void
arb_sin_cos_pi(arb_t s, arb_t c, const arb_t x, long prec)
{
arb_t t;
arb_t u;
fmpz_t v;
if (arf_cmpabs_2exp_si(arb_midref(x), FLINT_MAX(65536, (4*prec))) > 0)
{
arf_zero(arb_midref(s));
mag_one(arb_radref(s));
arf_zero(arb_midref(c));
mag_one(arb_radref(c));
return;
}
arb_init(t);
arb_init(u);
fmpz_init(v);
arb_mul_2exp_si(t, x, 1);
arf_get_fmpz(v, arb_midref(t), ARF_RND_NEAR);
arb_sub_fmpz(t, t, v, prec);
arb_const_pi(u, prec);
arb_mul(t, t, u, prec);
arb_mul_2exp_si(t, t, -1);
switch (fmpz_fdiv_ui(v, 4))
{
case 0:
arb_sin_cos(s, c, t, prec);
break;
case 1:
arb_sin_cos(c, s, t, prec);
arb_neg(c, c);
break;
case 2:
arb_sin_cos(s, c, t, prec);
arb_neg(s, s);
arb_neg(c, c);
break;
default:
arb_sin_cos(c, s, t, prec);
arb_neg(s, s);
break;
}
fmpz_clear(v);
arb_clear(t);
arb_clear(u);
}
int
arf_sub_special(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd)
{
if (arf_is_zero(x))
{
if (arf_is_zero(y))
{
arf_zero(z);
return 0;
}
else
return arf_neg_round(z, y, prec, rnd);
}
else if (arf_is_zero(y))
{
return arf_set_round(z, x, prec, rnd);
}
else if (arf_is_nan(x) || arf_is_nan(y)
|| (arf_is_pos_inf(x) && arf_is_pos_inf(y))
|| (arf_is_neg_inf(x) && arf_is_neg_inf(y)))
{
arf_nan(z);
return 0;
}
else if (arf_is_special(x))
{
arf_set(z, x);
return 0;
}
else
{
arf_neg(z, y);
return 0;
}
}
void
arf_ceil(arf_t z, const arf_t x)
{
if (arf_is_special(x) || arf_is_int(x))
{
arf_set(z, x);
}
else
{
slong exp = ARF_EXP(x);
/* now exp cannot be too large, as we would have
caught this in arf_is_int() */
if (COEFF_IS_MPZ(exp) || exp <= 0)
{
if (ARF_SGNBIT(x))
arf_zero(z);
else
arf_one(z);
}
else if (exp == 1)
{
arf_set_si(z, ARF_SGNBIT(x) ? -1 : 2);
}
else
{
arf_set_round(z, x, exp, ARF_RND_CEIL);
}
}
}
void
acb_hypgeom_erf_asymp(acb_t res, const acb_t z, slong prec, slong prec2)
{
acb_t a, t, u;
acb_init(a);
acb_init(t);
acb_init(u);
acb_one(a);
acb_mul_2exp_si(a, a, -1);
acb_mul(t, z, z, prec2);
acb_hypgeom_u_asymp(u, a, a, t, -1, prec2);
acb_neg(t, t);
acb_exp(t, t, prec2);
acb_mul(u, u, t, prec2);
acb_const_pi(t, prec2);
acb_sqrt(t, t, prec2);
acb_mul(t, t, z, prec2);
acb_div(u, u, t, prec2);
/* branch cut term: -1 or 1 */
if (arb_contains_zero(acb_realref(z)))
{
arb_zero(acb_imagref(t));
arf_zero(arb_midref(acb_realref(t)));
mag_one(arb_radref(acb_realref(t)));
}
else
{
acb_set_si(t, arf_sgn(arb_midref(acb_realref(z))));
}
acb_sub(t, t, u, prec);
if (arb_is_zero(acb_imagref(z)))
arb_zero(acb_imagref(t));
else if (arb_is_zero(acb_realref(z)))
arb_zero(acb_realref(t));
acb_set(res, t);
acb_clear(a);
acb_clear(t);
acb_clear(u);
}
void
arb_sinc(arb_t z, const arb_t x, slong prec)
{
mag_t c, r;
mag_init(c);
mag_init(r);
mag_set_ui_2exp_si(c, 5, -1);
arb_get_mag_lower(r, x);
if (mag_cmp(c, r) < 0)
{
/* x is not near the origin */
_arb_sinc_direct(z, x, prec);
