float
j0f(float x) /* wrapper j0f */
{
#ifdef _IEEE_LIBM
return __ieee754_j0f(x);
#else
float z = __ieee754_j0f(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(fabsf(x)>(float)X_TLOSS) {
/* j0f(|x|>X_TLOSS) */
return (float)__kernel_standard((double)x,(double)x,134);
} else
return z;
#endif
}
/* wrapper j0f */
float
j0f (float x)
{
if (__builtin_expect (isgreater (fabsf (x), (float) X_TLOSS), 0)
&& _LIB_VERSION != _IEEE_)
/* j0(|x|>X_TLOSS) */
return __kernel_standard_f (x, x, 134);
return __ieee754_j0f (x);
}
float
__ieee754_y0f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(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 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = sinf(x);
c = cosf(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = -cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
#ifdef DEAD_CODE
if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
else
#endif
{
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
}
return z;
}
if(ix<=0x32000000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_logf(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
}