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glibc  2.9
Functions | Variables
e_j1l.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

static long double pone ()
static long double qone ()
long double __ieee754_j1l (long double x)
long double __ieee754_y1l (long double x)
static long double pone (long double x)
static long double qone (long double x)

Variables

static long double huge = 1e4930L
static long double one = 1.0L
static long double invsqrtpi = 5.6418958354775628694807945156077258584405e-1L
static long double tpi = 6.3661977236758134307553505349005744813784e-1L
static long double R [5]
static long double S [4]
static long double zero = 0.0
static long double U0 [6]
static long double V0 [5]
static long double pr8 [7]
static long double ps8 [6]
static long double pr5 [7]
static long double ps5 [6]
static long double pr3 [7]
static long double ps3 [6]
static long double pr2 [7]
static long double ps2 [6]
static long double qr8 [7]
static long double qs8 [7]
static long double qr5 [7]
static long double qs5 [7]
static long double qr3 [7]
static long double qs3 [7]
static long double qr2 [7]
static long double qs2 [7]

Function Documentation

long double __ieee754_j1l ( long double  x)

Definition at line 125 of file e_j1l.c.

{
  long double z, c, r, s, ss, cc, u, v, y;
  int32_t ix;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;
  if (ix >= 0x7fff)
    return one / x;
  y = fabsl (x);
  if (ix >= 0x4000)
    {                       /* |x| >= 2.0 */
      __sincosl (y, &s, &c);
      ss = -s - c;
      cc = s - c;
      if (ix < 0x7ffe)
       {                    /* make sure y+y not overflow */
         z = __cosl (y + y);
         if ((s * c) > zero)
           cc = z / ss;
         else
           ss = z / cc;
       }
      /*
       * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
       * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
       */
      if (ix > 0x4080)
       z = (invsqrtpi * cc) / __ieee754_sqrtl (y);
      else
       {
         u = pone (y);
         v = qone (y);
         z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (y);
       }
      if (se & 0x8000)
       return -z;
      else
       return z;
    }
  if (ix < 0x3fde) /* |x| < 2^-33 */
    {
      if (huge + x > one)
       return 0.5 * x;             /* inexact if x!=0 necessary */
    }
  z = x * x;
  r = z * (R[0] + z * (R[1]+ z * (R[2] + z * (R[3] + z * R[4]))));
  s = S[0] + z * (S[1] + z * (S[2] + z * (S[3] + z)));
  r *= x;
  return (x * 0.5 + r / s);
}

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long double __ieee754_y1l ( long double  x)

Definition at line 215 of file e_j1l.c.

{
  long double z, s, c, ss, cc, u, v;
  int32_t ix;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;
  /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
  if (se & 0x8000)
    return zero / (zero * x);
  if (ix >= 0x7fff)
    return one / (x + x * x);
  if ((i0 | i1) == 0)
    return -HUGE_VALL + x;  /* -inf and overflow exception.  */
  if (ix >= 0x4000)
    {                       /* |x| >= 2.0 */
      __sincosl (x, &s, &c);
      ss = -s - c;
      cc = s - c;
      if (ix < 0x7fe00000)
       {                    /* make sure x+x not overflow */
         z = __cosl (x + x);
         if ((s * c) > zero)
           cc = z / ss;
         else
           ss = z / cc;
       }
      /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
       * where x0 = x-3pi/4
       *      Better formula:
       *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
       *                      =  1/sqrt(2) * (sin(x) - cos(x))
       *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
       *                      = -1/sqrt(2) * (cos(x) + sin(x))
       * To avoid cancellation, use
       *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
       * to compute the worse one.
       */
      if (ix > 0x4080)
       z = (invsqrtpi * ss) / __ieee754_sqrtl (x);
      else
       {
         u = pone (x);
         v = qone (x);
         z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x);
       }
      return z;
    }
  if (ix <= 0x3fbe)
    {                       /* x < 2**-65 */
      return (-tpi / x);
    }
  z = x * x;
 u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * (U0[4] + z * U0[5]))));
 v = V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * (V0[4] + z))));
  return (x * (u / v) +
         tpi * (__ieee754_j1l (x) * __ieee754_logl (x) - one / x));
}

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static long double pone ( ) [static]
static long double pone ( long double  x) [static]

Definition at line 415 of file e_j1l.c.