}
else if (mag_cmp_2exp_si(arb_radref(x), 1) < 0)
{
/* determine error magnitude using the derivative bound */
if (arb_is_exact(x))
{
mag_zero(c);
}
else
{
_arb_sinc_derivative_bound(r, x);
mag_mul(c, arb_radref(x), r);
}
/* evaluate sinc at the midpoint of x */
if (arf_is_zero(arb_midref(x)))
{
arb_one(z);
}
else
{
arb_get_mid_arb(z, x);
_arb_sinc_direct(z, z, prec);
}
/* add the error */
mag_add(arb_radref(z), arb_radref(z), c);
}
else
{
/* x has a large radius and includes points near the origin */
arf_zero(arb_midref(z));
mag_one(arb_radref(z));
}
mag_clear(c);
mag_clear(r);
}
void
arf_set_fmpr(arf_t y, const fmpr_t x)
{
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
arf_zero(y);
else if (fmpr_is_pos_inf(x))
arf_pos_inf(y);
else if (fmpr_is_neg_inf(x))
arf_neg_inf(y);
else
arf_nan(y);
}
else
{
arf_set_fmpz(y, fmpr_manref(x));
fmpz_add_inline(ARF_EXPREF(y), ARF_EXPREF(y), fmpr_expref(x));
}
}
void
arb_mul_naive(arb_t z, const arb_t x, const arb_t y, slong prec)
{
arf_t zm_exact, zm_rounded, zr, t, u;
arf_init(zm_exact);
arf_init(zm_rounded);
arf_init(zr);
arf_init(t);
arf_init(u);
arf_mul(zm_exact, arb_midref(x), arb_midref(y), ARF_PREC_EXACT, ARF_RND_DOWN);
arf_set_round(zm_rounded, zm_exact, prec, ARB_RND);
/* rounding error */
if (arf_equal(zm_exact, zm_rounded))
{
arf_zero(zr);
}
else
{
fmpz_t e;
fmpz_init(e);
/* more accurate, but not what we are testing
arf_sub(zr, zm_exact, zm_rounded, MAG_BITS, ARF_RND_UP);
arf_abs(zr, zr); */
fmpz_sub_ui(e, ARF_EXPREF(zm_rounded), prec);
arf_one(zr);
arf_mul_2exp_fmpz(zr, zr, e);
fmpz_clear(e);
}
/* propagated error */
if (!arb_is_exact(x))
{
arf_set_mag(t, arb_radref(x));
arf_abs(u, arb_midref(y));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
if (!arb_is_exact(y))
{
arf_set_mag(t, arb_radref(y));
arf_abs(u, arb_midref(x));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
if (!arb_is_exact(x) && !arb_is_exact(y))
{
arf_set_mag(t, arb_radref(x));
arf_set_mag(u, arb_radref(y));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
arf_set(arb_midref(z), zm_rounded);
arf_get_mag(arb_radref(z), zr);
arf_clear(zm_exact);
arf_clear(zm_rounded);
arf_clear(zr);
arf_clear(t);
arf_clear(u);
}
int arb_mat_jacobi(arb_mat_t D, arb_mat_t P, const arb_mat_t A, slong prec) {
//
// Given a d x d real symmetric matrix A, compute an orthogonal matrix
// P and a diagonal D such that A = P D P^t = P D P^(-1).
//
// D should have already been initialized as a d x 1 matrix, and Pp
// should have already been initialized as a d x d matrix.
//
// If the eigenvalues can be certified as unique, then a nonzero int is
// returned, and the eigenvectors should have reasonable error bounds. If
// the eigenvalues cannot be certified as unique, then some of the
// eigenvectors will have infinite error radius.
