expm1 # Name of the function to test # expm1.testdata # copyright (C) 2005 Ch. Q. Lauter and V.Lefevre # This file is part of crlibm and is distributed under the GNU Public Licence # See file COPYING for details # The following lines are either comments (beginning with a #) # or give # 1/ a rounding mode : RN|RU|RD|RZ (crlibm syntax) or N|P|M|Z (libmcr syntax) # 2/ The high and low hexadecimal halves of an input # 3/ The high and low hexadecimal halves of the expected corresponding output # TODO: VERIFY THIS VALUES # Special cases N 00000000 00000000 00000000 00000000 # zero N 80000000 00000000 80000000 00000000 # -zero P 00000000 00000000 00000000 00000000 # zero P 80000000 00000000 80000000 00000000 # -zero M 00000000 00000000 00000000 00000000 # zero M 80000000 00000000 80000000 00000000 # -zero Z 00000000 00000000 00000000 00000000 # zero Z 80000000 00000000 80000000 00000000 # -zero N 00000000 00000001 00000000 00000001 # smallest denorm positive N 80000000 00000001 80000000 00000001 # smallest denorm negative P 00000000 00000001 00000000 00000002 # smallest denorm positive P 80000000 00000001 80000000 00000000 # smallest denorm negative M 00000000 00000001 00000000 00000001 # smallest denorm positive M 80000000 00000001 80000000 00000001 # smallest denorm negative Z 00000000 00000001 00000000 00000001 # smallest denorm positive Z 80000000 00000001 80000000 00000000 # smallest denorm negative N 7ff00000 00000000 7ff00000 00000000 # +inf N fff00000 00000000 bff00000 00000000 # -inf P 7ff00000 00000000 7ff00000 00000000 # +inf P fff00000 00000000 bff00000 00000000 # -inf M 7ff00000 00000000 7ff00000 00000000 # +inf M fff00000 00000000 bff00000 00000000 # -inf Z 7ff00000 00000000 7ff00000 00000000 # +inf Z fff00000 00000000 bff00000 00000000 # -inf N fff80000 00000000 fff80000 00000000 # NaN P fff80000 00000000 fff80000 00000000 # NaN M fff80000 00000000 fff80000 00000000 # NaN Z fff80000 00000000 fff80000 00000000 # NaN # Overflows N 40862E42 FEFA39EE 7fefffff fffffb2a N 40862E42 FEFA39EF 7fefffff ffffff2a N 40862E42 FEFA39F0 7ff00000 00000000 N 40862E42 FEFA39F1 7ff00000 00000000 P 40862E42 FEFA39EE 7fefffff fffffb2b P 40862E42 FEFA39EF 7fefffff ffffff2b P 40862E42 FEFA39F0 7ff00000 00000000 P 40862E42 FEFA39F1 7ff00000 00000000 M 40862E42 FEFA39EE 7fefffff fffffb2a M 40862E42 FEFA39EF 7fefffff ffffff2a M 40862E42 FEFA39F0 7fefffff ffffffff M 40862E42 FEFA39F1 7fefffff ffffffff Z 40862E42 FEFA39EE 7fefffff fffffb2a Z 40862E42 FEFA39EF 7fefffff ffffff2a Z 40862E42 FEFA39F0 7fefffff ffffffff Z 40862E42 FEFA39F1 7fefffff ffffffff # -1.0 + correction in result N C0420596 6F2B4F12 bfefffff fffffffe N C042B708 872320E1 bfefffff ffffffff N C042B708 872320E2 bff00000 00000000 