int main()
{
slong iter;
flint_rand_t state;
flint_printf("acos_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, qbits, rbits1, rbits2;
fmpq_poly_t A;
arb_poly_t a, b, c, d;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
fmpq_poly_init(A);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
fmpq_poly_randtest(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5);
arb_poly_acos_series(b, a, n, rbits2);
/* Check cos(acos(x)) = x */
arb_poly_sin_cos_series_basecase(d, c, b, n, rbits2, 0);
fmpq_poly_truncate(A, n);
if (!arb_poly_contains_fmpq_poly(c, A))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
arb_poly_acos_series(a, a, n, rbits2);
if (!arb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(A);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("theta_const_sum_rs....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 5000 * arb_test_multiplier(); iter++)
{
acb_t q, t2a, t2b, t3a, t3b, t4a, t4b;
slong prec1, prec2, N;
acb_init(q);
acb_init(t2a);
acb_init(t2b);
acb_init(t3a);
acb_init(t3b);
acb_init(t4a);
acb_init(t4b);
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
N = n_randint(state, 300);
acb_randtest(q, state, prec1, 3);
acb_randtest(t2a, state, prec1, 3);
acb_randtest(t2b, state, prec1, 3);
acb_randtest(t3a, state, prec1, 3);
acb_randtest(t3b, state, prec1, 3);
acb_randtest(t4a, state, prec1, 3);
acb_randtest(t4b, state, prec1, 3);
acb_modular_theta_const_sum_basecase(t2a, t3a, t4a, q, N, prec1);
acb_modular_theta_const_sum_rs(t2b, t3b, t4b, q, N, prec2);
if (!acb_overlaps(t2a, t2b) || !acb_overlaps(t3a, t3b) || !acb_overlaps(t4a, t4b))
{
flint_printf("FAIL (overlap) iter = %wd\n", iter);
flint_printf("N = %wd\n", N);
flint_printf("q = "); acb_printd(q, 50); flint_printf("\n\n");
flint_printf("t2a = "); acb_printd(t2a, 50); flint_printf("\n\n");
flint_printf("t2b = "); acb_printd(t2b, 50); flint_printf("\n\n");
flint_printf("t3a = "); acb_printd(t3a, 50); flint_printf("\n\n");
flint_printf("t3b = "); acb_printd(t3b, 50); flint_printf("\n\n");
flint_printf("t4a = "); acb_printd(t4a, 50); flint_printf("\n\n");
flint_printf("t4b = "); acb_printd(t4b, 50); flint_printf("\n\n");
abort();
}
acb_clear(q);
acb_clear(t2a);
acb_clear(t2b);
acb_clear(t3a);
acb_clear(t3b);
acb_clear(t4a);
acb_clear(t4b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("complex_mul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arf_t e1, f1, e2, f2, a, b, c, d;
slong prec, r1, r2;
arf_rnd_t rnd;
arf_init(a);
arf_init(b);
arf_init(c);
arf_init(d);
arf_init(e1);
arf_init(f1);
arf_init(e2);
arf_init(f2);
for (iter2 = 0; iter2 < 100; iter2++)
{
arf_randtest_special(a, state, 3000, 100);
arf_randtest_special(b, state, 3000, 100);
arf_randtest_special(c, state, 3000, 100);
arf_randtest_special(d, state, 3000, 100);
prec = 2 + n_randint(state, 3000);
switch (n_randint(state, 5))
{
case 0: rnd = ARF_RND_DOWN; break;
case 1: rnd = ARF_RND_UP; break;
case 2: rnd = ARF_RND_FLOOR; break;
case 3: rnd = ARF_RND_CEIL; break;
default: rnd = ARF_RND_NEAR; break;
}
switch (n_randint(state, 5))
{
case 0:
r1 = arf_complex_mul(e1, f1, a, b, c, d, prec, rnd);
r2 = arf_complex_mul_fallback(e2, f2, a, b, c, d, prec, rnd);
if (!arf_equal(e1, e2) || !arf_equal(f1, f2) || r1 != r2)
{
flint_printf("FAIL!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("c = "); arf_print(c); flint_printf("\n\n");
flint_printf("d = "); arf_print(d); flint_printf("\n\n");
flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("e2 = "); arf_print(e2); flint_printf("\n\n");
flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
case 1:
arf_set(c, a);
arf_set(d, b);
r1 = arf_complex_mul(e1, f1, a, b, a, b, prec, rnd);
r2 = arf_complex_mul_fallback(e2, f2, a, b, c, d, prec, rnd);
if (!arf_equal(e1, e2) || !arf_equal(f1, f2) || r1 != r2)
{
flint_printf("FAIL! (aliasing 1)\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("c = "); arf_print(c); flint_printf("\n\n");
flint_printf("d = "); arf_print(d); flint_printf("\n\n");
flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("e2 = "); arf_print(e2); flint_printf("\n\n");
flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
case 2:
r1 = arf_complex_mul_fallback(e1, f1, a, b, a, b, prec, rnd);
r2 = arf_complex_mul(a, b, a, b, a, b, prec, rnd);
if (!arf_equal(e1, a) || !arf_equal(f1, b) || r1 != r2)
{
flint_printf("FAIL! (aliasing 2)\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
case 3:
r1 = arf_complex_mul_fallback(e1, f1, a, b, c, d, prec, rnd);
r2 = arf_complex_mul(a, b, a, b, c, d, prec, rnd);
if (!arf_equal(e1, a) || !arf_equal(f1, b) || r1 != r2)
{
flint_printf("FAIL! (aliasing 3)\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("c = "); arf_print(c); flint_printf("\n\n");
flint_printf("d = "); arf_print(d); flint_printf("\n\n");
flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
default:
r1 = arf_complex_mul_fallback(e1, f1, a, b, c, d, prec, rnd);
r2 = arf_complex_mul(c, d, a, b, c, d, prec, rnd);
if (!arf_equal(e1, c) || !arf_equal(f1, d) || r1 != r2)
{
flint_printf("FAIL! (aliasing 4)\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("c = "); arf_print(c); flint_printf("\n\n");