#define B(i,j) arb_mat_entry(B, i, j)
#define D(i) arb_mat_entry(D, i, 0)
#define P(i,j) arb_mat_entry(P, i, j)
int dim = arb_mat_nrows(A);
if(dim == 1) {
arb_mat_set(D, A);
arb_mat_one(P);
return 0;
}
arb_mat_t B;
arb_mat_init(B, dim, dim);
arf_t * B1 = (arf_t*)malloc(dim * sizeof(arf_t));
arf_t * B2 = (arf_t*)malloc(dim * sizeof(arf_t));
arf_t * row_max = (arf_t*)malloc((dim - 1) * sizeof(arf_t));
int * row_max_indices = (int*)malloc((dim - 1) * sizeof(int));
for(int k = 0; k < dim; k++) {
arf_init(B1[k]);
arf_init(B2[k]);
}
for(int k = 0; k < dim - 1; k++) {
arf_init(row_max[k]);
}
arf_t x1, x2;
arf_init(x1);
arf_init(x2);
arf_t Gii, Gij, Gji, Gjj;
arf_init(Gii);
arf_init(Gij);
arf_init(Gji);
arf_init(Gjj);
arb_mat_set(B, A);
arb_mat_one(P);
for(int i = 0; i < dim - 1; i++) {
for(int j = i + 1; j < dim; j++) {
arf_abs(x1, arb_midref(B(i,j)));
if(arf_cmp(row_max[i], x1) < 0) {
arf_set(row_max[i], x1);
row_max_indices[i] = j;
}
}
}
int finished = 0;
while(!finished) {
arf_zero(x1);
int i = 0;
int j = 0;
for(int k = 0; k < dim - 1; k++) {
if(arf_cmp(x1, row_max[k]) < 0) {
arf_set(x1, row_max[k]);
i = k;
}
}
j = row_max_indices[i];
slong bound = arf_abs_bound_lt_2exp_si(x1);
if(bound < -prec * .9) {
finished = 1;
break;
}
else {
//printf("%ld\n", arf_abs_bound_lt_2exp_si(x1));
//arb_mat_printd(B, 10);
//printf("\n");
}
arf_twobytwo_diag(Gii, Gij, arb_midref(B(i,i)), arb_midref(B(i,j)), arb_midref(B(j,j)), 2*prec);
arf_neg(Gji, Gij);
arf_set(Gjj, Gii);
//printf("%d %d\n", i, j);
//arf_printd(Gii, 100);
//printf(" ");
//arf_printd(Gij, 100);
//printf("\n");
if(arf_is_zero(Gij)) { // If this happens, we're
finished = 1; // not going to do any better
break; // without increasing the precision.
}
for(int k = 0; k < dim; k++) {
arf_mul(B1[k], Gii, arb_midref(B(i,k)), prec, ARF_RND_NEAR);
arf_addmul(B1[k], Gji, arb_midref(B(j,k)), prec, ARF_RND_NEAR);
arf_mul(B2[k], Gij, arb_midref(B(i,k)), prec, ARF_RND_NEAR);
arf_addmul(B2[k], Gjj, arb_midref(B(j,k)), prec, ARF_RND_NEAR);
}
for(int k = 0; k < dim; k++) {
arf_set(arb_midref(B(i,k)), B1[k]);
arf_set(arb_midref(B(j,k)), B2[k]);
}
for(int k = 0; k < dim; k++) {
arf_mul(B1[k], Gii, arb_midref(B(k,i)), prec, ARF_RND_NEAR);
arf_addmul(B1[k], Gji, arb_midref(B(k,j)), prec, ARF_RND_NEAR);
arf_mul(B2[k], Gij, arb_midref(B(k,i)), prec, ARF_RND_NEAR);
arf_addmul(B2[k], Gjj, arb_midref(B(k,j)), prec, ARF_RND_NEAR);
}
for(int k = 0; k < dim; k++) {
arf_set(arb_midref(B(k,i)), B1[k]);
arf_set(arb_midref(B(k,j)), B2[k]);
}
for(int k = 0; k < dim; k++) {
arf_mul(B1[k], Gii, arb_midref(P(k,i)), prec, ARF_RND_NEAR);
arf_addmul(B1[k], Gji, arb_midref(P(k,j)), prec, ARF_RND_NEAR);
arf_mul(B2[k], Gij, arb_midref(P(k,i)), prec, ARF_RND_NEAR);
arf_addmul(B2[k], Gjj, arb_midref(P(k,j)), prec, ARF_RND_NEAR);
}
for(int k = 0; k < dim; k++) {
arf_set(arb_midref(P(k,i)), B1[k]);
arf_set(arb_midref(P(k,j)), B2[k]);
}
if(i < dim - 1)
arf_set_ui(row_max[i], 0);
if(j < dim - 1)
arf_set_ui(row_max[j], 0);
// Update the max in any row where the maximum
// was in a column that changed.
for(int k = 0; k < dim - 1; k++) {
if(row_max_indices[k] == j || row_max_indices[k] == i) {
arf_abs(row_max[k], arb_midref(B(k,k+1)));
row_max_indices[k] = k+1;
for(int l = k+2; l < dim; l++) {
arf_abs(x1, arb_midref(B(k,l)));
if(arf_cmp(row_max[k], x1) < 0) {
arf_set(row_max[k], x1);
row_max_indices[k] = l;
}
}
}
}
// Update the max in the ith row.
