mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
add acb_agm
This commit is contained in:
fredrik
parent
cf7492dbc4
commit
7b31f65f88
6 changed files with 673 additions and 22 deletions
1
acb.h
1
acb.h
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@ -780,6 +780,7 @@ void acb_polylog_si(acb_t w, slong s, const acb_t z, slong prec);
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void acb_agm1(acb_t m, const acb_t z, slong prec);
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void acb_agm1_cpx(acb_ptr m, const acb_t z, slong len, slong prec);
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void acb_agm(acb_t res, const acb_t a, const acb_t b, slong prec);
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#define ACB_LAMBERTW_LEFT 2
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#define ACB_LAMBERTW_MIDDLE 4
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152
acb/agm.c
Normal file
152
acb/agm.c
Normal file
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@ -0,0 +1,152 @@
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/*
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Copyright (C) 2020 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb.h"
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void mag_agm(mag_t res, const mag_t x, const mag_t y);
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static void
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agm_helper(acb_t res, const acb_t a, const acb_t b, slong prec)
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{
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if (acb_rel_accuracy_bits(b) >= acb_rel_accuracy_bits(a))
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{
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acb_div(res, a, b, prec);
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acb_agm1(res, res, prec);
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acb_mul(res, res, b, prec);
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}
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else
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{
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acb_div(res, b, a, prec);
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acb_agm1(res, res, prec);
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acb_mul(res, res, a, prec);
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}
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}
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void
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acb_agm(acb_t res, const acb_t a, const acb_t b, slong prec)
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{
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acb_t t, u, v;
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if (!acb_is_finite(a) || !acb_is_finite(b))
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{
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acb_indeterminate(res);
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return;
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}
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if (acb_is_zero(a) || acb_is_zero(b))
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{
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acb_zero(res);
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return;
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}
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if (arb_is_zero(acb_imagref(a)) && arb_is_zero(acb_imagref(b)))
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{
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if (arb_is_nonnegative(acb_realref(a)) && arb_is_nonnegative(acb_realref(b)))
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{
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arb_agm(acb_realref(res), acb_realref(a), acb_realref(b), prec);
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arb_zero(acb_imagref(res));
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return;
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}
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}
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if (acb_contains_zero(a) || acb_contains_zero(b))
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{
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mag_t ra, rb;
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mag_init(ra);
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mag_init(rb);
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acb_get_mag(ra, a);
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acb_get_mag(rb, b);
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mag_agm(ra, ra, rb);
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acb_zero(res);
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acb_add_error_mag(res, ra);
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mag_clear(ra);
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mag_clear(rb);
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return;
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}
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acb_init(t);
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acb_add(t, a, b, prec);
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acb_mul_2exp_si(t, t, -1);