flint_printf("d = "); arf_print(d); flint_printf("\n\n");
flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
}
}
arf_clear(a);
arf_clear(b);
arf_clear(c);
arf_clear(d);
arf_clear(e1);
arf_clear(f1);
arf_clear(e2);
arf_clear(f2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_ui_euler_product....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t r;
ulong n;
mpfr_t s;
slong prec, accuracy;
do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n < 6);
prec = 2 + n_randint(state, n * FLINT_BIT_COUNT(n));
arb_init(r);
mpfr_init2(s, prec + 100);
arb_zeta_ui_euler_product(r, n, prec);
mpfr_zeta_ui(s, n, MPFR_RNDN);
if (!arb_contains_mpfr(r, s))
{
flint_printf("FAIL: containment\n\n");
flint_printf("n = %wu\n\n", n);
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n");
flint_abort();
}
accuracy = arb_rel_accuracy_bits(r);
if (accuracy < prec - 4)
{
flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec);
flint_printf("n = %wu\n\n", n);
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
flint_abort();
}
arb_clear(r);
mpfr_clear(s);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("add....");
fflush(stdout);
/* Check aliasing of a and c */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_randtest(b, state, n_randint(state, 100), 200);
fmpq_poly_add(c, a, b);
fmpq_poly_add(a, a, b);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
fmpq_poly_debug(c), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Check aliasing of b and c */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_randtest(b, state, n_randint(state, 100), 200);
fmpq_poly_add(c, a, b);
fmpq_poly_add(b, a, b);
cflags |= fmpq_poly_is_canonical(b) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(b, c) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
fmpq_poly_debug(c), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("resultant_div....");
fflush(stdout);
for (i = 0; i < 50; i++)
{
fmpq_poly_t f, g, h, p;
fmpq_t x, y, z, zz;
fmpz_t den;
slong nbits;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(p);
fmpq_poly_init(h);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_init(zz);
fmpz_init(den);
fmpq_poly_randtest(f, state, n_randint(state, 50), 100);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 50), 100);
fmpz_set(den, fmpq_poly_denref(f));
fmpq_poly_scalar_mul_fmpz(f, f, den);
fmpz_set(den, fmpq_poly_denref(g));
fmpq_poly_scalar_mul_fmpz(g, g, den);
fmpz_set(den, fmpq_poly_denref(h));
fmpq_poly_scalar_mul_fmpz(h, h, den);
fmpq_poly_mul(p, f, g);
fmpq_poly_resultant(x, f, h);
if (!fmpz_is_one(fmpq_denref(x)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("f = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(y, g, h);
if (!fmpz_is_one(fmpq_denref(y)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("h = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(z, p, h);
if (!fmpz_is_one(fmpq_denref(z)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("p = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
if (fmpq_is_zero(z))
{
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
continue;
}
nbits = (slong)fmpz_bits(fmpq_numref(y)) + 1;
fmpq_poly_resultant_div(z, p, h, fmpq_numref(x), nbits);
fmpq_poly_resultant(zz, p, h);
result = fmpq_equal(z, y);
if (!result)
{
flint_printf("FAIL (res(p, g)/div == res(p, g)/div:\n");
flint_printf("p = "), fmpq_poly_print_pretty(p, "x"), flint_printf("\n\n");
flint_printf("h = "), fmpq_poly_print_pretty(h, "x"), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(zz), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(x), flint_printf(" * "), fmpq_print(y), flint_printf("\n\n");
flint_printf("supplied divisor = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("nbits = %wu\n\n", nbits);
flint_printf("divisor found = "), fmpq_print(z), flint_printf("\n\n");
flint_printf("correct result = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main(void)
{
int i, j, result;
ulong count = UWORD(0);
gmp_randstate_t st;
FLINT_TEST_INIT(state);
gmp_randinit_default(st);
flint_printf("factor_pp1....");
fflush(stdout);
for (i = 0; i < 50 * flint_test_multiplier(); i++) /* Test random numbers */
{
mp_bitcnt_t bits;
mpz_t m, n;
fmpz_t n1, n2, r;
mpz_init(n);
mpz_init(m);
fmpz_init(n1);
fmpz_init(n2);
fmpz_init(r);
do {
mpz_urandomb(n, st, n_randint(state, 128) + 2);
} while (flint_mpz_cmp_ui(n, 2) < 0);
do {
mpz_urandomb(m, st, n_randint(state, 50) + 2);
} while (!mpz_probab_prime_p(m, 20));
mpz_mul(n, n, m);
fmpz_set_mpz(n1, n);
bits = FLINT_MIN(fmpz_bits(n1), FLINT_BITS);
for (j = 0; j < 20; j++)
{
fmpz_factor_pp1(n2, n1, 10000, 10000, n_randbits(state, bits - 2) + 3);
if (fmpz_cmp_ui(n2, 1) > 0) break;
}
if (fmpz_cmp_ui(n2, 1) > 0)
{
count++;
fmpz_mod(r, n1, n2);
result = (fmpz_is_zero(r));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n1 = ");
fmpz_print(n1);
flint_printf(", n2 = ");
fmpz_print(n2);
flint_printf("\n");
fmpz_print(r); flint_printf("\n");
abort();
}
}
fmpz_clear(n1);
fmpz_clear(n2);
fmpz_clear(r);
mpz_clear(m);
mpz_clear(n);
}
if (count < 49 * flint_test_multiplier())
{
flint_printf("FAIL:\n");
flint_printf("Only %wu numbers factored\n", count);
abort();
}