{
#ifdef __STDC__
  const long double *p, *q;
#else
  long double *p, *q;
#endif
  long double z, r, s;
  int32_t ix;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;
  if (ix >= 0x4002) /* x >= 8 */
    {
      p = pr8;
      q = ps8;
    }
  else
    {
      i1 = (ix << 16) | (i0 >> 16);
      if (i1 >= 0x40019174) /* x >= 4.54541015625 */
       {
         p = pr5;
         q = ps5;
       }
      else if (i1 >= 0x4000b6db)   /* x >= 2.85711669921875 */
       {
         p = pr3;
         q = ps3;
       }
      else if (ix >= 0x4000)       /* x better be >= 2 */
       {
         p = pr2;
         q = ps2;
       }
    }
  z = one / (x * x);
 r = p[0] + z * (p[1] +
               z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6])))));
 s = q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * (q[5] + z)))));
  return one + z * r / s;
}
static long double qone ( )
static long double qone ( long double  x) [static]

Definition at line 603 of file e_j1l.c.

{
#ifdef __STDC__
  const long double *p, *q;
#else
  long double *p, *q;
#endif
  static long double s, r, z;
  int32_t ix;
  u_int32_t se, i0, i1;

  GET_LDOUBLE_WORDS (se, i0, i1, x);
  ix = se & 0x7fff;
  if (ix >= 0x4002)         /* x >= 8 */
    {
      p = qr8;
      q = qs8;
    }
  else
    {
      i1 = (ix << 16) | (i0 >> 16);
      if (i1 >= 0x40019174) /* x >= 4.54541015625 */
       {
         p = qr5;
         q = qs5;
       }
      else if (i1 >= 0x4000b6db)   /* x >= 2.85711669921875 */
       {
         p = qr3;
         q = qs3;
       }
      else if (ix >= 0x4000)       /* x better be >= 2 */
       {
         p = qr2;
         q = qs2;
       }
    }
  z = one / (x * x);
  r =
    p[0] + z * (p[1] +
              z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6])))));
  s =
    q[0] + z * (q[1] +
              z * (q[2] +
                   z * (q[3] + z * (q[4] + z * (q[5] + z * (q[6] + z))))));
  return (.375 + z * r / s) / x;
}

Variable Documentation

long double huge = 1e4930L [static]

Definition at line 88 of file e_j1l.c.

long double invsqrtpi = 5.6418958354775628694807945156077258584405e-1L [static]

Definition at line 90 of file e_j1l.c.

long double one = 1.0L [static]

Definition at line 89 of file e_j1l.c.

long double pr2[7] [static]
Initial value:
 {

  2.795623248568412225239401141338714516445E-4L,
  1.092578168441856711925254839815430061135E-2L,
  1.278024620468953761154963591853679640560E-1L,
  5.469680473691500673112904286228351988583E-1L,
  8.313769490922351300461498619045639016059E-1L,
  3.544176317308370086415403567097130611468E-1L,
  1.604142674802373041247957048801599740644E-2L,
}

Definition at line 385 of file e_j1l.c.

long double pr3[7] [static]
Initial value:
 {

  1.265251153957366716825382654273326407972E-5L,
  8.031057269201324914127680782288352574567E-4L,
  1.581648121115028333661412169396282881035E-2L,
  1.179534658087796321928362981518645033967E-1L,
  3.227936912780465219246440724502790727866E-1L,
  2.559223765418386621748404398017602935764E-1L,
  2.277136933287817911091370397134882441046E-2L,
}

Definition at line 354 of file e_j1l.c.

long double pr5[7] [static]
Initial value:
 {

  4.318486887948814529950980396300969247900E-7L,
  4.715341880798817230333360497524173929315E-5L,
  1.642719430496086618401091544113220340094E-3L,
  2.228688005300803935928733750456396149104E-2L,
  1.142773760804150921573259605730018327162E-1L,
  1.755576530055079253910829652698703791957E-1L,
  3.218803858282095929559165965353784980613E-2L,
}

