void
fmprb_sqrt(fmprb_t z, const fmprb_t x, slong prec)
{
slong r;
if (fmprb_contains_negative(x))
{
fmpr_nan(fmprb_midref(z));
fmpr_pos_inf(fmprb_radref(z));
return;
}
if (fmprb_is_exact(x))
{
r = fmpr_sqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN);
fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r);
}
else
{
fmpr_t err;
fmpr_init(err);
fmpr_sub(err, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_DOWN);
fmpr_rsqrt(err, err, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul(err, fmprb_radref(x), err, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul_2exp_si(err, err, -1);
r = fmpr_sqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN);
fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r,
FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_clear(err);
}
fmprb_adjust(z);
}
void
fmprb_mul_fmpr_naive(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec)
{
/* (x+a) * y = x*y + y*a */
if (fmpr_is_pos_inf(fmprb_radref(x)))
{
fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN);
fmpr_pos_inf(fmprb_radref(z));
}
else if (fmpr_is_zero(fmprb_radref(x)))
{
slong r;
r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN);
fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r);
}
else
{
slong r;
fmpr_mul(fmprb_radref(z), fmprb_radref(x), y, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_abs(fmprb_radref(z), fmprb_radref(z));
r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN);
fmpr_add_error_result(fmprb_radref(z), fmprb_radref(z),
fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sub....");
fflush(stdout);
flint_randinit(state);
/* test exact subtraction: (x - y) - z == (x - z) - y */
for (iter = 0; iter < 100000; iter++)
{
slong bits, res1, res2, res3, res4;
fmpr_t x, y, z, t, u;
bits = 2 + n_randint(state, 200);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(t);
fmpr_init(u);
fmpr_randtest_special(x, state, bits, 10);
fmpr_randtest_special(y, state, bits, 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_randtest_special(t, state, bits, 10);
fmpr_randtest_special(u, state, bits, 10);
res1 = fmpr_sub(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res2 = fmpr_sub(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res3 = fmpr_sub(u, x, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res4 = fmpr_sub(u, u, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
if (!fmpr_equal(t, u) ||
res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT ||
res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT)
{
flint_printf("FAIL\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("t = "); fmpr_print(t); flint_printf("\n\n");
flint_printf("u = "); fmpr_print(u); flint_printf("\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(t);
fmpr_clear(u);
}
/* compare rounding with mpfr */
for (iter = 0; iter < 100000; iter++)
{
slong bits, res;
int mpfr_res;
fmpr_t x, y, z, w;
mpfr_t X, Y, Z;
bits = 2 + n_randint(state, 200);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(w);
mpfr_init2(X, bits + 100);
mpfr_init2(Y, bits + 100);
mpfr_init2(Z, bits);
fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10);
fmpr_randtest_special(y, state, bits + n_randint(state, 100), 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_get_mpfr(X, x, MPFR_RNDN);
fmpr_get_mpfr(Y, y, MPFR_RNDN);
switch (n_randint(state, 4))
{
case 0:
mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDZ);
res = fmpr_sub(z, x, y, bits, FMPR_RND_DOWN);
break;
case 1:
mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDA);
res = fmpr_sub(z, x, y, bits, FMPR_RND_UP);
break;
case 2:
mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDD);
res = fmpr_sub(z, x, y, bits, FMPR_RND_FLOOR);
break;
default:
mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDU);
res = fmpr_sub(z, x, y, bits, FMPR_RND_CEIL);
break;
}
fmpr_set_mpfr(w, Z);
if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0)
|| !fmpr_check_ulp(z, res, bits))
{
flint_printf("FAIL\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_printf("returned: %wd, %d\n", res, mpfr_res);
abort();
}
/* check error bound */
if (!fmpr_is_nan(z) && !fmpr_is_inf(z))
{
fmpr_t z_exact, error_bound, true_error;
fmpr_init(z_exact);
fmpr_init(error_bound);
fmpr_init(true_error);
fmpr_set_error_result(error_bound, z, res);
fmpr_sub(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_abs(true_error, true_error);
if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) ||
fmpr_cmp(true_error, error_bound) > 0)
{
flint_printf("FAIL: error bound\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n");
flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n");
flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n");
abort();
}
fmpr_clear(z_exact);
fmpr_clear(error_bound);
fmpr_clear(true_error);
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(w);
mpfr_clear(X);
mpfr_clear(Y);
mpfr_clear(Z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("add....");
fflush(stdout);
flint_randinit(state);
/* test exact addition: (x + y) + z == x + (y + z) */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong bits, res1, res2, res3, res4;
fmpr_t x, y, z, t, u;
bits = 2 + n_randint(state, 200);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(t);
fmpr_init(u);
fmpr_randtest_special(x, state, bits, 10);
fmpr_randtest_special(y, state, bits, 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_randtest_special(t, state, bits, 10);
fmpr_randtest_special(u, state, bits, 10);