gmp_randclear(st);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("revert_series_lagrange_fast....");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
fmpz_poly_t f, g;
slong n;
fmpz_poly_init(f);
fmpz_poly_init(g);
fmpz_poly_randtest(g, state, n_randint(state, 50),
1+n_randint(state,100));
fmpz_poly_set_coeff_ui(g, 0, 0);
fmpz_poly_set_coeff_ui(g, 1, 1);
if (n_randlimb(state) % 2)
fmpz_poly_neg(g, g); /* get -x term */
n = n_randint(state, 50);
fmpz_poly_revert_series_lagrange_fast(f, g, n);
fmpz_poly_revert_series_lagrange_fast(g, g, n);
result = (fmpz_poly_equal(f, g));
if (!result)
{
flint_printf("FAIL (aliasing):\n");
fmpz_poly_print(f), flint_printf("\n\n");
fmpz_poly_print(g), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(f);
fmpz_poly_clear(g);
}
/* Check f(f^(-1)) = id */
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
fmpz_poly_t f, g, h;
slong n;
fmpz_poly_init(f);
fmpz_poly_init(g);
fmpz_poly_init(h);
fmpz_poly_randtest(g, state, n_randint(state, 50), 1+n_randint(state,100));
fmpz_poly_set_coeff_ui(g, 0, 0);
fmpz_poly_set_coeff_ui(g, 1, 1);
if (n_randlimb(state) % 2)
fmpz_poly_neg(g, g); /* get -x term */
n = n_randint(state, 50);
fmpz_poly_revert_series_lagrange_fast(f, g, n);
fmpz_poly_compose_series(h, g, f, n);
result = ((n <= 1 && fmpz_poly_is_zero(h)) ||
(h->length == 2 && fmpz_is_zero(h->coeffs + 0) &&
fmpz_is_one(h->coeffs + 1)));
if (!result)
{
flint_printf("FAIL (comparison):\n");
fmpz_poly_print(f), flint_printf("\n\n");
fmpz_poly_print(g), flint_printf("\n\n");
fmpz_poly_print(h), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(f);
fmpz_poly_clear(g);
fmpz_poly_clear(h);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("union....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmprb_t x, y, z;
slong prec;
int alias;
fmprb_init(x);
fmprb_init(y);
fmprb_init(z);
fmprb_randtest_special(x, state, 200, 10);
fmprb_randtest_special(y, state, 200, 10);
fmprb_randtest_special(z, state, 200, 10);
prec = 2 + n_randint(state, 200);
fmprb_union(z, x, y, prec);
if (!fmprb_contains(z, x) || !fmprb_contains(z, y))
{
flint_printf("FAIL:\n\n");
flint_printf("x = "); fmprb_print(x); flint_printf("\n\n");
flint_printf("y = "); fmprb_print(y); flint_printf("\n\n");
flint_printf("z = "); fmprb_print(z); flint_printf("\n\n");
abort();
}
if (n_randint(state, 2))
{
fmprb_union(x, x, y, prec);
alias = fmprb_equal(x, z);
}
else
{
fmprb_union(y, x, y, prec);
alias = fmprb_equal(y, z);
}
if (!alias)
{
flint_printf("FAIL (aliasing):\n\n");
flint_printf("x = "); fmprb_print(x); flint_printf("\n\n");
flint_printf("y = "); fmprb_print(y); flint_printf("\n\n");
flint_printf("z = "); fmprb_print(z); flint_printf("\n\n");
abort();
}
fmprb_clear(x);
fmprb_clear(y);
fmprb_clear(z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sqrt_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 5000; iter++)
{
slong m, n, qbits, rbits1, rbits2;
fmpq_poly_t A;
acb_poly_t a, b, c;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
fmpq_poly_init(A);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
fmpq_poly_randtest_not_zero(A, state, m, qbits);
acb_poly_set_fmpq_poly(a, A, rbits1);
acb_poly_sqrt_series(b, a, n, rbits2);
/* Check sqrt(a)^2 = a */
acb_poly_mullow(c, b, b, n, rbits2);
fmpq_poly_truncate(A, n);
if (!acb_poly_contains_fmpq_poly(c, A))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
acb_poly_sqrt_series(a, a, n, rbits2);
if (!acb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(A);
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("interpolate_barycentric....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t P;
arb_poly_t R, S;
fmpq_t t, u;
arb_ptr xs, ys;
fmpq_poly_init(P);
arb_poly_init(R);
arb_poly_init(S);
fmpq_init(t);
fmpq_init(u);
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 5);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1);
n = P->length;
xs = _arb_vec_init(n);
ys = _arb_vec_init(n);
arb_poly_set_fmpq_poly(R, P, rbits1);
if (n > 0)
{
fmpq_randtest(t, state, qbits2);
arb_set_fmpq(xs, t, rbits2);
for (i = 1; i < n; i++)
{
fmpq_randtest_not_zero(u, state, qbits2);
fmpq_abs(u, u);
fmpq_add(t, t, u);
arb_set_fmpq(xs + i, t, rbits2);
}
}
for (i = 0; i < n; i++)
arb_poly_evaluate(ys + i, R, xs + i, rbits2);
arb_poly_interpolate_barycentric(S, xs, ys, n, rbits3);
if (!arb_poly_contains_fmpq_poly(S, P))
{
flint_printf("FAIL:\n");
flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n");
flint_printf("R = "); arb_poly_printd(R, 15); flint_printf("\n\n");
flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n");
flint_abort();
}
fmpq_poly_clear(P);
arb_poly_clear(R);
arb_poly_clear(S);
fmpq_clear(t);
fmpq_clear(u);
_arb_vec_clear(xs, n);
_arb_vec_clear(ys, n);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int iter;
flint_rand_t state;
flint_printf("set_trunc_round....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arb_poly_t a, b, c, d, e;
slong n, prec;
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
arb_poly_init(e);
arb_poly_randtest(a, state, n_randint(state, 10), 2 + n_randint(state, 200), 10);
arb_poly_randtest(b, state, n_randint(state, 10), 2 + n_randint(state, 200), 10);
arb_poly_randtest(c, state, n_randint(state, 10), 2 + n_randint(state, 200), 10);
