void
check_overflow ()
{
mpfr_t max;
mpfi_t a;
mpz_t z;
int inexact;
mpz_init (z);
mpfi_init2 (a, 53);
mpfr_init2 (max, 53);
mpz_set_ui (z, 4096);
mpfr_set_ui (&(a->left), 1, MPFI_RNDD);
mpfr_set_inf (max, +1);
mpfr_nextbelow (max);
mpfr_set (&(a->right), max, MPFI_RNDU);
inexact = mpfi_mul_z (a, a, z);
if (!mpfr_inf_p (&(a->right))) {
printf ("Error: mpfi_mul_z does not correctly handle positive "
"overflow.\n");
exit (1);
}
if (!MPFI_RIGHT_IS_INEXACT (inexact)) {
printf ("Error: mpfi_mul_z 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);
inexact = mpfi_mul_z (a, a, z);
if (!mpfr_inf_p (&(a->left))) {
printf ("Error: mpfi_mul_z does not correctly handle negative "
"overflow.\n");
exit (1);
}
if (!MPFI_LEFT_IS_INEXACT (inexact)) {
printf ("Error: mpfi_mul_z does not return correct value when negative "
"overflow.\n");
exit (1);
}
mpz_clear (z);
mpfi_clear (a);
mpfr_clear (max);
}
/*Returns in chebCoeffs the coeffs of the finite Chebyshev basis expansion
of the polynomial p of degree n-1, over [-1,1];
The coefficients in monomial basis of p are in *p
This algorithm uses simply euclidean division.
*/
void getPolyCoeffsChebBasis(sollya_mpfi_t *chebCoeffs, sollya_mpfi_t *p, int n){
sollya_mpfi_t *pAux, temp;
mpz_t *chebMatrix;
int i,j;
mp_prec_t prec;
prec = sollya_mpfi_get_prec(chebCoeffs[0]);
pAux=safeMalloc((n)*sizeof(sollya_mpfi_t));
for (i=0;i<n;i++){
sollya_mpfi_init2(pAux[i],prec);
sollya_mpfi_set(pAux[i], p[i]);
}
chebMatrix=(mpz_t *)safeMalloc((n*n)*sizeof(mpz_t));
for (i=0;i<n*n;i++){
mpz_init2(chebMatrix[i],prec);
}
getChebPolyCoeffs(chebMatrix, n, prec);
sollya_mpfi_init2(temp,prec);
for(i=n-1; i>=0;i--){
mpfi_div_z(chebCoeffs[i],pAux[i],chebMatrix[i*n+i]);
for(j=i-1;j>=0;j--){
mpfi_mul_z(temp,chebCoeffs[i],chebMatrix[i*n+j]);
mpfi_sub(pAux[j],pAux[j],temp);
}
}
for (i=0;i<n;i++){
sollya_mpfi_clear(pAux[i]);
}
safeFree(pAux);
for (i=0;i<n*n;i++){
mpz_clear(chebMatrix[i]);
}
safeFree(chebMatrix);
sollya_mpfi_clear(temp);
}
/*Wrapper to get directly the coeffs in the monomial basis
from a polynomial in the Chebyshev basis, over a given interval x*/
void getCoeffsFromChebPolynomial(sollya_mpfi_t**coeffs, sollya_mpfi_t *chebCoeffs, int n, sollya_mpfi_t x){
sollya_mpfi_t z1, z2, ui, vi, temp;
int j,i;
sollya_mpfi_t *c;
mpfr_t u,v;
mpz_t *chebMatrix;
mp_prec_t prec;
prec = sollya_mpfi_get_prec(chebCoeffs[0]);
sollya_mpfi_init2(temp, prec);
chebMatrix= (mpz_t *)safeMalloc((n*n)*sizeof(mpz_t));
for (i=0;i<n*n;i++){
mpz_init2(chebMatrix[i], prec);
}
getChebPolyCoeffs(chebMatrix, n,prec);
*coeffs= (sollya_mpfi_t *)safeMalloc((n)*sizeof(sollya_mpfi_t));
c=(sollya_mpfi_t *)safeMalloc((n)*sizeof(sollya_mpfi_t));
for (i=0;i<n;i++){
sollya_mpfi_init2((*coeffs)[i],prec);
sollya_mpfi_init2(c[i],prec);
sollya_mpfi_set_ui(c[i],0);
}
for (j=0;j<n;j++){
for (i=j;i<n;i++){
mpfi_mul_z(temp, chebCoeffs[i], chebMatrix[i*n+j]);
sollya_mpfi_add(c[j], c[j], temp);
}
}
/*we have in c_i the values of the coefs of P(2/(b-a)x- (b+a)/(b-a)) = \sum c_i (2/(b-a)x- (b+a)/(b-a))^i*/
/*we need to the translation*/
/*we compute z1=2/(b-a); z2=-(b+a)/(b-a)*/
sollya_mpfi_init2(ui, prec);
sollya_mpfi_init2(vi, prec);
mpfr_init2(u, prec);
mpfr_init2(v, prec);
sollya_mpfi_init2(z1, prec);
sollya_mpfi_init2(z2, prec);
sollya_mpfi_get_left(u,x);
sollya_mpfi_get_right(v,x);
sollya_mpfi_set_fr(ui,u);
sollya_mpfi_set_fr(vi,v);
sollya_mpfi_sub(z2,vi,ui);
sollya_mpfi_ui_div(z1,2,z2);
sollya_mpfi_add(temp, ui, vi);
sollya_mpfi_div(z2, temp, z2);
sollya_mpfi_neg(z2, z2);
getTranslatedPolyCoeffs((*coeffs), c, n, z1,z2);
/*cleaning*/
sollya_mpfi_clear(z1);
sollya_mpfi_clear(z2);
sollya_mpfi_clear(ui);
sollya_mpfi_clear(vi);
sollya_mpfi_clear(temp);
mpfr_clear(u);
mpfr_clear(v);
for (i=0;i<n*n;i++){
mpz_clear(chebMatrix[i]);
}
safeFree(chebMatrix);
for (i=0;i<n;i++){
sollya_mpfi_clear(c[i]);
}
safeFree(c);
}