res1 = fmpr_add(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res2 = fmpr_add(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res3 = fmpr_add(u, y, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res4 = fmpr_add(u, x, u, FMPR_PREC_EXACT, FMPR_RND_DOWN);
if (!fmpr_equal(t, u) ||
res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT ||
res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT)
{
flint_printf("FAIL\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("t = "); fmpr_print(t); flint_printf("\n\n");
flint_printf("u = "); fmpr_print(u); flint_printf("\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(t);
fmpr_clear(u);
}
/* compare with add_naive */
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong prec, ret1, ret2;
fmpr_t x, y, z, w;
fmpr_rnd_t rnd;
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(w);
fmpr_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
fmpr_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
fmpr_randtest_special(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
prec = 2 + n_randint(state, 1000);
if (n_randint(state, 10) == 0 &&
fmpz_bits(fmpr_expref(x)) < 10 &&
fmpz_bits(fmpr_expref(y)) < 10)
prec = FMPR_PREC_EXACT;
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
ret1 = fmpr_add(z, x, y, prec, rnd);
ret2 = fmpr_add_naive(w, x, y, prec, rnd);
if (!fmpr_equal(z, w) || ret1 != ret2 ||
!fmpr_check_ulp(z, ret1, prec) || !fmpr_check_ulp(w, ret2, prec))
{
flint_printf("FAIL\n\n");
flint_printf("iter %wd\n", iter);
flint_printf("prec = %wd\n", prec);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_printf("ret1 = %wd, ret2 = %wd\n", ret1, ret2);
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(w);
}
/* compare rounding with mpfr */
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong bits, res;
int mpfr_res;
fmpr_t x, y, z, w;
mpfr_t X, Y, Z;
bits = 2 + n_randint(state, 500);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(w);
mpfr_init2(X, bits + 500);
mpfr_init2(Y, bits + 500);
mpfr_init2(Z, bits);
fmpr_randtest_special(x, state, bits + n_randint(state, 500), 10);
fmpr_randtest_special(y, state, bits + n_randint(state, 500), 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_get_mpfr(X, x, MPFR_RNDN);
fmpr_get_mpfr(Y, y, MPFR_RNDN);
switch (n_randint(state, 4))
{
case 0:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDZ);
res = fmpr_add(z, x, y, bits, FMPR_RND_DOWN);
break;
case 1:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDA);
res = fmpr_add(z, x, y, bits, FMPR_RND_UP);
break;
case 2:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDD);
res = fmpr_add(z, x, y, bits, FMPR_RND_FLOOR);
break;
default:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDU);
res = fmpr_add(z, x, y, bits, FMPR_RND_CEIL);
break;
}
fmpr_set_mpfr(w, Z);
if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0)
|| !fmpr_check_ulp(z, res, bits))
{
flint_printf("FAIL\n\n");
flint_printf("iter %wd\n", iter);
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_printf("returned: %wd, %d\n", res, mpfr_res);
abort();
}
/* check error bound */
if (!fmpr_is_nan(z) && !fmpr_is_inf(z))
{
fmpr_t z_exact, error_bound, true_error;
fmpr_init(z_exact);
fmpr_init(error_bound);
fmpr_init(true_error);
fmpr_set_error_result(error_bound, z, res);
fmpr_add(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_abs(true_error, true_error);
if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) ||
fmpr_cmp(true_error, error_bound) > 0)
{
flint_printf("FAIL: error bound\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n");
flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n");
flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n");
abort();
}
fmpr_clear(z_exact);
fmpr_clear(error_bound);
fmpr_clear(true_error);
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(w);
mpfr_clear(X);
mpfr_clear(Y);
mpfr_clear(Z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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, res1, res2;
fmpr_t s1, s2, s3, err, err_bound;
fmpr_struct terms[20];
fmpr_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);
fmpr_init(s1);
fmpr_init(s2);
fmpr_init(s3);
fmpr_init(err);
fmpr_init(err_bound);
for (i = 0; i < len; i++)
{
fmpr_init(terms + i);
fmpr_randtest_special(terms + i, state, bits, expbits);
}
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
res1 = fmpr_sum(s1, terms, len, prec, rnd);
fmpr_zero(s2);
for (i = 0; i < len; i++)
fmpr_add(s2, s2, terms + i, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res2 = fmpr_set_round(s3, s2, prec, rnd);
if (!fmpr_equal(s1, s3) || res1 != res2 ||
!fmpr_check_ulp(s1, res1, prec) || !fmpr_check_ulp(s3, res2, prec))
{
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); fmpr_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n");
flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2);
abort();
}
fmpr_sub(err, s1, s2, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_abs(err, err);
fmpr_set_error_result(err_bound, s1, res1);
if (fmpr_cmp(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); fmpr_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n");
flint_printf("error: "); fmpr_print(err); flint_printf("\n\n");
flint_printf("error bound: "); fmpr_print(err_bound); flint_printf("\n\n");
flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2);
abort();
}
fmpr_clear(s1);
fmpr_clear(s2);
fmpr_clear(s3);
fmpr_clear(err);
fmpr_clear(err_bound);
for (i = 0; i < len; i++)
fmpr_clear(terms + i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}