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This commit is contained in:
Fredrik Johansson 2013-03-26 13:39:06 +01:00
parent a694da2f10
commit f1d6faaf07
8 changed files with 392 additions and 38 deletions
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16
doc/source/fmpcb.rst
View file

@ -168,7 +168,7 @@ Complex parts
the special value `\operatorname{arg}(0) = 0`, and
`\operatorname{arg}(a+0i) = \pi` for `a < 0`. Equivalently, if
`z = a+bi`, the argument is given by `\operatorname{atan2}(b,a)`
(see *fmprb_atan2*).
(see :funct:`fmprb_atan2`).
.. function:: void fmpcb_abs(fmprb_t r, const fmpcb_t z, long prec)
@ -308,11 +308,19 @@ Elementary functions
.. function:: void fmpcb_pow_ui(fmpcb_t y, const fmpcb_t b, ulong e, long prec)
Sets *y* to *b* raised to the power *e*, computed using binary exponentiation.
Sets `y = b^e` using binary exponentiation (with an initial division
if `e < 0`). Provided that *b* and *e*
are small enough and the exponent is positive, the exact power can be
computed by setting the precision to *FMPR_PREC_EXACT*.
.. function:: void fmpcb_pow(fmpcb_t r, const fmpcb_t x, const fmpcb_t y, long prec)
Note that these functions can get slow if the exponent is
extremely large (in such cases :func:`fmpcb_pow` may be superior).
Sets *r* to *x* raised to the power *y*, computed as `x^y = \exp(y \log x)`.
.. function:: void fmpcb_pow(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
Sets `z = x^y`, computed using binary exponentiation if `y` if
a small exact integer, as `z = (x^{1/2})^{2y}` if `y` is a small exact
half-integer, and generally as `z = \exp(y \log x)`.
.. function:: void fmpcb_sqrt(fmpcb_t r, const fmpcb_t z, long prec)

24
fmpcb.h
View file

@ -461,28 +461,7 @@ fmpcb_submul_fmprb(fmpcb_t z, const fmpcb_t x, const fmprb_t y, long prec)
fmprb_submul(fmpcb_imagref(z), fmpcb_imagref(x), y, prec);
}
static __inline__ void
fmpcb_inv(fmpcb_t z, const fmpcb_t x, long prec)
{
fmprb_t t;
fmprb_init(t);
#define a fmpcb_realref(x)
#define b fmpcb_imagref(x)
fmprb_mul(t, a, a, prec);
fmprb_addmul(t, b, b, prec);
fmprb_div(fmpcb_realref(z), a, t, prec);
fmprb_div(fmpcb_imagref(z), b, t, prec);
fmprb_neg(fmpcb_imagref(z), fmpcb_imagref(z));
#undef a
#undef b
fmprb_clear(t);
}
void fmpcb_inv(fmpcb_t z, const fmpcb_t x, long prec);
static __inline__ void
fmpcb_div(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
@ -531,6 +510,7 @@ void fmpcb_sin_cos(fmpcb_t s, fmpcb_t c, const fmpcb_t z, long prec);
void fmpcb_sin_pi(fmpcb_t r, const fmpcb_t z, long prec);
void fmpcb_sin_cos_pi(fmpcb_t s, fmpcb_t c, const fmpcb_t z, long prec);
void fmpcb_pow_fmprb(fmpcb_t z, const fmpcb_t x, const fmprb_t y, long prec);
void fmpcb_pow(fmpcb_t r, const fmpcb_t x, const fmpcb_t y, long prec);
void fmpcb_sqrt(fmpcb_t y, const fmpcb_t x, long prec);

68
fmpcb/inv.c Normal file
View file

@ -0,0 +1,68 @@
/*=============================================================================
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) 2013 Fredrik Johansson
******************************************************************************/
#include "fmpcb.h"
void
fmpcb_inv(fmpcb_t z, const fmpcb_t x, long prec)
{
#define a fmpcb_realref(x)
#define b fmpcb_imagref(x)
#define c fmpcb_realref(z)
#define d fmpcb_imagref(z)
if (fmprb_is_zero(b))
{
fmprb_ui_div(c, 1, a, prec);
fmprb_zero(d);
}
else if (fmprb_is_zero(a))
{
fmprb_ui_div(d, 1, b, prec);
fmprb_neg(d, d);
fmprb_zero(c);
}
else
{
fmprb_t t;
fmprb_init(t);
fmprb_mul(t, a, a, prec);
fmprb_addmul(t, b, b, prec);
fmprb_div(c, a, t, prec);
fmprb_div(d, b, t, prec);
fmprb_neg(d, d);
fmprb_clear(t);
}
#undef a
#undef b
#undef c
#undef d
}