for(int k = i + 1; k < dim; k++) {
arf_abs(x1, arb_midref(B(i, k)));
if(arf_cmp(row_max[i], x1) < 0) {
arf_set(row_max[i], x1);
row_max_indices[i] = k;
}
}
// Update the max in the jth row.
for(int k = j + 1; k < dim; k++) {
arf_abs(x1, arb_midref(B(j, k)));
if(arf_cmp(row_max[j], x1) < 0) {
arf_set(row_max[j], x1);
row_max_indices[j] = k;
}
}
// Go through column i to see if any of
// the new entries are larger than the
// max of their row.
for(int k = 0; k < i; k++) {
if(k == dim) continue;
arf_abs(x1, arb_midref(B(k, i)));
if(arf_cmp(row_max[k], x1) < 0) {
arf_set(row_max[k], x1);
row_max_indices[k] = i;
}
}
// And then column j.
for(int k = 0; k < j; k++) {
if(k == dim) continue;
arf_abs(x1, arb_midref(B(k, j)));
if(arf_cmp(row_max[k], x1) < 0) {
arf_set(row_max[k], x1);
row_max_indices[k] = j;
}
}
}
for(int k = 0; k < dim; k++) {
arb_set(D(k), B(k,k));
arb_set_exact(D(k));
}
// At this point we've done that diagonalization and all that remains is
// to certify the correctness and compute error bounds.
arb_mat_t e;
arb_t error_norms[dim];
for(int k = 0; k < dim; k++) arb_init(error_norms[k]);
arb_mat_init(e, dim, 1);
arb_t z1, z2;
arb_init(z1);
arb_init(z2);
for(int j = 0; j < dim; j++) {
arb_mat_set(B, A);
for(int k = 0; k < dim; k++) {
arb_sub(B(k, k), B(k, k), D(j), prec);
}
for(int k = 0; k < dim; k++) {
arb_set(arb_mat_entry(e, k, 0), P(k, j));
}
arb_mat_L2norm(z2, e, prec);
arb_mat_mul(e, B, e, prec);
arb_mat_L2norm(error_norms[j], e, prec);
arb_div(z2, error_norms[j], z2, prec); // and now z1 is an upper bound for the
// error in the eigenvalue
arb_add_error(D(j), z2);
}
int unique_eigenvalues = 1;
for(int j = 0; j < dim; j++) {
if(j == 0) {
arb_sub(z1, D(j), D(1), prec);
}
else {
arb_sub(z1, D(j), D(0), prec);
}
arb_get_abs_lbound_arf(x1, z1, prec);
for(int k = 1; k < dim; k++) {
if(k == j) continue;
arb_sub(z1, D(j), D(k), prec);
arb_get_abs_lbound_arf(x2, z1, prec);
if(arf_cmp(x2, x1) < 0) {
arf_set(x1, x2);
}
}
if(arf_is_zero(x1)) {
unique_eigenvalues = 0;
}
arb_div_arf(z1, error_norms[j], x1, prec);
for(int k = 0; k < dim; k++) {
arb_add_error(P(k, j), z1);
}
}
arb_mat_clear(e);
arb_clear(z1);
arb_clear(z2);
for(int k = 0; k < dim; k++) arb_clear(error_norms[k]);
arf_clear(x1);
arf_clear(x2);
arb_mat_clear(B);
for(int k = 0; k < dim; k++) {
arf_clear(B1[k]);
arf_clear(B2[k]);
}
for(int k = 0; k < dim - 1; k++) {
arf_clear(row_max[k]);
}
arf_clear(Gii);
arf_clear(Gij);
arf_clear(Gji);
arf_clear(Gjj);
free(B1);
free(B2);
free(row_max);
free(row_max_indices);
if(unique_eigenvalues) return 0;
else return 1;
#undef B
#undef D
#undef P
}
int main()
{
long iter;
flint_rand_t state;
printf("add_error....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
arf_t m, r;
arb_init(a);
arb_init(b);
arb_init(c);
arf_init(m);
arf_init(r);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 10);
arf_randtest_special(m, state, 1 + n_randint(state, 2000), 10);
arf_randtest_special(r, state, 1 + n_randint(state, 2000), 10);
/* c = a plus error bounds */
arb_set(c, a);
arf_set(arb_midref(b), m);
arf_get_mag(arb_radref(b), r);
arb_add_error(c, b);
/* b = a + random point */
arb_set(b, a);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), r, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), r, ARF_PREC_EXACT, ARF_RND_DOWN);
/* should this be done differently? */
if (arf_is_nan(arb_midref(b)))
arf_zero(arb_midref(b));
if (!arb_contains(c, b))
{
printf("FAIL (arb_add_error)\n\n");
printf("a = "); arb_printn(a, 50, 0); printf("\n\n");
printf("b = "); arb_printn(b, 50, 0); printf("\n\n");
