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speed up cauchy_bound by computing more accurate enclosures for the sine and cosine

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This commit is contained in:
Fredrik Johansson 2013-10-04 13:10:31 +02:00
parent f2a0e2b431
commit 1201456caa
1 changed files with 49 additions and 13 deletions
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62
fmpcb_calc/cauchy_bound.c
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@ -29,42 +29,70 @@ void
fmpcb_calc_cauchy_bound(fmprb_t bound, fmpcb_calc_func_t func, void * param,
const fmpcb_t x, const fmprb_t radius, long maxdepth, long prec)
{
long i, n, depth;
long i, n, depth, wp;
fmprb_t pi, theta, v;
fmprb_t pi, theta, v, s1, c1, s2, c2, st, ct;
fmpcb_t t, u;
fmprb_t b;
fmprb_init(pi);
fmprb_init(theta);
fmprb_init(v);
fmprb_init(s1);
fmprb_init(c1);
fmprb_init(s2);
fmprb_init(c2);
fmprb_init(st);
fmprb_init(ct);
fmpcb_init(t);
fmpcb_init(u);
fmprb_init(v);
fmprb_init(b);
fmprb_const_pi(pi, prec);
wp = prec + 20;
fmprb_const_pi(pi, wp);
fmprb_zero_pm_inf(b);
for (depth = 0, n = 16; depth < maxdepth; n *= 2, depth++)
{
fmprb_zero(b);
/* theta = 2 pi / n */
fmprb_div_ui(theta, pi, n, wp);
fmprb_mul_2exp_si(theta, theta, 1);
/* sine and cosine of i*theta and (i+1)*theta */
fmprb_zero(s1);
fmprb_one(c1);
fmprb_sin_cos(st, ct, theta, wp);
fmprb_set(s2, st);
fmprb_set(c2, ct);
for (i = 0; i < n; i++)
{
/* theta = 2 pi ([i,i+1]/n) */
fmpr_set_si(fmprb_midref(theta), 2 * i + 1);
fmpr_set_si(fmprb_radref(theta), 2);
fmprb_div_ui(theta, theta, n, prec);
fmprb_mul(theta, theta, pi, prec);
/* sine and cosine of 2 pi ([i,i+1]/n) */
fmprb_sin_cos(fmpcb_imagref(t), fmpcb_realref(t), theta, prec);
fmpcb_mul_fmprb(t, t, radius, prec);
/* since we use power of two subdivision points, the
sine and cosine are monotone on each subinterval */
fmprb_union(fmpcb_realref(t), c1, c2, wp);
fmprb_union(fmpcb_imagref(t), s1, s2, wp);
fmpcb_mul_fmprb(t, t, radius, wp);
fmpcb_add(t, t, x, prec);
/* next angle */
fmprb_mul(v, c2, ct, wp);
fmprb_mul(c1, s2, st, wp);
fmprb_sub(c1, v, c1, wp);
fmprb_mul(v, c2, st, wp);
fmprb_mul(s1, s2, ct, wp);
fmprb_add(s1, v, s1, wp);
fmprb_swap(c1, c2);
fmprb_swap(s1, s2);
func(u, t, param, 1, prec);
fmpcb_abs(v, u, prec);
fmprb_add(b, b, v, prec);
}
@ -78,9 +106,17 @@ fmpcb_calc_cauchy_bound(fmprb_t bound, fmpcb_calc_func_t func, void * param,
fmprb_clear(pi);
fmprb_clear(theta);
fmprb_clear(v);
fmpcb_clear(t);
fmpcb_clear(u);
fmprb_clear(v);
fmprb_clear(b);
fmprb_clear(s1);
fmprb_clear(c1);
fmprb_clear(s2);
fmprb_clear(c2);
fmprb_clear(st);
fmprb_clear(ct);
}