double j0(double x) /* wrapper j0 */ { #ifdef _IEEE_LIBM return __ieee754_j0(x); #else double z = __ieee754_j0(x); if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; if(fabs(x)>X_TLOSS) { return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */ } else return z; #endif }
double j0(double x) { double z = __ieee754_j0(x); if (_LIB_VERSION == _IEEE_ || isnan(x)) return z; if (fabs(x) > X_TLOSS) return __kernel_standard(x, x, 34); /* j0(|x|>X_TLOSS) */ return z; }
void Math_j0(void *fp) { F_Math_j0 *f; f = fp; *f->ret = __ieee754_j0(f->x); }
/* wrapper j0 */ double j0 (double x) { if (__builtin_expect (isgreater (fabs (x), X_TLOSS), 0) && _LIB_VERSION != _IEEE_ && _LIB_VERSION != _POSIX_) /* j0(|x|>X_TLOSS) */ return __kernel_standard (x, x, 34); return __ieee754_j0 (x); }
/* wrapper j0l */ long double j0l (long double x) { # if defined(__UCLIBC_HAS_FENV__) if (__builtin_expect (isgreater (fabsl (x), X_TLOSS), 0) && _LIB_VERSION != _IEEE_ && _LIB_VERSION != _POSIX_) /* j0(|x|>X_TLOSS) */ return __kernel_standard_l (x, x, 234); # endif /* __UCLIBC_HAS_FENV__ */ return (long double) __ieee754_j0 ((double)x); }
double __ieee754_y0(double x) { double z, s,c,ss,cc,u,v; int32_t hx,ix,lx; EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ if(ix>=0x7ff00000) return one/(x+x*x); if((ix|lx)==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 = sin(x); c = cos(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<0x7fe00000) { /* make sure x+x not overflow */ 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 = pzero(x); v = qzero(x); z = invsqrtpi*(u*ss+v*cc)/sqrt(x); } return z; } if(ix<=0x3e400000) { /* x < 2**-27 */ return(u00 + tpi*__ieee754_log(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_j0(x)*__ieee754_log(x))); }