/* @(#)s_erf.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#include <sys/cdefs.h>
/*
* See s_erf.c for complete comments.
*
* Converted to long double by Steven G. Kargl.
*/
#include <float.h>

#include "math.h"
#include "math_private.h"

/* XXX Prevent compilers from erroneously constant folding: */
static const volatile long double tiny = 0x1p-10000L;

static const double
half= 0.5,
one = 1,
two = 2;
/*
* In the domain [0, 2**-34], only the first term in the power series
* expansion of erf(x) is used.  The magnitude of the first neglected
* terms is less than 2**-102.
*/
static const union ieee_ext_u
efxu  = LD80C(0x8375d410a6db446c, -3,  1.28379167095512573902e-1L),
efx8u = LD80C(0x8375d410a6db446c,  0,  1.02703333676410059122e+0L),
/*
* Domain [0, 0.84375], range ~[-1.423e-22, 1.423e-22]:
* |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-72.573
*/
pp0u  = LD80C(0x8375d410a6db446c, -3,   1.28379167095512573902e-1L),
pp1u  = LD80C(0xa46c7d09ec3d0cec, -2,  -3.21140201054840180596e-1L),
pp2u  = LD80C(0x9b31e66325576f86, -5,  -3.78893851760347812082e-2L),
pp3u  = LD80C(0x804ac72c9a0b97dd, -7,  -7.83032847030604679616e-3L),
pp4u  = LD80C(0x9f42bcbc3d5a601d, -12, -3.03765663857082048459e-4L),
pp5u  = LD80C(0x9ec4ad6193470693, -16, -1.89266527398167917502e-5L),
qq1u  = LD80C(0xdb4b8eb713188d6b, -2,   4.28310832832310510579e-1L),
qq2u  = LD80C(0xa5750835b2459bd1, -4,   8.07896272074540216658e-2L),
qq3u  = LD80C(0x8b85d6bd6a90b51c, -7,   8.51579638189385354266e-3L),
qq4u  = LD80C(0x87332f82cff4ff96, -11,  5.15746855583604912827e-4L),
qq5u  = LD80C(0x83466cb6bf9dca00, -16,  1.56492109706256700009e-5L),
qq6u  = LD80C(0xf5bf98c2f996bf63, -24,  1.14435527803073879724e-7L);
#define efx     (efxu.extu_ld)
#define efx8    (efx8u.extu_ld)
#define pp0     (pp0u.extu_ld)
#define pp1     (pp1u.extu_ld)
#define pp2     (pp2u.extu_ld)
#define pp3     (pp3u.extu_ld)
#define pp4     (pp4u.extu_ld)
#define pp5     (pp5u.extu_ld)
#define qq1     (qq1u.extu_ld)
#define qq2     (qq2u.extu_ld)
#define qq3     (qq3u.extu_ld)
#define qq4     (qq4u.extu_ld)
#define qq5     (qq5u.extu_ld)
#define qq6     (qq6u.extu_ld)
static const union ieee_ext_u
erxu  = LD80C(0xd7bb3d0000000000, -1,  8.42700779438018798828e-1L),
/*
* Domain [0.84375, 1.25], range ~[-8.132e-22, 8.113e-22]:
* |(erf(x) - erx) - pa(x)/qa(x)| < 2**-71.762
*/
pa0u  = LD80C(0xe8211158da02c692, -27,  1.35116960705131296711e-8L),
pa1u  = LD80C(0xd488f89f36988618, -2,   4.15107507167065612570e-1L),
pa2u  = LD80C(0xece74f8c63fa3942, -4,  -1.15675565215949226989e-1L),
pa3u  = LD80C(0xc8d31e020727c006, -4,   9.80589241379624665791e-2L),
pa4u  = LD80C(0x985d5d5fafb0551f, -5,   3.71984145558422368847e-2L),
pa5u  = LD80C(0xa5b6c4854d2f5452, -8,  -5.05718799340957673661e-3L),
pa6u  = LD80C(0x85c8d58fe3993a47, -8,   4.08277919612202243721e-3L),
pa7u  = LD80C(0xddbfbc23677b35cf, -13,  2.11476292145347530794e-4L),
qa1u  = LD80C(0xb8a977896f5eff3f, -1,   7.21335860303380361298e-1L),
