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glibc  2.9
Functions | Variables
s_erfl.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

long double __erfl (long double x)
 weak_alias (__erfl, erfl)

Variables

static long double tiny = 1e-4931L
static long double half = 0.5L
static long double one = 1.0L
static long double two = 2.0L
static long double erx = 0.845062911510467529296875L
static long double efx = 1.2837916709551257389615890312154517168810E-1L
static long double efx8 = 1.0270333367641005911692712249723613735048E0L
static long double pp [6]
static long double qq [6]
static long double pa [8]
static long double qa [7]
static long double ra []
static long double sa []
static long double rb []
static long double sb []
static long double rc []
static long double sc []

Function Documentation

long double __erfl ( long double  x)

Definition at line 261 of file s_erfl.c.

{
  long double R, S, P, Q, s, y, z, r;
  int32_t ix, i;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;

  if (ix >= 0x7fff)
    {                       /* erf(nan)=nan */
      i = ((se & 0xffff) >> 15) << 1;
      return (long double) (1 - i) + one / x;    /* erf(+-inf)=+-1 */
    }

  ix = (ix << 16) | (i0 >> 16);
  if (ix < 0x3ffed800) /* |x|<0.84375 */
    {
      if (ix < 0x3fde8000) /* |x|<2**-33 */
       {
         if (ix < 0x00080000)
           return 0.125 * (8.0 * x + efx8 * x);  /*avoid underflow */
         return x + efx * x;
       }
      z = x * x;
      r = pp[0] + z * (pp[1]
          + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5]))));
      s = qq[0] + z * (qq[1]
         + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z)))));
      y = r / s;
      return x + x * y;
    }
  if (ix < 0x3fffa000) /* 1.25 */
    {                       /* 0.84375 <= |x| < 1.25 */
      s = fabsl (x) - one;
      P = pa[0] + s * (pa[1] + s * (pa[2]
        + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
      Q = qa[0] + s * (qa[1] + s * (qa[2]
        + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
      if ((se & 0x8000) == 0)
       return erx + P / Q;
      else
       return -erx - P / Q;
    }
  if (ix >= 0x4001d555) /* 6.6666259765625 */
    {                       /* inf>|x|>=6.666 */
      if ((se & 0x8000) == 0)
       return one - tiny;
      else
       return tiny - one;
    }
  x = fabsl (x);
  s = one / (x * x);
  if (ix < 0x4000b6db) /* 2.85711669921875 */
    {
      R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
          s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
      S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
          s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
    }
  else
    {                       /* |x| >= 1/0.35 */
      R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
         s * (rb[5] + s * (rb[6] + s * rb[7]))))));
      S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
         s * (sb[5] + s * (sb[6] + s))))));
    }
  z = x;
  GET_LDOUBLE_WORDS (i, i0, i1, z);
  i1 = 0;
  SET_LDOUBLE_WORDS (z, i, i0, i1);
  r =
    __ieee754_expl (-z * z - 0.5625) * __ieee754_expl ((z - x) * (z + x) +
                                               R / S);
  if ((se & 0x8000) == 0)
    return one - r / x;
  else
    return r / x - one;
}

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weak_alias ( __erfl  ,
erfl   
)

Definition at line 343 of file s_erfl.c.

{
  int32_t hx, ix;
  long double R, S, P, Q, s, y, z, r;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;
  if (ix >= 0x7fff)
    {                       /* erfc(nan)=nan */
      /* erfc(+-inf)=0,2 */
      return (long double) (((se & 0xffff) >> 15) << 1) + one / x;
    }