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/* a ~= -b; bound magnitude */
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if (acb_contains_zero(t))
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{
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mag_t ra, rb;
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mag_init(ra);
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mag_init(rb);
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acb_get_mag(ra, a);
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acb_get_mag(rb, b);
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mag_mul(rb, ra, rb);
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mag_sqrt(rb, rb);
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acb_get_mag(ra, t);
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mag_agm(ra, ra, rb);
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acb_zero(res);
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acb_add_error_mag(res, ra);
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mag_clear(ra);
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mag_clear(rb);
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acb_clear(t);
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return;
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}
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/* Do the initial step with the optimal square root, reducing to agm1 */
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acb_init(u);
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acb_init(v);
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acb_mul(u, a, b, prec);
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/* we can compute either square root here; avoid the branch cut */
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if (arf_sgn(arb_midref(acb_realref(u))) >= 0)
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{
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acb_sqrt(u, u, prec);
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}
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else
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{
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acb_neg(u, u);
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acb_sqrt(u, u, prec);
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acb_mul_onei(u, u);
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}
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acb_div(v, t, u, prec);
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if (arb_is_nonnegative(acb_realref(v)))
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{
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agm_helper(res, t, u, prec);
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}
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else if (arb_is_negative(acb_realref(v)))
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{
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acb_neg(u, u);
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agm_helper(res, t, u, prec);
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}
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else
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{
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agm_helper(v, t, u, prec);
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acb_neg(u, u);
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agm_helper(res, t, u, prec);
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acb_union(res, res, v, prec);
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}
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acb_clear(t);
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acb_clear(u);
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acb_clear(v);
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}
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95
acb/agm1.c
95
acb/agm1.c
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@ -12,6 +12,8 @@
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#include "acb.h"
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#include "acb_poly.h"
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void mag_agm(mag_t res, const mag_t x, const mag_t y);
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/* Checks that |arg(z)| <= 3 pi / 4 */
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static int
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acb_check_arg(const acb_t z)
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@ -96,6 +98,21 @@ acb_agm_close_taylor(acb_t res, acb_t z, acb_t z2,
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acb_mul(res, res, aplusb, prec);
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}
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static void
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acb_agm1_around_zero(acb_t res, const acb_t z, slong prec)
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{
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mag_t a, b;
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mag_init(a);
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mag_init(b);
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mag_one(a);
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acb_get_mag(b, z);
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mag_agm(a, a, b);
