mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
implement binary splitting acb_hypgeom summation
This commit is contained in:
Fredrik Johansson
parent
d7519e76ff
commit
57b1dd98d1
7 changed files with 458 additions and 3 deletions
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@ -45,12 +45,21 @@ void acb_hypgeom_pfq_sum_forward(acb_t s, acb_t t, acb_srcptr a, long p, acb_src
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void acb_hypgeom_pfq_sum_rs(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q,
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const acb_t z, long n, long prec);
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void acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q,
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const acb_t z, long n, long prec);
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void acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q,
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const acb_t z, long n, long prec);
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void acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q,
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const acb_t z, long n, long prec);
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void acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t,
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acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec);
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void acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, long p,
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acb_srcptr b, long q, const acb_t z, const acb_t zinv, long n, long prec);
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void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, long p, acb_srcptr b, long q,
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const acb_t z, long n, long prec);
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@ -32,7 +32,32 @@ acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, long p,
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if (n > 4 && prec >= 128
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&& _acb_vec_bits(a, p) * p + _acb_vec_bits(b, q) * q + 10 < prec / 2)
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{
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acb_hypgeom_pfq_sum_rs(s, t, a, p, b, q, z, n, prec);
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if (prec >= 256 && acb_bits(z) < prec * 0.01)
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acb_hypgeom_pfq_sum_bs(s, t, a, p, b, q, z, n, prec);
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else
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acb_hypgeom_pfq_sum_rs(s, t, a, p, b, q, z, n, prec);
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}
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else if (prec >= 1500 && n >= 30 + 100000 / (prec - 1000))
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{
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acb_hypgeom_pfq_sum_fme(s, t, a, p, b, q, z, n, prec);
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}
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else
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{
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acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec);
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}
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}
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void
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acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, long p,
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acb_srcptr b, long q, const acb_t z, const acb_t zinv, long n, long prec)
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{
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if (n > 4 && prec >= 128
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&& _acb_vec_bits(a, p) * p + _acb_vec_bits(b, q) * q + 10 < prec / 2)
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{
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if (prec >= 256 && acb_bits(zinv) < prec * 0.01)
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acb_hypgeom_pfq_sum_bs_invz(s, t, a, p, b, q, zinv, n, prec);
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else
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acb_hypgeom_pfq_sum_rs(s, t, a, p, b, q, z, n, prec);
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}
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else if (prec >= 1500 && n >= 30 + 100000 / (prec - 1000))
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{
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202
acb_hypgeom/pfq_sum_bs.c
Normal file
202
acb_hypgeom/pfq_sum_bs.c
Normal file
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@ -0,0 +1,202 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2015 Fredrik Johansson
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******************************************************************************/
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#include "acb_hypgeom.h"
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/*
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[S(k+1)] = [ R(k) 0 ] [S(k)]
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[T(k+1)] [ 1 1 ] [T(k)]
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[S(k+1)] = [ P(k) / Q(k) 0 ] [S(k)]
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[T(k+1)] [ 1 1 ] [T(k)]
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1 [ P(k) ]
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---- [ ]
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Q(k) [ Q(k) Q(k) ]
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[[A2 0] [B2 C2]] . [[A1 0] [B1 C1]] = [[A1 A2 0] [A1 B2 + B1 C2 C1 C2]
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A1 B2 + B1 B2 = B2 (A1 + B1) -- use to save time?
