f7p1
0x1.7667d46544feap887, -0x1.e92ef7681c985p-3
0x1.776f45edc5aa6p967, -0x1.8b34366de0584p-3
0x1.77d4e3169e8fdp889, -0x1.7159c5a0e440ep-4
0x1.792c56f01b25ep-474, 0x1.45237144dc76dp-2
0x1.7c4d814b67ce3p-30, 0x1.32f4217aa69bfp2
0x1.7fec1487cd8c2p-790, 0x1.373ec1a13952fp-4
0x1.8280e15921e7bp-544, 0x1.17f4d1f294f23p-2
0x1.8be4858d98288p395, -0x1.8ecf7076c1cadp-3
0x1.8c1a3651b2a3cp251, -0x1.fe464693b592fp-1
0x1.95b8339b15437p-805, 0x1.c590d48f70e09p-4
0x1.9ea712eab015cp643, -0x1.9f9a2005cd04dp-2
0x1.9ec010ebb0fb4p966, -0x1.322de55e2f27dp-3
0x1.a055b4cacfb90p692, -0x1.45a6d0302680bp-4
0x1.a2541721f7549p508, -0x1.46b5008fed93ap0
0x1.aa4ea2a62e6d3p146, -0x1.4948a7f0b9447p-2
0x1.aeab6627bd7fep-883, 0x1.e334b6e331bcfp-4
0x1.afc9062dd5d6cp285, -0x1.704640b7e8a60p0
0x1.b2e0e5768b8a4p700, -0x1.e3cc63841415cp-1
0x1.b44dd7483ff8fp762, -0x1.376275f0c7542p0
0x1.b461c649ef81fp-297, 0x1.757d3606ad420p-2
0x1.b47177acf880bp162, -0x1.dbc2c7336fcdcp-3
0x1.b5d597a5647bep312, -0x1.0d87f0669fd98p-3
0x1.b5f5f6894898fp824, -0x1.aeec9752febccp-2
0x1.b78b84a583db6p711, -0x1.443983558960ap-1
0x1.ba15f474f95a7p250, -0x1.9d46c49adf4ecp1
0x1.ba6e74fdcaafap685, -0x1.c69a403d3e719p-3
0x1.c14ed18d4eb53p652, -0x1.231bb32f82a5fp-1
0x1.c44727ecf4620p-965, 0x1.c61391aad6567p-6
0x1.c492c6882ec27p-423, 0x1.6bb9123ab40fdp-1
0x1.c525d219db143p-681, 0x1.5e10738bb6aefp-5
0x1.ca9510663b619p878, -0x1.8966f1a726428p-2
0x1.d2d4d70d57384p-769, 0x1.eec5e348f3c65p-5
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0x1.dabf72e2c886fp642, -0x1.e930d581ea0c3p-3
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0x1.db25c4ae37695p710, -0x1.ff84b0c08defdp-3
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0x1.e09726def851ap-784, 0x1.8d62918b2f6a5p-5
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0x1.eca182884f17fp-295, 0x1.af55d3375f461p-3
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0x1.f244722a51df2p548, -0x1.20f7a2f2fc3e8p-2
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0x1.f8b79758182dap-884, 0x1.ed6174093fca4p-6
0x1.fa5c677254961p133, -0x1.c91962524971ep-1
0x1.ff0544adacb78p649, -0x1.6c17c3a7210e2p-1