//////////////////////////////////////////////////////////////////////
// scattering function at a point
//////////////////////////////////////////////////////////////////////
float APSF::pointAPSF(float mu)
{
float total = 0.0f;
for (int m = 0; m < _maxTerms; m++)
total += (gM(_I0, m) + gM(_I0, m + 1)) * legendreM(m, mu);
return total;
}
double fd_nextafter(double x, double y)
{
int hx,hy,ix,iy;
unsigned lx,ly;
hx = FD_HI(x); /* high word of x */
lx = FD_LO(x); /* low word of x */
hy = FD_HI(y); /* high word of y */
ly = FD_LO(y); /* low word of y */
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffff; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
return x+y;
if(x==y) return x; /* x=y, return x */
if((ix|lx)==0) { /* x == 0 */
FD_HI(x) = hy&0x80000000; /* return +-minsubnormal */
FD_LO(x) = 1;
y = x*x;
if(y==x) return y; else return x; /* raise underflow flag */
}
if(hx>=0) { /* x > 0 */
if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
} else { /* x < 0 */
if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
}
hy = hx&0x7ff00000;
if(hy>=0x7ff00000) return gA(x,x); /* overflow */
if(hy<0x00100000) { /* underflow */
y = gM(x,x);
if(y!=x) { /* raise underflow flag */
FD_HI(y) = hx; FD_LO(y) = lx;
return y;
}
}
FD_HI(x) = hx; FD_LO(x) = lx;
return x;
}
double fd_remainder(double x, double p) /* wrapper fd_remainder */
{
int hx,hp;
unsigned sx,lx,lp;
double p_half;
hx = FD_HI(x); /* high word of x */
lx = FD_LO(x); /* low word of x */
hp = FD_HI(p); /* high word of p */
lp = FD_LO(p); /* low word of p */
sx = hx&0x80000000;
hp &= 0x7fffffff;
hx &= 0x7fffffff;
/* purge off fd_exception values */
if((hp|lp)==0) return gD(gM(x,p),gM(x,p)); /* p = 0 */
if((hx>=0x7ff00000)|| /* x not fd_finite */
((hp>=0x7ff00000)&& /* p is NaN */
(((hp-0x7ff00000)|lp)!=0)))
return gD(gM(x,p),gM(x,p));
if (hp<=0x7fdfffff) x = fd_fmod(x,gA(p,p)); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return gM(zero,x);
x = fd_fabs(x);
p = fd_fabs(p);
if (hp<0x00200000) {
if(gA(x,x) > p) {
x = gS(x,p);
if(gA(x,x) >= p) x = gS(x,p);
}
} else {
p_half = gM(0.5,p);
if(x>p_half) {
x = gS(x,p);
if(x>=p_half) x = gS(x,p);
}
}
FD_HI(x) ^= sx;
return x;
}
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))));
}
double fd_j0(double x) /* wrapper fd_j0 */
{
double z, s,c,ss,cc,r,u,v;
int hx,ix;
hx = FD_HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return gD(one, gM(x,x));
x = fd_fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = fd_sin(x);
c = fd_cos(x);
ss = gS(s,c);
cc = gA(s,c);
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);
}
/*
* 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>0x48000000) z = gD(gM(invsqrtpi,cc),gSqrt(x));
else {
u = pzero(x); v = qzero(x);
z = gD(gM(invsqrtpi, (gS(gM(u,cc), gM(v,ss)))), gSqrt(x));
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
if(huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return gS(one, gM(gM(0.25,x),x));
}
}
z = gM(x,x);
r = gM(z,gA(R02, gM(z,gA(R03, gM(z,gA(R04, gM(z,R05)))))));
s = gA(one, gM(z,gA(S01, gM(z,gA(S02, gM(z,gA(S03, gM(z,S04))))))));
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return gA(one, gM(z,gA(-0.25,gD(r,s))));
} else {
u = gM(0.5,x);
return(gM(gA(one, u), gS(one, u)) + gM(z, gD(r,s)));
}
}
static double qzero(double x)
{
const double *p,*q;
double s,r,z;
int ix;
ix = 0x7fffffff&FD_HI(x);
if(ix>=0x40200000) {p = qR8; q= qS8;}
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
else if(ix>=0x4006DB6D){p = qR3; q= qS3_;}
else if(ix>=0x40000000){p = qR2; q= qS2_;}
z = gD(one, gM(x,x));
r = gA(p[0], gM(z,gA(p[1], gM(z,gA(p[2], gM(z,gA(p[3], gM(z,gA(p[4], gM(z,p[5]))))))))));
s = gA(one , gM(z,gA(q[0], gM(z,gA(q[1], gM(z,gA(q[2], gM(z,gA(q[3], gM(z,gA(q[4], gM(z,q[5]))))))))))));
return gD(gA(-.125, gD(r,s)), x);
}
static double pzero(double x)
{
const double *p,*q;
double z,r,s;
int ix;
ix = 0x7fffffff&FD_HI(x);
if(ix>=0x40200000) {p = pR8; q= pS8;}
else if(ix>=0x40122E8B){p = pR5; q= pS5_;}
else if(ix>=0x4006DB6D){p = pR3; q= pS3_;}
else if(ix>=0x40000000){p = pR2; q= pS2_;}
z = gD(one, gM(x,x));
r = gA(p[0], gM(z,gA(p[1], gM(z,gA(p[2], gM(z,gA(p[3], gM(z,gA(p[4], gM(z,p[5]))))))))));
s = gA(one , gM(z,gA(q[0], gM(z,gA(q[1], gM(z,gA(q[2], gM(z,gA(q[3], gM(z,q[4]))))))))));
return gA(one, gD(r,s));
}
