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glibc  2.9
Functions | Variables
e_j1.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

static double pone ()
static double qone ()
double __ieee754_j1 (double x)
double __ieee754_y1 (double x)
static double pone (double x)
static double qone (double x)

Variables

static double huge = 1e300
static double one = 1.0
static double invsqrtpi = 5.64189583547756279280e-01
static double tpi = 6.36619772367581382433e-01
static double R []
static double S []
static double zero = 0.0
static double U0 [5]
static double V0 [5]
static double pr8 [6]
static double ps8 [5]
static double pr5 [6]
static double ps5 [5]
static double pr3 [6]
static double ps3 [5]
static double pr2 [6]
static double ps2 [5]
static double qr8 [6]
static double qs8 [6]
static double qr5 [6]
static double qs5 [6]
static double qr3 [6]
static double qs3 [6]
static double qr2 [6]
static double qs2 [6]

Function Documentation

double __ieee754_j1 ( double  x)

Definition at line 103 of file e_j1.c.

{
       double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4;
       int32_t hx,ix;

       GET_HIGH_WORD(hx,x);
       ix = hx&0x7fffffff;
       if(ix>=0x7ff00000) return one/x;
       y = fabs(x);
       if(ix >= 0x40000000) {      /* |x| >= 2.0 */
              __sincos (y, &s, &c);
              ss = -s-c;
              cc = s-c;
              if(ix<0x7fe00000) {  /* make sure y+y not overflow */
                  z = __cos(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>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
              else {
                  u = pone(y); v = qone(y);
                  z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
              }
              if(hx<0) return -z;
              else    return  z;
       }
       if(ix<0x3e400000) {  /* |x|<2**-27 */
           if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
       }
       z = x*x;
#ifdef DO_NOT_USE_THIS
       r =  z*(r00+z*(r01+z*(r02+z*r03)));
       s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
       r *= x;
#else
       r1 = z*R[0]; z2=z*z;
       r2 = R[1]+z*R[2]; z4=z2*z2;
       r = r1 + z2*r2 + z4*R[3];
       r *= x;
       s1 = one+z*S[1];
       s2 = S[2]+z*S[3];
       s3 = S[4]+z*S[5];
       s = s1 + z2*s2 + z4*s3;
#endif
       return(x*0.5+r/s);
}

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double __ieee754_y1 ( double  x)

Definition at line 182 of file e_j1.c.

{
       double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4;
       int32_t hx,ix,lx;

       EXTRACT_WORDS(hx,lx,x);
        ix = 0x7fffffff&hx;
    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
       if(ix>=0x7ff00000) return  one/(x+x*x);
        if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception.  */;
        if(hx<0) return zero/(zero*x);
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
              __sincos (x, &s, &c);
                ss = -s-c;
                cc = s-c;
                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
                    z = __cos(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>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
                else {
                    u = pone(x); v = qone(x);
                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
                }
                return z;
        }
        if(ix<=0x3c900000) {    /* x < 2**-54 */
            return(-tpi/x);
        }
        z = x*x;
#ifdef DO_NOT_USE_THIS
        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
#else
       u1 = U0[0]+z*U0[1];z2=z*z;
       u2 = U0[2]+z*U0[3];z4=z2*z2;
       u  = u1 + z2*u2 + z4*U0[4];
       v1 = one+z*V0[0];
       v2 = V0[1]+z*V0[2];
       v3 = V0[3]+z*V0[4];
       v = v1 + z2*v2 + z4*v3;
#endif
        return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}

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static double pone ( ) [static]

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static double pone ( double  x) [static]

Definition at line 350 of file e_j1.c.

{
#ifdef __STDC__
       const double *p,*q;
#else
       double *p,*q;
#endif
       double z,r,s,r1,r2,r3,s1,s2,s3,z2,z4;
        int32_t ix;
       GET_HIGH_WORD(ix,x);
       ix &= 0x7fffffff;
        if(ix>=0x40200000)     {p = pr8; q= ps8;}
        else if(ix>=0x40122E8B){p = pr5; q= ps5;}
        else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
        else if(ix>=0x40000000){p = pr2; q= ps2;}
        z = one/(x*x);
#ifdef DO_NOT_USE_THIS
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
#else
       r1 = p[0]+z*p[1]; z2=z*z;
       r2 = p[2]+z*p[3]; z4=z2*z2;
       r3 = p[4]+z*p[5];
       r = r1 + z2*r2 + z4*r3;
       s1 = one+z*q[0];
       s2 = q[1]+z*q[2];
       s3 = q[3]+z*q[4];
       s = s1 + z2*s2 + z4*s3;
#endif
        return one+ r/s;
}
static double qone ( )

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static double qone ( double  x) [static]

Definition at line 498 of file e_j1.c.