Definition at line 323 of file e_j1l.c.

long double pr8[7] [static]
Initial value:
 {

  8.402048819032978959298664869941375143163E-9L,
  1.813743245316438056192649247507255996036E-6L,
  1.260704554112906152344932388588243836276E-4L,
  3.439294839869103014614229832700986965110E-3L,
  3.576910849712074184504430254290179501209E-2L,
  1.131111483254318243139953003461511308672E-1L,
  4.480715825681029711521286449131671880953E-2L,
}

Definition at line 292 of file e_j1l.c.

long double ps2[6] [static]
Initial value:
 {

  2.385605161555183386205027000675875235980E-3L,
  9.616778294482695283928617708206967248579E-2L,
  1.195215570959693572089824415393951258510E0L,
  5.718412857897054829999458736064922974662E0L,
  1.065626298505499086386584642761602177568E1L,
  6.809140730053382188468983548092322151791E0L,
 
}

Definition at line 398 of file e_j1l.c.

long double ps3[6] [static]
Initial value:
 {

  1.079681071833391818661952793568345057548E-4L,
  6.986017817100477138417481463810841529026E-3L,
  1.429403701146942509913198539100230540503E-1L,
  1.148392024337075609460312658938700765074E0L,
  3.643663015091248720208251490291968840882E0L,
  3.990702269032018282145100741746633960737E0L,
  
}

Definition at line 367 of file e_j1l.c.

long double ps5[6] [static]
Initial value:
 {

  3.685108812227721334719884358034713967557E-6L,
  4.069102509511177498808856515005792027639E-4L,
  1.449728676496155025507893322405597039816E-2L,
  2.058869213229520086582695850441194363103E-1L,
  1.164890985918737148968424972072751066553E0L,
  2.274776933457009446573027260373361586841E0L,
  
}

Definition at line 336 of file e_j1l.c.

long double ps8[6] [static]
Initial value:
 {

  7.169748325574809484893888315707824924354E-8L,
  1.556549720596672576431813934184403614817E-5L,
  1.094540125521337139209062035774174565882E-3L,
  3.060978962596642798560894375281428805840E-2L,
  3.374146536087205506032643098619414507024E-1L,
  1.253830208588979001991901126393231302559E0L,
  
}

Definition at line 305 of file e_j1l.c.

long double qr2[7] [static]
Initial value:
 {

  -1.372751603025230017220666013816502528318E-4L,
  -6.879190253347766576229143006767218972834E-3L,
  -1.061253572090925414598304855316280077828E-1L,
  -6.262164224345471241219408329354943337214E-1L,
  -1.423149636514768476376254324731437473915E0L,
  -1.087955310491078933531734062917489870754E0L,
  -1.826821119773182847861406108689273719137E-1L,
}

Definition at line 572 of file e_j1l.c.

long double qr3[7] [static]
Initial value:
 {

  -3.618746299358445926506719188614570588404E-6L,
  -2.951146018465419674063882650970344502798E-4L,
  -7.728518171262562194043409753656506795258E-3L,
  -8.058010968753999435006488158237984014883E-2L,
  -3.356232856677966691703904770937143483472E-1L,
  -4.858192581793118040782557808823460276452E-1L,
  -1.592399251246473643510898335746432479373E-1L,
}

Definition at line 540 of file e_j1l.c.

long double qr5[7] [static]
Initial value:
 {

  -6.719134139179190546324213696633564965983E-8L,
  -9.467871458774950479909851595678622044140E-6L,
  -4.429341875348286176950914275723051452838E-4L,
  -8.539898021757342531563866270278505014487E-3L,
  -6.818691805848737010422337101409276287170E-2L,
  -1.964432669771684034858848142418228214855E-1L,
  -1.333896496989238600119596538299938520726E-1L,
}

Definition at line 508 of file e_j1l.c.