qa2u  = LD80C(0x9fcd662c3d4eac86, -1,   6.24227891731886593333e-1L),
qa3u  = LD80C(0x9d0b618eac67ba07, -2,   3.06727455774491855801e-1L),
qa4u  = LD80C(0x881a4293f6d6c92d, -3,   1.32912674218195890535e-1L),
qa5u  = LD80C(0xbab144f07dea45bf, -5,   4.55792134233613027584e-2L),
qa6u  = LD80C(0xa6c34ba438bdc900, -7,   1.01783980070527682680e-2L),
qa7u  = LD80C(0x8fa866dc20717a91, -9,   2.19204436518951438183e-3L);
#define erx     (erxu.extu_ld)
#define pa0     (pa0u.extu_ld)
#define pa1     (pa1u.extu_ld)
#define pa2     (pa2u.extu_ld)
#define pa3     (pa3u.extu_ld)
#define pa4     (pa4u.extu_ld)
#define pa5     (pa5u.extu_ld)
#define pa6     (pa6u.extu_ld)
#define pa7     (pa7u.extu_ld)
#define qa1     (qa1u.extu_ld)
#define qa2     (qa2u.extu_ld)
#define qa3     (qa3u.extu_ld)
#define qa4     (qa4u.extu_ld)
#define qa5     (qa5u.extu_ld)
#define qa6     (qa6u.extu_ld)
#define qa7     (qa7u.extu_ld)
static const union ieee_ext_u
/*
* Domain [1.25,2.85715], range ~[-2.334e-22,2.334e-22]:
* |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-71.860
*/
ra0u  = LD80C(0xa1a091e0fb4f335a, -7, -9.86494298915814308249e-3L),
ra1u  = LD80C(0xc2b0d045ae37df6b, -1, -7.60510460864878271275e-1L),
ra2u  = LD80C(0xf2cec3ee7da636c5, 3,  -1.51754798236892278250e+1L),
ra3u  = LD80C(0x813cc205395adc7d, 7,  -1.29237335516455333420e+2L),
ra4u  = LD80C(0x8737c8b7b4062c2f, 9,  -5.40871625829510494776e+2L),
ra5u  = LD80C(0x8ffe5383c08d4943, 10, -1.15194769466026108551e+3L),
ra6u  = LD80C(0x983573e64d5015a9, 10, -1.21767039790249025544e+3L),
ra7u  = LD80C(0x92a794e763a6d4db, 9,  -5.86618463370624636688e+2L),
ra8u  = LD80C(0xd5ad1fae77c3d9a3, 6,  -1.06838132335777049840e+2L),
ra9u  = LD80C(0x934c1a247807bb9c, 2,  -4.60303980944467334806e+0L),
sa1u  = LD80C(0xd342f90012bb1189, 4,   2.64077014928547064865e+1L),
sa2u  = LD80C(0x839be13d9d5da883, 8,   2.63217811300123973067e+2L),
sa3u  = LD80C(0x9f8cba6d1ae1b24b, 10,  1.27639775710344617587e+3L),
sa4u  = LD80C(0xcaa83f403713e33e, 11,  3.24251544209971162003e+3L),
sa5u  = LD80C(0x8796aff2f3c47968, 12,  4.33883591261332837874e+3L),
sa6u  = LD80C(0xb6ef97f9c753157b, 11,  2.92697460344182158454e+3L),
sa7u  = LD80C(0xe02aee5f83773d1c, 9,   8.96670799139389559818e+2L),
sa8u  = LD80C(0xc82b83855b88e07e, 6,   1.00084987800048510018e+2L),
sa9u  = LD80C(0x92f030aefadf28ad, 1,   2.29591004455459083843e+0L);
#define ra0     (ra0u.extu_ld)
#define ra1     (ra1u.extu_ld)
#define ra2     (ra2u.extu_ld)
#define ra3     (ra3u.extu_ld)
#define ra4     (ra4u.extu_ld)
#define ra5     (ra5u.extu_ld)
#define ra6     (ra6u.extu_ld)
#define ra7     (ra7u.extu_ld)
#define ra8     (ra8u.extu_ld)
#define ra9     (ra9u.extu_ld)
#define sa1     (sa1u.extu_ld)
#define sa2     (sa2u.extu_ld)
#define sa3     (sa3u.extu_ld)
#define sa4     (sa4u.extu_ld)
#define sa5     (sa5u.extu_ld)
#define sa6     (sa6u.extu_ld)
#define sa7     (sa7u.extu_ld)
#define sa8     (sa8u.extu_ld)