arb_poly_randtest(d, state, n_randint(state, 10), 2 + n_randint(state, 200), 10);
arb_poly_randtest(e, state, n_randint(state, 10), 2 + n_randint(state, 200), 10);
n = n_randint(state, 10);
prec = 2 + n_randint(state, 200);
arb_poly_set_trunc(b, a, n);
arb_poly_set_round(b, b, prec);
arb_poly_set_round(c, a, prec);
arb_poly_set_trunc(c, c, n);
arb_poly_set_trunc_round(d, a, n, prec);
arb_poly_set(e, a);
arb_poly_set_trunc_round(e, e, n, prec);
if (!arb_poly_equal(b, c) || !arb_poly_equal(c, d) || !arb_poly_equal(d, e))
{
flint_printf("FAIL\n\n");
arb_poly_printd(a, 50), flint_printf("\n\n");
arb_poly_printd(b, 50), flint_printf("\n\n");
arb_poly_printd(c, 50), flint_printf("\n\n");
arb_poly_printd(d, 50), flint_printf("\n\n");
arb_poly_printd(e, 50), flint_printf("\n\n");
flint_abort();
}
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
arb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return 0;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("dlog....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
dlog_table_t table;
dlog_bsgs_t bsgs;
dlog_crt_t crt;
dlog_precomp_t pre1, pre100;
ulong p, a, k;
nmod_t modp;
if (iter < 10)
p = n_nth_prime(iter + 2);
else
p = n_randprime(state, 15, 0);
nmod_init(&modp, p);
a = n_primitive_root_prime(p);
dlog_table_init(table, a, p);
dlog_bsgs_init(bsgs, a, p, p-1, dlog_bsgs_size(p, 1));
dlog_crt_init(crt, a, p, p-1, 10);
dlog_precomp_n_init(pre1, a, p, p-1, 1);
dlog_precomp_n_init(pre100, a, p, p-1, 100);
for (k = 1; k < 100 && k < p; k++)
{
ulong l0, l1, l2, l3, l4, l5;
l1 = dlog_table(table, k);
l2 = dlog_bsgs(bsgs, k);
l3 = dlog_crt(crt, k);
l4 = dlog_precomp(pre1, k);
l5 = dlog_precomp(pre100, k);
if (iter < 50 && k <= 7)
l0 = dlog_once(k, a, modp, p-1);
else
l0 = l1;
if (l0 != l1 || l1 != l2 || l1 != l3 || l1 != l4 || l1 != l5)
{
flint_printf("\n\nFAIL: log(%wu,%wu) mod %wu\n\n",k,a,p);
flint_printf("once: %wu\ntable: %wu\nbsgs: %wu\ncrt: %wu\nprecomp1: %wu\nprecomp100: %wu\n\n",
l0, l1, l2, l3, l4, l5);
abort();
}
}
dlog_table_clear(table);
dlog_bsgs_clear(bsgs);
dlog_crt_clear(crt);
dlog_precomp_clear(pre1);
dlog_precomp_clear(pre100);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp_pi_i....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, d;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_randtest(a, state, 1 + n_randint(state, 200), 3);
acb_randtest(b, state, 1 + n_randint(state, 200), 3);
acb_randtest(c, state, 1 + n_randint(state, 200), 3);
acb_randtest(d, state, 1 + n_randint(state, 200), 3);
prec = 2 + n_randint(state, 200);
acb_exp_pi_i(b, a, prec);
acb_const_pi(c, prec);
acb_mul(c, c, a, prec);
acb_mul_onei(c, c);
acb_exp(d, c, prec);
if (!acb_overlaps(d, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("d = "); acb_printd(d, 30); flint_printf("\n\n");
abort();
}
acb_set(c, a);
acb_exp_pi_i(c, c, prec);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_printf("d = "); acb_print(d); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("div....");
fflush(stdout);
flint_randinit(state);
/* test aliasing of c and a */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_div(c, a, b, prec);
acb_div(a, a, b, prec);
if (!acb_equal(a, c))
{
flint_printf("FAIL: aliasing c, a\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test aliasing of c and b */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_div(c, a, b, prec);
acb_div(b, a, b, prec);
if (!acb_equal(b, c))
{
flint_printf("FAIL: aliasing c, b\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test aliasing a, a */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, d;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_set(b, a);
acb_div(c, a, a, prec);
acb_div(d, a, b, prec);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: aliasing a, a\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_printf("d = "); acb_print(d); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
}
/* test aliasing a, a, a */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_set(b, a);
acb_div(c, a, b, prec);
acb_div(a, a, a, prec);
if (!acb_overlaps(a, c))
{
flint_printf("FAIL: aliasing a, a, a\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test (a+b)/c = a/c + b/c */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, d, e, f;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_init(e);
acb_init(f);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
acb_add(d, a, b, 2 + n_randint(state, 200));
acb_div(e, d, c, 2 + n_randint(state, 200));
acb_div(d, a, c, 2 + n_randint(state, 200));
acb_div(f, b, c, 2 + n_randint(state, 200));
acb_add(f, d, f, 2 + n_randint(state, 200));
if (!acb_overlaps(e, f))
{
flint_printf("FAIL: (a+b)/c = a/c + b/c\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_printf("e = "); acb_print(e); flint_printf("\n\n");
flint_printf("f = "); acb_print(f); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
acb_clear(e);
acb_clear(f);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rsqrt....");
fflush(stdout);
flint_randinit(state);
/* check (a^(-1/2))^(-2) = a */
for (iter = 0; iter < 10000; iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 2000), 10);