N C042B708 872320E3 bff00000 00000000 N C5000000 00000000 bff00000 00000000 P C0420596 6F2B4F12 bfefffff fffffffd P C0425000 00000000 bfefffff fffffffe P C042B708 872320E1 bfefffff ffffffff P C042B708 872320E2 bfefffff ffffffff P C042B708 872320E3 bfefffff ffffffff P C5000000 00000000 bfefffff ffffffff M C0420596 6F2B4F12 bfefffff fffffffe M C0425000 00000000 bfefffff ffffffff M C042B708 872320E1 bff00000 00000000 M C042B708 872320E2 bff00000 00000000 M C042B708 872320E3 bff00000 00000000 M C5000000 00000000 bff00000 00000000 Z C0420596 6F2B4F12 bfefffff fffffffd Z C0425000 00000000 bfefffff fffffffe Z C042B708 872320E1 bfefffff ffffffff Z C042B708 872320E2 bfefffff ffffffff Z C042B708 872320E3 bfefffff ffffffff Z C5000000 00000000 bfefffff ffffffff # Passing into "x + correction is result" path N 3c8fffff fffffffe 3c8fffff fffffffe N 3c8fffff ffffffff 3c8fffff ffffffff N 3c900000 00000000 3c900000 00000000 N 3c900000 00000001 3c900000 00000001 N 3c900000 00000002 3c900000 00000002 P 3c8fffff fffffffd 3c8fffff fffffffe P 3c8fffff fffffffe 3c8fffff ffffffff P 3c8fffff ffffffff 3c900000 00000000 P 3c900000 00000000 3c900000 00000001 P 3c900000 00000001 3c900000 00000002 P 3c900000 00000002 3c900000 00000003 M 3c8fffff fffffffe 3c8fffff fffffffe M 3c8fffff ffffffff 3c8fffff ffffffff M 3c900000 00000000 3c900000 00000000 M 3c900000 00000001 3c900000 00000001 M 3c900000 00000002 3c900000 00000002 Z 3c8fffff fffffffe 3c8fffff fffffffe Z 3c8fffff ffffffff 3c8fffff ffffffff Z 3c900000 00000000 3c900000 00000000 Z 3c900000 00000001 3c900000 00000001 Z 3c900000 00000002 3c900000 00000002 N bc8fffff fffffffe bc8fffff fffffffe N bc8fffff ffffffff bc8fffff ffffffff N bc900000 00000000 bc900000 00000000 N bc900000 00000001 bc900000 00000001 N bc900000 00000002 bc900000 00000002 P bc8fffff fffffffd bc8fffff fffffffc P bc8fffff fffffffe bc8fffff fffffffd P bc8fffff ffffffff bc8fffff fffffffe P bc900000 00000000 bc8fffff ffffffff P bc900000 00000001 bc900000 00000000 P bc900000 00000002 bc900000 00000001 M bc8fffff fffffffe bc8fffff fffffffe M bc8fffff ffffffff bc8fffff ffffffff M bc900000 00000000 bc900000 00000000 M bc900000 00000001 bc900000 00000001 M bc900000 00000002 bc900000 00000002 Z bc8fffff fffffffe bc8fffff fffffffd Z bc8fffff ffffffff bc8fffff fffffffe Z bc900000 00000000 bc8fffff ffffffff Z bc900000 00000001 bc900000 00000000 Z bc900000 00000002 bc900000 00000001 # Regression test: the bug found by Morten N c010a29d 7d64ae2c bfef7ffd 67be64da # Some difficult cases N 3FE4297E C53F6B7F 3fec1664 0ad39959 N 3FEACCFB E46B4EF0 3ff4f85c 9783dce1 N 3FD8BBE2 FB45C151 3fde3186 ba9d4d49 N 3FC4E88C 5ACCFDA5 3fc6b684 47b2f2fd N 3FBE923C 188EA79B 3fc03c5a 420857cf M 3FE4297E C53F6B7F 3fec1664 