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acb_zero(res);
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acb_add_error_mag(res, a);
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mag_clear(a);
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mag_clear(b);
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}
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void
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acb_agm1_basecase(acb_t res, const acb_t z, slong prec)
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{
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@ -129,16 +146,7 @@ acb_agm1_basecase(acb_t res, const acb_t z, slong prec)
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if (!acb_check_arg(z))
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{
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mag_t one;
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mag_init(one);
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mag_init(err);
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mag_one(one);
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acb_get_mag(err, z);
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mag_max(err, err, one);
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acb_zero(res);
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acb_add_error_mag(res, err);
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mag_clear(err);
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mag_clear(one);
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acb_agm1_around_zero(res, z, prec);
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return;
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}
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@ -417,28 +425,73 @@ acb_agm1_deriv_right(acb_t Mz, acb_t Mzp, const acb_t z, slong prec)
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}
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void
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acb_agm1(acb_t m, const acb_t z, slong prec)
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acb_agm1(acb_t res, const acb_t z, slong prec)
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{
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if (arf_sgn(arb_midref(acb_realref(z))) >= 0)
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if (acb_is_zero(z))
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{
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acb_agm1_basecase(m, z, prec);
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acb_zero(res);
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}
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else if (!acb_is_finite(z))
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{
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acb_indeterminate(res);
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}
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else if (acb_contains_zero(z))
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{
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acb_agm1_around_zero(res, z, prec);
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}
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else if (arf_sgn(arb_midref(acb_realref(z))) >= 0)
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{
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acb_agm1_basecase(res, z, prec);
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}
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else if (acb_equal_si(z, -1))
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{
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acb_zero(m);
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acb_zero(res);
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}
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else
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{
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/* use M(z) = (z+1)/2 * M(2 sqrt(z) / (z+1)) */
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/* use M(1,z) = M((z+1)/2, sqrt(z))
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= (z+1)/2 * M(1, 2 sqrt(z) / (z+1))
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= sqrt(z) * M(1, (z+1) / (2 sqrt(z)) */
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acb_t t;
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acb_init(t);
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acb_add_ui(t, z, 1, prec);
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acb_sqrt(m, z, prec);
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acb_div(m, m, t, prec);
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acb_mul_2exp_si(m, m, 1);
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acb_agm1_basecase(m, m, prec);
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acb_mul(m, m, t, prec);
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acb_mul_2exp_si(m, m, -1);
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acb_mul_2exp_si(t, t, -1);
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if (acb_contains_zero(t))
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{
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mag_t ra, rb;
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mag_init(ra);
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mag_init(rb);