acb_randtest(b, state, 1 + n_randint(state, 2000), 10);
prec = 2 + n_randint(state, 2000);
acb_rsqrt(b, a, prec);
acb_inv(c, b, prec);
acb_mul(c, c, c, prec);
if (!acb_contains(c, a))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
abort();
}
acb_rsqrt(a, a, prec);
if (!acb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("spd_solve....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, QX, QB;
arb_mat_t A, X, B;
slong n, m, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 8);
m = n_randint(state, 8);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(QX, n, m);
fmpq_mat_init(QB, n, m);
arb_mat_init(A, n, n);
arb_mat_init(X, n, m);
arb_mat_init(B, n, m);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
fmpq_mat_randtest(QB, state, qbits);
q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_abort();
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_set_fmpq_mat(B, QB, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_abort();
}
prec *= 2;
}
}
if (!arb_mat_contains_fmpq_mat(X, QX))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
flint_abort();
}
/* test aliasing */
r_invertible2 = arb_mat_spd_solve(B, A, B, prec);
if (!arb_mat_equal(X, B) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
flint_abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(QB);
fmpq_mat_clear(QX);
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("erfc....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec1, prec2, prec3, prec4;
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
prec3 = 2 + n_randint(state, 1000);
prec4 = 2 + n_randint(state, 1000);
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest_special(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_special(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_special(c, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_erf_asymp(b, a, 1, prec1, prec3);
break;
case 1:
acb_hypgeom_erf(b, a, prec1);
acb_sub_ui(b, b, 1, prec1);
acb_neg(b, b);
break;
default:
acb_hypgeom_erfc(b, a, prec1);
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_erf_asymp(c, a, 1, prec2, prec4);
break;
case 1:
acb_hypgeom_erf(c, a, prec2);
acb_sub_ui(c, c, 1, prec2);
acb_neg(c, c);
break;
default:
acb_hypgeom_erfc(c, a, prec2);
}
if (!acb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("integrate_taylor....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 150 * arb_test_multiplier(); iter++)
{
acb_t ans, res, a, b;
arf_t inr, outr;
double t;
slong goal, prec;
acb_init(ans);
acb_init(res);
acb_init(a);
acb_init(b);
arf_init(inr);
arf_init(outr);
goal = 2 + n_randint(state, 300);
prec = 2 + n_randint(state, 300);
acb_randtest(a, state, 1 + n_randint(state, 200), 2);
acb_randtest(b, state, 1 + n_randint(state, 200), 2);
acb_cos(ans, a, prec);
acb_cos(res, b, prec);
acb_sub(ans, ans, res, prec);
t = (1 + n_randint(state, 20)) / 10.0;
arf_set_d(inr, t);
arf_set_d(outr, t + (1 + n_randint(state, 20)) / 5.0);
acb_calc_integrate_taylor(res, sin_x, NULL,
a, b, inr, outr, goal, prec);
if (!acb_overlaps(res, ans))
{
flint_printf("FAIL! (iter = %wd)\n", iter);
flint_printf("prec = %wd, goal = %wd\n", prec, goal);
flint_printf("inr = "); arf_printd(inr, 15); flint_printf("\n");
flint_printf("outr = "); arf_printd(outr, 15); flint_printf("\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n");
flint_printf("res = "); acb_printd(res, 15); flint_printf("\n\n");
flint_printf("ans = "); acb_printd(ans, 15); flint_printf("\n\n");
abort();
}
acb_clear(ans);
acb_clear(res);
acb_clear(a);
acb_clear(b);
arf_clear(inr);
arf_clear(outr);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
/*
Given T(K), compute bound for T(n) z^n.
We need to multiply by
z^n * 1/rf(K+1,m)^r * (rf(K+1,m)/rf(K+1-A,m)) * (rf(K+1-B,m)/rf(K+1-2B,m))
where m = n - K. This is equal to
z^n *
(K+A)! (K-2B)! (K-B+m)!
----------------------- * ((K+m)! / K!)^(1-r)
(K-B)! (K-A+m)! (K-2B+m)!
*/
void
hypgeom_term_bound(mag_t Tn, const mag_t TK, slong K, slong A, slong B, int r, const mag_t z, slong n)
{
mag_t t, u, num;
slong m;
mag_init(t);
mag_init(u);
mag_init(num);
m = n - K;
if (m < 0)
{
flint_printf("hypgeom term bound\n");
abort();
}
/* TK * z^n */
mag_pow_ui(t, z, n);
mag_mul(num, TK, t);
/* numerator: (K+A)! (K-2B)! (K-B+m)! */
mag_fac_ui(t, K+A);
mag_mul(num, num, t);
mag_fac_ui(t, K-2*B);
mag_mul(num, num, t);
mag_fac_ui(t, K-B+m);
mag_mul(num, num, t);
/* denominator: (K-B)! (K-A+m)! (K-2B+m)! */
mag_rfac_ui(t, K-B);
mag_mul(num, num, t);
mag_rfac_ui(t, K-A+m);
mag_mul(num, num, t);
mag_rfac_ui(t, K-2*B+m);
mag_mul(num, num, t);
/* ((K+m)! / K!)^(1-r) */
if (r == 0)
{
mag_fac_ui(t, K+m);
mag_mul(num, num, t);
mag_rfac_ui(t, K);
mag_mul(num, num, t);
}
else if (r != 1)
{
mag_fac_ui(t, K);
mag_rfac_ui(u, K+m);
mag_mul(t, t, u);
mag_pow_ui(t, t, r-1);
mag_mul(num, num, t);
}
mag_set(Tn, num);
mag_clear(t);
mag_clear(u);
mag_clear(num);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c, d;
fmpz_t x;
slong prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_mul_fmpz(c, a, x, prec);
arb_mul(d, a, b, prec);
if (!arb_equal(c, d))
{
flint_printf("FAIL\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
fmpz_clear(x);
