compiler/stdc/math/ld128/s_erfl.c

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