static void
check_round_p (void)
{
mp_limb_t buf[MAX_LIMB_SIZE];
mp_size_t n, i;
mp_prec_t p;
mp_exp_t err;
int r1, r2;
for (n = 2 ; n <= MAX_LIMB_SIZE ; n++)
{
/* avoid mpn_random which leaks memory */
for (i = 0; i < n; i++)
buf[i] = randlimb ();
p = (mp_prec_t) randlimb() % ((n-1) * BITS_PER_MP_LIMB) + MPFR_PREC_MIN;
err = p + randlimb () % BITS_PER_MP_LIMB;
r1 = mpfr_round_p (buf, n, err, p);
r2 = mpfr_can_round_raw (buf, n, MPFR_SIGN_POS, err,
GMP_RNDN, GMP_RNDZ, p);
if (r1 != r2)
{
printf ("mpfr_round_p(%d) != mpfr_can_round(%d)!\n"
"bn = %ld, err0 = %ld, prec = %lu\nbp = ",
r1, r2, n, err, (unsigned long) p);
gmp_printf ("%NX\n", buf, n);
exit (1);
}
}
}
int
mpfr_round_p (mp_limb_t *bp, mp_size_t bn, mpfr_exp_t err0, mpfr_prec_t prec)
{
int i1, i2;
i1 = mpfr_round_p_2 (bp, bn, err0, prec);
i2 = mpfr_can_round_raw (bp, bn, MPFR_SIGN_POS, err0,
MPFR_RNDN, MPFR_RNDZ, prec);
if (i1 != i2)
{
fprintf (stderr, "mpfr_round_p(%d) != mpfr_can_round(%d)!\n"
"bn = %lu, err0 = %ld, prec = %lu\nbp = ", i1, i2,
(unsigned long) bn, (long) err0, (unsigned long) prec);
gmp_fprintf (stderr, "%NX\n", bp, bn);
MPFR_ASSERTN (0);
}
return i1;
}
int
mpfr_div (mpfr_ptr q, mpfr_srcptr u, mpfr_srcptr v, mp_rnd_t rnd_mode)
{
mp_srcptr up, vp, bp;
mp_size_t usize, vsize;
mp_ptr ap, qp, rp;
mp_size_t asize, bsize, qsize, rsize;
mp_exp_t qexp;
mp_size_t err, k;
mp_limb_t tonearest;
int inex, sh, can_round = 0, sign_quotient;
unsigned int cc = 0, rw;
TMP_DECL (marker);
/**************************************************************************
* *
* This part of the code deals with special cases *
* *
**************************************************************************/
if (MPFR_ARE_SINGULAR(u,v))
{
if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v))
{
MPFR_SET_NAN(q);
MPFR_RET_NAN;
}
sign_quotient = MPFR_MULT_SIGN( MPFR_SIGN(u) , MPFR_SIGN(v) );
MPFR_SET_SIGN(q, sign_quotient);
if (MPFR_IS_INF(u))
{
if (MPFR_IS_INF(v))
{
MPFR_SET_NAN(q);
MPFR_RET_NAN;
}
else
{
MPFR_SET_INF(q);
MPFR_RET(0);
}
}
else if (MPFR_IS_INF(v))
{
MPFR_SET_ZERO(q);
MPFR_RET(0);
}
else if (MPFR_IS_ZERO(v))
{
if (MPFR_IS_ZERO(u))
{
MPFR_SET_NAN(q);
MPFR_RET_NAN;
}
else
{
MPFR_SET_INF(q);
MPFR_RET(0);
}
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(u));
MPFR_SET_ZERO(q);
MPFR_RET(0);
}
}
MPFR_CLEAR_FLAGS(q);
/**************************************************************************
* *
* End of the part concerning special values. *
* *
**************************************************************************/
sign_quotient = MPFR_MULT_SIGN( MPFR_SIGN(u) , MPFR_SIGN(v) );
up = MPFR_MANT(u);
vp = MPFR_MANT(v);
MPFR_SET_SIGN(q, sign_quotient);
TMP_MARK (marker);
usize = MPFR_LIMB_SIZE(u);
vsize = MPFR_LIMB_SIZE(v);
/**************************************************************************
* *
* First try to use only part of u, v. If this is not sufficient, *
* use the full u and v, to avoid long computations eg. in the case *
* u = v. *
* *
**************************************************************************/
/* The dividend is a, length asize. The divisor is b, length bsize. */
qsize = (MPFR_PREC(q) + 3) / BITS_PER_MP_LIMB + 1;
/* in case PREC(q)=PREC(v), then vsize=qsize with probability 1-4/b
where b is the number of bits per limb */
if (MPFR_LIKELY(vsize <= qsize))
{
bsize = vsize;
bp = vp;
}
else /* qsize < vsize: take only the qsize high limbs of the divisor */
{
bsize = qsize;
bp = (mp_srcptr) vp + (vsize - qsize);
}
/* we have {bp, bsize} * (1 + errb) = (true divisor)
with 0 <= errb < 2^(-qsize*BITS_PER_MP_LIMB+1) */
asize = bsize + qsize;
ap = (mp_ptr) TMP_ALLOC (asize * BYTES_PER_MP_LIMB);
/* if all arguments have same precision, then asize will be about 2*usize */
if (MPFR_LIKELY(asize > usize))
{
/* copy u into the high limbs of {ap, asize}, and pad with zeroes */
/* FIXME: could we copy only the qsize high limbs of the dividend? */
MPN_COPY (ap + asize - usize, up, usize);
MPN_ZERO (ap, asize - usize);
}
else /* truncate the high asize limbs of u into {ap, asize} */
MPN_COPY (ap, up + usize - asize, asize);
/* we have {ap, asize} = (true dividend) * (1 - erra)
with 0 <= erra < 2^(-asize*BITS_PER_MP_LIMB).