105
fmpcb/pow.c
View file

@ -26,13 +26,25 @@
#include "fmpcb.h"
void
fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
fmpcb_pow_fmpz_binexp(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
{
long i, wp, bits;
if (fmpz_is_zero(e))
if (-2L <= *e && *e <= 2L)
{
fmpcb_one(y);
if (*e == 0L)
fmpcb_one(y);
else if (*e == 1L)
fmpcb_set_round(y, b, prec);
else if (*e == -1L)
fmpcb_inv(y, b, prec);
else if (*e == 2L)
fmpcb_mul(y, b, b, prec);
else
{
fmpcb_inv(y, b, prec);
fmpcb_mul(y, y, y, prec);
}
return;
}
@ -41,7 +53,7 @@ fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
fmpcb_pow_fmpz(y, b, f, prec + 2);
fmpcb_pow_fmpz_binexp(y, b, f, prec + 2);
fmpcb_inv(y, y, prec);
fmpz_clear(f);
return;
@ -52,7 +64,7 @@ fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
fmpcb_t t;
fmpcb_init(t);
fmpcb_set(t, b);
fmpcb_pow_fmpz(y, t, e, prec);
fmpcb_pow_fmpz_binexp(y, t, e, prec);
fmpcb_clear(t);
return;
}
@ -70,6 +82,12 @@ fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
}
}
void
fmpcb_pow_fmpz(fmpcb_t y, const fmpcb_t b, const fmpz_t e, long prec)
{
fmpcb_pow_fmpz_binexp(y, b, e, prec);
}
void
fmpcb_pow_ui(fmpcb_t y, const fmpcb_t b, ulong e, long prec)
{
@ -90,13 +108,86 @@ fmpcb_pow_si(fmpcb_t y, const fmpcb_t b, long e, long prec)
}
void
fmpcb_pow(fmpcb_t r, const fmpcb_t x, const fmpcb_t y, long prec)
_fmpcb_pow_exp(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
fmpcb_t t;
fmpcb_init(t);
fmpcb_log(t, x, prec);
fmpcb_mul(t, t, y, prec);
fmpcb_exp(r, t, prec);
fmpcb_exp(z, t, prec);
fmpcb_clear(t);
}
void
_fmpcb_pow_fmprb_exp(fmpcb_t z, const fmpcb_t x, const fmprb_t y, long prec)
{
fmpcb_t t;
fmpcb_init(t);
fmpcb_log(t, x, prec);
fmpcb_mul_fmprb(t, t, y, prec);
fmpcb_exp(z, t, prec);
fmpcb_clear(t);
}
void
fmpcb_pow_fmprb(fmpcb_t z, const fmpcb_t x, const fmprb_t y, long prec)
{
if (fmprb_is_exact(y))
{
if (fmpr_is_zero(fmprb_midref(y)))
{
fmpcb_one(z);
return;
}
if (!fmpr_is_special(fmprb_midref(y)))
{
const fmpz * exp_exp = fmpr_expref(fmprb_midref(y));
/* smallish integer powers and square roots */
if (!COEFF_IS_MPZ(*exp_exp) && (*exp_exp >= -1L))
{
long exp_bits;
exp_bits = *exp_exp + fmpz_bits(fmpr_manref(fmprb_midref(y)));
if (exp_bits < 64)
{
fmpz_t e;
fmpz_init(e);
if (*exp_exp == -1L)
{
fmpcb_sqrt(z, x, prec + exp_bits);
fmpz_set(e, fmpr_manref(fmprb_midref(y)));
fmpcb_pow_fmpz(z, z, e, prec);
}
else
{
fmpz_mul_2exp(e, fmpr_manref(fmprb_midref(y)), *exp_exp);
fmpcb_pow_fmpz(z, x, e, prec);
}
fmpz_clear(e);
return;
}
}
}
}
_fmpcb_pow_fmprb_exp(z, x, y, prec);
}
void
fmpcb_pow(fmpcb_t z, const fmpcb_t x, const fmpcb_t y, long prec)
{
if (fmprb_is_zero(fmpcb_imagref(y)))
{
fmpcb_pow_fmprb(z, x, fmpcb_realref(y), prec);
}
else
{
_fmpcb_pow_exp(z, x, y, prec);
}
}

103
fmpcb/test/t-pow.c Normal file
View file

@ -0,0 +1,103 @@
/*=============================================================================
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) 2012, 2013 Fredrik Johansson
******************************************************************************/
#include "fmpcb.h"
int main()
{
long iter;
flint_rand_t state;
printf("pow....");
fflush(stdout);
flint_randinit(state);
/* check large arguments */
for (iter = 0; iter < 10000; iter++)
{
fmpcb_t a, b, c, d, e, f;
long prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
fmpcb_init(a);
fmpcb_init(b);
fmpcb_init(c);
fmpcb_init(d);
fmpcb_init(e);
fmpcb_init(f);
fmpcb_randtest(a, state, 1 + n_randint(state, 1000), 200);
fmpcb_randtest(b, state, 1 + n_randint(state, 1000), 200);
fmpcb_pow(c, a, b, prec1);
fmpcb_pow(d, a, b, prec2);
if (!fmpcb_overlaps(c, d))
{
printf("FAIL: overlap\n\n");
printf("a = "); fmpcb_print(a); printf("\n\n");
printf("b = "); fmpcb_print(b); printf("\n\n");
printf("c = "); fmpcb_print(c); printf("\n\n");
printf("d = "); fmpcb_print(d); printf("\n\n");
abort();
}
fmpcb_randtest(c, state, 1 + n_randint(state, 1000), 200);
/* check a^(b+c) = a^b*a^c */
fmpcb_add(e, b, c, prec1);
fmpcb_pow(d, a, e, prec1);
fmpcb_pow(e, a, b, prec1);
fmpcb_pow(f, a, c, prec1);
fmpcb_mul(e, e, f, prec1);
if (!fmpcb_overlaps(d, e))
{
printf("FAIL: functional equation\n\n");
printf("a = "); fmpcb_print(a); printf("\n\n");
printf("b = "); fmpcb_print(b); printf("\n\n");
printf("c = "); fmpcb_print(c); printf("\n\n");
printf("d = "); fmpcb_print(d); printf("\n\n");
printf("e = "); fmpcb_print(e); printf("\n\n");
abort();
}
fmpcb_clear(a);
fmpcb_clear(b);
fmpcb_clear(c);
fmpcb_clear(d);
fmpcb_clear(e);
fmpcb_clear(f);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

