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/* mpfr_cmp2 -- exponent shift when subtracting two 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 "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* returns the number of cancelled bits when one subtracts abs(c) from abs(b).
Assumes |b| >= |c|, which implies MPFR_EXP(b)>=MPFR_EXP(c).
if |b| = |c|, returns prec(b).
Assumes neither of b or c is NaN or +/- infinity.
In other terms mpfr_cmp2 (b, c) returns EXP(b) - EXP(b-c).
*/
mp_prec_t
mpfr_cmp2 (mpfr_srcptr b, mpfr_srcptr c)
{
mp_limb_t *bp, *cp, bb, cc = 0, lastc = 0, dif, high_dif = 0;
mp_size_t bn, cn;
mp_exp_unsigned_t diff_exp;
mp_prec_t res = 0;
MPFR_ASSERTN(MPFR_IS_FP(b));
MPFR_ASSERTN(MPFR_IS_FP(c));
if (MPFR_IS_ZERO(c))
return 0;
MPFR_ASSERTN(MPFR_NOTZERO(b));
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
bn = (MPFR_PREC(b) - 1) / BITS_PER_MP_LIMB;
cn = (MPFR_PREC(c) - 1) / BITS_PER_MP_LIMB;
MPFR_ASSERTN(MPFR_EXP(b) >= MPFR_EXP(c));
diff_exp = (mp_exp_unsigned_t) MPFR_EXP(b) - MPFR_EXP(c);
if (diff_exp == 0) /* otherwise the shifted most significant limb of c
cannot match bp[bn] */
{
while (bn>=0 && cn>=0 && bp[bn] == cp[cn])
{
bn--;
cn--;
res += BITS_PER_MP_LIMB;
}
if (bn < 0) /* b = c */
return MPFR_PREC(b);
if (cn < 0) /* c discards exactly the upper part of b */
{
unsigned int z;
while (bn>=0 && bp[bn]==0)
{
bn--;
res += BITS_PER_MP_LIMB;
}
if (bn < 0) /* b = c */
return MPFR_PREC(b);
count_leading_zeros(z, bp[bn]); /* bp[bn] <> 0 */
return res + z;
}
}
/* now we have removed the identical upper limbs of b and c
(can happen only when diff_exp = 0): bp[bn] > cc, bn>=0, cn>=0 */
if (diff_exp < BITS_PER_MP_LIMB)
{
cc = cp[cn] >> diff_exp;
/* warning: a shift by BITS_PER_MP_LIMB may give wrong results */
if (diff_exp)
lastc = cp[cn] << (BITS_PER_MP_LIMB - diff_exp);
cn--;
}
else
diff_exp -= BITS_PER_MP_LIMB;
dif = bp[bn--] - cc; /* necessarily dif >= 1 */
while ((cn >= 0 || lastc != 0) && (high_dif == 0) && (dif == 1))
{ /* dif=1 implies diff_exp = 0 or 1 */
bb = (bn >= 0) ? bp[bn] : 0;
cc = lastc;
if (cn >= 0)
{
if (diff_exp == 0)
{
cc += cp[cn];
}
else /* diff_exp = 1 */
{
cc += cp[cn] >> 1;
lastc = cp[cn] << (BITS_PER_MP_LIMB - 1);
}
}
else
lastc = 0;
high_dif = 1 - mpn_sub_n (&dif, &bb, &cc, 1);
bn--;
cn--;
res += BITS_PER_MP_LIMB;
}
/* (cn<0 and lastc=0) or (high_dif,dif)<>(0,1) */
if (high_dif != 0) /* necessarily high_dif = 1 */
{
res--;
if (dif != 0)
return res;
}
else /* high_dif = 0 */
{
unsigned int z;
count_leading_zeros(z, dif); /* dif > 1 here */
res += z;
if (dif != (MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - z - 1)))
return res; /* dif is not a power of two */
}
/* now result is res + (low(b) < low(c)) */
while (bn >= 0 && (cn >= 0 || lastc != 0))
{
if (diff_exp >= BITS_PER_MP_LIMB)
diff_exp -= BITS_PER_MP_LIMB;
else
{
cc = lastc;
if (cn >= 0)
{
cc += cp[cn] >> diff_exp;
if (diff_exp != 0)
lastc = cp[cn] << (BITS_PER_MP_LIMB - diff_exp);
}
else
lastc = 0;
cn--;
}
if (bp[bn] != cc)
return res + (bp[bn] < cc);
bn--;
}
if (bn < 0)
{
if (lastc != 0)
return res + 1;
while (cn >= 0 && cp[cn] == 0)
cn--;
return res + (cn >= 0);
}
return res; /* remainder from c is 0 */
}
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