#define sa9     (sa9u.extu_ld)
/*
* Domain [2.85715,7], range ~[-8.323e-22,8.390e-22]:
* |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-70.326
*/
static const union ieee_ext_u
rb0u = LD80C(0xa1a091cf43abcd26, -7, -9.86494292470284646962e-3L),
rb1u = LD80C(0xd19d2df1cbb8da0a, -1, -8.18804618389296662837e-1L),
rb2u = LD80C(0x9a4dd1383e5daf5b, 4,  -1.92879967111618594779e+1L),
rb3u = LD80C(0xbff0ae9fc0751de6, 7,  -1.91940164551245394969e+2L),
rb4u = LD80C(0xdde08465310b472b, 9,  -8.87508080766577324539e+2L),
rb5u = LD80C(0xe796e1d38c8c70a9, 10, -1.85271506669474503781e+3L),
rb6u = LD80C(0xbaf655a76e0ab3b5, 10, -1.49569795581333675349e+3L),
rb7u = LD80C(0x95d21e3e75503c21, 8,  -2.99641547972948019157e+2L),
sb1u = LD80C(0x814487ed823c8cbd, 5,   3.23169247732868256569e+1L),
sb2u = LD80C(0xbe4bfbb1301304be, 8,   3.80593618534539961773e+2L),
sb3u = LD80C(0x809c4ade46b927c7, 11,  2.05776827838541292848e+3L),
sb4u = LD80C(0xa55284359f3395a8, 12,  5.29031455540062116327e+3L),
sb5u = LD80C(0xbcfa72da9b820874, 12,  6.04730608102312640462e+3L),
sb6u = LD80C(0x9d09a35988934631, 11,  2.51260238030767176221e+3L),
sb7u = LD80C(0xd675bbe542c159fa, 7,   2.14459898308561015684e+2L);
#define rb0     (rb0u.extu_ld)
#define rb1     (rb1u.extu_ld)
#define rb2     (rb2u.extu_ld)
#define rb3     (rb3u.extu_ld)
#define rb4     (rb4u.extu_ld)
#define rb5     (rb5u.extu_ld)
#define rb6     (rb6u.extu_ld)
#define rb7     (rb7u.extu_ld)
#define sb1     (sb1u.extu_ld)
#define sb2     (sb2u.extu_ld)
#define sb3     (sb3u.extu_ld)
#define sb4     (sb4u.extu_ld)
#define sb5     (sb5u.extu_ld)
#define sb6     (sb6u.extu_ld)
#define sb7     (sb7u.extu_ld)
/*
* Domain [7,108], range ~[-4.422e-22,4.422e-22]:
* |log(x*erfc(x)) + x**2 + 0.5625 - rc(x)/sc(x)| < 2**-70.938
*/
static const union ieee_ext_u
/* err = -4.422092275318925082e-22 -70.937689 */
rc0u = LD80C(0xa1a091cf437a17ad, -7, -9.86494292470008707260e-3L),
rc1u = LD80C(0xbe79c5a978122b00, -1, -7.44045595049165939261e-1L),
rc2u = LD80C(0xdb26f9bbe31a2794, 3,  -1.36970155085888424425e+1L),
rc3u = LD80C(0xb5f69a38f5747ac8, 6,  -9.09816453742625888546e+1L),
rc4u = LD80C(0xd79676d970d0a21a, 7,  -2.15587750997584074147e+2L),
rc5u = LD80C(0xfe528153c45ec97c, 6,  -1.27161142938347796666e+2L),
sc1u = LD80C(0xc5e8cd46d5604a96, 4,   2.47386727842204312937e+1L),
sc2u = LD80C(0xc5f0f5a5484520eb, 7,   1.97941248254913378865e+2L),
sc3u = LD80C(0x964e3c7b34db9170, 9,   6.01222441484087787522e+2L),
sc4u = LD80C(0x99be1b89faa0596a, 9,   6.14970430845978077827e+2L),
sc5u = LD80C(0xf80dfcbf37ffc5ea, 6,   1.24027318931184605891e+2L);
#define rc0     (rc0u.extu_ld)
#define rc1     (rc1u.extu_ld)
#define rc2     (rc2u.extu_ld)
#define rc3     (rc3u.extu_ld)
#define rc4     (rc4u.extu_ld)
#define rc5     (rc5u.extu_ld)
#define sc1     (sc1u.extu_ld)
#define sc2     (sc2u.extu_ld)
#define sc3     (sc3u.extu_ld)
#define sc4     (sc4u.extu_ld)
#define sc5     (sc5u.extu_ld)

