1 /* @(#)s_erf.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 __FBSDID("$FreeBSD$"); 15 16 /* 17 * See s_erf.c for complete comments. 18 * 19 * Converted to long double by Steven G. Kargl. 20 */ 21 #include <float.h> 22 23 #include "fpmath.h" 24 #include "math.h" 25 #include "math_private.h" 26 27 /* XXX Prevent compilers from erroneously constant folding these: */ 28 static const volatile long double tiny = 0x1p-10000L; 29 30 static const double 31 half= 0.5, 32 one = 1, 33 two = 2; 34 /* 35 * In the domain [0, 2**-40], only the first term in the power series 36 * expansion of erf(x) is used. The magnitude of the first neglected 37 * terms is less than 2**-120. 38 */ 39 static const long double 40 efx = 1.28379167095512573896158903121545167e-01L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06fc3f */ 41 efx8 = 1.02703333676410059116927122497236133e+00L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06ff3f */ 42 /* 43 * Domain [0, 0.84375], range ~[-1.919e-38, 1.919e-38]: 44 * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-125.29 45 */ 46 pp0 = 1.28379167095512573896158903121545167e-01L, /* 0x3ffc06eb, 0xa8214db6, 0x88d71d48, 0xa7f6bfec */ 47 pp1 = -3.14931554396568573802046931159683404e-01L, /* 0xbffd427d, 0x6ada7263, 0x547eb096, 0x95f37463 */ 48 pp2 = -5.27514920282183487103576956956725309e-02L, /* 0xbffab023, 0xe5a271e3, 0xb0e79b01, 0x2f7ac962 */ 49 pp3 = -1.13202828509005281355609495523452713e-02L, /* 0xbff872f1, 0x6a5023a1, 0xe08b3884, 0x326af20f */ 50 pp4 = -9.18626155872522453865998391206048506e-04L, /* 0xbff4e19f, 0xea5fb024, 0x43247a37, 0xe430b06c */ 51 pp5 = -7.87518862406176274922506447157284230e-05L, /* 0xbff14a4f, 0x31a85fe0, 0x7fff2204, 0x09c49b37 */ 52 pp6 = -3.42357944472240436548115331090560881e-06L, /* 0xbfeccb81, 0x4b43c336, 0xcd2eb6c2, 0x903f2d87 */ 53 pp7 = -1.37317432573890412634717890726745428e-07L, /* 0xbfe826e3, 0x0e915eb6, 0x42aee414, 0xf7e36805 */ 54 pp8 = -2.71115170113861755855049008732113726e-09L, /* 0xbfe2749e, 0x2b94fd00, 0xecb4d166, 0x0efb91f8 */ 55 pp9 = -3.37925756196555959454018189718117864e-11L, /* 0xbfdc293e, 0x1d9060cb, 0xd043204a, 0x314cd7f0 */ 56 qq1 = 4.76672625471551170489978555182449450e-01L, /* 0x3ffde81c, 0xde6531f0, 0x76803bee, 0x526e29e9 */ 57 qq2 = 1.06713144672281502058807525850732240e-01L, /* 0x3ffbb518, 0xd7a6bb74, 0xcd9bdd33, 0x7601eee5 */ 58 qq3 = 1.47747613127513761102189201923147490e-02L, /* 0x3ff8e423, 0xae527e18, 0xf12cb447, 0x723b4749 */ 59 qq4 = 1.39939377672028671891148770908874816e-03L, /* 0x3ff56ed7, 0xba055d84, 0xc21b45c4, 0x388d1812 */ 60 qq5 = 9.44302939359455241271983309378738276e-05L, /* 0x3ff18c11, 0xc18c99a4, 0x86d0fe09, 0x46387b4c */ 61 qq6 = 4.56199342312522842161301671745365650e-06L, /* 0x3fed3226, 0x73421d05, 0x08875300, 