{
#ifdef __STDC__
       const double *p,*q;
#else
       double *p,*q;
#endif
       double  s,r,z,r1,r2,r3,s1,s2,s3,z2,z4,z6;
       int32_t ix;
       GET_HIGH_WORD(ix,x);
       ix &= 0x7fffffff;
       if(ix>=0x40200000)     {p = qr8; q= qs8;}
       else if(ix>=0x40122E8B){p = qr5; q= qs5;}
       else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
       else if(ix>=0x40000000){p = qr2; q= qs2;}
       z = one/(x*x);
#ifdef DO_NOT_USE_THIS
       r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
       s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
#else
       r1 = p[0]+z*p[1]; z2=z*z;
       r2 = p[2]+z*p[3]; z4=z2*z2;
       r3 = p[4]+z*p[5]; z6=z4*z2;
       r = r1 + z2*r2 + z4*r3;
       s1 = one+z*q[0];
       s2 = q[1]+z*q[2];
       s3 = q[3]+z*q[4];
       s = s1 + z2*s2 + z4*s3 + z6*q[5];
#endif
       return (.375 + r/s)/x;
}

Variable Documentation

double huge = 1e300 [static]

Definition at line 79 of file e_j1.c.

double invsqrtpi = 5.64189583547756279280e-01 [static]

Definition at line 81 of file e_j1.c.

double one = 1.0 [static]

Definition at line 80 of file e_j1.c.

double pr2[6] [static]
Initial value:
 {

  1.07710830106873743082e-07, 
  1.17176219462683348094e-01, 
  2.36851496667608785174e+00, 
  1.22426109148261232917e+01, 
  1.76939711271687727390e+01, 
  5.07352312588818499250e+00, 
}

Definition at line 326 of file e_j1.c.

double pr3[6] [static]
Initial value:
 {

  3.02503916137373618024e-09, 
  1.17186865567253592491e-01, 
  3.93297750033315640650e+00, 
  3.51194035591636932736e+01, 
  9.10550110750781271918e+01, 
  4.85590685197364919645e+01, 
}

Definition at line 302 of file e_j1.c.

double pr5[6] [static]
Initial value:
 { 

  1.31990519556243522749e-11, 
  1.17187493190614097638e-01, 
  6.80275127868432871736e+00, 
  1.08308182990189109773e+02, 
  5.17636139533199752805e+02, 
  5.28715201363337541807e+02, 
}

Definition at line 278 of file e_j1.c.

double pr8[6] [static]
Initial value:
 { 

  0.00000000000000000000e+00, 
  1.17187499999988647970e-01, 
  1.32394806593073575129e+01, 
  4.12051854307378562225e+02, 
  3.87474538913960532227e+03, 
  7.91447954031891731574e+03, 
}

Definition at line 254 of file e_j1.c.

double ps2[5] [static]
Initial value:
 {

  2.14364859363821409488e+01, 
  1.25290227168402751090e+02, 
  2.32276469057162813669e+02, 
  1.17679373287147100768e+02, 
  8.36463893371618283368e+00, 
}

Definition at line 338 of file e_j1.c.

double ps3[5] [static]
Initial value:
 {

  3.47913095001251519989e+01, 
  3.36762458747825746741e+02, 
  1.04687139975775130551e+03, 
  8.90811346398256432622e+02, 
  1.03787932439639277504e+02, 
}

Definition at line 314 of file e_j1.c.

double ps5[5] [static]
Initial value:
 {

  5.92805987221131331921e+01, 
  9.91401418733614377743e+02, 
  5.35326695291487976647e+03, 
  7.84469031749551231769e+03, 
  1.50404688810361062679e+03, 
}

Definition at line 290 of file e_j1.c.

