int
cxrec (struct cxpr z, struct cxpr *w)
{
struct xpr x;
int sa, sb, ea, eb;
if (xprcmp (&z.re, &xZero) == 0 && xprcmp (&z.im, &xZero) == 0)
return 0;
else
{
sa = z.re.nmm[0] & xM_sgn;
sb = z.im.nmm[0] & xM_sgn;
ea = (z.re.nmm[0] &= xM_exp) - xBias;
eb = (z.im.nmm[0] &= xM_exp) - xBias;
if (ea > eb + XBOUND)
x = z.re;
else if (eb > ea + XBOUND)
x = z.im;
else
{
z.re.nmm[0] -= eb;
z.im.nmm[0] = xBias;
x = xsqrt (xadd (xmul (z.re, z.re), xmul (z.im, z.im), 0));
x.nmm[0] += eb;
z.re.nmm[0] += eb;
z.im.nmm[0] += eb;
}
w->re = xdiv (xdiv (z.re, x), x);
w->im = xdiv (xdiv (z.im, x), x);
w->re.nmm[0] |= sa;
w->im.nmm[0] |= xM_sgn ^ sb;
return 1;
}
}
struct xpr
cxabs (struct cxpr z)
{
struct xpr x;
int ea, eb;
if (xprcmp (&z.re, &xZero) == 0 && xprcmp (&z.im, &xZero) == 0)
return xZero;
else
{
ea = (z.re.nmm[0] &= xM_exp) - xBias;
eb = (z.im.nmm[0] &= xM_exp) - xBias;
if (ea > eb + XBOUND)
return z.re;
else if (eb > ea + XBOUND)
return z.im;
else
{
z.re.nmm[0] -= eb;
z.im.nmm[0] = xBias;
x = xsqrt (xadd (xmul (z.re, z.re), xmul (z.im, z.im), 0));
x.nmm[0] += eb;
return x;
}
}
}
struct cxpr
cxacosh (struct cxpr z)
{
struct cxpr w;
struct xpr ls, rs;
w = cxsqrt (cxsub (cxsqr (z), cxOne));
ls = cxabs (cxsum (z, w));
rs = xmul (xVSV, cxabs (z));
if (xprcmp (&ls, &rs) < 0)
return cxneg (cxlog (cxsub (z, w)));
else
return cxlog (cxsum (z, w));
}
int
main (int na, char **av)
{
struct xpr s, t, f;
char nbx[64], nby[64];
FILE *fp;
if (na != 2)
{
printf ("para: input_file\n");
exit (-1);
}
fp = fopen (*++av, "r");
printf (" Test of Elementary Operations\n");
while (fscanf (fp, "%s %s", nbx, nby) != EOF)
{
s = atox (nbx);
t = atox (nby);
printf ("\n x= ");
xprxpr (s, decd);
printf ("\n y= ");
xprxpr (t, decd);
/* extended precision addition */
printf ("\nadd\n");
f = xadd (s, t, 0);
printf (" %16.10f\n", xtodbl (f));
xprxpr (f, decd);
/* extended precision subtraction */
printf ("\nsubtract\n");
f = xadd (s, t, 1);
printf (" %16.10f\n", xtodbl (f));
xprxpr (f, decd);
/* extended precision multiplication */
printf ("\nmultiply\n");
f = xmul (s, t);
printf (" %16.10f\n", xtodbl (f));
xprxpr (f, decd);
/* extended precision division */
printf ("\ndivide\n");
f = xdiv (s, t);
printf (" %16.10f\n", xtodbl (f));
xprxpr (f, decd);
}
putchar ('\n');
return 0;
}
struct xpr
xsin (struct xpr z)
{
int k;
z = rred (z, 's', &k);
if (x_exp (&z) >= xK_lin)
{
z = c_tan (xpr2 (z, -1));
z = xdiv (xpr2 (z, 1), xadd (xOne, xmul (z, z), 0));
}
if ((k))
return xneg (z);
else
return z;
}
struct cxpr
cxasinh (struct cxpr z)
{
struct cxpr w;
struct xpr ls, rs;
/* In this way, cxasinh() works fine also with real numbers */
/* very near to -oo. */
w = cxsqrt (cxsum (cxOne, cxsqr (z)));
ls = cxabs (cxsum (z, w));
rs = xmul (xVSV, cxabs (z));
if (xprcmp (&ls, &rs) < 0)
return cxneg (cxlog (cxsub (w, z)));
else
return cxlog (cxsum (z, w));
}
struct xpr
xcos (struct xpr z)
{
int k;
z = rred (z, 'c', &k);
if (x_exp (&z) < xK_lin)
{
if ((k))
return xneg (xOne);
else
return xOne;
}
z = c_tan (xpr2 (z, -1));
z = xmul (z, z);
z = xdiv (xadd (xOne, z, 1), xadd (xOne, z, 0));
if ((k))
return xneg (z);
else
return z;
}
static struct xpr
c_tan (struct xpr z)
{
struct xpr s, f, d;
int m;
unsigned short k;
if (x_exp (&z) < xK_lin)
return z;
s = xneg (xmul (z, z));
for (k = 1; k <= XDIM && s.nmm[k] == 0; k++);
if ((xsigerr (s.nmm[0] == 0xffff && k > XDIM, XFPOFLOW, NULL)))
return xZero;
else
{
f = xZero;
for (d = inttox (m = xMS_trg); m > 1;)
{
f = xdiv (s, xadd (d, f, 0));
d = inttox (m -= 2);
}
return xdiv (z, xadd (d, f, 0));
}
}
vector3D MakeNormal(point3D &p1, point3D &p2, point3D &p3) {
vector3D ans = xmul(p2-p1, p3-p1);
normal(ans);
return ans;
}