0x32fa1432 */ 62 qq7 = 1.53019260483764773845294600092361197e-07L, /* 0x3fe8489b, 0x3a63f627, 0x2b9ad2ce, 0x26516e57 */ 63 qq8 = 3.25542691121324805094777901250005508e-09L, /* 0x3fe2bf6c, 0x26d93a29, 0x9142be7c, 0x9f1dd043 */ 64 qq9 = 3.37405581964478060434410167262684979e-11L; /* 0x3fdc28c8, 0xfb8fa1be, 0x10e57eec, 0xaa19e49f */ 65 66 static const long double 67 erx = 8.42700792949714894142232424201210961e-01L, /* 0x3ffeaf76, 0x7a741088, 0xb0000000, 0x00000000 */ 68 /* 69 * Domain [0.84375, 1.25], range ~[-2.521e-36, 2.523e-36]: 70 * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-120.15 71 */ 72 pa0 = -2.48010117891186017024438233323795897e-17L, /* 0xbfc7c97f, 0x77812279, 0x6c877f22, 0xef4bfb2e */ 73 pa1 = 4.15107497420594680894327969504526489e-01L, /* 0x3ffda911, 0xf096fbc2, 0x55662005, 0x2337fa64 */ 74 pa2 = -3.94180628087084846724448515851892609e-02L, /* 0xbffa42e9, 0xab54528c, 0xad529da1, 0x6efc2af3 */ 75 pa3 = 4.48897599625192107295954790681677462e-02L, /* 0x3ffa6fbc, 0xa65edba1, 0x0e4cbcea, 0x73ef9a31 */ 76 pa4 = 8.02069252143016600110972019232995528e-02L, /* 0x3ffb4887, 0x0e8b548e, 0x3230b417, 0x11b553b3 */ 77 pa5 = -1.02729816533435279443621120242391295e-02L, /* 0xbff850a0, 0x041de3ee, 0xd5bca6c9, 0x4ef5f9f2 */ 78 pa6 = 5.70777694530755634864821094419982095e-03L, /* 0x3ff77610, 0x9b501e10, 0x4c978382, 0x742df68f */ 79 pa7 = 1.22635150233075521018231779267077071e-03L, /* 0x3ff5417b, 0x0e623682, 0x60327da0, 0x96b9219e */ 80 pa8 = 5.36100234820204569428412542856666503e-04L, /* 0x3ff41912, 0x27ceb4c1, 0x1d3298ec, 0x84ced627 */ 81 pa9 = -1.97753571846365167177187858667583165e-04L, /* 0xbff29eb8, 0x23f5bcf3, 0x15c83c46, 0xe4fda98b */ 82 pa10 = 6.19333039900846970674794789568415105e-05L, /* 0x3ff103c4, 0x60f88e46, 0xc0c9fb02, 0x13cc7fc1 */ 83 pa11 = -5.40531400436645861492290270311751349e-06L, /* 0xbfed6abe, 0x9665f8a8, 0xdd0ad3ba, 0xe5dc0ee3 */ 84 qa1 = 9.05041313265490487793231810291907851e-01L, /* 0x3ffecf61, 0x93340222, 0xe9930620, 0xc4e61168 */ 85 qa2 = 6.79848064708886864767240880834868092e-01L, /* 0x3ffe5c15, 0x0ba858dc, 0xf7900ae9, 0xfea1e09a */ 86 qa3 = 4.04720609926471677581066689316516445e-01L, /* 0x3ffd9e6f, 0x145e9b00, 0x6d8c1749, 0xd2928623 */ 87 qa4 = 1.69183273898369996364661075664302225e-01L, /* 0x3ffc5a7c, 0xc2a363c1, 0xd6c19097, 0xef9b4063 */ 88 qa5 = 7.44476185988067992342479750486764248e-02L, /* 0x3ffb30ef, 0xfc7259ef, 0x1bcbb089, 0x686dd62d */ 89 qa6 = 2.02981172725892407200420389604788573e-02L, /* 0x3ff94c90, 0x7976cb0e, 0x21e1d36b, 0x0f09ca2b */ 90 qa7 = 6.94281866271607668268269403102277234e-03L, /* 0x3ff7c701, 0x2b193250, 0xc5d46ecc, 0x374843d8 */ 91 qa8 = 1.12952275469171559611651594706820034e-03L, /* 0x3ff52818, 0xfd2a7c06, 0xd13e38fd, 0xda4b34f5 */ 92 qa9 = 