mirror of
https://sourceware.org/git/glibc.git
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c3d466cba1
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.
510 lines
23 KiB
Plaintext
510 lines
23 KiB
Plaintext
## args: double:double
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## ret: double
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## includes: math.h
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42.0, 42.0
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0x1.8368e4ed700bbp-57, 0x1.0000000000000p-64
|
|
-0x1.7c5d037e915cep538, -0x1.aa30914f141e5p-886
|
|
-0x1.9ff485cb26fa7p227, 0x1.82c1703140ceep465
|
|
-0x1.bc56157fec778p-542, -0x1.898e228074677p-385
|
|
0x1.eb16d56eb1d78p-224, 0x1.393ef32f107adp205
|
|
-0x1.10bf71d60a4d1p-524, 0x1.335ac0ca90f62p1004
|
|
0x1.392bc7ade8723p528, -0x1.50ea12907473fp21
|
|
0x1.a26d44e3b408fp-896, 0x1.beda15a2a2799p129
|
|
0x1.6d0d67d7d2ad2p627, 0x1.35c77413a4d2fp190
|
|
-0x1.47a744db0c087p689, -0x1.0445309d5d5bdp-205
|
|
0x1.0d3c074692057p781, -0x1.885716d3dcfbap146
|
|
0x1.5feca3ddab161p-509, 0x1.3e0c341715e1cp217
|
|
0x1.001af5dcc9beep589, 0x1.0000000000000p-64
|
|
0x1.0b0f700297c73p388, 0x1.0000000000000p-64
|
|
-0x1.4591e2de659a7p796, 0x1.4ab1a273f0697p736
|
|
0x1.1e68964b6cc85p6, -0x1.d50762f9e9ce4p59
|
|
0x1.40a7f08b7509dp-373, 0x1.6784b7c373049p207
|
|
0x1.c43b310d38279p-924, 0x1.d4b5d23a0b96dp239
|
|
0x1.421436f55761ep-12, 0x1.320481b0055a7p227
|
|
-0x1.135fa0f337e6ep856, -0x1.ed172226e05edp335
|
|
-0x1.d0a84005691b7p763, -0x1.68f840a20c734p60
|
|
-0x1.6153c39025700p908, -0x1.87eff6801054cp257
|
|
0x1.ad64258a1c8aep201, -0x1.eb202553cc800p129
|
|
0x1.09a810c8ff945p866, -0x1.0000000000000p-64
|
|
0x1.d14433f742c09p-360, 0x1.f4ff819b628ddp21
|
|
0x1.0c04a59d1fa4fp562, 0x1.66b354392a531p134
|
|
-0x1.84297333218cep712, 0x1.497396c926ddfp73
|
|
-0x1.fb9fd6c57d283p-969, -0x1.eb21f1c75479dp195
|
|
0x1.dd87e7279e72bp748, -0x1.0000000000000p-64
|
|
0x1.e494b3d72a143p612, -0x1.3b94e6aa337a0p-57
|
|
0x1.4a6b277bdabe4p-613, -0x1.0000000000000p-64
|
|
0x1.aa78012aaa9c7p338, 0x1.0000000000000p-64
|
|
-0x1.ab74577adade9p149, -0x1.2057c78ee21ccp31
|
|
0x1.3974c5e1e2049p105, -0x1.d3dbb0fb0baf1p54
|
|
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
|
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0x1.14f5b49e12b8fp-751, 0x1.522c717bca3eap0
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0x1.4ba3f35d2f4afp-333, 0x1.6e39f0895a072p-3
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0x1.c14ed18d4eb53p652, -0x1.231bb32f82a5fp-1
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0x1.c44727ecf4620p-965, 0x1.c61391aad6567p-6
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0x1.c492c6882ec27p-423, 0x1.6bb9123ab40fdp-1
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0x1.c525d219db143p-681, 0x1.5e10738bb6aefp-5
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0x1.ca9510663b619p878, -0x1.8966f1a726428p-2
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0x1.d2d4d70d57384p-769, 0x1.eec5e348f3c65p-5
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0x1.d3275243b3fd2p-203, 0x1.a56f87acf7afbp1
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0x1.d5d3022665384p-509, 0x1.d4f984b477a34p-5
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0x1.dabf72e2c886fp642, -0x1.e930d581ea0c3p-3
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0x1.daffa04064cf7p799, -0x1.b944c271f477bp-1
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0x1.db25c4ae37695p710, -0x1.ff84b0c08defdp-3
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0x1.dc06652f06a70p-689, 0x1.f2eb368dd304ap-3
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0x1.e09726def851ap-784, 0x1.8d62918b2f6a5p-5
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0x1.e1561576de8f5p-470, 0x1.983137f5396b2p-2
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0x1.e5e4c7891da9bp-871, 0x1.5775130263654p-5
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0x1.eca182884f17fp-295, 0x1.af55d3375f461p-3
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0x1.f1c172bc4f401p-360, 0x1.f40476496c282p-4
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0x1.f244722a51df2p548, -0x1.20f7a2f2fc3e8p-2
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0x1.f422f159f235bp126, -0x1.339620de97b69p1
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0x1.f43463d9cef16p-845, 0x1.2c364792462fep-3
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0x1.f8b79758182dap-884, 0x1.ed6174093fca4p-6
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0x1.fa5c677254961p133, -0x1.c91962524971ep-1
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0x1.ff0544adacb78p649, -0x1.6c17c3a7210e2p-1
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