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*/
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static void
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bsplit(acb_t A1, acb_t B1, acb_t C1,
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acb_srcptr a, long p,
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acb_srcptr b, long q,
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const acb_t z,
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long aa,
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long bb,
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long prec,
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int invz)
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{
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if (bb - aa == 1)
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{
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long i;
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if (p == 0)
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{
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if (invz)
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acb_one(A1);
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else
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acb_set(A1, z);
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}
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else
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{
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acb_add_ui(A1, a, aa, prec);
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for (i = 1; i < p; i++)
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{
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acb_add_ui(B1, a + i, aa, prec);
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acb_mul(A1, A1, B1, prec);
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}
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if (!invz)
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acb_mul(A1, A1, z, prec);
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}
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if (q == 0)
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{
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if (invz)
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acb_set(C1, z);
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else
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acb_one(C1);
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}
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else
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{
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acb_add_ui(C1, b, aa, prec);
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for (i = 1; i < q; i++)
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{
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acb_add_ui(B1, b + i, aa, prec);
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acb_mul(C1, C1, B1, prec);
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}
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if (invz)
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acb_mul(C1, C1, z, prec);
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}
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/* acb_set(B1, C1); but we skip this */
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}
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else
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{
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long m;
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acb_t A2, B2, C2;
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acb_init(A2);
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acb_init(B2);
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acb_init(C2);
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m = aa + (bb - aa) / 2;
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bsplit(A1, B1, C1, a, p, b, q, z, aa, m, prec, invz);
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bsplit(A2, B2, C2, a, p, b, q, z, m, bb, prec, invz);
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if (bb - m == 1) /* B2 = C2 */
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{
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if (m - aa == 1)
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acb_add(B2, A1, C1, prec);
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else
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acb_add(B2, A1, B1, prec);
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acb_mul(B1, B2, C2, prec);
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}
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else
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{
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if (m - aa == 1)
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acb_mul(B1, C1, C2, prec);
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else
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acb_mul(B1, B1, C2, prec);
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acb_addmul(B1, A1, B2, prec);
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}
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acb_mul(A1, A1, A2, prec);
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acb_mul(C1, C1, C2, prec);
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acb_clear(A2);
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acb_clear(B2);
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acb_clear(C2);
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}
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}
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void
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acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t,
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acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
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{
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acb_t u, v, w;
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if (n < 4)
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{
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acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec);
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return;
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}
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acb_init(u);
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acb_init(v);
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acb_init(w);
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bsplit(u, v, w, a, p, b, q, z, 0, n, prec, 0);
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acb_div(t, u, w, prec);
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acb_div(s, v, w, prec);
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acb_clear(u);
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acb_clear(v);
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acb_clear(w);
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}
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void
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acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t,
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acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
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{
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acb_t u, v, w;
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if (n < 4)
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{
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acb_init(u);
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acb_inv(u, z, prec);
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acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, u, n, prec);
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acb_clear(u);
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return;
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}
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acb_init(u);
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acb_init(v);
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acb_init(w);
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bsplit(u, v, w, a, p, b, q, z, 0, n, prec, 1);
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acb_div(t, u, w, prec);
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acb_div(s, v, w, prec);
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acb_clear(u);
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acb_clear(v);
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acb_clear(w);
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}
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98
acb_hypgeom/test/t-pfq_sum_bs.c
Normal file
98
acb_hypgeom/test/t-pfq_sum_bs.c
Normal file
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@ -0,0 +1,98 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2014 Fredrik Johansson
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******************************************************************************/
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#include "acb_hypgeom.h"
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("pfq_sum_bs....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 10000; iter++)
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{
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acb_ptr a, b;
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acb_t z, s1, s2, t1, t2;
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long i, p, q, n, prec1, prec2;
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p = n_randint(state, 5);
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q = n_randint(state, 5);
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n = n_randint(state, 300);
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prec1 = 2 + n_randint(state, 500);
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prec2 = 2 + n_randint(state, 500);
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acb_init(z);
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acb_init(s1);
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acb_init(s2);
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acb_init(t1);
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acb_init(t2);
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acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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a = _acb_vec_init(p);
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b = _acb_vec_init(q);
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for (i = 0; i < p; i++)
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acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
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for (i = 0; i < q; i++)
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acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
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acb_hypgeom_pfq_sum_forward(s1, t1, a, p, b, q, z, n, prec1);
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acb_hypgeom_pfq_sum_bs(s2, t2, a, p, b, q, z, n, prec2);
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if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2))
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{
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printf("FAIL: overlap\n\n");
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printf("z = "); acb_print(a); printf("\n\n");
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printf("s1 = "); acb_print(s1); printf("\n\n");
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printf("s2 = "); acb_print(s2); printf("\n\n");
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printf("t1 = "); acb_print(t1); printf("\n\n");
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printf("t2 = "); acb_print(t2); printf("\n\n");
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abort();
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}
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_acb_vec_clear(a, p);
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_acb_vec_clear(b, q);
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acb_clear(z);
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acb_clear(s1);
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acb_clear(s2);
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acb_clear(t1);
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acb_clear(t2);
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}
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flint_randclear(state);
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flint_cleanup();
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printf("PASS\n");
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return EXIT_SUCCESS;
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}
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107
acb_hypgeom/test/t-pfq_sum_invz.c
Normal file
107
acb_hypgeom/test/t-pfq_sum_invz.c
Normal file
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@ -0,0 +1,107 @@
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/*=============================================================================
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|
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This file is part of ARB.
