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/* mpfr_cmp -- compare two floating-point numbers
Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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 "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
/* returns 0 iff b = c
a positive value iff b > c
a negative value iff b < c
More precisely, in case b and c are of same sign, the absolute value
of the result is one plus the absolute difference between the exponents
of b and c, i.e. one plus the number of bits shifts to align b and c
(this value is useful in mpfr_sub).
*/
/* #define DEBUG */
/* compares b and sign(s)*c */
int
#if __STDC__
mpfr_cmp3 ( mpfr_srcptr b, mpfr_srcptr c, long int s)
#else
mpfr_cmp3(b, c, s)
mpfr_srcptr b;
mpfr_srcptr c;
long int s;
#endif
{
long int diff_exp;
unsigned long bn, cn;
mp_limb_t *bp, *cp;
if (!NOTZERO(b)) {
if (!NOTZERO(c)) return 0; else return -(MPFR_SIGN(c));
}
else if (!NOTZERO(c)) return MPFR_SIGN(b);
s = s * MPFR_SIGN(b) * MPFR_SIGN(c);
if (s<0) return(MPFR_SIGN(b));
/* now signs are equal */
diff_exp = EXP(b)-EXP(c);
s = (MPFR_SIGN(b) > 0) ? 1 : -1;
if (diff_exp>0) return(s*(1+diff_exp));
else if (diff_exp<0) return(s*(-1+diff_exp));
/* both signs and exponents are equal */
bn = (PREC(b)-1)/mp_bits_per_limb+1;
cn = (PREC(c)-1)/mp_bits_per_limb+1;
bp = MANT(b); cp = MANT(c);
while (bn && cn) {
if (bp[--bn] != cp[--cn])
return((bp[bn]>cp[cn]) ? s : -s);
}
if (bn) { while (bn) if (bp[--bn]) return(s); }
else if (cn) while (cn) if (cp[--cn]) return(-s);
return 0;
}
/* returns the number of cancelled bits when one subtracts abs(c) from abs(b).
Assumes b>=c, which implies EXP(b)>=EXP(c).
if b=c, returns prec(b).
*/
int
#if __STDC__
mpfr_cmp2 ( mpfr_srcptr b, mpfr_srcptr c )
#else
mpfr_cmp2(b, c)
mpfr_srcptr b;
mpfr_srcptr c;
#endif
{
long int d, bn, cn, k, z;
mp_limb_t *bp, *cp, t, u=0, cc=0;
#ifdef DEBUG
printf("b="); mpfr_print_raw(b); putchar('\n');
printf("c="); mpfr_print_raw(c); putchar('\n');
#endif
if (NOTZERO(c)==0) return (NOTZERO(b)) ? 0 : PREC(b);
d = EXP(b)-EXP(c);
k = 0; /* result can be d or d+1 if d>1, or >= d otherwise */
/* k is the number of identical bits in the high part,
then z is the number of possibly cancelled bits */
#ifdef DEBUG
if (d<0) { printf("assumption EXP(b)<EXP(c) violated\n"); exit(1); }
#endif
bn = (PREC(b)-1)/mp_bits_per_limb;
cn = (PREC(c)-1)/mp_bits_per_limb;
bp = MANT(b); cp = MANT(c);
/* subtract c from b from most significant to less significant limbs,
and first determines first non zero limb difference */
if (d)
{
cc = bp[bn--];
if (d<mp_bits_per_limb)
cc -= cp[cn]>>d;
}
else { /* d=0 */
while (bn>=0 && cn>=0 && (cc=(bp[bn--]-cp[cn--]))==0) {
k+=mp_bits_per_limb;
}
if (cc==0) { /* either bn<0 or cn<0 */
while (bn>=0 && (cc=bp[bn--])==0) k+=mp_bits_per_limb;
}
/* now bn<0 or cc<>0 */
if (cc==0 && bn<0) return(PREC(b));
}
/* the first non-zero limb difference is cc, and the number
of cancelled bits in the upper limbs is k */
count_leading_zeros(u, cc);
k += u;
if (cc != ((mp_limb_t)1<<(mp_bits_per_limb-u-1))) return k;
/* now cc is an exact power of two */
if (cc != 1)
/* We just need to compare the following limbs */
/* until two of them differ. The result is either k or k+1. */
{
/* First flush all the unmatched limbs of b ; they all have to
be 0 in order for the process to go on */
while (bn >= 0)
{
if (cn < 0) { return k; }
t = bp[bn--];
if (d < mp_bits_per_limb)
{
if (d)
{
u = cp[cn--] << (mp_bits_per_limb - d);
if (cn >= 0) u+=(cp[cn]>>d);
}
else u = cp[cn--];
if (t > u || (t == u && cn < 0)) return k;
if (t < u) return k+1;
}
else
if (t) return k; else d -= mp_bits_per_limb;
}
/* bn < 0; if some limb of c is nonzero, return k+1, otherwise return k*/
if (cn>=0 && (cp[cn--] << (mp_bits_per_limb - d))) { return k+1; }
while (cn >= 0)
if (cp[cn--]) return k+1;
return k;
}
/* cc = 1. Too bad. */
z = 0; /* number of possibly cancelled bits - 1 */
/* thus result is either k if low(b) >= low(c)
or k+z+1 if low(b) < low(c) */
if (d > mp_bits_per_limb) { return k; }
while (bn >= 0)
{
if (cn < 0) { return k; }
if (d)
{
u = cp[cn--] << (mp_bits_per_limb - d);
if (cn >= 0) u+=(cp[cn]>>d);
}
else u = cp[cn--];
/* bp[bn--] > cp[cn--] : no borrow possible, k unchanged
bp[bn--] = cp[cn--] : need to consider next limbs
bp[bn--] < cp[cn--] : borrow
*/
if ((cc = bp[bn--]) != u) {
if (cc>u) return k;
else { count_leading_zeros(u, cc-u); return k + 1 + z + u; }
}
else z += mp_bits_per_limb;
}
if (cn >= 0)
count_leading_zeros(cc, ~(cp[cn--] << (mp_bits_per_limb - d)));
else { cc = 0; }
k += cc;
if (cc < d) return k;
while (cn >= 0 && !~cp[cn--]) { z += mp_bits_per_limb; }
if (cn >= 0) { count_leading_zeros(cc, ~cp[cn--]); return (k + z + cc); }
return k; /* We **need** that the nonsignificant limbs of c are set
to zero there */
}
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