void acb_lgamma(acb_t y, const acb_t x, long prec) { int reflect; long r, n, wp; acb_t t, u; wp = prec + FLINT_BIT_COUNT(prec); acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 0, 0, wp); /* log(gamma(x)) = log(gamma(x+r)) - log(rf(x,r)) */ acb_init(t); acb_init(u); acb_add_ui(t, x, r, wp); acb_gamma_stirling_eval(u, t, n, 0, wp); acb_rising_ui_rec(t, x, r, prec); acb_log(t, t, prec); _acb_log_rising_correct_branch(t, t, x, r, wp); acb_sub(y, u, t, prec); acb_clear(t); acb_clear(u); }
static void _acb_gamma(acb_t y, const acb_t x, long prec, int inverse) { int reflect; long r, n, wp; acb_t t, u, v; wp = prec + FLINT_BIT_COUNT(prec); acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 0, wp); acb_init(t); acb_init(u); acb_init(v); if (reflect) { /* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */ acb_sub_ui(t, x, 1, wp); acb_neg(t, t); acb_rising_ui_rec(u, t, r, wp); arb_const_pi(acb_realref(v), wp); acb_mul_arb(u, u, acb_realref(v), wp); acb_add_ui(t, t, r, wp); acb_gamma_stirling_eval(v, t, n, 0, wp); acb_exp(v, v, wp); acb_sin_pi(t, x, wp); acb_mul(v, v, t, wp); } else { /* gamma(x) = gamma(x+r) / rf(x,r) */ acb_add_ui(t, x, r, wp); acb_gamma_stirling_eval(u, t, n, 0, wp); acb_exp(u, u, prec); acb_rising_ui_rec(v, x, r, wp); } if (inverse) acb_div(y, v, u, prec); else acb_div(y, u, v, prec); acb_clear(t); acb_clear(u); acb_clear(v); }
void acb_rising_ui(acb_t y, const acb_t x, ulong n, long prec) { if (n < FLINT_MAX(prec, 100)) { acb_rising_ui_rec(y, x, n, prec); } else { acb_t t; acb_init(t); acb_add_ui(t, x, n, prec); acb_gamma(t, t, prec); acb_rgamma(y, x, prec); acb_mul(y, y, t, prec); acb_clear(t); } }
void acb_rising(acb_t y, const acb_t x, const acb_t n, long prec) { if (acb_is_int(n) && arf_sgn(arb_midref(acb_realref(n))) >= 0 && arf_cmpabs_ui(arb_midref(acb_realref(n)), FLINT_MAX(prec, 100)) < 0) { acb_rising_ui_rec(y, x, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), prec); } else { acb_t t; acb_init(t); acb_add(t, x, n, prec); acb_gamma(t, t, prec); acb_rgamma(y, x, prec); acb_mul(y, y, t, prec); acb_clear(t); } }