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acb_get_mag(ra, t);
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acb_get_mag(rb, z);
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mag_sqrt(rb, rb);
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mag_agm(ra, ra, rb);
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acb_zero(res);
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acb_add_error_mag(res, ra);
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mag_clear(ra);
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mag_clear(rb);
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}
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else if (acb_rel_accuracy_bits(t) > acb_rel_accuracy_bits(z))
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{
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acb_sqrt(res, z, prec);
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acb_div(res, res, t, prec);
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acb_agm1_basecase(res, res, prec);
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acb_mul(res, res, t, prec);
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}
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else
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{
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acb_sqrt(res, z, prec);
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acb_div(t, t, res, prec);
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acb_agm1_basecase(t, t, prec);
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acb_mul(res, res, t, prec);
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}
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acb_clear(t);
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}
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}
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435
acb/test/t-agm.c
Normal file
435
acb/test/t-agm.c
Normal file
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@ -0,0 +1,435 @@
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/*
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Copyright (C) 2020 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb.h"
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#define NUM_TESTS 256
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const double agm_testdata[NUM_TESTS][6] = {
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{-1, -1, -1, -1, -1.00000000000000, -1.00000000000000},
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{-1, -1, -1, 0, -1.04916052873278, -0.478155746088161},
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{-1, -1, -1, 1, -1.19814023473559, 0.000000000000000},
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{-1, -1, -1, 2, -1.35980258211696, 0.412918513270561},
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{-1, -1, 0, -1, -0.478155746088161, -1.04916052873278},
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{-1, -1, 0, 0, 0.000000000000000, 0.000000000000000},
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{-1, -1, 0, 1, -0.778004078788958, 0.188411067988680},
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{-1, -1, 0, 2, -0.966415146777638, 0.589593010800278},
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{-1, -1, 1, -1, 0.000000000000000, -1.19814023473559},
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{-1, -1, 1, 0, 0.188411067988680, -0.778004078788958},
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{-1, -1, 1, 1, 0.000000000000000, 0.000000000000000},
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{-1, -1, 1, 2, -0.574659643809835, 0.810208383866421},
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{-1, -1, 2, -1, 0.412918513270561, -1.35980258211696},
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{-1, -1, 2, 0, 0.589593010800278, -0.966415146777638},
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{-1, -1, 2, 1, 0.810208383866421, -0.574659643809835},
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{-1, -1, 2, 2, 1.08423239187061, -0.238299975053003},
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{-1, 0, -1, -1, -1.04916052873278, -0.478155746088161},
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{-1, 0, -1, 0, -1.00000000000000, 0.000000000000000},
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{-1, 0, -1, 1, -1.04916052873278, 0.478155746088161},
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{-1, 0, -1, 2, -1.13815978557677, 0.897764105638205},
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{-1, 0, 0, -1, -0.599070117367796, -0.599070117367796},
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{-1, 0, 0, 0, 0.000000000000000, 0.000000000000000},
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{-1, 0, 0, 1, -0.599070117367796, 0.599070117367796},
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{-1, 0, 0, 2, -0.742646422399778, 1.01005159361958},
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{-1, 0, 1, -1, -0.188411067988680, -0.778004078788958},
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{-1, 0, 1, 0, 0.000000000000000, 0.000000000000000},
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{-1, 0, 1, 1, -0.188411067988680, 0.778004078788958},
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{-1, 0, 1, 2, -0.363823969691055, 1.15631976909117},