0ad39959 M 3FEACCFB E46B4EF0 3ff4f85c 9783dce0 M 3FD8BBE2 FB45C151 3fde3186 ba9d4d49 M 3FC4E88C 5ACCFDA5 3fc6b684 47b2f2fc M 3FBE923C 188EA79B 3fc03c5a 420857cf P 3FE4297E C53F6B7F 3fec1664 0ad3995a P 3FEACCFB E46B4EF0 3ff4f85c 9783dce1 P 3FD8BBE2 FB45C151 3fde3186 ba9d4d4a P 3FC4E88C 5ACCFDA5 3fc6b684 47b2f2fd P 3FBE923C 188EA79B 3fc03c5a 420857d0 Z 3FE4297E C53F6B7F 3fec1664 0ad39959 Z 3FEACCFB E46B4EF0 3ff4f85c 9783dce0 Z 3FD8BBE2 FB45C151 3fde3186 ba9d4d49 Z 3FC4E88C 5ACCFDA5 3fc6b684 47b2f2fc Z 3FBE923C 188EA79B 3fc03c5a 420857cf # Very worst case. 95 identical bits, it's probably our best. It is not a random one, though. Z 0x3CE7FFFF 0xFFFFFFFD 0x3CE80000 0x00000005 # 2.664535259100374513725358171900e-15 # One in five of the very worst cases computed by Lefevre and Muller. # Rounding these values requires evaluating the function to at least 2^(-100). # These worst cases have been selected thanks to the filterlists 5 script # If you want the full list please contact Jean-Michel Muller Z 0x3FE005AE 0x04256BAB 0x3FE4CBB1 0x357E7A3D # 5.006933289508784801213892023952e-01 Z 0x3FE0727A 0xF5FEE8F6 0x3FE58065 0x51A5D846 # 5.139746479610767249113223442691e-01 Z 0x3FE12FCC 0xE02EFB32 0x3FE6C09C 0x32841319 # 5.370849970421203156689671232016e-01 Z 0x3FE41C9E 0x095CD545 0x3FEBFE3A 0x84BBD0F1 # 6.284933264602520219810344315192e-01 Z 0x3FEACCFB 0xE46B4EF0 0x3FF4F85C 0x9783DCE0 # 8.375224553405740124389922129922e-01 Z 0x3F54B7B1 0x868AB960 0x3F54BB0C 0x524BB555 # 1.264499058531841357844172080149e-03 N 0x3F574C94 0xBF209126 0x3F5750D2 0xF63268FD # 1.422066936819518703088993660799e-03 Z 0x3F59FD79 0x1855C814 0x3F5A02C0 0xC886FB74 # 1.586311585324744373448613288247e-03 Z 0x3F5A77EB 0x3F6D31C5 0x3F5A7D65 0x289493FA # 1.615504964962531349662033797188e-03 N 0x3F5ACF4B 0xCBF84D75 0x3F5AD4EA 0x1B49C9A0 # 1.636337299605409136352140997417e-03 N 0x3F5D68E0 0xCE210935 0x3F5D6FA3 0xB3048628 # 1.795024429626379926586143831457e-03 N 0x3F4ABCCF 0x85927836 0x3F4ABF9A 0x9CC4B305 # 8.159650125383391666006316356174e-04 N 0x3F342391 0xDA930C99 0x3F34245C 0xA9C2261D # 3.072959030527372078535341959338e-04 Z 0x3F3581FC 0x77565990 0x3F3582E3 0xC886ABA8 # 3.281823513473719824973251490974e-04 Z 0x3F39B2EB 0xD6CE08AE 0x3F39B436 0x19696F09 # 3.921342638976238427137022135582e-04 N 0x3F3BBF2D 0x53E60743 0x3F3BC0AE 0x52F8E3CA # 4.233823455238492033773922695872e-04 N 0x3F226F95 0x1DE92A8B 0x3F226FEA 0x1754F931 # 1.406545188323459134090848143828e-04 Z 0x3F2BADF1 0xEFCA64D6 0x3F2BAEB1 0x7D0C6B9E # 2.111776192535222136485717481236e-04 Z 0x3F2C6A98 0x0FFB27B4 0x3F2C6B61 0xF320BB96 # 2.167997954443647229752500926736e-04 N 0x3F2E1DE9 0x6FADA839 0x3F2E1ECC 0x35AD2463 # 2.297732788421618006519803190102e-04 N 0x3F16A6B3 