3.13736683241992737197226578597710179e-04L, /* 0x3ff348fa, 0x0cb48d18, 0x051f849b, 0x135ccf74 */ 93 qa10 = 1.17037675204033225470121134087771410e-05L, /* 0x3fee88b6, 0x98f47704, 0xa5d8f8f2, 0xc6422e11 */ 94 qa11 = 4.61312518293853991439362806880973592e-06L, /* 0x3fed3594, 0xe31db94f, 0x3592b693, 0xed4386b4 */ 95 qa12 = -1.02158572037456893687737553657431771e-06L; /* 0xbfeb123a, 0xd60d9b1e, 0x1f6fdeb9, 0x7dc8410a */ 96 /* 97 * Domain [1.25,2.85715], range ~[-2.922e-37,2.922e-37]: 98 * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-121.36 99 */ 100 static const long double 101 ra0 = -9.86494292470069009555706994426014461e-03L, /* 0xbff84341, 0x239e8709, 0xe941b06a, 0xcb4b6ec5 */ 102 ra1 = -1.13580436992565640457579040117568870e+00L, /* 0xbfff22c4, 0x133f7c0d, 0x72d5e231, 0x2eb1ee3f */ 103 ra2 = -4.89744330295291950661185707066921755e+01L, /* 0xc00487cb, 0xa38b4fc2, 0xc136695b, 0xc1df8047 */ 104 ra3 = -1.10766149300215937173768072715352140e+03L, /* 0xc00914ea, 0x55e6beb3, 0xabc50e07, 0xb6e5664d */ 105 ra4 = -1.49991031232170934967642795601952100e+04L, /* 0xc00cd4b8, 0xd33243e6, 0xffbf6545, 0x3c57ef6e */ 106 ra5 = -1.29805749738318462882524181556996692e+05L, /* 0xc00ffb0d, 0xbfeed9b6, 0x5b2a3ff4, 0xe245bd3c */ 107 ra6 = -7.42828497044940065828871976644647850e+05L, /* 0xc0126ab5, 0x8fe7caca, 0x473352d9, 0xcd4e0c90 */ 108 ra7 = -2.85637299581890734287995171242421106e+06L, /* 0xc0145cad, 0xa7f76fe7, 0x3e358051, 0x1799f927 */ 109 ra8 = -7.40674797129824999383748865571026084e+06L, /* 0xc015c412, 0x6fe29c02, 0x298ad158, 0x7d24e45c */ 110 ra9 = -1.28653420911930973914078724204151759e+07L, /* 0xc016889e, 0x7c2eb0dc, 0x95d5863b, 0x0aa34dc3 */ 111 ra10 = -1.47198163599330179552932489109452638e+07L, /* 0xc016c136, 0x90b84923, 0xf9bcb497, 0x19bbd0f5 */ 112 ra11 = -1.07812992258382800318665248311522624e+07L, /* 0xc0164904, 0xe673a113, 0x35d7f079, 0xe13701f3 */ 113 ra12 = -4.83545565681708642630419905537756076e+06L, /* 0xc0152721, 0xfea094a8, 0x869eb39d, 0x413d6f13 */ 114 ra13 = -1.23956521201673964822976917356685286e+06L, /* 0xc0132ea0, 0xd3646baa, 0x2fe62b0d, 0xbae5ce85 */ 115 ra14 = -1.62289333553652417591275333240371812e+05L, /* 0xc0103cf8, 0xaab1e2d6, 0x4c25e014, 0x248d76ab */ 116 ra15 = -8.82890392601176969729168894389833110e+03L, /* 0xc00c13e7, 0x3b3d8f94, 0x6fbda6f6, 0xe7049a82 */ 117 ra16 = -1.22591866337261720023681535568334619e+02L, /* 0xc005ea5e, 0x12358891, 0xcfa712c5, 0x77f050d4 */ 118 sa1 = 6.44508918884710829371852723353794047e+01L, /* 0x400501cd, 0xb69a6c0f, 0x5716de14, 0x47161af6 */ 119 sa2 = 1.76118475473171481523704824327358534e+03L, /* 0x4009b84b, 0xd305829f, 0xc4c771b0, 0xbf1f7f9b */ 120 sa3 = 2.69448346969488374857087646131950188e+04L, /* 0x400da503, 0x56bacc05, 0x4fdba68d, 0x2cca27e6 */ 121 sa4 = 2.56826633369941456778326497384543763e+05L, /* 