}
/* aliasing */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c;
fmpz_t x;
slong prec;
arb_init(a);
arb_init(b);
arb_init(c);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_mul_fmpz(c, a, x, prec);
arb_mul_fmpz(a, a, x, prec);
if (!arb_equal(a, c))
{
flint_printf("FAIL (aliasing)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpz_clear(x);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("get_interval_arf....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t x, y;
arf_t a, b;
arb_init(x);
arf_init(a);
arf_init(b);
arb_init(y);
arb_randtest_special(x, state, 200, 100);
arb_get_interval_arf(a, b, x, 2 + n_randint(state, 200));
arb_set_interval_arf(y, a, b, 2 + n_randint(state, 200));
if (!arb_contains(y, x))
{
flint_printf("FAIL:\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("a = "); arf_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
abort();
}
arb_clear(x);
arf_clear(a);
arf_clear(b);
arb_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong i;
mpfr_t tabx, logx, y1, y2;
mpz_t tt;
flint_printf("log_tab....");
fflush(stdout);
{
slong prec, bits, num;
prec = ARB_LOG_TAB1_LIMBS * FLINT_BITS;
bits = ARB_LOG_TAB11_BITS;
num = 1 << ARB_LOG_TAB11_BITS;
mpfr_init2(tabx, prec);
mpfr_init2(logx, prec);
mpfr_init2(y1, prec);
mpfr_init2(y2, prec);
for (i = 0; i < num; i++)
{
tt->_mp_d = (mp_ptr) arb_log_tab11[i];
tt->_mp_size = prec / FLINT_BITS;
tt->_mp_alloc = tt->_mp_size;
while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0)
tt->_mp_size--;
mpfr_set_z(tabx, tt, MPFR_RNDD);
mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD);
mpfr_set_ui(logx, i, MPFR_RNDD);
mpfr_div_2ui(logx, logx, bits, MPFR_RNDD);
mpfr_add_ui(logx, logx, 1, MPFR_RNDD);
mpfr_log(logx, logx, MPFR_RNDD);
mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD);
mpfr_floor(y1, y1);
mpfr_div_2ui(y1, y1, prec, MPFR_RNDD);
mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD);
mpfr_floor(y2, y2);
mpfr_div_2ui(y2, y2, prec, MPFR_RNDD);
if (!mpfr_equal_p(y1, y2))
{
flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec);
mpfr_printf("y1 = %.1500Rg\n", y1);
mpfr_printf("y2 = %.1500Rg\n", y2);
flint_abort();
}
}
mpfr_clear(tabx);
mpfr_clear(logx);
mpfr_clear(y1);
mpfr_clear(y2);
}
{
slong prec, bits, num;
prec = ARB_LOG_TAB1_LIMBS * FLINT_BITS;
bits = ARB_LOG_TAB11_BITS + ARB_LOG_TAB12_BITS;
num = 1 << ARB_LOG_TAB12_BITS;
mpfr_init2(tabx, prec);
mpfr_init2(logx, prec);
mpfr_init2(y1, prec);
mpfr_init2(y2, prec);
for (i = 0; i < num; i++)
{
tt->_mp_d = (mp_ptr) arb_log_tab12[i];
tt->_mp_size = prec / FLINT_BITS;
tt->_mp_alloc = tt->_mp_size;
while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0)
tt->_mp_size--;
mpfr_set_z(tabx, tt, MPFR_RNDD);
mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD);
mpfr_set_ui(logx, i, MPFR_RNDD);
mpfr_div_2ui(logx, logx, bits, MPFR_RNDD);
mpfr_add_ui(logx, logx, 1, MPFR_RNDD);
mpfr_log(logx, logx, MPFR_RNDD);
mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD);
mpfr_floor(y1, y1);
mpfr_div_2ui(y1, y1, prec, MPFR_RNDD);
mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD);
mpfr_floor(y2, y2);
mpfr_div_2ui(y2, y2, prec, MPFR_RNDD);
if (!mpfr_equal_p(y1, y2))
{
flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec);
mpfr_printf("y1 = %.1500Rg\n", y1);
mpfr_printf("y2 = %.1500Rg\n", y2);
flint_abort();
}
}
mpfr_clear(tabx);
mpfr_clear(logx);
mpfr_clear(y1);
mpfr_clear(y2);
}
{
slong prec, bits, num;
prec = ARB_LOG_TAB2_LIMBS * FLINT_BITS;
bits = ARB_LOG_TAB21_BITS;
num = 1 << ARB_LOG_TAB21_BITS;
mpfr_init2(tabx, prec);
mpfr_init2(logx, prec);
mpfr_init2(y1, prec);
mpfr_init2(y2, prec);
for (i = 0; i < num; i++)
{
tt->_mp_d = (mp_ptr) arb_log_tab21[i];
tt->_mp_size = prec / FLINT_BITS;
tt->_mp_alloc = tt->_mp_size;
while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0)
tt->_mp_size--;
mpfr_set_z(tabx, tt, MPFR_RNDD);
mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD);
mpfr_set_ui(logx, i, MPFR_RNDD);
mpfr_div_2ui(logx, logx, bits, MPFR_RNDD);
mpfr_add_ui(logx, logx, 1, MPFR_RNDD);
mpfr_log(logx, logx, MPFR_RNDD);
mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD);
mpfr_floor(y1, y1);
mpfr_div_2ui(y1, y1, prec, MPFR_RNDD);
mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD);
mpfr_floor(y2, y2);
mpfr_div_2ui(y2, y2, prec, MPFR_RNDD);
if (!mpfr_equal_p(y1, y2))
{
flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec);
mpfr_printf("y1 = %.1500Rg\n", y1);
mpfr_printf("y2 = %.1500Rg\n", y2);
flint_abort();
}
}
mpfr_clear(tabx);
mpfr_clear(logx);
mpfr_clear(y1);
mpfr_clear(y2);
}
{
slong prec, bits, num;
prec = ARB_LOG_TAB2_LIMBS * FLINT_BITS;
bits = ARB_LOG_TAB21_BITS + ARB_LOG_TAB22_BITS;
num = 1 << ARB_LOG_TAB22_BITS;
mpfr_init2(tabx, prec);
mpfr_init2(logx, prec);
mpfr_init2(y1, prec);
mpfr_init2(y2, prec);
for (i = 0; i < num; i++)
{
tt->_mp_d = (mp_ptr) arb_log_tab22[i];
tt->_mp_size = prec / FLINT_BITS;
tt->_mp_alloc = tt->_mp_size;
while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0)
tt->_mp_size--;
mpfr_set_z(tabx, tt, MPFR_RNDD);
mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD);
mpfr_set_ui(logx, i, MPFR_RNDD);
mpfr_div_2ui(logx, logx, bits, MPFR_RNDD);