0x6BE58808 0x3F16A6F3 0x8ECB0F3A # 8.640737630608030534623553720053e-05 Z 0x3F165530 0x0604782A 0x3F16556E 0x5E8BBE3C # 8.519273388116256639536472139440e-05 N 0x3F1A2533 0x42489FF1 0x3F1A2588 0xB57CF6FE # 9.973645553229528381514873425218e-05 N 0x3F027B36 0x6256F194 0x3F027B4B 0xBB56940E # 3.525027959081213448956637623866e-05 N 0x3F0DEC50 0x4595F456 0x3F0DEC88 0x3C20F85D # 5.707378358985801247976049621613e-05 N 0x3EF04289 0x07E1378F 0x3EF04291 0x4AF76376 # 1.550665228249693011904584982741e-05 N 0x3EF2F985 0x6C3059EF 0x3EF2F990 0xAC848CD1 # 1.809567653418027235469843494453e-05 Z 0x3EF450E4 0x9B4A3789 0x3EF450F1 0x8139EC99 # 1.937483621588341402655099321439e-05 Z 0x3EF31B6A 0x89DB0407 0x3EF31B75 0xF2858F83 # 1.822194518897107413913337425893e-05 N 0x3EF51FCE 0x10251A48 0x3EF51FDC 0x02094EF7 # 2.014564325605376041324057201365e-05 N 0x3EF7CBE2 0xAD7E2C54 0x3EF7CBF4 0x5FAFD5DA # 2.269404180270066112307808525728e-05 Z 0x3EFADC6B 0xB5B1C2E0 0x3EFADC82 0x41DBB2AC # 2.561666347528329234356503363301e-05 Z 0x3EE0B0C6 0x2F2B5CC6 0x3EE0B0CA 0x89777A80 # 7.958662057756793055699959249516e-06 Z 0x3EEC8D9B 0x5668584E 0x3EEC8DA8 0x138D5FCC # 1.361520362501088989687879349244e-05 Z 0x3EEDBE37 0x6499989C 0x3EEDBE45 0x37356D33 # 1.418258320313682600789448318146e-05 Z 0x3ED9149D 0x0F28BBF7 0x3ED914A1 0xF93A0C0E # 5.979662307128110624915209164731e-06 Z 0x3EDD8B91 0xFB7C7038 0x3EDD8B98 0xCD53D288 # 7.044123712576142142937490886467e-06 N 0x3EDB8C6E 0xB5FFAC92 0x3EDB8C74 0xA3D94DB0 # 6.568089560214601817689401841438e-06 N 0x3EC67BA8 0x0988725A 0x3EC67BAA 0x03052C7D # 2.680186366411837655982387113029e-06 Z 0x3EC84709 0xFFC724E4 0x3EC8470C 0x4D2CE0A9 # 2.894103088933566825355532536879e-06 N 0x3EC99213 0x264807DC 0x3EC99215 0xB4234AB9 # 3.048253619520621701221956001415e-06 Z 0x3ECB7F93 0x4085ACB6 0x3ECB7F96 0x34AE85E7 # 3.278057651259065677351849793508e-06 Z 0x3ECCF8EE 0xB2D2568B 0x3ECCF8F1 0xFA38DC57 # 3.453778296756361789512359758425e-06 Z 0x3ECF0077 0x055498F1 0x3ECF007A 0xC671BA0A # 3.695704473688427787130385618330e-06 Z 0x3ECE98F1 0x67ABEA1A 0x3ECE98F5 0x0FE0288D # 3.647498315271071024038385816057e-06 Z 0x3FDA3A7A 0xDD74F25A 0x3FE0359F 0x11A22A8D # 4.098193323768889451130803536216e-01 Z 0x3FDBCAB2 0x7D05ABDE 0x3FE166CE 0x703B05E9 # 4.342466565055341787271458997566e-01 N 0x3EB1B990 0xCAB42256 0x3EB1B991 0x67CA04B7 # 1.056484317642688086023297286409e-06 N 0x3EB11E54 0x952CC21E 0x3EB11E55 0x27B22F41 # 1.020340808021689558477860734764e-06 Z 0x3EB3763A 0x907B12F8 0x3EB3763B 0x4DDCBD83 # 1.160015530675047266680015300988e-06 N 0x3EBA4406 0xCB34C9D4 0x3EBA4408 0x24269011 # 1.565559426830292909422776698181e-06 Z 0x3EBE7385 0x6741E035 0x3EBE7387 0x36E5A540 # 1.815036196920968968257785632059e-06 Z 0x3EA6A2E7 