/* wrapper j1 */
double
j1 (double x)
{
if (__builtin_expect (fabs (x) > X_TLOSS, 0) && _LIB_VERSION != _IEEE_)
/* j1(|x|>X_TLOSS) */
return __kernel_standard (x, x, 36);
return __ieee754_j1 (x);
}
void
Math_j1(void *fp)
{
F_Math_j1 *f;
f = fp;
*f->ret = __ieee754_j1(f->x);
}
double
__ieee754_y1(double x)
{
double z, s,c,ss,cc,u,v;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/*
* y1(NaN) = NaN.
* y1(Inf) = 0.
* y1(-Inf) = NaN and raise invalid exception.
*/
if(ix>=0x7ff00000) return vone/(x+x*x);
/* y1(+-0) = -inf and raise divide-by-zero exception. */
if((ix|lx)==0) return -one/vzero;
/* y1(x<0) = NaN and raise invalid exception. */
if(hx<0) return vzero/vzero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
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)/sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
}
if(ix<=0x3c900000) { /* x < 2**-54 */
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));
}
/*
* @unimplemented
*/
double _j1(double num)
{
if (!_finite(num)) *_errno() = EDOM;
return __ieee754_j1(num);
}
/*
* @unimplemented
*/
double _j1(double num)
{
/* FIXME: errno handling */
return __ieee754_j1(num);
}