mpfr_add_ui(logx, logx, 1, MPFR_RNDD);
mpfr_log(logx, logx, MPFR_RNDD);
mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD);
mpfr_floor(y1, y1);
mpfr_div_2ui(y1, y1, prec, MPFR_RNDD);
mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD);
mpfr_floor(y2, y2);
mpfr_div_2ui(y2, y2, prec, MPFR_RNDD);
if (!mpfr_equal_p(y1, y2))
{
flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec);
mpfr_printf("y1 = %.1500Rg\n", y1);
mpfr_printf("y2 = %.1500Rg\n", y2);
flint_abort();
}
}
mpfr_clear(tabx);
mpfr_clear(logx);
mpfr_clear(y1);
mpfr_clear(y2);
}
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("mul_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arf_t x, z, v;
fmpz_t y;
slong prec, r1, r2;
arf_rnd_t rnd;
arf_init(x);
arf_init(z);
arf_init(v);
fmpz_init(y);
for (iter2 = 0; iter2 < 100; iter2++)
{
arf_randtest_special(x, state, 2000, 10);
fmpz_randtest(y, state, 2000);
prec = 2 + n_randint(state, 2000);
if (n_randint(state, 10))
prec = ARF_PREC_EXACT;
switch (n_randint(state, 5))
{
case 0: rnd = ARF_RND_DOWN; break;
case 1: rnd = ARF_RND_UP; break;
case 2: rnd = ARF_RND_FLOOR; break;
case 3: rnd = ARF_RND_CEIL; break;
default: rnd = ARF_RND_NEAR; break;
}
switch (n_randint(state, 2))
{
case 0:
r1 = arf_mul_fmpz(z, x, y, prec, rnd);
r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd);
if (!arf_equal(z, v) || r1 != r2)
{
flint_printf("FAIL!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpz_print(y); flint_printf("\n\n");
flint_printf("z = "); arf_print(z); flint_printf("\n\n");
flint_printf("v = "); arf_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
default:
r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd);
r1 = arf_mul_fmpz(x, x, y, prec, rnd);
if (!arf_equal(x, v) || r1 != r2)
{
flint_printf("FAIL (aliasing)!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpz_print(y); flint_printf("\n\n");
flint_printf("v = "); arf_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
}
}
arf_clear(x);
arf_clear(z);
arf_clear(v);
fmpz_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void _arb_sin_cos_taylor_rs(mp_ptr ysin, mp_ptr ycos,
mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N,
int sinonly, int alternating)
{
mp_ptr s, t, xpow;
mp_limb_t new_denom, old_denom, c;
slong power, k, m;
int cosorsin;
TMP_INIT;
TMP_START;
if (2 * N >= FACTORIAL_TAB_SIZE - 1)
{
flint_printf("_arb_sin_cos_taylor_rs: N too large!\n");
abort();
}
if (N <= 1)
{
if (N == 0)
{
flint_mpn_zero(ysin, xn);
if (!sinonly) flint_mpn_zero(ycos, xn);
error[0] = 0;
}
else if (N == 1)
{
flint_mpn_copyi(ysin, x, xn);
if (!sinonly) flint_mpn_store(ycos, xn, LIMB_ONES);
error[0] = 1;
}
}
else
{
/* Choose m ~= sqrt(num_terms) (m must be even, >= 2) */
m = 2;
while (m * m < N)
m += 2;
/* todo: merge allocations */
xpow = TMP_ALLOC_LIMBS((m + 1) * xn);
s = TMP_ALLOC_LIMBS(xn + 2);
t = TMP_ALLOC_LIMBS(2 * xn + 2); /* todo: 1 limb too much? */
/* higher index ---> */
/* | ---xn--- | */
/* xpow = | <temp> | x^m | x^(m-1) | ... | x^2 | x | */
#define XPOW_WRITE(__k) (xpow + (m - (__k)) * xn)
#define XPOW_READ(__k) (xpow + (m - (__k) + 1) * xn)
mpn_sqr(XPOW_WRITE(1), x, xn);
mpn_sqr(XPOW_WRITE(2), XPOW_READ(1), xn);
for (k = 4; k <= m; k += 2)
{
mpn_mul_n(XPOW_WRITE(k - 1), XPOW_READ(k / 2), XPOW_READ(k / 2 - 1), xn);
mpn_sqr(XPOW_WRITE(k), XPOW_READ(k / 2), xn);
}
for (cosorsin = sinonly; cosorsin < 2; cosorsin++)
{
flint_mpn_zero(s, xn + 1);
/* todo: skip one nonscalar multiplication (use x^m)
when starting on x^0 */
power = (N - 1) % m;
for (k = N - 1; k >= 0; k--)
{
c = factorial_tab_numer[2 * k + cosorsin];
new_denom = factorial_tab_denom[2 * k + cosorsin];
old_denom = factorial_tab_denom[2 * k + cosorsin + 2];
/* change denominators */
if (new_denom != old_denom && k < N - 1)
{
if (alternating && (k % 2 == 0))
s[xn] += old_denom;
mpn_divrem_1(s, 0, s, xn + 1, old_denom);
if (alternating && (k % 2 == 0))
s[xn] -= 1;
}
if (power == 0)
{
/* add c * x^0 -- only top limb is affected */
if (alternating & k)
s[xn] -= c;
else
s[xn] += c;
/* Outer polynomial evaluation: multiply by x^m */
if (k != 0)
{
mpn_mul(t, s, xn + 1, XPOW_READ(m), xn);
flint_mpn_copyi(s, t + xn, xn + 1);
}
power = m - 1;
}
else
{
if (alternating & k)
s[xn] -= mpn_submul_1(s, XPOW_READ(power), xn, c);
else
s[xn] += mpn_addmul_1(s, XPOW_READ(power), xn, c);
power--;
}
}
/* finally divide by denominator */
if (cosorsin == 0)
{
mpn_divrem_1(t, 0, s, xn + 1, factorial_tab_denom[0]);
/* perturb down to a number < 1 if necessary. note that this
does not invalidate the error bound: 1 - ulp is either
1 ulp too small or must be closer to the exact value */
if (t[xn] == 0)
flint_mpn_copyi(ycos, t, xn);
else
flint_mpn_store(ycos, xn, LIMB_ONES);
}
else
{
mpn_divrem_1(s, 0, s, xn + 1, factorial_tab_denom[0]);
mpn_mul(t, s, xn + 1, x, xn);
flint_mpn_copyi(ysin, t + xn, xn);
}
}
/* error bound (ulp) */
error[0] = 2;
}
TMP_END;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("agm....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c;
fmpq_t q, r;
mpfr_t t, u;
slong prec = 2 + n_randint(state, 200);
arb_init(a);
arb_init(b);
arb_init(c);
fmpq_init(q);
fmpq_init(r);
mpfr_init2(t, prec + 100);
