quad_float log(const quad_float& t) { // Newton method. See Bailey, MPFUN
if (t.hi <= 0.0) {
Error("log(quad_float): argument must be positive");
}
double s1 = log(t.hi);
ForceToMem(&s1); // Again, this is fairly paranoid.
quad_float s;
s = s1;
quad_float e;
e=exp(s);
return s+(t-e)/e; // Newton step
}
quad_float sqrt(const quad_float& y) {
if (y.hi < 0.0)
ArithmeticError("quad_float: square root of negative number");
if (y.hi == 0.0) return quad_float(0.0,0.0);
double c;
c = sqrt(y.hi);
ForceToMem(&c); // This is fairly paranoid, but it doesn't cost too much.
START_FIX
DOUBLE p,q,hx,tx,u,uu,cc;
DOUBLE t1;
p = Protect(NTL_QUAD_FLOAT_SPLIT*c);
hx = (c-p);
hx = hx+p;
tx = c-hx;
p = Protect(hx*hx);
q = Protect(hx*tx);
q = q+q;
u = p+q;
uu = p-u;
uu = uu+q;
t1 = Protect(tx*tx);
uu = uu+t1;
cc = y.hi-u;
cc = cc-uu;
cc = cc+y.lo;
t1 = c+c;
cc = cc/t1;
hx = c+cc;
tx = c-hx;
tx = tx+cc;
END_FIX
return quad_float(hx, tx);
}
xdouble ceil(const xdouble& aa)
{
xdouble z;
xdouble a = aa;
ForceToMem(&a.x);
if (a.e == 0) {
z.x = ceil(a.x);
z.e = 0;
z.normalize();
return z;
}
else if (a.e > 0) {
return a;
}
else {
if (a.x < 0)
return to_xdouble(0);
else
return to_xdouble(1);
}
}
