File: [local] / OpenXM_contrib / gmp / mpfr / Attic / pow.c (download)
Revision 1.1.1.2 (vendor branch), Mon Aug 25 16:06:07 2003 UTC (20 years, 10 months ago) by ohara
Branch: GMP
CVS Tags: VERSION_4_1_2, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX Changes since 1.1.1.1: +291 -42
lines
Import gmp 4.1.2
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/* mpfr_pow -- power function x^y
Copyright 2001, 2002 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
static int mpfr_pow_is_exact _PROTO((mpfr_srcptr, mpfr_srcptr));
/* return non zero iff x^y is exact.
Assumes x and y are ordinary numbers (neither NaN nor Inf),
and y is not zero.
*/
int
mpfr_pow_is_exact (mpfr_srcptr x, mpfr_srcptr y)
{
mp_exp_t d;
unsigned long i, c;
mp_limb_t *yp;
if ((mpfr_sgn (x) < 0) && (mpfr_isinteger (y) == 0))
return 0;
if (mpfr_sgn (y) < 0)
return mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0;
/* compute d such that y = c*2^d with c odd integer */
d = MPFR_EXP(y) - MPFR_PREC(y);
/* since y is not zero, necessarily one of the mantissa limbs is not zero,
thus we can simply loop until we find a non zero limb */
yp = MPFR_MANT(y);
for (i = 0; yp[i] == 0; i++, d += BITS_PER_MP_LIMB);
/* now yp[i] is not zero */
count_trailing_zeros (c, yp[i]);
d += c;
if (d < 0)
{
mpz_t a;
mp_exp_t b;
mpz_init (a);
b = mpfr_get_z_exp (a, x); /* x = a * 2^b */
c = mpz_scan1 (a, 0);
mpz_div_2exp (a, a, c);
b += c;
/* now a is odd */
while (d != 0)
{
if (mpz_perfect_square_p (a))
{
d++;
mpz_sqrt (a, a);
}
else
{
mpz_clear (a);
return 0;
}
}
mpz_clear (a);
}
return 1;
}
/* The computation of z = pow(x,y) is done by
z = exp(y * log(x)) = x^y */
int
mpfr_pow (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd_mode)
{
int inexact = 0;
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y))
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
if (MPFR_IS_INF(y))
{
mpfr_t one;
int cmp;
if (MPFR_SIGN(y) > 0)
{
if (MPFR_IS_INF(x))
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(x) > 0)
MPFR_SET_INF(z);
else
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
MPFR_CLEAR_FLAGS(z);
if (MPFR_IS_ZERO(x))
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
mpfr_init2(one, BITS_PER_MP_LIMB);
mpfr_set_ui(one, 1, GMP_RNDN);
cmp = mpfr_cmp_abs(x, one);
mpfr_clear(one);
if (cmp > 0)
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else if (cmp < 0)
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
else
{
if (MPFR_IS_INF(x))
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(x) > 0)
MPFR_SET_ZERO(z);
else
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
if (MPFR_IS_ZERO(x))
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
mpfr_init2(one, BITS_PER_MP_LIMB);
mpfr_set_ui(one, 1, GMP_RNDN);
cmp = mpfr_cmp_abs(x, one);
mpfr_clear(one);
MPFR_CLEAR_FLAGS(z);
if (cmp > 0)
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else if (cmp < 0)
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
}
if (MPFR_IS_ZERO(y))
{
return mpfr_set_ui (z, 1, GMP_RNDN);
}
if (mpfr_isinteger (y))
{
mpz_t zi;
long int zii;
int exptol;
mpz_init(zi);
exptol = mpfr_get_z_exp (zi, y);
if (exptol>0)
mpz_mul_2exp(zi, zi, exptol);
else
mpz_tdiv_q_2exp(zi, zi, (unsigned long int) (-exptol));
zii=mpz_get_ui(zi);
mpz_clear(zi);
return mpfr_pow_si (z, x, zii, rnd_mode);
}
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0)
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(y) > 0)
MPFR_SET_INF(z);
else
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
if (MPFR_IS_ZERO(x))
{
MPFR_CLEAR_FLAGS(z);
MPFR_SET_ZERO(z);
MPFR_SET_SAME_SIGN(z, x);
MPFR_RET(0);
}
if (MPFR_SIGN(x) < 0)
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
MPFR_CLEAR_FLAGS(z);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te, ti;
int loop = 0, ok;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt=Nt+5+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(ti);
mpfr_init(te);
do
{
loop ++;
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (ti, Nt);
mpfr_set_prec (te, Nt);
/* compute exp(y*ln(x)) */
mpfr_log (ti, x, GMP_RNDU); /* ln(n) */
mpfr_mul (te, y, ti, GMP_RNDU); /* y*ln(n) */
mpfr_exp (t, te, GMP_RNDN); /* exp(x*ln(n))*/
/* estimation of the error -- see pow function in algorithms.ps*/
err = Nt - (MPFR_EXP(te) + 3);
/* actualisation of the precision */
Nt += 10;
ok = mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny);
/* check exact power */
if (ok == 0 && loop == 1)
ok = mpfr_pow_is_exact (x, y);
}
while (err < 0 || ok == 0);
inexact = mpfr_set (z, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
}
return inexact;
}