printf("c = "); arb_printn(c, 50, 0); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arf_clear(m);
arf_clear(r);
}
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
arf_t m;
arb_init(a);
arb_init(b);
arb_init(c);
arf_init(m);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 10);
arf_randtest_special(m, state, 1 + n_randint(state, 2000), 10);
/* c = a plus error bounds */
arb_set(c, a);
arb_add_error_arf(c, m);
/* b = a + random point */
arb_set(b, a);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN);
/* should this be done differently? */
if (arf_is_nan(arb_midref(b)))
arf_zero(arb_midref(b));
if (!arb_contains(c, b))
{
printf("FAIL (arb_add_error_arf)\n\n");
printf("a = "); arb_printn(a, 50, 0); printf("\n\n");
printf("b = "); arb_printn(b, 50, 0); printf("\n\n");
printf("c = "); arb_printn(c, 50, 0); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arf_clear(m);
}
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
arf_t t;
mag_t r;
arb_init(a);
arb_init(b);
arb_init(c);
mag_init(r);
arf_init(t);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10);
mag_randtest(r, state, 10);
/* c = a plus error bounds */
arb_set(c, a);
arb_add_error_mag(c, r);
/* b = a + random point */
arb_set(b, a);
arf_set_mag(t, r);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
/* should this be done differently? */
if (arf_is_nan(arb_midref(b)))
arf_zero(arb_midref(b));
if (!arb_contains(c, b))
{
printf("FAIL (arb_add_error_mag)\n\n");
printf("a = "); arb_printn(a, 50, 0); printf("\n\n");
printf("b = "); arb_printn(b, 50, 0); printf("\n\n");
printf("c = "); arb_printn(c, 50, 0); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
mag_clear(r);
arf_clear(t);
}
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
arf_t t;
long e;
arb_init(a);
arb_init(b);
arb_init(c);
arf_init(t);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10);
e = n_randint(state, 10) - 10;
/* c = a plus error bounds */
arb_set(c, a);
arb_add_error_2exp_si(c, e);
/* b = a + random point */
arb_set(b, a);
arf_one(t);
arf_mul_2exp_si(t, t, e);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
/* should this be done differently? */
if (arf_is_nan(arb_midref(b)))
arf_zero(arb_midref(b));
if (!arb_contains(c, b))
{
printf("FAIL (arb_add_error_2exp_si)\n\n");
printf("a = "); arb_printn(a, 50, 0); printf("\n\n");
printf("b = "); arb_printn(b, 50, 0); printf("\n\n");
printf("c = "); arb_printn(c, 50, 0); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arf_clear(t);
}
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
arf_t t;
fmpz_t e;
arb_init(a);
arb_init(b);
arb_init(c);
arf_init(t);
fmpz_init(e);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10);
fmpz_randtest(e, state, 10);
/* c = a plus error bounds */
arb_set(c, a);
arb_add_error_2exp_fmpz(c, e);
/* b = a + random point */
arb_set(b, a);
arf_one(t);
arf_mul_2exp_fmpz(t, t, e);
if (n_randint(state, 2))
arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
else
arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN);
/* should this be done differently? */
if (arf_is_nan(arb_midref(b)))
arf_zero(arb_midref(b));
if (!arb_contains(c, b))
{
printf("FAIL (arb_add_error_2exp_fmpz)\n\n");
printf("a = "); arb_printn(a, 50, 0); printf("\n\n");
printf("b = "); arb_printn(b, 50, 0); printf("\n\n");
printf("c = "); arb_printn(c, 50, 0); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arf_clear(t);
fmpz_clear(e);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
arf_sum(arf_t s, arf_srcptr terms, long len, long prec, arf_rnd_t rnd)
{
arf_ptr blocks;
long i, j, used;
int have_merged, res;
/* first check if the result is inf or nan */