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{-1, 0, 2, -1, 0.178866979357132, -0.985872907297986},
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{-1, 0, 2, 0, 0.422966208408802, 0.661266183461805},
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{-1, 0, 2, 1, 0.178866979357132, 0.985872907297986},
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{-1, 0, 2, 2, -0.0126420344317752, 1.32391495927282},
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{-1, 1, -1, -1, -1.19814023473559, 0.000000000000000},
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{-1, 1, -1, 0, -1.04916052873278, 0.478155746088161},
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{-1, 1, -1, 1, -1.00000000000000, 1.00000000000000},
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{-1, 1, -1, 2, -1.02005412633766, 1.47134936286465},
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{-1, 1, 0, -1, -0.778004078788958, -0.188411067988680},
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{-1, 1, 0, 0, 0.000000000000000, 0.000000000000000},
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{-1, 1, 0, 1, -0.478155746088161, 1.04916052873278},
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{-1, 1, 0, 2, -0.571004782644619, 1.52731627482094},
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{-1, 1, 1, -1, 0.000000000000000, 0.000000000000000},
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{-1, 1, 1, 0, 0.188411067988680, 0.778004078788958},
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{-1, 1, 1, 1, 0.000000000000000, 1.19814023473559},
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{-1, 1, 1, 2, -0.136827548397369, 1.62780548487271},
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{-1, 1, 2, -1, 0.810208383866421, 0.574659643809835},
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{-1, 1, 2, 0, 0.589593010800278, 0.966415146777638},
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{-1, 1, 2, 1, 0.412918513270561, 1.35980258211696},
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{-1, 1, 2, 2, 0.267405171219803, 1.75269801601936},
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{-1, 2, -1, -1, -1.35980258211696, 0.412918513270561},
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{-1, 2, -1, 0, -1.13815978557677, 0.897764105638205},
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{-1, 2, -1, 1, -1.02005412633766, 1.47134936286465},
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{-1, 2, -1, 2, -1.00000000000000, 2.00000000000000},
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{-1, 2, 0, -1, -0.985872907297986, 0.178866979357132},
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{-1, 2, 0, 0, 0.000000000000000, 0.000000000000000},
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{-1, 2, 0, 1, -0.420983902077155, 1.47839688785392},
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{-1, 2, 0, 2, -0.493004461502931, 2.02900451838781},
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{-1, 2, 1, -1, 0.574659643809835, 0.810208383866421},
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{-1, 2, 1, 0, 0.363823969691055, 1.15631976909117},
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{-1, 2, 1, 1, 0.136827548397369, 1.62780548487271},
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{-1, 2, 1, 2, 0.000000000000000, 2.11638793788003},
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{-1, 2, 2, -1, 0.963366302386887, 0.963366302386887},
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{-1, 2, 2, 0, 0.777111977967075, 1.37110999239961},
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{-1, 2, 2, 1, 0.599070117367796, 1.79721035210339},
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{-1, 2, 2, 2, 0.455159607692816, 2.23571522629432},
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{0, -1, -1, -1, -0.478155746088161, -1.04916052873278},
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{0, -1, -1, 0, -0.599070117367796, -0.599070117367796},
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{0, -1, -1, 1, -0.778004078788958, -0.188411067988680},
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{0, -1, -1, 2, -0.985872907297986, 0.178866979357132},
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{0, -1, 0, -1, 0.000000000000000, -1.00000000000000},
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{0, -1, 0, 0, 0.000000000000000, 0.000000000000000},
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{0, -1, 0, 1, 0.000000000000000, 0.000000000000000},
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{0, -1, 0, 2, 0.661266183461805, 0.422966208408802},
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{0, -1, 1, -1, 0.478155746088161, -1.04916052873278},
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{0, -1, 1, 0, 0.599070117367796, -0.599070117367796},
|
||||
{0, -1, 1, 1, 0.778004078788958, -0.188411067988680},
|
||||
{0, -1, 1, 2, 0.985872907297986, 0.178866979357132},
|
||||
{0, -1, 2, -1, 0.897764105638205, -1.13815978557677},
|
||||
{0, -1, 2, 0, 1.01005159361958, -0.742646422399778},
|
||||
{0, -1, 2, 1, 1.15631976909117, -0.363823969691055},
|
||||
{0, -1, 2, 2, 1.32391495927282, -0.0126420344317752},
|
||||
