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bugfix and test code for the theta derivatives

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This commit is contained in:
Fredrik Johansson 2014-10-20 13:21:17 +02:00
parent 1ae88cf2bd
commit 930801b0f9
2 changed files with 125 additions and 95 deletions
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112
acb_modular/test/t-theta_1234_sum.c
View file

@ -39,18 +39,11 @@ int main()
that we compute the right functions */
for (iter = 0; iter < 10000; iter++)
{
acb_t t1a, t1b, t2a, t2b, t3a, t3b, t4a, t4b, w, q;
acb_ptr t1a, t1b, t2a, t2b, t3a, t3b, t4a, t4b;
acb_t w, q;
int w_is_unit;
long prec0, e0, prec1, prec2;
long prec0, e0, prec1, prec2, len1, len2, i;
acb_init(t1a);
acb_init(t1b);
acb_init(t2a);
acb_init(t2b);
acb_init(t3a);
acb_init(t3b);
acb_init(t4a);
acb_init(t4b);
acb_init(w);
acb_init(q);
@ -58,6 +51,18 @@ int main()
prec0 = 2 + n_randint(state, 3000);
prec1 = 2 + n_randint(state, 3000);
prec2 = 2 + n_randint(state, 3000);
len1 = 1 + n_randint(state, 30);
len2 = 1 + n_randint(state, 30);
t1a = _acb_vec_init(len1);
t2a = _acb_vec_init(len1);
t3a = _acb_vec_init(len1);
t4a = _acb_vec_init(len1);
t1b = _acb_vec_init(len2);
t2b = _acb_vec_init(len2);
t3b = _acb_vec_init(len2);
t4b = _acb_vec_init(len2);
if (n_randint(state, 2))
{
@ -74,43 +79,62 @@ int main()
acb_randtest(q, state, prec0, e0);
acb_randtest(t1a, state, prec0, e0);
acb_randtest(t1b, state, prec0, e0);
acb_randtest(t2a, state, prec0, e0);
acb_randtest(t2b, state, prec0, e0);
acb_randtest(t3a, state, prec0, e0);
acb_randtest(t3b, state, prec0, e0);
acb_randtest(t4a, state, prec0, e0);
acb_randtest(t4b, state, prec0, e0);
acb_modular_theta_1234_sum(t1a, t2a, t3a, t4a, w, w_is_unit, q, 1, prec1);
acb_modular_theta_1234_sum(t1b, t2b, t3b, t4b, w, w_is_unit & n_randint(state, 2), q, 1, prec2);
if (!acb_overlaps(t1a, t1b) || !acb_overlaps(t2a, t2b)
|| !acb_overlaps(t3a, t3b) || !acb_overlaps(t4a, t4b))
for (i = 0; i < len1; i++)
{
printf("FAIL (overlap)\n");
printf("q = "); acb_print(q); printf("\n\n");
printf("w = "); acb_print(w); printf("\n\n");
printf("t1a = "); acb_print(t1a); printf("\n\n");
printf("t1b = "); acb_print(t1b); printf("\n\n");
printf("t2a = "); acb_print(t2a); printf("\n\n");
printf("t2b = "); acb_print(t2b); printf("\n\n");
printf("t3a = "); acb_print(t3a); printf("\n\n");
printf("t3b = "); acb_print(t3b); printf("\n\n");
printf("t4a = "); acb_print(t4a); printf("\n\n");
printf("t4b = "); acb_print(t4b); printf("\n\n");
abort();
acb_randtest(t1a + i, state, prec0, e0);
acb_randtest(t2a + i, state, prec0, e0);
acb_randtest(t3a + i, state, prec0, e0);
acb_randtest(t4a + i, state, prec0, e0);
}
acb_clear(t1a);
acb_clear(t1b);
acb_clear(t2a);
acb_clear(t2b);
acb_clear(t3a);
acb_clear(t3b);
acb_clear(t4a);
acb_clear(t4b);
for (i = 0; i < len2; i++)
{
acb_randtest(t1b + i, state, prec0, e0);
acb_randtest(t2b + i, state, prec0, e0);
acb_randtest(t3b + i, state, prec0, e0);
acb_randtest(t4b + i, state, prec0, e0);
}
acb_modular_theta_1234_sum(t1a, t2a, t3a, t4a,
w, w_is_unit, q, len1, prec1);
acb_modular_theta_1234_sum(t1b, t2b, t3b, t4b,
w, w_is_unit & n_randint(state, 2), q, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
if (!acb_overlaps(t1a + i, t1b + i)
|| !acb_overlaps(t2a + i, t2b + i)
|| !acb_overlaps(t3a + i, t3b + i)
|| !acb_overlaps(t4a + i, t4b + i))
{
printf("FAIL (overlap) iter = %ld\n", iter);
printf("len1 = %ld, len2 = %ld, prec1 = %ld, prec2 = %ld\n\n",
len1, len2, prec1, prec2);
printf("i = %ld\n\n", i);
printf("q = "); acb_printd(q, 50); printf("\n\n");
printf("w = "); acb_printd(w, 50); printf("\n\n");
printf("t1a = "); acb_printd(t1a + i, 50); printf("\n\n");
printf("t1b = "); acb_printd(t1b + i, 50); printf("\n\n");
printf("t2a = "); acb_printd(t2a + i, 50); printf("\n\n");
printf("t2b = "); acb_printd(t2b + i, 50); printf("\n\n");
printf("t3a = "); acb_printd(t3a + i, 50); printf("\n\n");
printf("t3b = "); acb_printd(t3b + i, 50); printf("\n\n");
printf("t4a = "); acb_printd(t4a + i, 50); printf("\n\n");
printf("t4b = "); acb_printd(t4b + i, 50); printf("\n\n");
abort();
}
}
_acb_vec_clear(t1a, len1);
_acb_vec_clear(t2a, len1);
_acb_vec_clear(t3a, len1);
_acb_vec_clear(t4a, len1);
_acb_vec_clear(t1b, len2);
_acb_vec_clear(t2b, len2);
_acb_vec_clear(t3b, len2);
_acb_vec_clear(t4b, len2);
acb_clear(w);
acb_clear(q);
}

