static void
check_overflow ()
{
mpfr_t max;
mpfi_t a;
mpfr_t b;
int inexact;
mpfi_init2 (a, 53);
mpfr_init2 (max, 53);
mpfr_init2 (b, 53);
mpfr_set_ui (&(a->left), 1, MPFI_RNDD);
mpfr_set_inf (max, +1);
mpfr_nextbelow (max);
mpfr_set (&(a->right), max, MPFI_RNDU);
mpfr_set_ui (b, +1, MPFI_RNDD);
inexact = mpfi_add_fr (a, a, b);
if (!mpfr_inf_p (&(a->right))) {
printf ("Error: mpfi_add_fr does not correctly handle positive "
"overflow.\n");
exit (1);
}
if (!MPFI_RIGHT_IS_INEXACT (inexact)) {
printf ("Error: mpfi_add_fr does not return correct value when positive "
"overflow.\n");
exit (1);
}
mpfr_set_inf (max, -1);
mpfr_nextabove (max);
mpfr_set (&(a->left), max, MPFI_RNDD);
mpfr_set_ui (&(a->right), 1, MPFI_RNDU);
mpfr_set_si (b, -1, MPFI_RNDD);
inexact = mpfi_add_fr (a, a, b);
if (!mpfr_inf_p (&(a->left))) {
printf ("Error: mpfi_add_fr does not correctly handle negative "
"overflow.\n");
exit (1);
}
if (!MPFI_LEFT_IS_INEXACT (inexact)) {
printf ("Error: mpfi_add_fr does not return correct value when negative "
"overflow.\n");
exit (1);
}
mpfi_clear (a);
mpfr_clear (b);
mpfr_clear (max);
}
/* This function computes an interval bound for a polynomial in cheb basis.
by using Clenshaw's method --
The n coefficients are given in coeffs.*/
void evaluateChebPolynomialClenshaw(sollya_mpfi_t bound, int n, sollya_mpfi_t *coeffs, mpfi_t x,mpfi_t x0){
int i;
sollya_mpfi_t z, zz, z1,b0,b1;
mpfr_t a, b;
mp_prec_t prec;
prec = sollya_mpfi_get_prec(bound);
sollya_mpfi_init2(z, prec);
sollya_mpfi_init2(zz, prec);
sollya_mpfi_init2(z1, prec);
sollya_mpfi_init2(b0, prec);
sollya_mpfi_init2(b1, prec);
mpfr_init2(a, prec);
mpfr_init2(b, prec);
sollya_mpfi_get_right(b,x);
sollya_mpfi_get_left(a,x);
sollya_mpfi_set_fr(z1,b);
sollya_mpfi_sub_fr(z1,z1,a);
sollya_mpfi_inv(z1,z1);
sollya_mpfi_mul_ui(z,z1,2);
/*z=2/(b-a)*/
sollya_mpfi_set_fr(zz,b);
mpfi_add_fr(zz,zz,a);
sollya_mpfi_mul(zz,zz,z1);
/*zz=(b+a)/(b-a)*/
sollya_mpfi_mul(z,z,x0);
sollya_mpfi_sub(z,z,zz);
/*z=2/(b-a) * x0 - (b+a)/(b-a)*/
/*Do the clenshaw algo*/
/*b1:=[0.,0.];
b0:=[0.,0.];
for i from n to 2 by -1 do
bb:=(((2&*z)&*b0) &-b1) &+L[i];
b1:=b0;
b0:=bb;
end do;
bb:=((z&*b0) &-b1) &+L[1];
return bb;
*/
sollya_mpfi_set_ui(b0,0);
sollya_mpfi_set_ui(b1,0);
for(i=n-1;i>0; i--){
sollya_mpfi_mul(zz,z,b0);
sollya_mpfi_mul_ui(zz,zz,2);
sollya_mpfi_sub(zz,zz,b1);
sollya_mpfi_add(zz,zz,coeffs[i]);
sollya_mpfi_set(b1,b0);
sollya_mpfi_set(b0,zz);
}
sollya_mpfi_mul(zz,z,b0);
sollya_mpfi_sub(zz,zz,b1);
sollya_mpfi_add(zz,zz,coeffs[0]);
sollya_mpfi_set(bound, zz);
sollya_mpfi_clear(zz);
sollya_mpfi_clear(z);
sollya_mpfi_clear(z1);
sollya_mpfi_clear(b0);
sollya_mpfi_clear(b1);
mpfr_clear(b); mpfr_clear(a);
}