{0, 0, -1, -1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, -1, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, -1, 1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, -1, 2, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 0, -1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 0, 1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 0, 2, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 1, -1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 1, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 1, 1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 1, 2, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 2, -1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 2, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 2, 1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 0, 2, 2, 0.000000000000000, 0.000000000000000},
|
||||
{0, 1, -1, -1, -0.778004078788958, 0.188411067988680},
|
||||
{0, 1, -1, 0, -0.599070117367796, 0.599070117367796},
|
||||
{0, 1, -1, 1, -0.478155746088161, 1.04916052873278},
|
||||
{0, 1, -1, 2, -0.420983902077155, 1.47839688785392},
|
||||
{0, 1, 0, -1, 0.000000000000000, 0.000000000000000},
|
||||
{0, 1, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 1, 0, 1, 0.000000000000000, 1.00000000000000},
|
||||
{0, 1, 0, 2, 0.000000000000000, 1.45679103104691},
|
||||
{0, 1, 1, -1, 0.778004078788958, 0.188411067988680},
|
||||
{0, 1, 1, 0, 0.599070117367796, 0.599070117367796},
|
||||
{0, 1, 1, 1, 0.478155746088161, 1.04916052873278},
|
||||
{0, 1, 1, 2, 0.420983902077155, 1.47839688785392},
|
||||
{0, 1, 2, -1, 1.15631976909117, 0.363823969691055},
|
||||
{0, 1, 2, 0, 1.01005159361958, 0.742646422399778},
|
||||
{0, 1, 2, 1, 0.897764105638205, 1.13815978557677},
|
||||
{0, 1, 2, 2, 0.820905313474926, 1.53147158277780},
|
||||
{0, 2, -1, -1, -0.966415146777638, 0.589593010800278},
|
||||
{0, 2, -1, 0, -0.742646422399778, 1.01005159361958},
|
||||
{0, 2, -1, 1, -0.571004782644619, 1.52731627482094},
|
||||
{0, 2, -1, 2, -0.493004461502931, 2.02900451838781},
|
||||
{0, 2, 0, -1, 0.661266183461805, 0.422966208408802},
|
||||
{0, 2, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{0, 2, 0, 1, 0.000000000000000, 1.45679103104691},
|
||||
{0, 2, 0, 2, 0.000000000000000, 2.00000000000000},
|
||||
{0, 2, 1, -1, 0.966415146777638, 0.589593010800278},
|
||||
{0, 2, 1, 0, 0.742646422399778, 1.01005159361958},
|
||||
{0, 2, 1, 1, 0.571004782644619, 1.52731627482094},
|
||||
{0, 2, 1, 2, 0.493004461502931, 2.02900451838781},
|
||||
{0, 2, 2, -1, 1.37110999239961, 0.777111977967075},
|
||||
{0, 2, 2, 0, 1.19814023473559, 1.19814023473559},
|
||||
{0, 2, 2, 1, 1.05542091981433, 1.64623191253177},
|
||||
{0, 2, 2, 2, 0.956311492176322, 2.09832105746556},
|
||||
{1, -1, -1, -1, 0.000000000000000, -1.19814023473559},
|
||||
{1, -1, -1, 0, -0.188411067988680, -0.778004078788958},
|
||||
{1, -1, -1, 1, 0.000000000000000, 0.000000000000000},
|
||||
{1, -1, -1, 2, 0.574659643809835, 0.810208383866421},
|
||||
{1, -1, 0, -1, 0.478155746088161, -1.04916052873278},
|
||||
{1, -1, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{1, -1, 0, 1, 0.778004078788958, 0.188411067988680},
|
||||
{1, -1, 0, 2, 0.966415146777638, 0.589593010800278},
|
||||
{1, -1, 1, -1, 1.00000000000000, -1.00000000000000},
|
||||
{1, -1, 1, 0, 1.04916052873278, -0.478155746088161},
|
||||
{1, -1, 1, 1, 1.19814023473559, 0.000000000000000},
|
||||
{1, -1, 1, 2, 1.35980258211696, 0.412918513270561},
|
||||
{1, -1, 2, -1, 1.47134936286465, -1.02005412633766},
|
||||
{1, -1, 2, 0, 1.52731627482094, -0.571004782644619},
|
||||
{1, -1, 2, 1, 1.62780548487271, -0.136827548397369},
|
||||
{1, -1, 2, 2, 1.75269801601936, 0.267405171219803},
|
||||
{1, 0, -1, -1, 0.188411067988680, -0.778004078788958},
|
||||
{1, 0, -1, 0, 0.000000000000000, 0.000000000000000},
|
||||
{1, 0, -1, 1, 0.188411067988680, 0.778004078788958},
|
||||
{1, 0, -1, 2, 0.363823969691055, 1.15631976909117},
|
||||
{1, 0, 0, -1, 0.599070117367796, -0.599070117367796},
|
||||
{1, 0, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{1, 0, 0, 1, 0.599070117367796, 0.599070117367796},
|
||||
{1, 0, 0, 2, 0.742646422399778, 1.01005159361958},
|
||||
{1, 0, 1, -1, 1.04916052873278, -0.478155746088161},
|
||||
{1, 0, 1, 0, 1.00000000000000, 0.000000000000000},
|
||||
{1, 0, 1, 1, 1.04916052873278, 0.478155746088161},
|
||||
{1, 0, 1, 2, 1.13815978557677, 0.897764105638205},
|
||||
{1, 0, 2, -1, 1.47839688785392, -0.420983902077155},
|
||||
{1, 0, 2, 0, 1.45679103104691, 0.000000000000000},
|
||||
{1, 0, 2, 1, 1.47839688785392, 0.420983902077155},
|
||||
{1, 0, 2, 2, 1.53147158277780, 0.820905313474926},
|
||||
{1, 1, -1, -1, 0.000000000000000, 0.000000000000000},
|
||||
{1, 1, -1, 0, -0.188411067988680, 0.778004078788958},
|
||||
{1, 1, -1, 1, 0.000000000000000, 1.19814023473559},
|
||||
{1, 1, -1, 2, 0.136827548397369, 1.62780548487271},
|
||||
{1, 1, 0, -1, 0.778004078788958, -0.188411067988680},
|
||||
{1, 1, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{1, 1, 0, 1, 0.478155746088161, 1.04916052873278},
|
||||
{1, 1, 0, 2, 0.571004782644619, 1.52731627482094},
|
||||
{1, 1, 1, -1, 1.19814023473559, 0.000000000000000},
|
||||
{1, 1, 1, 0, 1.04916052873278, 0.478155746088161},
|
||||
{1, 1, 1, 1, 1.00000000000000, 1.00000000000000},
|
||||
{1, 1, 1, 2, 1.02005412633766, 1.47134936286465},
|
||||
{1, 1, 2, -1, 1.62780548487271, 0.136827548397369},
|
||||
{1, 1, 2, 0, 1.52731627482094, 0.571004782644619},
|
||||
{1, 1, 2, 1, 1.47134936286465, 1.02005412633766},
|
||||
{1, 1, 2, 2, 1.45679103104691, 1.45679103104691},
|
||||
{1, 2, -1, -1, -0.574659643809835, 0.810208383866421},
|
||||
{1, 2, -1, 0, -0.363823969691055, 1.15631976909117},
|
||||
{1, 2, -1, 1, -0.136827548397369, 1.62780548487271},
|
||||
{1, 2, -1, 2, 0.000000000000000, 2.11638793788003},
|
||||
{1, 2, 0, -1, 0.985872907297986, 0.178866979357132},
|
||||
{1, 2, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{1, 2, 0, 1, 0.420983902077155, 1.47839688785392},
|
||||
{1, 2, 0, 2, 0.493004461502931, 2.02900451838781},
|
||||
{1, 2, 1, -1, 1.35980258211696, 0.412918513270561},
|
||||
{1, 2, 1, 0, 1.13815978557677, 0.897764105638205},
|
||||
{1, 2, 1, 1, 1.02005412633766, 1.47134936286465},
|
||||
{1, 2, 1, 2, 1.00000000000000, 2.00000000000000},
|
||||
{1, 2, 2, -1, 1.79721035210339, 0.599070117367796},
|
||||
{1, 2, 2, 0, 1.64623191253177, 1.05542091981433},
|
||||
{1, 2, 2, 1, 1.54030226799894, 1.54030226799894},
|
||||
{1, 2, 2, 2, 1.48529284479956, 2.02010318723916},
|
||||
{2, -1, -1, -1, 0.412918513270561, -1.35980258211696},
|
||||
{2, -1, -1, 0, 0.178866979357132, -0.985872907297986},
|
||||
{2, -1, -1, 1, 0.810208383866421, 0.574659643809835},
|
||||
{2, -1, -1, 2, 0.963366302386887, 0.963366302386887},
|
||||
{2, -1, 0, -1, 0.897764105638205, -1.13815978557677},
|
||||
{2, -1, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{2, -1, 0, 1, 1.15631976909117, 0.363823969691055},
|
||||
{2, -1, 0, 2, 1.37110999239961, 0.777111977967075},
|
||||
{2, -1, 1, -1, 1.47134936286465, -1.02005412633766},
|
||||
{2, -1, 1, 0, 1.47839688785392, -0.420983902077155},
|
||||
{2, -1, 1, 1, 1.62780548487271, 0.136827548397369},
|
||||
{2, -1, 1, 2, 1.79721035210339, 0.599070117367796},
|
||||
{2, -1, 2, -1, 2.00000000000000, -1.00000000000000},
|
||||
{2, -1, 2, 0, 2.02900451838781, -0.493004461502931},
|
||||
{2, -1, 2, 1, 2.11638793788003, 0.000000000000000},
|
||||
{2, -1, 2, 2, 2.23571522629432, 0.455159607692816},
|
||||
{2, 0, -1, -1, 0.589593010800278, -0.966415146777638},
|
||||
{2, 0, -1, 0, 0.422966208408802, 0.661266183461805},
|
||||
{2, 0, -1, 1, 0.589593010800278, 0.966415146777638},
|
||||
{2, 0, -1, 2, 0.777111977967075, 1.37110999239961},
|
||||
{2, 0, 0, -1, 1.01005159361958, -0.742646422399778},
|
||||
{2, 0, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{2, 0, 0, 1, 1.01005159361958, 0.742646422399778},
|
||||
{2, 0, 0, 2, 1.19814023473559, 1.19814023473559},
|
||||
{2, 0, 1, -1, 1.52731627482094, -0.571004782644619},
|
||||
{2, 0, 1, 0, 1.45679103104691, 0.000000000000000},
|
||||
{2, 0, 1, 1, 1.52731627482094, 0.571004782644619},
|
||||
{2, 0, 1, 2, 1.64623191253177, 1.05542091981433},
|
||||
{2, 0, 2, -1, 2.02900451838781, -0.493004461502931},
|
||||
{2, 0, 2, 0, 2.00000000000000, 0.000000000000000},
|
||||
{2, 0, 2, 1, 2.02900451838781, 0.493004461502931},
|
||||
{2, 0, 2, 2, 2.09832105746556, 0.956311492176322},
|
||||
{2, 1, -1, -1, 0.810208383866421, -0.574659643809835},
|
||||
{2, 1, -1, 0, 0.178866979357132, 0.985872907297986},
|
||||
{2, 1, -1, 1, 0.412918513270561, 1.35980258211696},
|
||||
{2, 1, -1, 2, 0.599070117367796, 1.79721035210339},
|
||||
{2, 1, 0, -1, 1.15631976909117, -0.363823969691055},
|
||||
{2, 1, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{2, 1, 0, 1, 0.897764105638205, 1.13815978557677},
|
||||
{2, 1, 0, 2, 1.05542091981433, 1.64623191253177},
|
||||
{2, 1, 1, -1, 1.62780548487271, -0.136827548397369},
|
||||
{2, 1, 1, 0, 1.47839688785392, 0.420983902077155},
|
||||
{2, 1, 1, 1, 1.47134936286465, 1.02005412633766},
|
||||
{2, 1, 1, 2, 1.54030226799894, 1.54030226799894},
|
||||
{2, 1, 2, -1, 2.11638793788003, 0.000000000000000},
|
||||
{2, 1, 2, 0, 2.02900451838781, 0.493004461502931},
|
||||
{2, 1, 2, 1, 2.00000000000000, 1.00000000000000},
|
||||
{2, 1, 2, 2, 2.02010318723916, 1.48529284479956},
|
||||
{2, 2, -1, -1, 1.08423239187061, -0.238299975053003},
|
||||
{2, 2, -1, 0, -0.0126420344317752, 1.32391495927282},
|
||||
{2, 2, -1, 1, 0.267405171219803, 1.75269801601936},
|
||||
{2, 2, -1, 2, 0.455159607692816, 2.23571522629432},
|
||||
{2, 2, 0, -1, 1.32391495927282, -0.0126420344317752},
|
||||
{2, 2, 0, 0, 0.000000000000000, 0.000000000000000},
|
||||
{2, 2, 0, 1, 0.820905313474926, 1.53147158277780},
|
||||
{2, 2, 0, 2, 0.956311492176322, 2.09832105746556},
|
||||
{2, 2, 1, -1, 1.75269801601936, 0.267405171219803},
|
||||
{2, 2, 1, 0, 1.53147158277780, 0.820905313474926},
|
||||
{2, 2, 1, 1, 1.45679103104691, 1.45679103104691},
|
||||
{2, 2, 1, 2, 1.48529284479956, 2.02010318723916},
|
||||
{2, 2, 2, -1, 2.23571522629432, 0.455159607692816},
|
||||
{2, 2, 2, 0, 2.09832105746556, 0.956311492176322},
|
||||
{2, 2, 2, 1, 2.02010318723916, 1.48529284479956},
|
||||
{2, 2, 2, 2, 2.00000000000000, 2.00000000000000},
|
||||
};
|
||||
|
||||
int main()
|
||||
{
|
||||
slong iter;
|
||||
flint_rand_t state;
|
||||
|
||||
flint_printf("agm....");
|
||||
fflush(stdout);
|
||||
|
||||
flint_randinit(state);
|
||||
|
||||
|
||||
/* test particular values against table */
|
||||
{
|
||||
acb_t x, y, r, s;
|
||||
|
||||
acb_init(x);
|
||||
acb_init(y);
|
||||
acb_init(r);
|
||||
acb_init(s);
|
||||
|
||||
for (iter = 0; iter < NUM_TESTS; iter++)
|
||||
{
|
||||
acb_set_d_d(x, agm_testdata[iter][0], agm_testdata[iter][1]);
|
||||
acb_set_d_d(y, agm_testdata[iter][2], agm_testdata[iter][3]);
|
||||
acb_set_d_d(s, agm_testdata[iter][4], agm_testdata[iter][5]);
|
||||
mag_set_d(arb_radref(acb_realref(s)), 1e-13);
|
||||
mag_set_d(arb_radref(acb_imagref(s)), 1e-13);
|
||||
|
||||
acb_agm(r, x, y, 64);
|
||||
|
||||
if (!acb_overlaps(r, s))
|
||||
{
|
||||
flint_printf("FAIL\n\n");
|
||||
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
|
||||
flint_printf("y = "); acb_printd(y, 15); flint_printf("\n\n");
|
||||
flint_printf("r = "); acb_printd(r, 15); flint_printf("\n\n");
|
||||
flint_printf("s = "); acb_printd(s, 15); flint_printf("\n\n");
|
||||
flint_abort();
|
||||
}
|
||||
}
|
||||
|
||||
acb_clear(x);
|
||||
acb_clear(y);
|
||||
acb_clear(r);
|
||||
acb_clear(s);
|
||||
}
|
||||
|
||||
/* self-consistency test */
|
||||
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
|
||||
{
|
||||
acb_t m1, m2;
|
||||
acb_t x1, x2, y1, y2, t;
|
||||
slong prec1, prec2;
|
||||
|
||||
prec1 = 2 + n_randint(state, 200);
|
||||
prec2 = 2 + n_randint(state, 200);
|
||||
|
||||
acb_init(x1);
|
||||
acb_init(x2);
|
||||
acb_init(y1);
|
||||
acb_init(y2);
|
||||
acb_init(m1);
|
||||
acb_init(m2);
|
||||
acb_init(t);
|
||||
|
||||
acb_randtest(x1, state, prec1, 1 + n_randint(state, 100));
|
||||
acb_randtest(y1, state, prec1, 1 + n_randint(state, 100));
|
||||
acb_randtest(m1, state, prec1, 1 + n_randint(state, 100));
|
||||
acb_randtest(m2, state, prec1, 1 + n_randint(state, 100));
|
||||
|
||||
if (n_randint(state, 2))
|
||||
{
|
||||
acb_randtest(t, state, prec2, 1 + n_randint(state, 200));
|
||||
acb_mul(y1, x1, t, prec1);
|
||||
}
|
||||
|
||||
if (n_randint(state, 2))
|
||||
acb_swap(x1, y1);
|
||||
|
||||
if (n_randint(state, 2))
|
||||
{
|
||||
acb_set(x2, x1);
|
||||
}
|
||||
else
|
||||
{
|
||||
acb_randtest(t, state, prec2, 1 + n_randint(state, 200));
|
||||
acb_add(x2, x1, t, prec2);
|
||||
acb_sub(x2, x2, t, prec2);
|
||||
}
|
||||
|
||||
if (n_randint(state, 2))
|
||||
{
|
||||
acb_set(y2, y1);
|
||||
}
|
||||
else
|
||||
{
|
||||
acb_randtest(t, state, prec2, 1 + n_randint(state, 200));
|
||||
acb_add(y2, y1, t, prec2);
|
||||
acb_sub(y2, y2, t, prec2);
|
||||
}
|
||||
|
||||
acb_agm(m1, x1, y1, prec1);
|
||||
acb_agm(m2, x2, y2, prec2);
|
||||
|
||||
if (!acb_overlaps(m1, m2))
|
||||
{
|
||||
flint_printf("FAIL (overlap)\n\n");
|
||||
flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
|
||||
|
||||
flint_printf("x1 = "); acb_printd(x1, 30); flint_printf("\n\n");
|
||||
flint_printf("y1 = "); acb_printd(y1, 30); flint_printf("\n\n");
|
||||
flint_printf("x2 = "); acb_printd(x2, 30); flint_printf("\n\n");
|
||||
flint_printf("y2 = "); acb_printd(y2, 30); flint_printf("\n\n");
|
||||
flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n");
|
||||
flint_printf("m2 = "); acb_printd(m2, 30); flint_printf("\n\n");
|
||||
flint_abort();
|
||||
}
|
||||
|
||||
acb_div(t, x1, y1, prec1);
|
||||
if (acb_is_finite(t) && (!acb_is_real(t) || !arb_is_negative(acb_realref(t))))
|
||||
{
|
||||
if (n_randint(state, 2))
|
||||
{
|
||||
acb_div(t, x1, y1, prec1);
|
||||
acb_agm1(t, t, prec1);
|
||||
acb_mul(t, t, y1, prec1);
|
||||
}
|
||||
else
|
||||
{
|
||||
acb_div(t, y1, x1, prec1);
|
||||
acb_agm1(t, t, prec1);
|
||||
acb_mul(t, t, x1, prec1);
|
||||
}
|
||||
|
||||
if (!acb_overlaps(t, m1))
|
||||
{
|
||||
flint_printf("FAIL (overlap 2)\n\n");
|
||||
flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
|
||||
|
||||
flint_printf("x1 = "); acb_printd(x1, 30); flint_printf("\n\n");
|
||||
flint_printf("y1 = "); acb_printd(y1, 30); flint_printf("\n\n");
|
||||
flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n");
|
||||
flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n");
|
||||
flint_abort();
|
||||
}
|
||||
}
|
||||
|
||||
acb_clear(x1);
|
||||
acb_clear(x2);
|
||||
acb_clear(y1);
|
||||
acb_clear(y2);
|
||||
acb_clear(m1);
|
||||
acb_clear(m2);
|
||||
acb_clear(t);
|
||||
}
|
||||
|
||||
flint_randclear(state);
|
||||
flint_cleanup();
|
||||
flint_printf("PASS\n");
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
|
|
@ -1049,6 +1049,16 @@ See :ref:`algorithms_agm` for implementation details.
|
|||
arithmetic-geometric mean at the point *z* truncated to length *len*, i.e.
|
||||
`M(z+x) \in \mathbb{C}[[x]]`.
|
||||
|
||||
.. function:: void acb_agm(acb_t m, const acb_t x, const acb_t y, slong prec)
|
||||
|
||||
Sets *m* to the arithmetic-geometric mean of *x* and *y*. The square
|
||||
roots in the AGM iteration are chosen so as to form the "optimal"
|
||||
AGM sequence. This gives a well-defined function of *x* and *y* except
|
||||
when `x / y` is a negative real number, in which case there are two
|
||||
optimal AGM sequences. In that case, an arbitrary but consistent
|
||||
choice is made (if a decision cannot be made due to inexact arithmetic,
|
||||
the union of both choices is returned).
|
||||
|
||||
Other special functions
|
||||
-------------------------------------------------------------------------------
|
||||
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@ exact and therefore do not require separate *lower* versions.
|
|||
|
||||
A common mistake is to forget computing a lower bound for the argument
|
||||
of a decreasing function that is meant to be bounded from above,
|
||||
or vice versa. For example, to compute and upper bound for `(x+1)/(y+1)`,
|
||||
or vice versa. For example, to compute an upper bound for `(x+1)/(y+1)`,
|
||||
the parameter *x* should initially be an upper bound while *y* should be
|
||||
a lower bound, and one should do::
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue