float
j1f(float x) /* wrapper j1f */
{
#ifdef _IEEE_LIBM
return __ieee754_j1f(x);
#else
float z;
z = __ieee754_j1f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z;
if(fabsf(x)>(float)X_TLOSS) {
/* j1(|x|>X_TLOSS) */
return (float)__kernel_standard((double)x,(double)x,136);
} else
return z;
#endif
}
/* wrapper j1f */
float
j1f (float x)
{
if (__builtin_expect (fabsf (x) > X_TLOSS, 0) && _LIB_VERSION != _IEEE_)
/* j1(|x|>X_TLOSS) */
return __kernel_standard_f (x, x, 136);
return __ieee754_j1f (x);
}
/* wrapper j1f */
float
__j1f (float x)
{
if (__builtin_expect (isgreater (fabsf (x), X_TLOSS), 0)
&& _LIB_VERSION != _IEEE_ && _LIB_VERSION != _POSIX_)
/* j1(|x|>X_TLOSS) */
return __kernel_standard_f (x, x, 136);
return __ieee754_j1f (x);
}
float
__ieee754_y1f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(ix>=0x7f800000) return one/(x+x*x);
if(ix==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sinf(x);
c = cosf(x);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = cosf(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)/sqrtf(x);
else {
u = ponef(x); v = qonef(x);
z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
}
return z;
}
if(ix<=0x24800000) { /* 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_j1f(x)*__ieee754_logf(x)-one/x));
}