0x751F12F3 0x3EA6A2E7 0xF538F14F # 6.746156293526846286067052103907e-07 Z 0x3EA7170F 0x38AD676A 0x3EA7170F 0xBDF71D66 # 6.881378892084896807648840624805e-07 N 0x3EAAFB5C 0x5E4486F4 0x3EAAFB5D 0x1445EE81 # 8.041226320679659189986313722054e-07 Z 0x3EAD610B 0x08165E99 0x3EAD610B 0xDFDEB506 # 8.755646520473109463056815733595e-07 Z 0x3EAEFBD6 0x48CEF1D2 0x3EAEFBD7 0x38CE7467 # 9.233873626761688504762043763763e-07 Z 0x3E90F617 0x0091B49B 0x3E90F617 0x2487A2D7 # 2.527428937863281450681453548651e-07 N 0x3E9371A1 0xEC60762F 0x3E9371A2 0x1BA285AA # 2.897363454728492891089781154784e-07 Z 0x3E9EF8E3 0xDED3507F 0x3E9EF8E4 0x56BC3E05 # 4.615221474550486239562076869886e-07 Z 0x3E99FED4 0x2C04A907 0x3E99FED4 0x807D0D07 # 3.873620180334250951617711036107e-07 N 0x3E96EB68 0xE8C7B02A 0x3E96EB69 0x2A7180E1 # 3.415282001917601564412057570108e-07 N 0x3E85540C 0x0F13FD48 0x3E85540C 0x2B825688 # 1.589082852318328754247451009562e-07 N 0x3E8A3197 0x2381BD0C 0x3E8A3197 0x4E638221 # 1.951583656930781513543448311976e-07 Z 0x3E708E89 0xD859A836 0x3E708E89 0xE0EAACFB # 6.167885232560242796691471391796e-08 N 0x3E71A4D6 0xF93A29EF 0x3E71A4D7 0x02F49F7D # 6.572866900249659935210640301570e-08 Z 0x3E740174 0x397FD869 0x3E740174 0x4601A9C7 # 7.452696448848514941270014056221e-08 Z 0x3E7AD800 0xB3A6A7FD 0x3E7AD800 0xCA2B5B37 # 1.000008013398725021377989982847e-07 Z 0x3E781B0F 0x381CFF0C 0x3E781B0F 0x4A45ACCB # 8.980073398518289150930789081773e-08 N 0x3E7725D1 0x832DBE89 0x3E7725D1 0x93EC486F # 8.623200713013558743784897154053e-08 Z 0x3E6CDD26 0xCDB8D888 0x3E6CDD26 0xDABD56B0 # 5.376315367589579226827883363937e-08 Z 0x3E6D7A90 0xE8EA82C5 0x3E6D7A90 0xF67E80D5 # 5.490849474166313689473215031191e-08 N 0x3E6F21AC 0x1D3378F2 0x3E6F21AC 0x2C58296B # 5.798699800341913557350355607270e-08 Z 0x3E6FAD44 0xFD7AB54B 0x3E6FAD45 0x0D28653F # 5.900270111151337939155666115730e-08 Z 0x3E5B0E54 0xBEAA5F54 0x3E5B0E54 0xC4626CB0 # 2.519784551377563473767976680653e-08 N 0x3E570979 0x0C9CEF04 0x3E570979 0x10C25739 # 2.145488123900374738431499075167e-08 Z 0x3E497EF8 0xC7A6A15A 0x3E497EF8 0xCA30ACEA # 1.187249253495058302790544316630e-08 N 0x3E4BDDFE 0x561DBEF3 0x3E4BDDFE 0x5926531B # 1.297665858424598428062944399436e-08 Z 0x3E4E76EE 0x51AFCFBA 0x3E4E76EE 0x554FE6D6 # 1.418617272782483634263233425888e-08 Z 0x3E310D3E 0xD6D5160F 0x3E310D3E 0xD7667793 # 3.970167622884932487740220359010e-09 Z 0x3E3BE4C1 0xB571A289 0x3E3BE4C1 0xB6F6A92C # 6.494480362438469762460236230301e-09 Z 0x3E3CFDF2 0xA63E8C69 0x3E3CFDF2 0xA7E2D0E8 # 6.750222245670706013815512647408e-09 N 0x3E39D6F3 0x75A07C12 0x3E39D6F3 0x76EE5417 # 6.016262899351159692087286881990e-09 Z 0x3E3B5B7B 0x347EB1A5 0x3E3B5B7B 0x35F4E7FC # 6.369629108811366297460832545290e-09 Z 0x3E3FA3AD 