double ps8[5] [static]
Initial value:
 {

  1.14207370375678408436e+02, 
  3.65093083420853463394e+03, 
  3.69562060269033463555e+04, 
  9.76027935934950801311e+04, 
  3.08042720627888811578e+04, 
}

Definition at line 266 of file e_j1.c.

double qr2[6] [static]
Initial value:
 {

 -1.78381727510958865572e-07, 
 -1.02517042607985553460e-01, 
 -2.75220568278187460720e+00, 
 -1.96636162643703720221e+01, 
 -4.23253133372830490089e+01, 
 -2.13719211703704061733e+01, 
}

Definition at line 473 of file e_j1.c.

double qr3[6] [static]
Initial value:
 {

 -5.07831226461766561369e-09, 
 -1.02537829820837089745e-01, 
 -4.61011581139473403113e+00, 
 -5.78472216562783643212e+01, 
 -2.28244540737631695038e+02, 
 -2.19210128478909325622e+02, 
}

Definition at line 448 of file e_j1.c.

double qr5[6] [static]
Initial value:
 { 

 -2.08979931141764104297e-11, 
 -1.02539050241375426231e-01, 
 -8.05644828123936029840e+00, 
 -1.83669607474888380239e+02, 
 -1.37319376065508163265e+03, 
 -2.61244440453215656817e+03, 
}

Definition at line 423 of file e_j1.c.

double qr8[6] [static]
Initial value:
 { 

  0.00000000000000000000e+00, 
 -1.02539062499992714161e-01, 
 -1.62717534544589987888e+01, 
 -7.59601722513950107896e+02, 
 -1.18498066702429587167e+04, 
 -4.84385124285750353010e+04, 
}

Definition at line 398 of file e_j1.c.

double qs2[6] [static]
Initial value:
 {

  2.95333629060523854548e+01, 
  2.52981549982190529136e+02, 
  7.57502834868645436472e+02, 
  7.39393205320467245656e+02, 
  1.55949003336666123687e+02, 
 -4.95949898822628210127e+00, 
}

Definition at line 485 of file e_j1.c.

double qs3[6] [static]
Initial value:
 {

  4.76651550323729509273e+01, 
  6.73865112676699709482e+02, 
  3.38015286679526343505e+03, 
  5.54772909720722782367e+03, 
  1.90311919338810798763e+03, 
 -1.35201191444307340817e+02, 
}

Definition at line 460 of file e_j1.c.

double qs5[6] [static]
Initial value:
 {

  8.12765501384335777857e+01, 
  1.99179873460485964642e+03, 
  1.74684851924908907677e+04, 
  4.98514270910352279316e+04, 
  2.79480751638918118260e+04, 
 -4.71918354795128470869e+03, 
}

Definition at line 435 of file e_j1.c.

double qs8[6] [static]
Initial value:
 {

  1.61395369700722909556e+02, 
  7.82538599923348465381e+03, 
  1.33875336287249578163e+05, 
  7.19657723683240939863e+05, 
  6.66601232617776375264e+05, 
 -2.94490264303834643215e+05, 
}

Definition at line 410 of file e_j1.c.

double R[] [static]
Initial value:
 {-6.25000000000000000000e-02, 
  1.40705666955189706048e-03, 
 -1.59955631084035597520e-05, 
  4.96727999609584448412e-08}

Definition at line 84 of file e_j1.c.

double S[] [static]
Initial value:
  {0.0, 1.91537599538363460805e-02, 
  1.85946785588630915560e-04, 
  1.17718464042623683263e-06, 
  5.04636257076217042715e-09, 
  1.23542274426137913908e-11}

Definition at line 88 of file e_j1.c.

double tpi = 6.36619772367581382433e-01 [static]

Definition at line 82 of file e_j1.c.

double U0[5] [static]
Initial value:
 {

 -1.96057090646238940668e-01, 
  5.04438716639811282616e-02, 
 -1.91256895875763547298e-03, 
  2.35252600561610495928e-05, 
 -9.19099158039878874504e-08, 
}

Definition at line 159 of file e_j1.c.

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

  1.99167318236649903973e-02, 
  2.02552581025135171496e-04, 
  1.35608801097516229404e-06, 
  6.22741452364621501295e-09, 
  1.66559246207992079114e-11, 
}

Definition at line 170 of file e_j1.c.

double zero = 0.0 [static]

Definition at line 97 of file e_j1.c.