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/* tdiv -- test file for mpc_div.
Copyright (C) 2002 Andreas Enge, Paul Zimmermann
This file is part of the MPC Library.
The MPC 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 MPC 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 MPC 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 "mpfr.h"
#include "mpc.h"
#include "mpc-impl.h"
#define OUT(x) { mpc_out_str (stdout, 2, 0, x, MPC_RNDNN); putchar ('\n'); }
#define ERR(x) { mpc_out_str (stderr, 2, 0, x, MPC_RNDNN); \
fprintf (stderr, "\n"); }
int mpc_div_ref (mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t);
int
mpc_div_ref (mpc_ptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
{
int ok = 0, inexact_q, inex_re, inex_im = 0, cancel = 0, err, sgn;
mpfr_t u, v, q, t;
mp_prec_t prec;
mp_rnd_t rnd_re, rnd_im;
if (mpfr_cmp_ui (MPC_IM(c), 0) == 0) /* c is real */
{
/* compute imaginary part first in case a=b or a=c */
inex_im = mpfr_div (MPC_IM(a), MPC_IM(b), MPC_RE(c), MPC_RND_IM(rnd));
inex_re = mpfr_div (MPC_RE(a), MPC_RE(b), MPC_RE(c), MPC_RND_RE(rnd));
return MPC_INEX(inex_re, inex_im);
}
prec = MPC_MAX_PREC(a);
/* try to guess the signs of the real and imaginary parts */
sgn = mpfr_sgn (MPC_RE(b)) * mpfr_sgn (MPC_RE(c))
+ mpfr_sgn (MPC_IM(b)) * mpfr_sgn (MPC_IM(c));
rnd_re = (sgn > 0) ? GMP_RNDU : GMP_RNDD;
sgn = mpfr_sgn (MPC_RE(b)) * mpfr_sgn (MPC_IM(c))
- mpfr_sgn (MPC_IM(b)) * mpfr_sgn (MPC_RE(c));
rnd_im = (sgn > 0) ? GMP_RNDU : GMP_RNDD;
/* first try with only one real division */
prec += mpc_ceil_log2 (prec) + 3;
mpfr_init2 (u, prec);
mpfr_init2 (v, prec);
mpfr_init2 (q, prec);
mpfr_init2 (t, prec);
/* first compute 1/norm(c)^2 rounded away */
inexact_q = mpfr_mul (u, MPC_RE(c), MPC_RE(c), GMP_RNDZ);
inexact_q |= mpfr_mul (v, MPC_IM(c), MPC_IM(c), GMP_RNDZ);
inexact_q |= mpfr_add (q, u, v, GMP_RNDZ); /* 3 ulps */
inexact_q |= mpfr_ui_div (q, 1, q, GMP_RNDU); /* 7 ulps */
/* now compute b*conjugate(c) */
/* real part */
inex_re = mpfr_mul (u, MPC_RE(b), MPC_RE(c), rnd_re); /* 1 */
inex_re |= mpfr_mul (v, MPC_IM(b), MPC_IM(c), rnd_re); /* 1 */
inex_re |= mpfr_add (t, u, v, rnd_re);
if (MPFR_IS_ZERO(u))
{
if (MPFR_IS_ZERO(v))
cancel = 0;
else
cancel = MPFR_EXP(v) - MPFR_EXP(t);
}
else if (MPFR_IS_ZERO(v))
cancel = MPFR_EXP(u) - MPFR_EXP(t);
else
{
cancel = (MPFR_IS_ZERO(t)) ? prec
: MAX(MPFR_EXP(u), MPFR_EXP(v)) - MPFR_EXP(t);
}
/* err(t) <= [1 + 2*2^cancel] ulp(t) */
inex_re |= mpfr_mul (t, t, q, rnd_re) || inexact_q;
/* err(t) <= [1 + 3*(1 + 2*2^cancel) + 14] ulp(t)
*/
err = (cancel <= 1) ? 5 : ((cancel == 2) ? 6 :
((cancel <= 4) ? 7 : cancel + 3));