0xE2DDED37 0x3E3FA3AD 0xE4D27398 # 7.366615357536089054625238293833e-09 Z 0x3E2668E8 0x98383C47 0x3E2668E8 0x98B5C905 # 2.608843975707637591842709778411e-09 N 0x3FCC24B7 0x1882CFF3 0x3FCF7A27 0x4060D907 # 2.198704595263048788833515345686e-01 Z 0x3FCFDE31 0xA71DDBA9 0x3FD217C7 0x9B0566B5 # 2.489683214186844406601295531800e-01 N 0x3E1F75B2 0x0F5AC212 0x3E1F75B2 0x0FD678FA # 1.831198357374760117422428918580e-09 N 0x3E081606 0x0FBA05B5 0x3E081606 0x0FDE47E5 # 7.009957332081317687745861915295e-10 Z 0x3E0FCFFD 0xBC85BE3E 0x3E0FCFFD 0xBCC4FEC5 # 9.258646011715036043020402617052e-10 N 0x3E0EFC07 0x5BB4E78F 0x3E0EFC07 0x5BF0E82D # 9.017672645180203612081538623233e-10 N 0x3DF079DF 0x58D66228 0x3DF079DF 0x58DEDDD8 # 2.397582903371179136683931512131e-10 Z 0x3DF3BEC3 0x33A0F929 0x3DF3BEC3 0x33AD2822 # 2.873299824013314191185535394001e-10 Z 0x3DF48A85 0x1B06182A 0x3DF48A85 0x1B1347A7 # 2.989122517419990964741322775399e-10 Z 0x3DFAA288 0x4AE7DE9A 0x3DFAA288 0x4AFE09F1 # 3.875886928296320111934657270220e-10 Z 0x3DE01FFF 0xFFFEA550 0x3DE02000 0x0002B55F # 1.173248165264135572621242168062e-10 Z 0x3DE007FF 0xFFFEA955 0x3DE00800 0x0002AD55 # 1.166426955001104601102603458055e-10 Z 0x3DE07FFF 0xFFFE9500 0x3DE08000 0x0002D5FF # 1.200533006316243949059311638822e-10 Z 0x3DE097FF 0xFFFE90DD 0x3DE09800 0x0002DE45 # 1.207354216579267165759707664194e-10 Z 0x3DE187FF 0xFFFE6635 0x3DE18800 0x00033395 # 1.275566319209414029762998386941e-10 Z 0x3DE10FFF 0xFFFE7BD4 0x3DE11000 0x00030857 # 1.241460267894359984806959737154e-10 Z 0x3DE1FFFF 0xFFFE5000 0x3DE20000 0x00035FFF # 1.309672370524429300627823613556e-10 Z 0x3DE16FFF 0xFFFE6A94 0x3DE17000 0x00032AD7 # 1.268745108946406322699087730838e-10 Z 0x3DE1E7FF 0xFFFE547D 0x3DE1E800 0x00035705 # 1.302851160261429348382155642087e-10 Z 0x3DE0F7FF 0xFFFE8015 0x3DE0F800 0x0002FFD5 # 1.234639057631344522924806396416e-10 N 0x3DE22BE6 0x06863DB3 0x3DE22BE6 0x068B6682 # 1.322149085198737521897341807607e-10 Z 0x3DE277FF 0xFFFE3935 0x3DE27800 0x00038D95 # 1.343778421839405797401435416999e-10 Z 0x3DE2D7FF 0xFFFE268D 0x3DE2D800 0x0003B2E5 # 1.371063262891359077474651195070e-10 Z 0x3DE2EFFF 0xFFFE21D4 0x3DE2F000 0x0003BC57 # 1.377884473154343520083833797270e-10 Z 0x3DE52FFF 0xFFFDA974 0x3DE53000 0x0004AD17 # 1.541593519465504853609655172011e-10 Z 0x3DE547FF 0xFFFDA425 0x3DE54800 0x0004B7B5 # 1.548414729728450522127624351039e-10 Z 0x3DE6AFFF 0xFFFD51B4 0x3DE6B000 0x00055C97 # 1.650732883672449434259337605233e-10 Z 0x3DE367FF 0xFFFE09DD 0x3DE36800 0x0003EC45 # 1.411990524469242468675018754368e-10 Z 0x3DE3C7FF 0xFFFDF645 0x3DE3C800 0x00041375 # 1.439275365521133710202293055363e-10 Z 0x3DE4CFFF 0xFFFDBE74 0x3DE4D000 0x00048317 # 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