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legendre_p_ui_asymp: minor optimization

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Take advantage of the fact that |z|=1 in power computation.
This commit is contained in:
Marc Mezzarobba 2018-01-03 11:23:47 +01:00
parent 8ec2304863
commit 153747dce3
1 changed files with 12 additions and 3 deletions
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15
arb_hypgeom/legendre_p_ui_asymp.c
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@ -220,9 +220,18 @@ _arb_hypgeom_legendre_p_ui_asymp(arb_t res, ulong n, const arb_t x,
_arb_hypgeom_legendre_p_ui_asymp_error(err, n, err, K);
/* z = (x + yi)^(n+0.5) * (1-i) */
arb_set(acb_realref(z), x);
arb_set(acb_imagref(z), y);
acb_pow_arb(z, z, u, prec);
if (n < 256)
{
arb_set(acb_realref(z), x);
arb_set(acb_imagref(z), y);
acb_pow_arb(z, z, u, prec);
}
else
{
arb_atan2(t, y, x, prec);
arb_mul(t, t, u, prec);
arb_sin_cos(acb_imagref(z), acb_realref(z), t, prec);
}
arb_one(acb_realref(s));
arb_set_si(acb_imagref(s), -1);
acb_mul(z, z, s, prec);