/* series of c^(d+x) */
static __inline__ void
_fmprb_poly_pow_cpx(fmprb_ptr res, const fmprb_t c, const fmprb_t d, long trunc, long prec)
{
long i;
fmprb_t logc;
fmprb_init(logc);
fmprb_log(logc, c, prec);
fmprb_mul(res + 0, logc, d, prec);
fmprb_exp(res + 0, res + 0, prec);
for (i = 1; i < trunc; i++)
{
fmprb_mul(res + i, res + i - 1, logc, prec);
fmprb_div_ui(res + i, res + i, i, prec);
}
fmprb_clear(logc);
}
void
bound_K(fmprb_t C, const fmprb_t AN, const fmprb_t B, const fmprb_t T, long wp)
{
if (fmprb_is_zero(B) || fmprb_is_zero(T))
{
fmprb_one(C);
}
else
{
fmprb_div(C, B, AN, wp);
/* TODO: atan is dumb, should also bound by pi/2 */
fmprb_atan(C, C, wp);
fmprb_mul(C, C, T, wp);
if (fmprb_is_nonpositive(C))
fmprb_one(C);
else
fmprb_exp(C, C, wp);
}
}
int main()
{
long iter;
flint_rand_t state;
printf("exp....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmprb_t a, b;
fmpq_t q;
mpfr_t t;
long prec = 2 + n_randint(state, 200);
fmprb_init(a);
fmprb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
fmprb_randtest(a, state, 1 + n_randint(state, 200), 3);
fmprb_randtest(b, state, 1 + n_randint(state, 200), 3);
fmprb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_exp(t, t, MPFR_RNDN);
fmprb_exp(b, a, prec);
if (!fmprb_contains_mpfr(b, t))
{
printf("FAIL: containment\n\n");
printf("a = "); fmprb_print(a); printf("\n\n");
printf("b = "); fmprb_print(b); printf("\n\n");
abort();
}
fmprb_exp(a, a, prec);
if (!fmprb_equal(a, b))
{
printf("FAIL: aliasing\n\n");
abort();
}
fmprb_clear(a);
fmprb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
/* check large arguments */
for (iter = 0; iter < 100000; iter++)
{
fmprb_t a, b, c, d;
long prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
fmprb_init(a);
fmprb_init(b);
fmprb_init(c);
fmprb_init(d);
fmprb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
fmprb_exp(b, a, prec1);
fmprb_exp(c, a, prec2);
if (!fmprb_overlaps(b, c))
{
printf("FAIL: overlap\n\n");
printf("a = "); fmprb_print(a); printf("\n\n");
printf("b = "); fmprb_print(b); printf("\n\n");
printf("c = "); fmprb_print(c); printf("\n\n");
abort();
}
fmprb_randtest_precise(b, state, 1 + n_randint(state, 1000), 100);
/* check exp(a)*exp(b) = exp(a+b) */
fmprb_exp(c, a, prec1);
fmprb_exp(d, b, prec1);
fmprb_mul(c, c, d, prec1);
fmprb_add(d, a, b, prec1);
fmprb_exp(d, d, prec1);
if (!fmprb_overlaps(c, d))
{
printf("FAIL: functional equation\n\n");
printf("a = "); fmprb_print(a); printf("\n\n");
printf("b = "); fmprb_print(b); printf("\n\n");
printf("c = "); fmprb_print(c); printf("\n\n");
printf("d = "); fmprb_print(d); printf("\n\n");
abort();
}
fmprb_clear(a);
fmprb_clear(b);
fmprb_clear(c);
fmprb_clear(d);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
static void
_fmprb_gamma(fmprb_t y, const fmprb_t x, long prec, int inverse)
{
int reflect;
long r, n, wp;
fmprb_t t, u, v;
if (fmprb_is_exact(x))
{
const fmpr_struct * mid = fmprb_midref(x);
if (fmpr_is_special(mid))
{
if (!inverse && fmpr_is_pos_inf(mid))
{
fmprb_set(y, x);
}
else if (fmpr_is_nan(mid) || fmpr_is_neg_inf(mid) || !inverse)
{
fmpr_nan(fmprb_midref(y));
fmpr_pos_inf(fmprb_radref(y));
}
else
{
fmprb_zero(y);
}
return;
}
else
{
const fmpz exp = *fmpr_expref(mid);
const fmpz man = *fmpr_manref(mid);
/* fast gamma(n), gamma(n/2) or gamma(n/4) */
if (!COEFF_IS_MPZ(exp) && (exp >= -2) &&
((double) fmpz_bits(&man) + exp < prec))
{
fmpq_t a;
fmpq_init(a);
fmpr_get_fmpq(a, mid);
fmprb_gamma_fmpq(y, a, prec + 2 * inverse);
if (inverse)
fmprb_ui_div(y, 1, y, prec);
fmpq_clear(a);
return;
}
}
}
wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 1, 0, wp);
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
if (reflect)
{
/* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */
fmprb_sub_ui(t, x, 1, wp);
fmprb_neg(t, t);
gamma_rising_fmprb_ui_bsplit(u, t, r, wp);
fmprb_const_pi(v, wp);
fmprb_mul(u, u, v, wp);
fmprb_add_ui(t, t, r, wp);
gamma_stirling_eval_fmprb(v, t, n, 0, wp);
fmprb_exp(v, v, wp);
fmprb_sin_pi(t, x, wp);
fmprb_mul(v, v, t, wp);
}
else
{
/* gamma(x) = gamma(x+r) / rf(x,r) */
fmprb_add_ui(t, x, r, wp);
gamma_stirling_eval_fmprb(u, t, n, 0, wp);
fmprb_exp(u, u, prec);
gamma_rising_fmprb_ui_bsplit(v, x, r, wp);
}
if (inverse)
fmprb_div(y, v, u, prec);
else
fmprb_div(y, u, v, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
}