#warning obsolete and unnecessary?
#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_j1.c,v 1.10 1999/07/02 15:37:39 simonb Exp $");
#endif
#include "math.h"
#include "math_private.h"
static double pone(double), qone(double);
static const double
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01,
tpi = 6.36619772367581382433e-01,
r00 = -6.25000000000000000000e-02,
r01 = 1.40705666955189706048e-03,
r02 = -1.59955631084035597520e-05,
r03 = 4.96727999609584448412e-08,
s01 = 1.91537599538363460805e-02,
s02 = 1.85946785588630915560e-04,
s03 = 1.17718464042623683263e-06,
s04 = 5.04636257076217042715e-09,
s05 = 1.23542274426137913908e-11;
static const double zero = 0.0;
double j1(double x)
{
double z, s,c,ss,cc,r,u,v,y;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/x;
y = fabs(x);
if(ix >= 0x40000000) {
s = sin(y);
c = cos(y);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) {
z = cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(ix<0x3e400000) {
if(huge+x>one) return 0.5*x;
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*0.5+r/s);
}
static const double U0[5] = {
-1.96057090646238940668e-01,
5.04438716639811282616e-02,
-1.91256895875763547298e-03,
2.35252600561610495928e-05,
-9.19099158039878874504e-08,
};
static const double V0[5] = {
1.99167318236649903973e-02,
2.02552581025135171496e-04,
1.35608801097516229404e-06,
6.22741452364621501295e-09,
1.66559246207992079114e-11,
};
#define __ieee754_j1 j1
#define __ieee754_log log
double y1(double x)
{
double z, s,c,ss,cc,u,v;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) {
s = sin(x);
c = cos(x);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) {
z = cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
}
if(ix<=0x3c900000) {
return(-tpi/x);
}
z = x*x;
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]))));
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
#ifdef __STDC__
static const double pr8[6] = {
#else
static double pr8[6] = {
#endif
0.00000000000000000000e+00,
1.17187499999988647970e-01,
1.32394806593073575129e+01,
4.12051854307378562225e+02,
3.87474538913960532227e+03,
7.91447954031891731574e+03,
};
#ifdef __STDC__
static const double ps8[5] = {
#else
static double ps8[5] = {
#endif
1.14207370375678408436e+02,
3.65093083420853463394e+03,
3.69562060269033463555e+04,
9.76027935934950801311e+04,
3.08042720627888811578e+04,
};
#ifdef __STDC__
static const double pr5[6] = {
#else
static double pr5[6] = {
#endif
1.31990519556243522749e-11,
1.17187493190614097638e-01,
6.80275127868432871736e+00,
1.08308182990189109773e+02,
5.17636139533199752805e+02,
5.28715201363337541807e+02,
};
#ifdef __STDC__
static const double ps5[5] = {
#else
static double ps5[5] = {
#endif
5.92805987221131331921e+01,
9.91401418733614377743e+02,
5.35326695291487976647e+03,
7.84469031749551231769e+03,
1.50404688810361062679e+03,
};
#ifdef __STDC__
static const double pr3[6] = {
#else
static double pr3[6] = {
#endif
3.02503916137373618024e-09,
1.17186865567253592491e-01,
3.93297750033315640650e+00,
3.51194035591636932736e+01,
9.10550110750781271918e+01,
4.85590685197364919645e+01,
};
#ifdef __STDC__
static const double ps3[5] = {
#else
static double ps3[5] = {
#endif
3.47913095001251519989e+01,
3.36762458747825746741e+02,
1.04687139975775130551e+03,
8.90811346398256432622e+02,
1.03787932439639277504e+02,
};
#ifdef __STDC__
static const double pr2[6] = {
#else
static double pr2[6] = {
#endif
1.07710830106873743082e-07,
1.17176219462683348094e-01,
2.36851496667608785174e+00,
1.22426109148261232917e+01,
1.76939711271687727390e+01,
5.07352312588818499250e+00,
};
#ifdef __STDC__
static const double ps2[5] = {
#else
static double ps2[5] = {
#endif
2.14364859363821409488e+01,
1.25290227168402751090e+02,
2.32276469057162813669e+02,
1.17679373287147100768e+02,
8.36463893371618283368e+00,
};
#ifdef __STDC__
static double pone(double x)
#else
static double pone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
int32_t ix;
p = q = 0;
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);
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]))));
return one+ r/s;
}
#ifdef __STDC__
static const double qr8[6] = {
#else
static double qr8[6] = {
#endif
0.00000000000000000000e+00,
-1.02539062499992714161e-01,
-1.62717534544589987888e+01,
-7.59601722513950107896e+02,
-1.18498066702429587167e+04,
-4.84385124285750353010e+04,
};
#ifdef __STDC__
static const double qs8[6] = {
#else
static double qs8[6] = {
#endif
1.61395369700722909556e+02,
7.82538599923348465381e+03,
1.33875336287249578163e+05,
7.19657723683240939863e+05,
6.66601232617776375264e+05,
-2.94490264303834643215e+05,
};
#ifdef __STDC__
static const double qr5[6] = {
#else
static double qr5[6] = {
#endif
-2.08979931141764104297e-11,
-1.02539050241375426231e-01,
-8.05644828123936029840e+00,
-1.83669607474888380239e+02,
-1.37319376065508163265e+03,
-2.61244440453215656817e+03,
};
#ifdef __STDC__
static const double qs5[6] = {
#else
static double qs5[6] = {
#endif
8.12765501384335777857e+01,
1.99179873460485964642e+03,
1.74684851924908907677e+04,
4.98514270910352279316e+04,
2.79480751638918118260e+04,
-4.71918354795128470869e+03,
};
#ifdef __STDC__
static const double qr3[6] = {
#else
static double qr3[6] = {
#endif
-5.07831226461766561369e-09,
-1.02537829820837089745e-01,
-4.61011581139473403113e+00,
-5.78472216562783643212e+01,
-2.28244540737631695038e+02,
-2.19210128478909325622e+02,
};
#ifdef __STDC__
static const double qs3[6] = {
#else
static double qs3[6] = {
#endif
4.76651550323729509273e+01,
6.73865112676699709482e+02,
3.38015286679526343505e+03,
5.54772909720722782367e+03,
1.90311919338810798763e+03,
-1.35201191444307340817e+02,
};
#ifdef __STDC__
static const double qr2[6] = {
#else
static double qr2[6] = {
#endif
-1.78381727510958865572e-07,
-1.02517042607985553460e-01,
-2.75220568278187460720e+00,
-1.96636162643703720221e+01,
-4.23253133372830490089e+01,
-2.13719211703704061733e+01,
};
#ifdef __STDC__
static const double qs2[6] = {
#else
static double qs2[6] = {
#endif
2.95333629060523854548e+01,
2.52981549982190529136e+02,
7.57502834868645436472e+02,
7.39393205320467245656e+02,
1.55949003336666123687e+02,
-4.95949898822628210127e+00,
};
#ifdef __STDC__
static double qone(double x)
#else
static double qone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
int32_t ix;
p = q = 0;
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);
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])))));
return (.375 + r/s)/x;
}