long double
erfl(long double x)
{
       long double ax,R,S,P,Q,s,y,z,r;
       uint64_t lx __unused;
       int32_t i;
       uint16_t hx;

       EXTRACT_LDBL80_WORDS(hx, lx, x);

       if((hx & 0x7fff) == 0x7fff) {   /* erfl(nan)=nan */
               i = (hx>>15)<<1;
               return (1-i)+one/x;     /* erfl(+-inf)=+-1 */
       }

       ENTERI();

       ax = fabsl(x);
       if(ax < 0.84375) {
           if(ax < 0x1p-34L) {
               if(ax < 0x1p-16373L)
                   RETURNI((8*x+efx8*x)/8);    /* avoid spurious underflow */
               RETURNI(x + efx*x);
           }
           z = x*x;
           r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*pp5))));
           s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*qq6)))));
           y = r/s;
           RETURNI(x + x*y);
       }
       if(ax < 1.25) {
           s = ax-one;
           P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*pa7))))));
           Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*qa7))))));
           if(x>=0) RETURNI(erx + P/Q); else RETURNI(-erx - P/Q);
       }
       if(ax >= 7) {                   /* inf>|x|>= 7 */
           if(x>=0) RETURNI(one-tiny); else RETURNI(tiny-one);
       }
       s = one/(ax*ax);
       if(ax < 2.85715) {      /* |x| < 2.85715 */
           R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+
               s*(ra8+s*ra9))))))));
           S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
               s*(sa8+s*sa9))))))));
       } else {        /* |x| >= 2.85715 */
           R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*rb7))))));
           S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7))))));
       }
       z=(float)ax;
       r=expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);
       if(x>=0) RETURNI(one-r/ax); else RETURNI(r/ax-one);
}

long double
erfcl(long double x)
{
       long double ax,R,S,P,Q,s,y,z,r;
       uint64_t lx __unused;
       uint16_t hx;

       EXTRACT_LDBL80_WORDS(hx, lx, x);

       if((hx & 0x7fff) == 0x7fff) {   /* erfcl(nan)=nan */
                                       /* erfcl(+-inf)=0,2 */
           return ((hx>>15)<<1)+one/x;
       }

       ENTERI();

       ax = fabsl(x);
       if(ax < 0.84375L) {
           if(ax < 0x1p-34L)
               RETURNI(one-x);
           z = x*x;
           r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*pp5))));
           s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*qq6)))));
           y = r/s;
           if(ax < 0.25L) {    /* x<1/4 */
               RETURNI(one-(x+x*y));
           } else {
               r = x*y;
               r += (x-half);
              RETURNI(half - r);
           }
       }
       if(ax < 1.25L) {
           s = ax-one;
           P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*pa7))))));
           Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*qa7))))));
           if(x>=0) {
               z  = one-erx; RETURNI(z - P/Q);
           } else {
               z = (erx+P/Q); RETURNI(one+z);
           }
       }

       if(ax < 108) {                  /* |x| < 108 */
           s = one/(ax*ax);
           if(ax < 2.85715) {          /* |x| < 2.85715 */
               R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+
                   s*(ra8+s*ra9))))))));
               S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
                   s*(sa8+s*sa9))))))));
           } else if(ax < 7) {         /* | |x| < 7 */
               R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*rb7))))));
               S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7))))));
           } else {
               if(x < -7) RETURNI(two-tiny);/* x < -7 */
               R=rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*rc5))));
               S=one+s*(sc1+s*(sc2+s*(sc3+s*(sc4+s*sc5))));
           }
           z = (float)ax;
           r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);
           if(x>0) RETURNI(r/ax); else RETURNI(two-r/ax);
       } else {
           if(x>0) RETURNI(tiny*tiny); else RETURNI(two-tiny);
       }
}

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