long double qr8[7] [static]
Initial value:
 {

  -5.691925079044209246015366919809404457380E-10L,
  -1.632587664706999307871963065396218379137E-7L,
  -1.577424682764651970003637263552027114600E-5L,
  -6.377627959241053914770158336842725291713E-4L,
  -1.087408516779972735197277149494929568768E-2L,
  -6.854943629378084419631926076882330494217E-2L,
  -1.055448290469180032312893377152490183203E-1L,
}

Definition at line 476 of file e_j1l.c.

long double qs2[7] [static]
Initial value:
 {

  1.338768933634451601814048220627185324007E-3L,
  7.071099998918497559736318523932241901810E-2L,
  1.200511429784048632105295629933382142221E0L,
  8.327301713640367079030141077172031825276E0L,
  2.468479301872299311658145549931764426840E1L,
  2.961179686096262083509383820557051621644E1L,
  1.201402313144305153005639494661767354977E1L,
 
}

Definition at line 585 of file e_j1l.c.

long double qs3[7] [static]
Initial value:
 {

  3.529139957987837084554591421329876744262E-5L,
  2.973602667215766676998703687065066180115E-3L,
  8.273534546240864308494062287908662592100E-2L,
  9.613359842126507198241321110649974032726E-1L,
  4.853923697093974370118387947065402707519E0L,
  1.002671608961669247462020977417828796933E1L,
  7.028927383922483728931327850683151410267E0L,
  
}

Definition at line 553 of file e_j1l.c.

long double qs5[7] [static]
Initial value:
 {

  6.552755584474634766937589285426911075101E-7L,
  9.410814032118155978663509073200494000589E-5L,
  4.561677087286518359461609153655021253238E-3L,
  9.397742096177905170800336715661091535805E-2L,
  8.518538116671013902180962914473967738771E-1L,
  3.177729183645800174212539541058292579009E0L,
  4.006745668510308096259753538973038902990E0L,
  
}

Definition at line 521 of file e_j1l.c.

long double qs8[7] [static]
Initial value:
 {

  5.550982172325019811119223916998393907513E-9L,
  1.607188366646736068460131091130644192244E-6L,
  1.580792530091386496626494138334505893599E-4L,
  6.617859900815747303032860443855006056595E-3L,
  1.212840547336984859952597488863037659161E-1L,
  9.017885953937234900458186716154005541075E-1L,
  2.201114489712243262000939120146436167178E0L,
  
}

Definition at line 489 of file e_j1l.c.

long double R[5] [static]
Initial value:
 {
    -9.647406112428107954753770469290757756814E7L,
    2.686288565865230690166454005558203955564E6L,
    -3.689682683905671185891885948692283776081E4L,
    2.195031194229176602851429567792676658146E2L,
    -5.124499848728030297902028238597308971319E-1L,
}

Definition at line 96 of file e_j1l.c.

long double S[4] [static]
Initial value:
{
  1.543584977988497274437410333029029035089E9L,
  2.133542369567701244002565983150952549520E7L,
  1.394077011298227346483732156167414670520E5L,
  5.252401789085732428842871556112108446506E2L,
  
}

Definition at line 104 of file e_j1l.c.

long double tpi = 6.3661977236758134307553505349005744813784e-1L [static]

Definition at line 91 of file e_j1l.c.

long double U0[6] [static]
Initial value:
 {

  -5.908077186259914699178903164682444848615E10L,
  1.546219327181478013495975514375773435962E10L,
  -6.438303331169223128870035584107053228235E8L,
  9.708540045657182600665968063824819371216E6L,
  -6.138043997084355564619377183564196265471E4L,
  1.418503228220927321096904291501161800215E2L,
}

Definition at line 187 of file e_j1l.c.

long double V0[5] [static]
Initial value:
 {

  3.013447341682896694781964795373783679861E11L,
  4.669546565705981649470005402243136124523E9L,
  3.595056091631351184676890179233695857260E7L,
  1.761554028569108722903944659933744317994E5L,
  5.668480419646516568875555062047234534863E2L,
  
}

Definition at line 199 of file e_j1l.c.

long double zero = 0.0 [static]

Definition at line 116 of file e_j1l.c.