  ix = (ix << 16) | (i0 >> 16);
  if (ix < 0x3ffed800) /* |x|<0.84375 */
    {
      if (ix < 0x3fbe0000) /* |x|<2**-65 */
       return one - x;
      z = x * x;
      r = pp[0] + z * (pp[1]
          + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5]))));
      s = qq[0] + z * (qq[1]
         + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z)))));
      y = r / s;
      if (ix < 0x3ffd8000) /* x<1/4 */
       {
         return one - (x + x * y);
       }
      else
       {
         r = x * y;
         r += (x - half);
         return half - r;
       }
    }
  if (ix < 0x3fffa000) /* 1.25 */
    {                       /* 0.84375 <= |x| < 1.25 */
      s = fabsl (x) - one;
      P = pa[0] + s * (pa[1] + s * (pa[2]
        + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
      Q = qa[0] + s * (qa[1] + s * (qa[2]
        + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
      if ((se & 0x8000) == 0)
       {
         z = one - erx;
         return z - P / Q;
       }
      else
       {
         z = erx + P / Q;
         return one + z;
       }
    }
  if (ix < 0x4005d600) /* 107 */
    {                       /* |x|<107 */
      x = fabsl (x);
      s = one / (x * x);
      if (ix < 0x4000b6db) /* 2.85711669921875 */
       {                    /* |x| < 1/.35 ~ 2.857143 */
         R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
              s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
         S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
              s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
       }
      else if (ix < 0x4001d555) /* 6.6666259765625 */
       {                    /* 6.666 > |x| >= 1/.35 ~ 2.857143 */
         R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
             s * (rb[5] + s * (rb[6] + s * rb[7]))))));
         S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
              s * (sb[5] + s * (sb[6] + s))))));
       }
      else
       {                    /* |x| >= 6.666 */
         if (se & 0x8000)
           return two - tiny;      /* x < -6.666 */

         R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] +
                                              s * (rc[4] + s * rc[5]))));
         S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] +
                                              s * (sc[4] + s))));
       }
      z = x;
      GET_LDOUBLE_WORDS (hx, i0, i1, z);
      i1 = 0;
      i0 &= 0xffffff00;
      SET_LDOUBLE_WORDS (z, hx, i0, i1);
      r = __ieee754_expl (-z * z - 0.5625) *
       __ieee754_expl ((z - x) * (z + x) + R / S);
      if ((se & 0x8000) == 0)
       return r / x;
      else
       return two - r / x;
    }
  else
    {
      if ((se & 0x8000) == 0)
       return tiny * tiny;
      else
       return two - tiny;
    }
}

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Variable Documentation

long double efx = 1.2837916709551257389615890312154517168810E-1L [static]

Definition at line 125 of file s_erfl.c.

long double efx8 = 1.0270333367641005911692712249723613735048E0L [static]

Definition at line 127 of file s_erfl.c.

long double erx = 0.845062911510467529296875L [static]

Definition at line 120 of file s_erfl.c.

long double half = 0.5L [static]

Definition at line 116 of file s_erfl.c.

long double one = 1.0L [static]

Definition at line 117 of file s_erfl.c.

long double pa[8] [static]
Initial value:
 {
    -1.076952146179812072156734957705102256059E0L,
     1.884814957770385593365179835059971587220E2L,
    -5.339153975012804282890066622962070115606E1L,
     4.435910679869176625928504532109635632618E1L,
     1.683219516032328828278557309642929135179E1L,
    -2.360236618396952560064259585299045804293E0L,
     1.852230047861891953244413872297940938041E0L,
     9.394994446747752308256773044667843200719E-2L,
  }

Definition at line 155 of file s_erfl.c.

long double pp[6] [static]
Initial value:
 {
    1.122751350964552113068262337278335028553E6L,
    -2.808533301997696164408397079650699163276E6L,
    -3.314325479115357458197119660818768924100E5L,
    -6.848684465326256109712135497895525446398E4L,
    -2.657817695110739185591505062971929859314E3L,
    -1.655310302737837556654146291646499062882E2L,
  }

Definition at line 129 of file s_erfl.c.

