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/* mpfr_round_raw_generic, mpfr_round_raw2, mpfr_round_raw, mpfr_round_prec,
mpfr_can_round, mpfr_can_round_raw -- various rounding functions
Copyright 1999, 2000, 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 "mpfr.h"
#include "mpfr-impl.h"
#if (BITS_PER_MP_LIMB & (BITS_PER_MP_LIMB - 1))
#error "BITS_PER_MP_LIMB must be a power of 2"
#endif
/*
If flag = 0, puts in y the value of xp (with precision xprec and
sign 1 if negative=0, -1 otherwise) rounded to precision yprec and
direction rnd_mode. Supposes x is not zero nor NaN nor +/- Infinity
(i.e. *xp != 0). If inexp != NULL, computes the inexact flag of the
rounding.
In case of even rounding when rnd = GMP_RNDN, returns 2 or -2.
If flag = 1, just returns whether one should add 1 or not for rounding.
*/
int
mpfr_round_raw_generic(mp_limb_t *yp, mp_limb_t *xp, mp_prec_t xprec,
int neg, mp_prec_t yprec, mp_rnd_t rnd_mode,
int *inexp, int flag)
{
mp_size_t xsize, nw;
mp_limb_t himask, lomask;
int rw, carry = 0;
xsize = (xprec-1)/BITS_PER_MP_LIMB + 1;
nw = yprec / BITS_PER_MP_LIMB;
rw = yprec & (BITS_PER_MP_LIMB - 1);
if (flag && !inexp && (rnd_mode==GMP_RNDZ || xprec <= yprec
|| (rnd_mode==GMP_RNDU && neg)
|| (rnd_mode==GMP_RNDD && neg==0)))
return 0;
if (rw)
{
nw++;
lomask = ((MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw)) - MP_LIMB_T_ONE);
himask = ~lomask;
}
else
{
lomask = -1;
himask = -1;
}
MPFR_ASSERTN(nw >= 1);
if (xprec <= yprec)
{ /* No rounding is necessary. */
/* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */
MPFR_ASSERTN(nw >= xsize);
if (inexp)
*inexp = 0;
if (flag)
return 0;
MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
MPN_ZERO(yp, nw - xsize);
}
else
{
mp_limb_t sb;
if ((rnd_mode == GMP_RNDU && neg) ||
(rnd_mode == GMP_RNDD && !neg))
rnd_mode = GMP_RNDZ;
if (inexp || rnd_mode != GMP_RNDZ)
{
mp_size_t k;
k = xsize - nw;
if (!rw)
k--;
MPFR_ASSERTN(k >= 0);
sb = xp[k] & lomask; /* First non-significant bits */
if (rnd_mode == GMP_RNDN)
{
mp_limb_t rbmask = MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw - 1);
if (sb & rbmask) /* rounding bit */
sb &= ~rbmask; /* it is 1, clear it */
else
rnd_mode = GMP_RNDZ; /* it is 0, behave like rounding to 0 */
}
while (sb == 0 && k > 0)
sb = xp[--k];
if (rnd_mode == GMP_RNDN)
{ /* rounding to nearest, with rounding bit = 1 */
if (sb == 0) /* Even rounding. */
{
sb = xp[xsize - nw] & (himask ^ (himask << 1));
if (inexp)
*inexp = ((neg != 0) ^ (sb != 0))
? MPFR_EVEN_INEX : -MPFR_EVEN_INEX;
}
else /* sb != 0 */
{
if (inexp)
*inexp = (neg == 0) ? 1 : -1;
}
}
else if (inexp)
*inexp = sb == 0 ? 0
: (((neg != 0) ^ (rnd_mode != GMP_RNDZ)) ? 1 : -1);
}
else
sb = 0;
if (flag)
return sb != 0 && rnd_mode != GMP_RNDZ;
if (sb != 0 && rnd_mode != GMP_RNDZ)
carry = mpn_add_1(yp, xp + xsize - nw, nw,
rw ? MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw) : 1);
else
MPN_COPY_INCR(yp, xp + xsize - nw, nw);
yp[0] &= himask;
}
return carry;
}
int
mpfr_round_prec (mpfr_ptr x, mp_rnd_t rnd_mode, mp_prec_t prec)
{
mp_limb_t *tmp, *xp;
int carry, inexact;
mp_prec_t nw;
TMP_DECL(marker);
MPFR_ASSERTN(prec >= MPFR_PREC_MIN && prec <= MPFR_PREC_MAX);
nw = 1 + (prec - 1) / BITS_PER_MP_LIMB; /* needed allocated limbs */
/* check if x has enough allocated space for the mantissa */
if (nw > MPFR_ABSSIZE(x))
{
MPFR_MANT(x) = (mp_ptr) (*__gmp_reallocate_func)
(MPFR_MANT(x), (size_t) MPFR_ABSSIZE(x) * BYTES_PER_MP_LIMB,
(size_t) nw * BYTES_PER_MP_LIMB);
MPFR_SET_ABSSIZE(x, nw); /* new number of allocated limbs */
}
if (MPFR_IS_NAN(x))
MPFR_RET_NAN;
if (MPFR_IS_INF(x))
return 0; /* infinity is exact */
/* x is a real number */
TMP_MARK(marker);
tmp = TMP_ALLOC (nw * BYTES_PER_MP_LIMB);
xp = MPFR_MANT(x);
carry = mpfr_round_raw (tmp, xp, MPFR_PREC(x), MPFR_SIGN(x) < 0,
prec, rnd_mode, &inexact);
MPFR_PREC(x) = prec;
if (carry)
{
mp_exp_t exp = MPFR_EXP(x);
if (exp == __mpfr_emax)
(void) mpfr_set_overflow(x, rnd_mode, MPFR_SIGN(x));
else
{
MPFR_EXP(x)++;
xp[nw - 1] = MP_LIMB_T_HIGHBIT;
if (nw - 1 > 0)
MPN_ZERO(xp, nw - 1);
}
}
else
MPN_COPY(xp, tmp, nw);
TMP_FREE(marker);
return inexact;
}
/* assumption: BITS_PER_MP_LIMB is a power of 2 */
/* assuming b is an approximation of x in direction rnd1
with error at most 2^(MPFR_EXP(b)-err), returns 1 if one is
able to round exactly x to precision prec with direction rnd2,
and 0 otherwise.