This {ap, asize} / {bp, bsize} =
(true dividend) / (true divisor) * (1 - erra) (1 + errb) */
/* Allocate limbs for quotient and remainder. */
qp = (mp_ptr) TMP_ALLOC ((qsize + 1) * BYTES_PER_MP_LIMB);
rp = (mp_ptr) TMP_ALLOC (bsize * BYTES_PER_MP_LIMB);
rsize = bsize;
mpn_tdiv_qr (qp, rp, 0, ap, asize, bp, bsize);
sh = - (int) qp[qsize];
/* since u and v are normalized, sh is 0 or -1 */
/* we have {qp, qsize + 1} = {ap, asize} / {bp, bsize} (1 - errq)
with 0 <= errq < 2^(-qsize*BITS_PER_MP_LIMB+1+sh)
thus {qp, qsize + 1} =
(true dividend) / (true divisor) * (1 - erra) (1 + errb) (1 - errq).
In fact, since the truncated dividend and {rp, bsize} do not overlap,
we have: {qp, qsize + 1} =
(true dividend) / (true divisor) * (1 - erra') (1 + errb)
where 0 <= erra' < 2^(-qsize*BITS_PER_MP_LIMB+sh) */
/* Estimate number of correct bits. */
err = qsize * BITS_PER_MP_LIMB;
/* We want to check if rounding is possible, but without normalizing
because we might have to divide again if rounding is impossible, or
if the result might be exact. We have however to mimic normalization */
/*
To detect asap if the result is inexact, so as to avoid doing the
division completely, we perform the following check :
- if rnd_mode != GMP_RNDN, and the result is exact, we are unable
to round simultaneously to zero and to infinity ;
- if rnd_mode == GMP_RNDN, and if we can round to zero with one extra
bit of precision, we can decide rounding. Hence in that case, check
as in the case of GMP_RNDN, with one extra bit. Note that in the case
of close to even rounding we shall do the division completely, but
this is necessary anyway : we need to know whether this is really
even rounding or not.
*/
if (MPFR_UNLIKELY(asize < usize || bsize < vsize))
{
{
mp_rnd_t rnd_mode1, rnd_mode2;
mp_exp_t tmp_exp;
mp_prec_t tmp_prec;
if (bsize < vsize)
err -= 2; /* divisor is truncated */
#if 0 /* commented this out since the truncation of the dividend is already
taken into account in {rp, bsize}, which does not overlap with the
neglected part of the dividend */
else if (asize < usize)
err --; /* dividend is truncated */
#endif
if (MPFR_LIKELY(rnd_mode == GMP_RNDN))
{
rnd_mode1 = GMP_RNDZ;
rnd_mode2 = MPFR_IS_POS_SIGN(sign_quotient) ? GMP_RNDU : GMP_RNDD;
sh++;
}
else
{
rnd_mode1 = rnd_mode;
switch (rnd_mode)
{
case GMP_RNDU:
rnd_mode2 = GMP_RNDD; break;
case GMP_RNDD:
rnd_mode2 = GMP_RNDU; break;
default:
rnd_mode2 = MPFR_IS_POS_SIGN(sign_quotient) ?
GMP_RNDU : GMP_RNDD;
break;
}
}
tmp_exp = err + sh + BITS_PER_MP_LIMB;
tmp_prec = MPFR_PREC(q) + sh + BITS_PER_MP_LIMB;
can_round =
mpfr_can_round_raw (qp, qsize + 1, sign_quotient, tmp_exp,
GMP_RNDN, rnd_mode1, tmp_prec)
& mpfr_can_round_raw (qp, qsize + 1, sign_quotient, tmp_exp,
GMP_RNDN, rnd_mode2, tmp_prec);
/* restore original value of sh, i.e. sh = - qp[qsize] */
sh -= (rnd_mode == GMP_RNDN);
}