104
fmpcb/test/t-pow_fmpz.c Normal file
View file

@ -0,0 +1,104 @@
/*=============================================================================
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) 2012, 2013 Fredrik Johansson
******************************************************************************/
#include "fmpcb.h"
int main()
{
long iter;
flint_rand_t state;
printf("pow_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 5000; iter++)
{
fmpcb_t a, b, c, d;
fmpz_t e1, e2, e3;
long prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
fmpcb_init(a);
fmpcb_init(b);
fmpcb_init(c);
fmpcb_init(d);
fmpz_init(e1);
fmpz_init(e2);
fmpz_init(e3);
fmpcb_randtest(a, state, 1 + n_randint(state, 1000), 200);
fmpcb_randtest(b, state, 1 + n_randint(state, 1000), 200);
fmpz_randtest(e1, state, 200);
fmpz_randtest(e2, state, 200);
fmpcb_pow_fmpz(b, a, e1, prec1);
fmpcb_pow_fmpz(c, a, e1, prec2);
if (!fmpcb_overlaps(b, c))
{
printf("FAIL: overlap\n\n");
printf("a = "); fmpcb_print(a); printf("\n\n");
printf("b = "); fmpcb_print(b); printf("\n\n");
printf("c = "); fmpcb_print(c); printf("\n\n");
printf("e1 = "); fmpz_print(e1); printf("\n\n");
abort();
}
/* check a^(e1+e2) = a^e1*a^e2 */
fmpcb_pow_fmpz(c, a, e2, prec1);
fmpcb_mul(d, b, c, prec1);
fmpz_add(e3, e1, e2);
fmpcb_pow_fmpz(c, a, e3, prec1);
if (!fmpcb_overlaps(c, d))
{
printf("FAIL: functional equation\n\n");
printf("a = "); fmpcb_print(a); printf("\n\n");
printf("b = "); fmpcb_print(b); printf("\n\n");
printf("c = "); fmpcb_print(c); printf("\n\n");
printf("d = "); fmpcb_print(d); printf("\n\n");
printf("e1 = "); fmpz_print(e1); printf("\n\n");
printf("e2 = "); fmpz_print(e2); printf("\n\n");
abort();
}
fmpcb_clear(a);
fmpcb_clear(b);
fmpcb_clear(c);
fmpcb_clear(d);
fmpz_clear(e1);
fmpz_clear(e2);
fmpz_clear(e3);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}

4
fmprb/pow_fmpz_binexp.c
View file

@ -53,7 +53,7 @@ fmprb_pow_fmpz_binexp(fmprb_t y, const fmprb_t b, const fmpz_t e, long prec)
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
fmprb_pow_fmpz(y, b, f, prec + 2);
fmprb_pow_fmpz_binexp(y, b, f, prec + 2);
fmprb_ui_div(y, 1UL, y, prec);
fmpz_clear(f);
return;
@ -64,7 +64,7 @@ fmprb_pow_fmpz_binexp(fmprb_t y, const fmprb_t b, const fmpz_t e, long prec)
fmprb_t t;
fmprb_init(t);
fmprb_set(t, b);
fmprb_pow_fmpz(y, t, e, prec);
fmprb_pow_fmpz_binexp(y, t, e, prec);
fmprb_clear(t);
return;
}

6
fmprb/test/t-pow.c
View file

@ -51,8 +51,8 @@ int main()
fmprb_init(e);
fmprb_init(f);
fmprb_randtest_precise(a, state, 1 + n_randint(state, 1000), 200);
fmprb_randtest_precise(b, state, 1 + n_randint(state, 1000), 200);
fmprb_randtest(a, state, 1 + n_randint(state, 1000), 200);
fmprb_randtest(b, state, 1 + n_randint(state, 1000), 200);
fmprb_pow(c, a, b, prec1);
fmprb_pow(d, a, b, prec2);
@ -67,7 +67,7 @@ int main()
abort();
}
fmprb_randtest_precise(c, state, 1 + n_randint(state, 1000), 200);
fmprb_randtest(c, state, 1 + n_randint(state, 1000), 200);
/* check a^(b+c) = a^b*a^c */
fmprb_add(e, b, c, prec1);