mpfr_init2(u, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 200), 3);
arb_randtest(b, state, 1 + n_randint(state, 200), 3);
arb_randtest(c, state, 1 + n_randint(state, 200), 3);
arb_agm(c, a, b, prec);
if (arb_equal(a, b))
{
if (!arb_contains(c, a))
{
flint_printf("FAIL: containment (identity)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
}
else
{
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
arb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
fmpq_get_mpfr(u, r, MPFR_RNDN);
mpfr_agm(t, t, u, MPFR_RNDN);
if (!arb_contains_mpfr(c, t))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpq_clear(q);
fmpq_clear(r);
mpfr_clear(t);
mpfr_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pow_ui....");
fflush(stdout);
flint_randinit(state);
/* compare with fmpz_poly */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong zbits1, rbits1, rbits2;
ulong e;
fmpz_poly_t A, B;
arb_poly_t a, b;
zbits1 = 2 + n_randint(state, 100);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
e = n_randint(state, 30);
fmpz_poly_init(A);
fmpz_poly_init(B);
arb_poly_init(a);
arb_poly_init(b);
fmpz_poly_randtest(A, state, 1 + n_randint(state, 8), zbits1);
fmpz_poly_pow(B, A, e);
arb_poly_set_fmpz_poly(a, A, rbits1);
arb_poly_pow_ui(b, a, e, rbits2);
if (!arb_poly_contains_fmpz_poly(b, B))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("e = %wu\n", e);
flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
abort();
}
arb_poly_pow_ui(a, a, e, rbits2);
if (!arb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpz_poly_clear(A);
fmpz_poly_clear(B);
arb_poly_clear(a);
arb_poly_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t A, B, C;
arb_poly_t a, b, c, d;
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
fmpq_poly_init(A);
fmpq_poly_init(B);
fmpq_poly_init(C);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1);
fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2);
fmpq_poly_mul(C, A, B);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_set_fmpq_poly(b, B, rbits2);
arb_poly_mul(c, a, b, rbits3);
if (!arb_poly_contains_fmpq_poly(c, C))
{
flint_printf("FAIL\n\n");
flint_printf("bits3 = %wd\n", rbits3);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n");
flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
arb_poly_set(d, a);
arb_poly_mul(d, d, b, rbits3);
if (!arb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
abort();
}
arb_poly_set(d, b);
arb_poly_mul(d, a, d, rbits3);
if (!arb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
abort();
}
/* test squaring */
arb_poly_set(b, a);
arb_poly_mul(c, a, b, rbits3);
arb_poly_mul(d, a, a, rbits3);
if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */
{
flint_printf("FAIL (squaring)\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
arb_poly_mul(a, a, a, rbits3);
if (!arb_poly_equal(d, a))
{
flint_printf("FAIL (aliasing, squaring)\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
fmpq_poly_clear(A);
fmpq_poly_clear(B);
fmpq_poly_clear(C);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp_series_basecase....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, bits1, bits2, bits3;
acb_poly_t a, b, c, d;
bits1 = 2 + n_randint(state, 100);
bits2 = 2 + n_randint(state, 100);
bits3 = 2 + n_randint(state, 100);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
acb_poly_randtest(a, state, m, bits1, 5);
acb_poly_randtest(b, state, m, bits1, 5);
/* check exp(a+b) = exp(a) exp(b) */
acb_poly_exp_series_basecase(c, a, n, bits2);
acb_poly_exp_series_basecase(d, b, n, bits2);
acb_poly_mullow(c, c, d, n, bits2);
acb_poly_add(d, a, b, bits3);
acb_poly_exp_series_basecase(d, d, n, bits3); /* also aliasing test */
if (!acb_poly_overlaps(c, d))
{
flint_printf("FAIL\n\n");
flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
acb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("solve_tril....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
arb_mat_t A, X, B, Y;
slong rows, cols, prec, i, j;
int unit;
prec = 2 + n_randint(state, 200);
if (n_randint(state, 10) == 0)
{
rows = n_randint(state, 60);
cols = n_randint(state, 60);
}
else
{
rows = n_randint(state, 10);
cols = n_randint(state, 10);
}
unit = n_randint(state, 2);
arb_mat_init(A, rows, rows);
arb_mat_init(B, rows, cols);
arb_mat_init(X, rows, cols);
arb_mat_init(Y, rows, cols);
arb_mat_randtest(A, state, prec, 10);
arb_mat_randtest(X, state, prec, 10);
arb_mat_randtest(Y, state, prec, 10);
for (i = 0; i < rows; i++)
{
if (unit)
arb_one(arb_mat_entry(A, i, i));
else
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
for (j = i + 1; j < rows; j++)
arb_zero(arb_mat_entry(A, i, j));
}
arb_mat_mul(B, A, X, prec);
if (unit) /* check that diagonal entries are ignored */
{
for (i = 0; i < rows; i++)
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
}
/* Check Y = A^(-1) * (A * X) = X */
arb_mat_solve_tril(Y, A, B, unit, prec);
if (!arb_mat_overlaps(Y, X))
{
flint_printf("FAIL\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
/* Check aliasing */
arb_mat_solve_tril(B, A, B, unit, prec);
if (!arb_mat_equal(B, Y))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
arb_mat_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
