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avoiding one polynomial multiplication when computing many derivatives of zeta

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This commit is contained in:
Fredrik Johansson 2013-09-06 12:02:07 +02:00
parent fc95be3e29
commit d0176ed1f8
1 changed files with 14 additions and 10 deletions
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24
zeta/series_em_sum.c
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@ -102,17 +102,21 @@ zeta_series_em_sum(fmpcb_ptr z, const fmpcb_t s, const fmpcb_t a, int deflate, u
/* sum += (N+a) * 1/((s+x)-1) * t */
if (!deflate)
{
/* u = 1/(s+x) has series [1/(s-1), -1/(s-1)^2, 1/(s-1)^3, ...] */
fmpcb_sub_ui(u + 0, s, 1, prec);
fmpcb_inv(u + 0, u + 0, prec);
for (i = 1; i < d; i++)
fmpcb_mul(u + i, u + i - 1, u + 0, prec);
for (i = 1; i < d; i += 2)
fmpcb_neg(u + i, u + i);
/* u = (N+a)^(1-(s+x)) */
fmpcb_sub_ui(v, s, 1, prec);
_fmpcb_poly_fmpcb_invpow_cpx(u, Na, v, d, prec);
_fmpcb_poly_mullow(v, u, d, t, d, d, prec);
_fmpcb_vec_scalar_mul(v, v, d, Na, prec);
_fmpcb_vec_add(sum, sum, v, d, prec);
/* divide by 1/((s-1) + x) */
fmpcb_sub_ui(v, s, 1, prec);
fmpcb_div(u, u, v, prec);
for (i = 1; i < d; i++)
{
fmpcb_sub(u + i, u + i, u + i - 1, prec);
fmpcb_div(u + i, u + i, v, prec);
}
_fmpcb_vec_add(sum, sum, u, d, prec);
}
/* sum += ((N+a)^(1-(s+x)) - 1) / ((s+x) - 1) */
else