Side effects: none.
*/
int
mpfr_can_round (mpfr_ptr b, mp_exp_t err, mp_rnd_t rnd1,
mp_rnd_t rnd2, mp_prec_t prec)
{
return MPFR_IS_ZERO(b) ? 0 : /* we cannot round if b=0 */
mpfr_can_round_raw (MPFR_MANT(b),
(MPFR_PREC(b) - 1)/BITS_PER_MP_LIMB + 1,
MPFR_SIGN(b), err, rnd1, rnd2, prec);
}
int
mpfr_can_round_raw (mp_limb_t *bp, mp_size_t bn, int neg, mp_exp_t err0,
mp_rnd_t rnd1, mp_rnd_t rnd2, mp_prec_t prec)
{
mp_prec_t err;
mp_size_t k, k1, tn;
int s, s1;
mp_limb_t cc, cc2;
mp_limb_t *tmp;
TMP_DECL(marker);
if (err0 < 0 || (mp_exp_unsigned_t) err0 <= prec)
return 0; /* can't round */
neg = neg <= 0;
/* if the error is smaller than ulp(b), then anyway it will propagate
up to ulp(b) */
err = ((mp_exp_unsigned_t) err0 > (mp_prec_t) bn * BITS_PER_MP_LIMB) ?
(mp_prec_t) bn * BITS_PER_MP_LIMB : err0;
/* warning: if k = m*BITS_PER_MP_LIMB, consider limb m-1 and not m */
k = (err - 1) / BITS_PER_MP_LIMB;
s = err % BITS_PER_MP_LIMB;
if (s)
s = BITS_PER_MP_LIMB - s;
/* the error corresponds to bit s in limb k, the most significant limb
being limb 0 */
k1 = (prec - 1) / BITS_PER_MP_LIMB;
s1 = prec % BITS_PER_MP_LIMB;
if (s1)
s1 = BITS_PER_MP_LIMB - s1;
/* the last significant bit is bit s1 in limb k1 */
/* don't need to consider the k1 most significant limbs */
k -= k1;
bn -= k1;
prec -= (mp_prec_t) k1 * BITS_PER_MP_LIMB;
/* if when adding or subtracting (1 << s) in bp[bn-1-k], it does not
change bp[bn-1] >> s1, then we can round */
if (rnd1 == GMP_RNDU)
if (neg)
rnd1 = GMP_RNDZ;
if (rnd1 == GMP_RNDD)
rnd1 = neg ? GMP_RNDU : GMP_RNDZ;
/* in the sequel, RNDU = towards infinity, RNDZ = towards zero */
TMP_MARK(marker);
tn = bn;
k++; /* since we work with k+1 everywhere */
tmp = TMP_ALLOC(tn * BYTES_PER_MP_LIMB);
if (bn > k)
MPN_COPY (tmp, bp, bn - k);
if (rnd1 != GMP_RNDN)
{ /* GMP_RNDZ or GMP_RNDU */
cc = (bp[bn - 1] >> s1) & 1;
cc ^= mpfr_round_raw2(bp, bn, neg, rnd2, prec);
/* now round b +/- 2^(MPFR_EXP(b)-err) */
cc2 = rnd1 == GMP_RNDZ ?
mpn_add_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s) :
mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
}
else
{ /* GMP_RNDN */
/* first round b+2^(MPFR_EXP(b)-err) */
cc = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */
cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
/* now round b-2^(MPFR_EXP(b)-err) */
cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
}
if (cc2 && cc)
{
TMP_FREE(marker);
return 0;
}
cc2 = (tmp[bn - 1] >> s1) & 1;
cc2 ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
TMP_FREE(marker);
return cc == cc2;
}
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