108
acb_modular/theta_1234_sum.c
View file

@ -286,12 +286,15 @@ acb_modular_theta_1234_sum(acb_ptr theta1,
if (e == e1 + e2)
{
acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k2, term_prec, prec);
acb_mul_approx(qpow + k, tmp1, tmp2,
qpow + k1, qpow + k2, term_prec, prec);
}
else if (e == 2 * e1 + e2)
{
acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k1, term_prec, prec);
acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k, qpow + k2, term_prec, prec);
acb_mul_approx(qpow + k, tmp1, tmp2,
qpow + k1, qpow + k1, term_prec, prec);
acb_mul_approx(qpow + k, tmp1, tmp2,
qpow + k, qpow + k2, term_prec, prec);
}
else
{
@ -435,8 +438,57 @@ acb_modular_theta_1234_sum(acb_ptr theta1,
acb_add(theta2 + r, theta2 + r, (r % 2 == 0) ? tmp1 : tmp2, prec);
}
/* Add error bound. Note that this must be done after multiplying
by w above, and before scaling by pi^r / r! below. */
/*
Coefficient r in the z-expansion gains a factor: pi^r / r!
times a sign:
+ 2 cos = +1 * (exp + 1/exp)
- 2 sin = +i * (exp - 1/exp)
- 2 cos = -1 * (exp + 1/exp)
+ 2 sin = -i * (exp - 1/exp)
...
*/
acb_mul_onei(theta1, theta1);
acb_neg(theta1, theta1);
for (r = 1; r < len; r++)
{
if (r % 4 == 0)
{
acb_mul_onei(theta1 + r, theta1 + r);
acb_neg(theta1 + r, theta1 + r);
}
else if (r % 4 == 1)
{
acb_mul_onei(theta2 + r, theta2 + r);
acb_mul_onei(theta3 + r, theta3 + r);
acb_mul_onei(theta4 + r, theta4 + r);
}
else if (r % 4 == 2)
{
acb_mul_onei(theta1 + r, theta1 + r);
acb_neg(theta2 + r, theta2 + r);
acb_neg(theta3 + r, theta3 + r);
acb_neg(theta4 + r, theta4 + r);
}
else
{
acb_neg(theta1 + r, theta1 + r);
acb_mul_onei(theta2 + r, theta2 + r);
acb_mul_onei(theta3 + r, theta3 + r);
acb_mul_onei(theta4 + r, theta4 + r);
acb_neg(theta2 + r, theta2 + r);
acb_neg(theta3 + r, theta3 + r);
acb_neg(theta4 + r, theta4 + r);
}
}
/* Add error bound. Note that this must be done after the
rearrangements above, and before scaling by pi^r / r! below. */
for (r = 0; r < len; r++)
{
if (q_is_real && w_is_unit) /* result must be real */
@ -455,20 +507,6 @@ acb_modular_theta_1234_sum(acb_ptr theta1,
}
}
/*
Coefficient r in the z-expansion gains a factor: pi^r / r!
times a sign:
+ 2 cos = +1 * (exp + 1/exp)
- 2 sin = +i * (exp - 1/exp)
- 2 cos = -1 * (exp + 1/exp)
+ 2 sin = -i * (exp - 1/exp)
...
*/
acb_mul_onei(theta1, theta1);
acb_neg(theta1, theta1);
if (len > 1)
{
arb_t c, d;
@ -491,38 +529,6 @@ acb_modular_theta_1234_sum(acb_ptr theta1,
arb_mul(d, d, c, prec);
arb_div_ui(d, d, r + 1, prec);
}
if (r % 4 == 0)
{
acb_mul_onei(theta1 + r, theta1 + r);
acb_neg(theta1 + r, theta1 + r);
}
else if (r % 4 == 1)
{
acb_mul_onei(theta2 + r, theta2 + r);
acb_mul_onei(theta3 + r, theta3 + r);
acb_mul_onei(theta4 + r, theta4 + r);
}
else if (r % 4 == 2)
{
acb_mul_onei(theta1 + r, theta1 + r);
acb_neg(theta2 + r, theta2 + r);
acb_neg(theta3 + r, theta3 + r);
acb_neg(theta4 + r, theta4 + r);
}
else
{
acb_neg(theta1 + r, theta1 + r);
acb_mul_onei(theta2 + r, theta2 + r);
acb_mul_onei(theta3 + r, theta3 + r);
acb_mul_onei(theta4 + r, theta4 + r);
acb_neg(theta2 + r, theta2 + r);
acb_neg(theta3 + r, theta3 + r);
acb_neg(theta4 + r, theta4 + r);
}
}
arb_clear(c);