|
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|
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ARB is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
ARB is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
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/******************************************************************************
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|
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Copyright (C) 2014 Fredrik Johansson
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|
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******************************************************************************/
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#include "acb_hypgeom.h"
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("pfq_sum_invz....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 2000; iter++)
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{
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acb_ptr a, b;
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acb_t z, zinv, s1, s2, t1, t2;
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long i, p, q, n, prec1, prec2;
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p = n_randint(state, 5);
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q = n_randint(state, 5);
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n = n_randint(state, 300);
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prec1 = 2 + n_randint(state, 500);
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prec2 = 2 + n_randint(state, 500);
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acb_init(z);
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acb_init(zinv);
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acb_init(s1);
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acb_init(s2);
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acb_init(t1);
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acb_init(t2);
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acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
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acb_inv(zinv, z, 1 + n_randint(state, 500));
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a = _acb_vec_init(p);
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b = _acb_vec_init(q);
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for (i = 0; i < p; i++)
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acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
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for (i = 0; i < q; i++)
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acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
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if (n_randint(state, 2))
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acb_hypgeom_pfq_sum_invz(s1, t1, a, p, b, q, zinv, z, n, prec1);
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else
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acb_hypgeom_pfq_sum_bs_invz(s1, t1, a, p, b, q, z, n, prec1);
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acb_hypgeom_pfq_sum(s2, t2, a, p, b, q, zinv, n, prec2);
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if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2))
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{
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printf("FAIL: overlap\n\n");
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printf("n = %ld\n\n", n);
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printf("z = "); acb_printd(z, 15); printf("\n\n");
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printf("s1 = "); acb_printd(s1, 15); printf("\n\n");
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printf("s2 = "); acb_printd(s2, 15); printf("\n\n");
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printf("t1 = "); acb_printd(t1, 15); printf("\n\n");
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printf("t2 = "); acb_printd(t2, 15); printf("\n\n");
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abort();
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}
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_acb_vec_clear(a, p);
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_acb_vec_clear(b, q);
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acb_clear(z);
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acb_clear(zinv);
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acb_clear(s1);
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acb_clear(s2);
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acb_clear(t1);
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||||
acb_clear(t2);
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}
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||||
|
||||
flint_randclear(state);
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||||
flint_cleanup();
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printf("PASS\n");
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return EXIT_SUCCESS;
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||||
}
|
||||
|
|
@ -179,7 +179,7 @@ void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b,
|
|||
{
|
||||
mag_t C1, Cn, alpha, nu, sigma, rho, zinv, tmp, err;
|
||||
acb_struct aa[3];
|
||||
acb_t s, t, w;
|
||||
acb_t s, t, w, winv;
|
||||
int R, p, q, is_real;
|
||||
|
||||
if (!acb_is_finite(a) || !acb_is_finite(b) || !acb_is_finite(z))
|
||||
|
|
@ -204,6 +204,7 @@ void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b,
|
|||
acb_init(s);
|
||||
acb_init(t);
|
||||
acb_init(w);
|
||||
acb_init(winv);
|
||||
|
||||
/* special case, for incomplete gamma
|
||||
[todo: also when they happen to be exact and with difference 1...] */
|
||||
|
|
@ -228,6 +229,7 @@ void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b,
|
|||
|
||||
acb_neg(w, z);
|
||||
acb_inv(w, w, prec);
|
||||
acb_neg(winv, z);
|
||||
|
||||
if (n < 0)
|
||||
n = acb_hypgeom_pfq_choose_n(aa, p, aa + p, q, w, prec);
|
||||
|
|
@ -243,7 +245,7 @@ void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b,
|
|||
}
|
||||
else
|
||||
{
|
||||
acb_hypgeom_pfq_sum(s, t, aa, p, aa + p, q, w, n, prec);
|
||||
acb_hypgeom_pfq_sum_invz(s, t, aa, p, aa + p, q, w, winv, n, prec);
|
||||
|
||||
if (R == 1)
|
||||
{
|
||||
|
|
@ -307,5 +309,6 @@ void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b,
|
|||
acb_clear(s);
|
||||
acb_clear(t);
|
||||
acb_clear(w);
|
||||
acb_clear(winv);
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -86,6 +86,8 @@ or remove a 1 from the `a_i` parameters if there is one.
|
|||
|
||||
.. function:: void acb_hypgeom_pfq_sum_rs(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
|
||||
|
|
@ -97,6 +99,8 @@ or remove a 1 from the `a_i` parameters if there is one.
|
|||
The *forward* version computes the sum using forward
|
||||
recurrence.
|
||||
|
||||
The *bs* version computes the sum using binary splitting.
|
||||
|
||||
The *rs* version computes the sum in reverse order
|
||||
using rectangular splitting. It only computes a
|
||||
magnitude bound for the value of *t*.
|
||||
|
|
@ -106,6 +110,13 @@ or remove a 1 from the `a_i` parameters if there is one.
|
|||
The default version automatically chooses an algorithm
|
||||
depending on the inputs.
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t w, long n, long prec)
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, const acb_t w, long n, long prec)
|
||||
|
||||
Like :func:`acb_hypgeom_pfq_sum`, but taking advantage of
|
||||
`w = 1/z` possibly having few bits.
|
||||
|
||||
.. function:: void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, long p, acb_srcptr b, long q, const acb_t z, long n, long prec)
|
||||
|
||||
Computes
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue