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add complex sign function, acb_sgn

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This commit is contained in:
Fredrik Johansson 2016-02-18 00:55:43 +01:00
parent 28d78c7c43
commit d9c8a39a51
4 changed files with 164 additions and 0 deletions
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2
acb.h
View file

@ -424,6 +424,8 @@ acb_get_rad_ubound_arf(arf_t u, const acb_t z, slong prec)
void acb_arg(arb_t r, const acb_t z, slong prec);
void acb_sgn(acb_t res, const acb_t z, slong prec);
ACB_INLINE void
acb_add(acb_t z, const acb_t x, const acb_t y, slong prec)
{

62
acb/sgn.c Normal file
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@ -0,0 +1,62 @@
/*=============================================================================
This file is part of ARB.
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
=============================================================================*/
/******************************************************************************
Copyright (C) 2016 Fredrik Johansson
******************************************************************************/
#include "acb.h"
void
acb_sgn(acb_t res, const acb_t z, slong prec)
{
if (arb_is_zero(acb_imagref(z)))
{
arb_sgn(acb_realref(res), acb_realref(z));
arb_zero(acb_imagref(res));
}
else if (arb_is_zero(acb_realref(z)))
{
arb_sgn(acb_imagref(res), acb_imagref(z));
arb_zero(acb_realref(res));
}
else
{
arb_t t;
arb_init(t);
acb_abs(t, z, prec);
arb_inv(t, t, prec);
if (arb_is_finite(t))
{
acb_mul_arb(res, z, t, prec);
}
else
{
arf_zero(arb_midref(acb_realref(res)));
mag_one(arb_radref(acb_realref(res)));
arb_set(acb_imagref(res), acb_realref(res));
}
arb_clear(t);
}
}

95
acb/test/t-sgn.c Normal file
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@ -0,0 +1,95 @@
/*=============================================================================
This file is part of ARB.
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
=============================================================================*/
/******************************************************************************
Copyright (C) 2016 Fredrik Johansson
******************************************************************************/
#include "acb.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sgn....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_t x, a, b;
slong prec;
acb_init(x);
acb_init(a);
acb_init(b);
acb_randtest_special(x, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100));
acb_randtest_special(a, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100));
prec = 2 + n_randint(state, 200);
acb_sgn(a, x, prec);
if (acb_is_zero(x))
{
acb_zero(b);
}
else
{
arb_zero(acb_realref(b));
acb_arg(acb_imagref(b), x, prec);
acb_exp(b, b, prec);
}
if (!acb_overlaps(a, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n");
abort();
}
acb_sgn(x, x, prec);
if (!acb_overlaps(a, x))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n");
abort();
}
acb_clear(x);
acb_clear(a);
acb_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}

5
doc/source/acb.rst
View file

@ -331,6 +331,11 @@ Complex parts
Sets *r* to the absolute value of *z*.
.. function:: void acb_sgn(arb_t r, const acb_t z, slong prec)
Sets *r* to the complex sign of *z*, defined as 0 if *z* is exactly zero
and the projection onto the unit circle `z / |z| = \exp(i \arg(z))` otherwise.
Arithmetic
-------------------------------------------------------------------------------