/* compose by poly2 = a*x^n + c, no aliasing; n >= 1 */
void
_arb_poly_compose_axnc(arb_ptr res, arb_srcptr poly1, slong len1,
const arb_t c, const arb_t a, slong n, slong prec)
{
slong i;
_arb_vec_set_round(res, poly1, len1, prec);
/* shift by c (c = 0 case will be fast) */
_arb_poly_taylor_shift(res, c, len1, prec);
/* multiply by powers of a */
if (!arb_is_one(a))
{
if (arb_equal_si(a, -1))
{
for (i = 1; i < len1; i += 2)
arb_neg(res + i, res + i);
}
else if (len1 == 2)
{
arb_mul(res + 1, res + 1, a, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set(t, a);
for (i = 1; i < len1; i++)
{
arb_mul(res + i, res + i, t, prec);
if (i + 1 < len1)
arb_mul(t, t, a, prec);
}
arb_clear(t);
}
}
/* stretch */
for (i = len1 - 1; i >= 1 && n > 1; i--)
{
arb_swap(res + i * n, res + i);
_arb_vec_zero(res + (i - 1) * n + 1, n - 1);
}
}
void
_arb_poly_taylor_shift_horner(arb_ptr poly, const arb_t c, slong n, slong prec)
{
slong i, j;
if (arb_is_one(c))
{
for (i = n - 2; i >= 0; i--)
for (j = i; j < n - 1; j++)
arb_add(poly + j, poly + j, poly + j + 1, prec);
}
else if (arb_equal_si(c, -1))
{
for (i = n - 2; i >= 0; i--)
for (j = i; j < n - 1; j++)
arb_sub(poly + j, poly + j, poly + j + 1, prec);
}
else if (!arb_is_zero(c))
{
for (i = n - 2; i >= 0; i--)
for (j = i; j < n - 1; j++)
arb_addmul(poly + j, poly + j + 1, c, prec);
}
}
int main()
{
slong iter;
FLINT_TEST_INIT(state);
{
ulong k;
arb_t a,b;
arf_t c,d;
fmpq_poly_t p;
arb_init(a);
arb_init(b);
arf_init(c);
arf_init(d);
/* x+1 */
fmpq_poly_init(p);
fmpq_poly_set_coeff_si(p, 0, 1);
fmpq_poly_set_coeff_si(p, 1, 1);
for (iter = 0; iter < 5000; iter++)
{
k = n_randint(state, 10000);
arb_set_si(a, k);
fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100));
if (!arb_equal_si(b, k + 1))
{
printf("FAIL (fmpq_poly_evaluate_arb):\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
arf_set_si(c, k);
fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100));
if (!arf_equal_si(d, k + 1))
{
printf("FAIL (fmpq_poly_evaluate_arf):\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
}
/* x^2 */
fmpq_poly_zero(p);
fmpq_poly_set_coeff_si(p, 2, 1);
for (iter = 0; iter < 1000; iter++)
{
k = n_randint(state, 10000);
arb_set_si(a, k);
fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100));
if (!arb_equal_si(b, k * k))
{
printf("Error (test_fmpq_poly_evaluate_arb):\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
arf_set_si(c, k);
fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100));
if (!arf_equal_si(d, k * k))
{
printf("Error (test_fmpq_poly_evaluate_arf):\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
}
fmpq_poly_clear(p);
arb_clear(a);
arb_clear(b);
arf_clear(c);
arf_clear(d);
}
/* check evaluate_arb agains exact evaluate_fmpq */
for (iter = 0; iter < 1000; iter++)
{
fmpq_poly_t p;
fmpq_t x,y;
arb_t a,b;
fmpq_poly_init(p);
fmpq_init(x);
fmpq_init(y);
arb_init(a);
arb_init(b);
fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10);
fmpq_randtest(x, state, 10);
arb_set_fmpq(a, x, 64);
fmpq_poly_evaluate_fmpq(y, p, x);
fmpq_poly_evaluate_arb(b, p, a, 60);
if (!arb_contains_fmpq(b, y))
{
printf("FAIL (y not in b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("x = "); fmpq_print(x); printf("\n");
printf("y = "); fmpq_print(y); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_evaluate_arb(a, p, a, 60);
if (!arb_equal(a,b))
{
printf("FAIL (a not equal b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("x = "); fmpq_print(x); printf("\n");
printf("y = "); fmpq_print(y); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
arb_clear(a);
arb_clear(b);
}
/* test aliasing */
for (iter = 0; iter < 1000; iter++)
{
fmpq_poly_t p;
arb_t a,b;
arf_t c,d;
fmpq_poly_init(p);
arb_init(a);
arb_init(b);
arf_init(c);
arf_init(d);
fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10);
arb_randtest(a, state, 60, 10);
arb_randtest(b, state, 60, 10);
arf_randtest(c, state, 60, 10);
arf_randtest(d, state, 60, 10);
fmpq_poly_evaluate_arb(b, p, a, 60);
fmpq_poly_evaluate_arb(a, p, a, 60);
if (!arb_equal(a, b))
{
printf("FAIL (a not equal b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_evaluate_arf(d, p, c, 60);
fmpq_poly_evaluate_arf(c, p, c, 60);
if (!arf_equal(c, d))
{
printf("FAIL (c not equal d):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
}
fmpq_poly_clear(p);
arb_clear(a);
arb_clear(b);
arf_clear(c);
arf_clear(d);
}
FLINT_TEST_CLEANUP(state);
return 0;
}