ok = (inex_re == 0) || ((err < prec) && mpfr_can_round (t, prec - err,
rnd_re, MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a))));
if ((rnd_re == GMP_RNDU && mpfr_sgn (t) < 0)
|| (rnd_re == GMP_RNDD && mpfr_sgn (t) > 0))
{
ok = 0;
rnd_re = INV_RND(rnd_re);
}
if (ok) /* compute imaginary part */
{
inex_im = mpfr_mul (u, MPC_RE(b), MPC_IM(c), INV_RND(rnd_im));
inex_im |= mpfr_mul (v, MPC_IM(b), MPC_RE(c), rnd_im);
if (MPFR_IS_ZERO(u))
{
if (MPFR_IS_ZERO(v))
cancel = 0;
else
cancel = MPFR_EXP(v);
}
else if (MPFR_IS_ZERO(v))
cancel = MPFR_EXP(u);
else
cancel = MAX(MPFR_EXP(u), MPFR_EXP(v));
inex_im |= mpfr_sub (u, v, u, rnd_im);
if (!MPFR_IS_ZERO(u))
cancel = cancel - MPFR_EXP(u);
inex_im |= mpfr_mul (u, u, q, rnd_im) || inexact_q;
err = (cancel <= 1) ? 5 : ((cancel == 2) ? 6 :
((cancel <= 4) ? 7 : cancel + 3));
ok = (inex_im == 0) || ((err < prec) && mpfr_can_round (u,
prec - err, GMP_RNDN, MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a))));
if ((rnd_im == GMP_RNDU && mpfr_sgn (u) < 0)
|| (rnd_im == GMP_RNDD && mpfr_sgn (u) > 0))
{
ok = 0;
rnd_im = INV_RND(rnd_im);
}
}
/* now loop with two real divisions, to detect exact quotients */
while (ok == 0)
{
prec += mpc_ceil_log2 (prec) + 3;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
mpfr_set_prec (q, prec);
mpfr_set_prec (t, prec);
/* first compute 1/norm(c)^2 rounded away */
inexact_q = mpfr_mul (u, MPC_RE(c), MPC_RE(c), GMP_RNDZ);
inexact_q |= mpfr_mul (v, MPC_IM(c), MPC_IM(c), GMP_RNDZ);
inexact_q |= mpfr_add (q, u, v, GMP_RNDZ); /* 3 ulps */
/* now compute b*conjugate(c) */
/* real part */
inex_re = mpfr_mul (u, MPC_RE(b), MPC_RE(c), rnd_re); /* 1 */
inex_re |= mpfr_mul (v, MPC_IM(b), MPC_IM(c), rnd_re); /* 1 */
inex_re |= mpfr_add (t, u, v, rnd_re);
if (MPFR_IS_ZERO(u))
{
if (MPFR_IS_ZERO(v))
cancel = 0;
else
cancel = MPFR_EXP(v) - MPFR_EXP(t);
}
else if (MPFR_IS_ZERO(v))
cancel = MPFR_EXP(u) - MPFR_EXP(t);
else
cancel = (MPFR_IS_ZERO(t)) ? prec
: MAX(MPFR_EXP(u), MPFR_EXP(v)) - MPFR_EXP(t);
/* err(t) <= [1 + 2*2^cancel] ulp(t) */
inex_re |= mpfr_div (t, t, q, rnd_re) || inexact_q;
/* err(t) <= [1 + 2*(1 + 2*2^cancel) + 6] ulp(t)
*/
err = (cancel <= 0) ? 4 : cancel + 3;
ok = (inex_re == 0) || ((err < prec) && mpfr_can_round (t, prec - err,
rnd_re, MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a))));
if ((rnd_re == GMP_RNDU && mpfr_sgn (t) < 0)
|| (rnd_re == GMP_RNDD && mpfr_sgn (t) > 0))
{
ok = 0;
rnd_re = INV_RND(rnd_re);
}
if (ok) /* compute imaginary part */
{
inex_im = mpfr_mul (u, MPC_RE(b), MPC_IM(c), INV_RND(rnd_im));
inex_im |= mpfr_mul (v, MPC_IM(b), MPC_RE(c), rnd_im);
if (MPFR_IS_ZERO(u))
