double fd_y0(double x) /* wrapper fd_y0 */
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = FD_HI(x);
ix = 0x7fffffff&hx;
lx = FD_LO(x);
/* Y0(NaN) is NaN, fd_y0(-inf) is Nan, fd_y0(inf) is 0 */
if(ix>=0x7ff00000) return gD( one, gA(x, gM(x,x)));
if((ix|lx)==0) return gD(-one, zero);
if(hx<0) return gD(zero,zero);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* fd_y0(x) = fd_sqrt(2/(pi*x))*(p0(x)*fd_sin(x0)+q0(x)*fd_cos(x0))
* where x0 = x-pi/4
* Better formula:
* fd_cos(x0) = fd_cos(x)fd_cos(pi/4)+fd_sin(x)fd_sin(pi/4)
* = 1/fd_sqrt(2) * (fd_sin(x) + fd_cos(x))
* fd_sin(x0) = fd_sin(x)fd_cos(3pi/4)-fd_cos(x)fd_sin(3pi/4)
* = 1/fd_sqrt(2) * (fd_sin(x) - fd_cos(x))
* To avoid cancellation, use
* fd_sin(x) +- fd_cos(x) = -fd_cos(2x)/(fd_sin(x) -+ fd_cos(x))
* to compute the worse one.
*/
s = fd_sin(x);
c = fd_cos(x);
ss = gS(s,c);
cc = gA(s,c);
/*
* fd_j0(x) = 1/fd_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / fd_sqrt(x)
* fd_y0(x) = 1/fd_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / fd_sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -fd_cos(gA(x,x));
if (gM(s,c) < zero) cc = gD(z,ss);
else ss = gD(z,cc);
}
if(ix>0x48000000) z = gD(gM(invsqrtpi,ss), gSqrt(x));
else {
u = pzero(x); v = qzero(x);
z = gD(gM(invsqrtpi, gA(gM(u,ss), gM(v,cc))), gSqrt(x));
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return gA(u00, gM(tpi, fd_log(x)));
}
z = gM(x,x);
u = gA(u00, gM(z,gA(u01, gM(z,gA(u02, gM(z,gA(u03, gM(z,gA(u04, gM(z,gA(u05, gM(z,u06))))))))))));
v = gA(one, gM(z,gA(v01, gM(z,gA(v02, gM(z,gA(v03, gM(z,v04))))))));
return(gD(u,v) + gM(tpi,gM(fd_j0(x), fd_log(x))));
}
static JSBool
math_log(JSContext *cx, JSObject *obj, uintN argc, jsval *argv, jsval *rval)
{
jsdouble x, z;
if (!js_ValueToNumber(cx, argv[0], &x))
return JS_FALSE;
z = fd_log(x);
return js_NewNumberValue(cx, z, rval);
}