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/* mpfr_agm -- arithmetic-geometric mean of two floating-point numbers
Copyright (C) 1999, 2001 Free Software Foundation.
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 <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* returns ceil(log(d)/log(2)) */
long
_mpfr_ceil_log2 (double d)
{
long exp;
union ieee_double_extract x;
x.d = d;
exp = x.s.exp - 1023;
x.s.exp = 1023; /* value for 1 <= d < 2 */
if (x.d != 1.0) exp++;
return exp;
}
/* returns floor(log(d)/log(2)) */
long
_mpfr_floor_log2 (double d)
{
union ieee_double_extract x;
x.d = d;
return (long) x.s.exp - 1023;
}
/* returns y >= 2^d */
double
_mpfr_ceil_exp2 (double d)
{
long exp;
union ieee_double_extract x;
exp = (long) d;
if (d != (double) exp) exp++;
/* now exp = ceil(d) */
x.d = 1.0;
if (exp < -1022) exp = -1022;
else if (exp > 1024) {
fprintf (stderr, "Overflow in _mpfr_ceil_exp2\n");
exit (1);
}
x.s.exp = 1023 + exp;
return x.d;
}
void
mpfr_agm (mpfr_ptr r, mpfr_srcptr op2, mpfr_srcptr op1, mp_rnd_t rnd_mode)
{
int s, go_on, compare;
mp_prec_t p, q;
double uo, vo;
mp_limb_t *up, *vp, *tmpp, *tmpup, *tmpvp, *ap, *bp;
mpfr_t u, v, tmp, tmpu, tmpv, a, b;
TMP_DECL(marker1);
/* If a or b is NaN, the result is NaN */
if (MPFR_IS_NAN(op1) || MPFR_IS_NAN(op2))
{
MPFR_SET_NAN(r);
return;
}
/* If a or b is negative (including -Infinity), the result is NaN */
if ((MPFR_SIGN(op1) < 0) || (MPFR_SIGN(op2) < 0))
{
MPFR_SET_NAN(r);
return;
}
MPFR_CLEAR_NAN(r);
/* If a or b is +Infinity, the result is +Infinity */
if (MPFR_IS_INF(op1) || MPFR_IS_INF(op2))
{
MPFR_SET_INF(r);
MPFR_SET_SAME_SIGN(r, op1);
return;
}
MPFR_CLEAR_INF(r);
/* If a or b is 0, the result is 0 */
if ((MPFR_NOTZERO(op1) && MPFR_NOTZERO(op2)) == 0)
{
MPFR_SET_ZERO(r);
return;
}
/* precision of the following calculus */
q = MPFR_PREC(r);
p = q + 15;
/* Initialisations */
go_on=1;
TMP_MARK(marker1);
s=(p-1)/BITS_PER_MP_LIMB+1;
MPFR_INIT(ap, a, p, s);
MPFR_INIT(bp, b, p, s);
{
TMP_DECL(marker2);
TMP_MARK(marker2);
MPFR_INIT(up, u, p, s);
MPFR_INIT(vp, v, p, s);
MPFR_INIT(tmpup, tmpu, p, s);
MPFR_INIT(tmpvp, tmpv, p, s);
MPFR_INIT(tmpp, tmp, p, s);
/* b and a are the 2 operands but we want b >= a */
if ((compare = mpfr_cmp (op1,op2)) > 0)
{
mpfr_set (b,op1,GMP_RNDN);
mpfr_set (a,op2,GMP_RNDN);
}
else if (compare == 0)
{
mpfr_set (r, op1, rnd_mode);
return;
}
else
{
mpfr_set (b,op2,GMP_RNDN);
mpfr_set (a,op1,GMP_RNDN);
}
vo=mpfr_get_d(b);
uo=mpfr_get_d(a);
mpfr_set(u,a,GMP_RNDN);
mpfr_set(v,b,GMP_RNDN);
/* Main loop */
while (go_on) {
int err, eq, can_round;
eq=0;
err=1 + (int) ((3.0/2.0*(double)_mpfr_ceil_log2((double)p)+1.0)*_mpfr_ceil_exp2(-(double)p)
+3.0*_mpfr_ceil_exp2(-2.0*(double)p*uo/(vo-uo)));
if(p-err-3<=q) {
p=q+err+4;
err= 1 +
(int) ((3.0/2.0*_mpfr_ceil_log2((double)p)+1.0)*_mpfr_ceil_exp2(-(double)p)
+3.0*_mpfr_ceil_exp2(-2.0*(double)p*uo/(vo-uo)));
}
/* Calculus of un and vn */
while (eq<=p-2) {
mpfr_mul(tmp,u,v,GMP_RNDN);
mpfr_sqrt (tmpu, tmp, GMP_RNDN);
mpfr_add(tmp,u,v,GMP_RNDN);
mpfr_div_2exp(tmpv,tmp,1,GMP_RNDN);
mpfr_set(u,tmpu,GMP_RNDN);
mpfr_set(v,tmpv,GMP_RNDN);
if (mpfr_cmp(v,u) >= 0)
eq = mpfr_cmp2(v,u);
else
eq = mpfr_cmp2(u,v);
}
/* Roundability of the result */
can_round=mpfr_can_round(v,p-err-3,GMP_RNDN,rnd_mode,q);
if (can_round)
go_on=0;
else {
go_on=1;
p+=5;
TMP_FREE(marker2);
TMP_MARK(marker2);
s=(p-1)/BITS_PER_MP_LIMB+1;
MPFR_INIT(up, u, p, s);
MPFR_INIT(vp, v, p, s);
MPFR_INIT(tmpup, tmpu, p, s);
MPFR_INIT(tmpvp, tmpv, p, s);
MPFR_INIT(tmpp, tmp, p, s);
mpfr_set(u,a,GMP_RNDN);
mpfr_set(v,b,GMP_RNDN);
}
}
/* End of while */
/* Setting of the result */
mpfr_set(r,v,rnd_mode);
}
/* Let's clean */
TMP_FREE(marker1);
return ;
}
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