long double qa[7] [static]
Initial value:
  {
    4.559263722294508998149925774781887811255E2L,
    3.289248982200800575749795055149780689738E2L,
    2.846070965875643009598627918383314457912E2L,
    1.398715859064535039433275722017479994465E2L,
    6.060190733759793706299079050985358190726E1L,
    2.078695677795422351040502569964299664233E1L,
    4.641271134150895940966798357442234498546E0L,
    
  }

Definition at line 166 of file s_erfl.c.

long double qq[6] [static]
Initial value:
 {
    8.745588372054466262548908189000448124232E6L,
    3.746038264792471129367533128637019611485E6L,
    7.066358783162407559861156173539693900031E5L,
    7.448928604824620999413120955705448117056E4L,
    4.511583986730994111992253980546131408924E3L,
    1.368902937933296323345610240009071254014E2L,
    
  }

Definition at line 138 of file s_erfl.c.

long double ra[] [static]
Initial value:
 {
      1.363566591833846324191000679620738857234E-1L,
      1.018203167219873573808450274314658434507E1L,
      1.862359362334248675526472871224778045594E2L,
      1.411622588180721285284945138667933330348E3L,
      5.088538459741511988784440103218342840478E3L,
      8.928251553922176506858267311750789273656E3L,
      7.264436000148052545243018622742770549982E3L,
      2.387492459664548651671894725748959751119E3L,
      2.220916652813908085449221282808458466556E2L,
    }

Definition at line 184 of file s_erfl.c.

long double rb[] [static]
Initial value:
 {
      -4.869587348270494309550558460786501252369E-5L,
      -4.030199390527997378549161722412466959403E-3L,
      -9.434425866377037610206443566288917589122E-2L,
      -9.319032754357658601200655161585539404155E-1L,
      -4.273788174307459947350256581445442062291E0L,
      -8.842289940696150508373541814064198259278E0L,
      -7.069215249419887403187988144752613025255E0L,
      -1.401228723639514787920274427443330704764E0L,
    }

Definition at line 214 of file s_erfl.c.

long double rc[] [static]
Initial value:
 {
      -8.299617545269701963973537248996670806850E-5L,
      -6.243845685115818513578933902532056244108E-3L,
      -1.141667210620380223113693474478394397230E-1L,
      -7.521343797212024245375240432734425789409E-1L,
      -1.765321928311155824664963633786967602934E0L,
      -1.029403473103215800456761180695263439188E0L,
    }

Definition at line 238 of file s_erfl.c.

long double sa[] [static]
Initial value:
 {
      -1.382234625202480685182526402169222331847E1L,
      -3.315638835627950255832519203687435946482E2L,
      -2.949124863912936259747237164260785326692E3L,
      -1.246622099070875940506391433635999693661E4L,
      -2.673079795851665428695842853070996219632E4L,
      -2.880269786660559337358397106518918220991E4L,
      -1.450600228493968044773354186390390823713E4L,
      -2.874539731125893533960680525192064277816E3L,
      -1.402241261419067750237395034116942296027E2L,
      
    }

Definition at line 196 of file s_erfl.c.

long double sb[] [static]
Initial value:
 {
      4.936254964107175160157544545879293019085E-3L,
      1.583457624037795744377163924895349412015E-1L,
      1.850647991850328356622940552450636420484E0L,
      9.927611557279019463768050710008450625415E0L,
      2.531667257649436709617165336779212114570E1L,
      2.869752886406743386458304052862814690045E1L,
      1.182059497870819562441683560749192539345E1L,
      
    }

Definition at line 225 of file s_erfl.c.

long double sc[] [static]
Initial value:
 {
      8.413244363014929493035952542677768808601E-3L,
      2.065114333816877479753334599639158060979E-1L,
      1.639064941530797583766364412782135680148E0L,
      4.936788463787115555582319302981666347450E0L,
      5.005177727208955487404729933261347679090E0L,
      
    }

Definition at line 247 of file s_erfl.c.

long double tiny = 1e-4931L [static]

Definition at line 115 of file s_erfl.c.

long double two = 2.0L [static]

Definition at line 118 of file s_erfl.c.