0x4010f59d, 0x51124428, 0x69c41de6, 0xbd0d5753 */ 122 sa5 = 1.60647413092257206847700054645905859e+06L, /* 0x40138834, 0xa2184244, 0x557a1bed, 0x68c9d556 */ 123 sa6 = 6.76963075165099718574753447122393797e+06L, /* 0x40159d2f, 0x7b01b0cc, 0x8bac9e95, 0x5d35d56e */ 124 sa7 = 1.94295690905361884290986932493647741e+07L, /* 0x40172878, 0xc1172d61, 0x3068501e, 0x2f3c71da */ 125 sa8 = 3.79774781017759149060839255547073541e+07L, /* 0x401821be, 0xc30d06fe, 0x410563d7, 0x032111fd */ 126 sa9 = 5.00659831846029484248302236457727397e+07L, /* 0x40187df9, 0x1f97a111, 0xc51d6ac2, 0x4b389793 */ 127 sa10 = 4.36486287620506484276130525941972541e+07L, /* 0x40184d03, 0x3a618ae0, 0x2a723357, 0xfa45c60a */ 128 sa11 = 2.43779678791333894255510508253951934e+07L, /* 0x401773fa, 0x6fe10ee2, 0xc467850d, 0xc6b7ff30 */ 129 sa12 = 8.30732360384443202039372372212966542e+06L, /* 0x4015fb09, 0xee6a5631, 0xdd98de7e, 0x8b00461a */ 130 sa13 = 1.60160846942050515734192397495105693e+06L, /* 0x40138704, 0x8782bf13, 0x5b8fb315, 0xa898abe5 */ 131 sa14 = 1.54255505242533291014555153757001825e+05L, /* 0x40102d47, 0xc0abc98e, 0x843c9490, 0xb4352440 */ 132 sa15 = 5.87949220002375547561467275493888824e+03L, /* 0x400b6f77, 0xe00d21d1, 0xec4d41e8, 0x2f8e1673 */ 133 sa16 = 4.97272976346793193860385983372237710e+01L; /* 0x40048dd1, 0x816c1b3f, 0x24f540a6, 0x4cfe03cc */ 134 /* 135 * Domain [2.85715,9], range ~[-7.886e-37,7.918e-37]: 136 * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-120 137 */ 138 static const long double 139 rb0 = -9.86494292470008707171371994479162369e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e561, 0xf4469360 */ 140 rb1 = -1.57047326624110727986326503729442830L, /* 0xbfff920a, 0x8935bf73, 0x8803b894, 0x4656482d */ 141 rb2 = -1.03228196364885474342132255440317065e2L, /* 0xc0059ce9, 0xac4ed0ff, 0x2cff0ff7, 0x5e70d1ab */ 142 rb3 = -3.74000570653418227179358710865224376e3L, /* 0xc00ad380, 0x2ebf7835, 0xf6b07ed2, 0x861242f7 */ 143 rb4 = -8.35435477739098044190860390632813956e4L, /* 0xc00f4657, 0x8c3ae934, 0x3647d7b3, 0x80e76fb7 */ 144 rb5 = -1.21398672055223642118716640216747152e6L, /* 0xc0132862, 0x2b8761c8, 0x27d18c0f, 0x137c9463 */ 145 rb6 = -1.17669175877248796101665344873273970e7L, /* 0xc0166719, 0x0b2cea46, 0x81f14174, 0x11602ea5 */ 146 rb7 = -7.66108006086998253606773064264599615e7L, /* 0xc019243f, 0x3c26f4f0, 0x1cc05241, 0x3b953728 */ 147 rb8 = -3.32547117558141845968704725353130804e8L, /* 0xc01b3d24, 0x42d8ee26, 0x24ef6f3b, 0x604a8c65 */ 148 rb9 = -9.41561252426350696802167711221739746e8L, /* 0xc01cc0f8, 0xad23692a, 0x8ddb2310, 0xe9937145 */ 149 rb10 = -1.67157110805390944549427329626281063e9L, /* 0xc01d8e88, 0x9a903734, 0x09a55fa3, 0xd205c903 */ 150 rb11 = -1.74339631004410841337645931421427373e9L, /* 