{
if (MPFR_IS_ZERO(v))
cancel = 0;
else
cancel = MPFR_EXP(v);
}
else if (MPFR_IS_ZERO(v))
cancel = MPFR_EXP(u);
else
cancel = MAX(MPFR_EXP(u), MPFR_EXP(v));
inex_im |= mpfr_sub (u, v, u, rnd_im);
if (!MPFR_IS_ZERO(u))
cancel = cancel - MPFR_EXP(u);
inex_im |= mpfr_div (u, u, q, rnd_im) || inexact_q;
err = (cancel <= 0) ? 4 : cancel + 3;
ok = (inex_im == 0) || ((err < prec) && mpfr_can_round (u,
prec - err, GMP_RNDN, MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a))));
if ((rnd_im == GMP_RNDU && mpfr_sgn (u) < 0)
|| (rnd_im == GMP_RNDD && mpfr_sgn (u) > 0))
{
ok = 0;
rnd_im = INV_RND(rnd_im);
}
}
}
inex_re = mpfr_set (MPC_RE(a), t, MPC_RND_RE(rnd)) || inex_re;
inex_im = mpfr_set (MPC_IM(a), u, MPC_RND_IM(rnd)) || inex_im;
mpfr_clear (u);
mpfr_clear (v);
mpfr_clear (q);
mpfr_clear (t);
return MPC_INEX(inex_re, inex_im);
}
int
main()
{
mpc_t b, c, q, q_ref;
int inex, i;
mp_prec_t prec;
mp_rnd_t rnd_re, rnd_im;
mpc_rnd_t rnd;
mpc_init (b);
mpc_init (c);
mpc_init (q);
mpc_init (q_ref);
mpc_set_prec (b, 10);
mpc_set_prec (c, 10);
mpc_set_prec (q, 10);
mpc_set_ui_ui (b, 973, 964, MPC_RNDNN);
mpc_set_ui_ui (c, 725, 745, MPC_RNDNN);
inex = mpc_div (q, b, c, MPC_RNDZZ);
mpc_set_si_si (b, 43136, -787, MPC_RNDNN);
mpc_div_2exp (b, b, 15, MPC_RNDNN);
if (mpc_cmp (q, b))
{
fprintf (stderr, "mpc_div failed for (973+I*964)/(725+I*745)\n");
exit (1);
}
mpc_set_si_si (b, -837, 637, MPC_RNDNN);
mpc_set_si_si (c, 63, -5, MPC_RNDNN);
inex = mpc_div (q, b, c, MPC_RNDZN);
mpc_set_prec (b, 2);
mpc_set_prec (c, 2);
mpc_set_prec (q, 2);
mpc_set_ui_ui (b, 4, 3, MPC_RNDNN);
mpc_set_ui_ui (c, 1, 2, MPC_RNDNN);
inex = mpc_div (q, b, c, MPC_RNDNN);
for (prec = 2; prec < 1000; prec++)
{
mpc_set_prec (b, prec);
mpc_set_prec (c, prec);
mpc_set_prec (q, prec);
mpc_set_prec (q_ref, prec);
for (i = 0; i < 1000/prec; i++)
{
mpc_random (b);
/* generate a non-zero divisor */
do
{
mpc_random (c);
}
while (mpfr_sgn (MPC_RE(c)) == 0 && mpfr_sgn (MPC_IM(c)) == 0);
for (rnd_re = (mp_rnd_t)0; rnd_re < (mp_rnd_t)4; ++rnd_re)
for (rnd_im = (mp_rnd_t)0; rnd_im < (mp_rnd_t)4; ++rnd_im)
{
rnd = RNDC(rnd_re, rnd_im);
mpc_div (q, b, c, rnd);
mpc_div_ref (q_ref, b, c, rnd);
if (mpc_cmp (q, q_ref))
{
fprintf (stderr, "mpc_div and mpc_div_ref differ"
"for prec=%lu rnd=(%s,%s)\n", prec,
mpfr_print_rnd_mode (rnd_re),
mpfr_print_rnd_mode (rnd_im));
fprintf (stderr, "b=");
ERR(b);
fprintf (stderr, "c=");
ERR(c);
fprintf (stderr, "q=");
ERR(q);
fprintf (stderr, "q_ref=");
ERR(q_ref);
exit (1);
}
}
}
}
mpc_clear (b);
mpc_clear (c);
mpc_clear (q);
mpc_clear (q_ref);
return 0;
}
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