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implement mag_root

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This commit is contained in:
Fredrik Johansson 2015-07-21 15:09:06 +02:00
parent bd446004c7
commit 7b6828df42
4 changed files with 176 additions and 0 deletions
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6
doc/source/mag.rst
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@ -285,6 +285,12 @@ Powers and logarithms
Sets *z* to an upper bound for `\sqrt{x^2 + y^2}`.
.. function:: void mag_root(mag_t z, const mag_t x, ulong n)
Sets *z* to an upper bound for `x^{1/n}`.
We evaluate `\exp(\log(1+2^{kn}x)/n) 2^{-n}`, where *k* is chosen
so that `2^{kn}x \approx 2^{30}`.
.. function:: void mag_log1p(mag_t z, const mag_t x)
Sets *z* to an upper bound for `\log(1+x)`. The bound is computed

2
mag.h
View file

@ -581,6 +581,8 @@ void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t man, const fmpz_t exp);
void mag_sqrt(mag_t y, const mag_t x);
void mag_rsqrt(mag_t y, const mag_t x);
void mag_root(mag_t y, const mag_t x, ulong n);
void mag_hypot(mag_t z, const mag_t x, const mag_t y);
void mag_binpow_uiui(mag_t b, ulong m, ulong n);

69
mag/root.c Normal file
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@ -0,0 +1,69 @@
/*=============================================================================
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) 2015 Fredrik Johansson
******************************************************************************/
#include "mag.h"
void
mag_root(mag_t y, const mag_t x, ulong n)
{
if (n == 0)
{
mag_inf(y);
}
else if (n == 1 || mag_is_special(x))
{
mag_set(y, x);
}
else if (n == 2)
{
mag_sqrt(y, x);
}
else if (n == 4)
{
mag_sqrt(y, x);
mag_sqrt(y, y);
}
else
{
fmpz_t e, f;
fmpz_init_set_ui(e, MAG_BITS);
fmpz_init(f);
fmpz_sub(e, e, MAG_EXPREF(x));
fmpz_cdiv_q_ui(e, e, n);
fmpz_mul_ui(f, e, n);
mag_mul_2exp_fmpz(y, x, f);
mag_log1p(y, y);
mag_div_ui(y, y, n);
mag_exp(y, y);
fmpz_neg(e, e);
mag_mul_2exp_fmpz(y, y, e);
fmpz_clear(e);
fmpz_clear(f);
}
}

99
mag/test/t-root.c Normal file
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@ -0,0 +1,99 @@
/*=============================================================================
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) 2014 Fredrik Johansson
******************************************************************************/
#include "mag.h"
int main()
{
long iter;
flint_rand_t state;
printf("root....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpr_t x, y, z, z2;
mag_t xb, yb;
ulong n;
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(z2);
mag_init(xb);
mag_init(yb);
mag_randtest_special(xb, state, 1 + n_randint(state, 200));
mag_randtest_special(yb, state, 1 + n_randint(state, 200));
n = n_randint(state, 30);
mag_root(yb, xb, n);
mag_get_fmpr(x, xb);
mag_get_fmpr(y, yb);
fmpr_root(z, x, n, MAG_BITS, FMPR_RND_UP);
fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP);
fmpr_mul_2exp_si(z2, z2, -10);
MAG_CHECK_BITS(xb)
MAG_CHECK_BITS(yb)
if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0))
{
printf("FAIL\n\n");
printf("x = "); fmpr_print(x); printf("\n\n");
printf("y = "); fmpr_print(y); printf("\n\n");
printf("z = "); fmpr_print(z); printf("\n\n");
printf("z2 = "); fmpr_print(z2); printf("\n\n");
abort();
}
mag_root(xb, xb, n);
if (!mag_equal(xb, yb))
{
printf("FAIL (aliasing)\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(z2);
mag_clear(xb);
mag_clear(yb);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}