0xc01d9fa8, 0x77582d2a, 0xc183b8ab, 0x7e00cb05 */ 151 rb12 = -9.57655233596934915727573141357471703e8L, /* 0xc01cc8a5, 0x460cc685, 0xd0271fa0, 0x6a70e3da */ 152 rb13 = -2.26320062731339353035254704082495066e8L, /* 0xc01aafab, 0xd7d76721, 0xc9720e11, 0x6a8bd489 */ 153 rb14 = -1.42777302996263256686002973851837039e7L, /* 0xc016b3b8, 0xc499689f, 0x2b88d965, 0xc32414f9 */ 154 sb1 = 1.08512869705594540211033733976348506e2L, /* 0x4005b20d, 0x2db7528d, 0x00d20dcb, 0x858f6191 */ 155 sb2 = 5.02757713761390460534494530537572834e3L, /* 0x400b3a39, 0x3bf4a690, 0x3025d28d, 0xfd40a891 */ 156 sb3 = 1.31019107205412870059331647078328430e5L, /* 0x400fffcb, 0x1b71d05e, 0x3b28361d, 0x2a3c3690 */ 157 sb4 = 2.13021555152296846166736757455018030e6L, /* 0x40140409, 0x3c6984df, 0xc4491d7c, 0xb04aa08d */ 158 sb5 = 2.26649105281820861953868568619768286e7L, /* 0x401759d6, 0xce8736f0, 0xf28ad037, 0x2a901e0c */ 159 sb6 = 1.61071939490875921812318684143076081e8L, /* 0x401a3338, 0x686fb541, 0x6bd27d06, 0x4f95c9ac */ 160 sb7 = 7.66895673844301852676056750497991966e8L, /* 0x401c6daf, 0x31cec121, 0x54699126, 0x4bd9bf9e */ 161 sb8 = 2.41884450436101936436023058196042526e9L, /* 0x401e2059, 0x46b0b8d7, 0x87b64cbf, 0x78bc296d */ 162 sb9 = 4.92403055884071695093305291535107666e9L, /* 0x401f257e, 0xbe5ed739, 0x39e17346, 0xcadd2e55 */ 163 sb10 = 6.18627786365587486459633615573786416e9L, /* 0x401f70bb, 0x1be7a7e7, 0x6a45b5ae, 0x607c70f0 */ 164 sb11 = 4.45898013426501378097430226324743199e9L, /* 0x401f09c6, 0xa32643d7, 0xf1724620, 0x9ea46c32 */ 165 sb12 = 1.63006115763329848117160344854224975e9L, /* 0x401d84a3, 0x0996887f, 0x65a4f43b, 0x978c1d74 */ 166 sb13 = 2.39216717012421697446304015847567721e8L, /* 0x401ac845, 0x09a065c2, 0x30095da7, 0x9d72d6ae */ 167 sb14 = 7.84837329009278694937250358810225609e6L; /* 0x4015df06, 0xd5290e15, 0x63031fac, 0x4d9c894c */ 168 /* 169 * Domain [9,108], range ~[-5.324e-38,5.340e-38]: 170 * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-124 171 */ 172 static const long double 173 rc0 = -9.86494292470008707171367567652935673e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e55b, 0x1aa10fd3 */ 174 rc1 = -1.26229447747315096406518846411562266L, /* 0xbfff4325, 0xbb1aab28, 0xda395cd9, 0xfb861c15 */ 175 rc2 = -6.13742634438922591780742637728666162e1L, /* 0xc004eafe, 0x7dd51cd8, 0x3c7c5928, 0x751e50cf */ 176 rc3 = -1.50455835478908280402912854338421517e3L, /* 0xc0097823, 0xbc15b9ab, 0x3d60745c, 0x523e80a5 */ 177 rc4 = -2.04415631865861549920184039902945685e4L, /* 0xc00d3f66, 0x40b3fc04, 0x5388f2ec, 0xb009e1f0 */ 178 rc5 = -1.57625662981714582753490610560037638e5L, /* 0xc01033dc, 0xd4dc95b6, 0xfd4da93b, 0xf355b4a9 */ 179 rc6 = -6.73473451616752528402917538033283794e5L, /* 0xc01248d8, 0x2e73a4f9, 0xcded49c5, 0xfa3bfeb7 */ 180 rc7 = -1.47433165421387483167186683764364857e6L, /* 0xc01367f1, 0xba77a8f7, 0xcfdd0dbb, 0x25d554b3 */ 181 rc8 = -1.38811981807868828563794929997744139e6L, /* 0xc01352e5, 0x7d16d9ad, 0xbbdcbf38, 0x38fbc5ea */ 182 rc9 = -3.59659700530831825640766479698155060e5L, /* 0xc0115f3a, 0xecd57f45, 0x21f8ad6c, 0x910a5958 */ 183 sc1 = 7.72730753022908298637508998072635696e1L, /* 0x40053517, 0xa10d52bc, 0xdabb55b6, 0xbd0328cd */ 184 sc2 = 2.36825757341694050500333261769082182e3L, /* 0x400a2808, 0x3e0a9b42, 0x82977842, 0x9c5de29e */ 185 sc3 = 3.72210540173034735352888847134073099e4L, /* 0x400e22ca, 0x1ba827ef, 0xac8390d7, 0x1fc39a41 */ 186 sc4 = 3.24136032646418336712461033591393412e5L, /* 0x40113c8a, 0x0216e100, 0xc59d1e44, 0xf0e68d9d */ 187 sc5 = 1.57836135851134393802505823370009175e6L, /* 0x40138157, 0x95bc7664, 0x17575961, 0xdbe58eeb */ 188 sc6 = 4.12881981392063738026679089714182355e6L, /* 0x4014f801, 0x9e82e8d2, 0xb8b3a70e, 0xfd84185d */ 189 sc7 = 5.24438427289213488410596395361544142e6L, /* 0x40154017, 0x81177109, 0x2aa6c3b0, 0x1f106625 */ 190 sc8 = 2.59909544563616121735963429710382149e6L, /* 0x40143d45, 0xbb90a9b1, 0x12bf9390, 0xa827a700 */ 191 sc9 = 2.80930665169282501639651995082335693e5L; /* 0x40111258, 0xaa92222e, 0xa97e3216, 0xa237fa6c */ 192 193 long double 194 erfl(long double x) 195 { 196 long double ax,R,S,P,Q,s,y,z,r; 197 uint64_t lx, llx; 198 int32_t i; 199 uint16_t hx; 200 201 EXTRACT_LDBL128_WORDS(hx, lx, llx, x); 202 203 if((hx & 0x7fff) == 0x7fff) { /* erfl(nan)=nan */ 204 i = (hx>>15)<<1; 205 return (1-i)+one/x; /* erfl(+-inf)=+-1 */ 206 } 207 208 ax = fabsl(x); 209 if(ax < 0.84375) { 210 if(ax < 0x1p-40L) { 211 if(ax < 0x1p-16373L) 212 return (8*x+efx8*x)/8; /* avoid spurious underflow */ 213 return x + efx*x; 214 } 215 z = x*x; 216 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+ 217 z*(pp8+z*pp9)))))))); 218 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+ 219 z*(qq8+z*qq9)))))))); 220 y = r/s; 221 return x + x*y; 222 } 223 if(ax < 1.25) { 224 s = ax-one; 225 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+ 226 s*(pa8+s*(pa9+s*(pa10+s*pa11)))))))))); 227 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+ 228 s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12))))))))))); 229 if(x>=0) return (erx + P/Q); else return (-erx - P/Q); 230 } 231 if (ax >= 9) { /* inf>|x|>= 9 */ 232 if(x>=0) return (one-tiny); else return (tiny-one); 233 } 234 s = one/(ax*ax); 235 if(ax < 2.85715) { /* |x| < 2.85715 */ 236 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ 237 s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+ 238 s*(ra15+s*ra16))))))))))))))); 239 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ 240 s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+ 241 