{
int have_pos_inf = 0;
int have_neg_inf = 0;
for (i = 0; i < len; i++)
{
if (arf_is_pos_inf(terms + i))
{
if (have_neg_inf)
{
arf_nan(s);
return 0;
}
have_pos_inf = 1;
}
else if (arf_is_neg_inf(terms + i))
{
if (have_pos_inf)
{
arf_nan(s);
return 0;
}
have_neg_inf = 1;
}
else if (arf_is_nan(terms + i))
{
arf_nan(s);
return 0;
}
}
if (have_pos_inf)
{
arf_pos_inf(s);
return 0;
}
if (have_neg_inf)
{
arf_neg_inf(s);
return 0;
}
}
blocks = flint_malloc(sizeof(arf_struct) * len);
for (i = 0; i < len; i++)
arf_init(blocks + i);
/* put all terms into blocks */
used = 0;
for (i = 0; i < len; i++)
{
if (!arf_is_zero(terms + i))
{
arf_set(blocks + used, terms + i);
used++;
}
}
/* merge blocks until all are well separated */
have_merged = 1;
while (used >= 2 && have_merged)
{
have_merged = 0;
for (i = 0; i < used && !have_merged; i++)
{
for (j = i + 1; j < used && !have_merged; j++)
{
if (_arf_are_close(blocks + i, blocks + j, prec))
{
arf_add(blocks + i, blocks + i, blocks + j,
ARF_PREC_EXACT, ARF_RND_DOWN);
/* remove the merged block */
arf_swap(blocks + j, blocks + used - 1);
used--;
/* remove the updated block if the sum is zero */
if (arf_is_zero(blocks + i))
{
arf_swap(blocks + i, blocks + used - 1);
used--;
}
have_merged = 1;
}
}
}
}
if (used == 0)
{
arf_zero(s);
res = 0;
}
else if (used == 1)
{
res = arf_set_round(s, blocks + 0, prec, rnd);
}
else
{
/* find the two largest blocks */
for (i = 1; i < used; i++)
if (arf_cmpabs(blocks + 0, blocks + i) < 0)
arf_swap(blocks + 0, blocks + i);
for (i = 2; i < used; i++)
if (arf_cmpabs(blocks + 1, blocks + i) < 0)
arf_swap(blocks + 1, blocks + i);
res = _arf_add_eps(s, blocks + 0, arf_sgn(blocks + 1), prec, rnd);
}
for (i = 0; i < len; i++)
arf_clear(blocks + i);
flint_free(blocks);
return res;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sum....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong i, len, prec, bits, expbits;
int res1, res2;
arf_t s1, s2, s3, err;
mag_t err_bound;
arf_struct terms[20];
arf_rnd_t rnd;
len = n_randint(state, 20);
bits = 2 + n_randint(state, 1000);
prec = 2 + n_randint(state, 1000);
expbits = n_randint(state, 14);
arf_init(s1);
arf_init(s2);
arf_init(s3);
arf_init(err);
mag_init(err_bound);
for (i = 0; i < len; i++)
{
arf_init(terms + i);
arf_randtest_special(terms + i, state, bits, expbits);
}
switch (n_randint(state, 4))
{
case 0: rnd = ARF_RND_DOWN; break;
case 1: rnd = ARF_RND_UP; break;
case 2: rnd = ARF_RND_FLOOR; break;
default: rnd = ARF_RND_CEIL; break;
}
res1 = arf_sum(s1, terms, len, prec, rnd);
arf_zero(s2);
for (i = 0; i < len; i++)
arf_add(s2, s2, terms + i, ARF_PREC_EXACT, ARF_RND_DOWN);
res2 = arf_set_round(s3, s2, prec, rnd);
if (!arf_equal(s1, s3) || res1 != res2)
{
flint_printf("FAIL (%wd)\n\n", iter);
flint_printf("prec = %wd\n\n", prec);
for (i = 0; i < len; i++)
{
flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
arf_sub(err, s1, s2, ARF_PREC_EXACT, ARF_RND_DOWN);
arf_abs(err, err);
if (res1)
arf_mag_set_ulp(err_bound, s1, prec);
else
mag_zero(err_bound);
if (arf_cmpabs_mag(err, err_bound) > 0)
{
flint_printf("FAIL (error bound)!\n");
flint_printf("prec = %wd\n\n", prec);
for (i = 0; i < len; i++)
{
flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n");
flint_printf("error: "); arf_print(err); flint_printf("\n\n");
flint_printf("error bound: "); mag_print(err_bound); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
arf_clear(s1);
arf_clear(s2);
arf_clear(s3);
arf_clear(err);
mag_clear(err_bound);
for (i = 0; i < len; i++)
arf_clear(terms + i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