s*(sa15+s*sa16))))))))))))))); 242 } else { /* |x| >= 2.85715 */ 243 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+ 244 s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+ 245 s*rb14))))))))))))); 246 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+ 247 s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+ 248 s*sb14))))))))))))); 249 } 250 z = (float)ax; 251 r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); 252 if(x>=0) return (one-r/ax); else return (r/ax-one); 253 } 254 255 long double 256 erfcl(long double x) 257 { 258 long double ax,R,S,P,Q,s,y,z,r; 259 uint64_t lx, llx; 260 uint16_t hx; 261 262 EXTRACT_LDBL128_WORDS(hx, lx, llx, x); 263 264 if((hx & 0x7fff) == 0x7fff) { /* erfcl(nan)=nan */ 265 /* erfcl(+-inf)=0,2 */ 266 return ((hx>>15)<<1)+one/x; 267 } 268 269 ax = fabsl(x); 270 if(ax < 0.84375L) { 271 if(ax < 0x1p-34L) 272 return one-x; 273 z = x*x; 274 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+ 275 z*(pp8+z*pp9)))))))); 276 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+ 277 z*(qq8+z*qq9)))))))); 278 y = r/s; 279 if(ax < 0.25L) { /* x<1/4 */ 280 return one-(x+x*y); 281 } else { 282 r = x*y; 283 r += (x-half); 284 return half - r; 285 } 286 } 287 if(ax < 1.25L) { 288 s = ax-one; 289 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+ 290 s*(pa8+s*(pa9+s*(pa10+s*pa11)))))))))); 291 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+ 292 s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12))))))))))); 293 if(x>=0) { 294 z = one-erx; return z - P/Q; 295 } else { 296 z = erx+P/Q; return one+z; 297 } 298 } 299 300 if(ax < 108) { /* |x| < 108 */ 301 s = one/(ax*ax); 302 if(ax < 2.85715) { /* |x| < 2.85715 */ 303 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ 304 s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+ 305 s*(ra15+s*ra16))))))))))))))); 306 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ 307 s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+ 308 s*(sa15+s*sa16))))))))))))))); 309 } else if(ax < 9) { 310 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+ 311 s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+ 312 s*rb14))))))))))))); 313 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+ 314 s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+ 315 s*sb14))))))))))))); 316 } else { 317 if(x < -9) return two-tiny; /* x < -9 */ 318 R=rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+s*(rc6+s*(rc7+ 319 s*(rc8+s*rc9)))))))); 320 S=one+s*(sc1+s*(sc2+s*(sc3+s*(sc4+s*(sc5+s*(sc6+s*(sc7+ 321 s*(sc8+s*sc9)))))))); 322 } 323 z = (float)ax; 324 r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); 325 if(x>0) return r/ax; else return two-r/ax; 326 } else { 327 if(x>0) return tiny*tiny; else return two-tiny; 328 } 329 } 330