int
mpfr_mul_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode)
{
mp_limb_t *yp;
mp_size_t xn;
int cnt, inexact;
MPFR_TMP_DECL (marker);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (u != 0)
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* infinity is exact */
}
else /* 0 * infinity */
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
}
else if (MPFR_UNLIKELY (u <= 1))
{
if (u < 1)
{
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
else
return mpfr_set (y, x, rnd_mode);
}
else if (MPFR_UNLIKELY (IS_POW2 (u)))
return mpfr_mul_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode);
yp = MPFR_MANT (y);
xn = MPFR_LIMB_SIZE (x);
MPFR_ASSERTD (xn < MP_SIZE_T_MAX);
MPFR_TMP_MARK(marker);
yp = MPFR_TMP_LIMBS_ALLOC (xn + 1);
MPFR_ASSERTN (u == (mp_limb_t) u);
yp[xn] = mpn_mul_1 (yp, MPFR_MANT (x), xn, u);
/* x * u is stored in yp[xn], ..., yp[0] */
/* since the case u=1 was treated above, we have u >= 2, thus
yp[xn] >= 1 since x was msb-normalized */
MPFR_ASSERTD (yp[xn] != 0);
if (MPFR_LIKELY (MPFR_LIMB_MSB (yp[xn]) == 0))
{
count_leading_zeros (cnt, yp[xn]);
mpn_lshift (yp, yp, xn + 1, cnt);
}
else
{
cnt = 0;
}
/* now yp[xn], ..., yp[0] is msb-normalized too, and has at most
PREC(x) + (GMP_NUMB_BITS - cnt) non-zero bits */
MPFR_RNDRAW (inexact, y, yp, (mpfr_prec_t) (xn + 1) * GMP_NUMB_BITS,
rnd_mode, MPFR_SIGN (x), cnt -- );
MPFR_TMP_FREE (marker);
cnt = GMP_NUMB_BITS - cnt;
if (MPFR_UNLIKELY (__gmpfr_emax < MPFR_EMAX_MIN + cnt
|| MPFR_GET_EXP (x) > __gmpfr_emax - cnt))
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(x));
MPFR_SET_EXP (y, MPFR_GET_EXP (x) + cnt);
MPFR_SET_SAME_SIGN (y, x);
return inexact;
}
int
mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t bx,cx;
mpfr_uexp_t d;
mpfr_prec_t p, sh, cnt;
mp_size_t n;
mp_limb_t *ap, *bp, *cp;
mp_limb_t limb;
int inexact;
mp_limb_t bcp,bcp1; /* Cp and C'p+1 */
mp_limb_t bbcp = (mp_limb_t) -1, bbcp1 = (mp_limb_t) -1; /* Cp+1 and C'p+2,
gcc claims that they might be used uninitialized. We fill them with invalid
values, which should produce a failure if so. See README.dev file. */
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c));
MPFR_ASSERTD(MPFR_IS_PURE_FP(b));
MPFR_ASSERTD(MPFR_IS_PURE_FP(c));
/* Read prec and num of limbs */
p = MPFR_PREC (b);
n = MPFR_PREC2LIMBS (p);
/* Fast cmp of |b| and |c|*/
bx = MPFR_GET_EXP (b);
cx = MPFR_GET_EXP (c);
if (MPFR_UNLIKELY(bx == cx))
{
mp_size_t k = n - 1;
/* Check mantissa since exponent are equals */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
while (k>=0 && MPFR_UNLIKELY(bp[k] == cp[k]))
k--;
if (MPFR_UNLIKELY(k < 0))
/* b == c ! */
{
/* Return exact number 0 */
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET(0);
}
else if (bp[k] > cp[k])
goto BGreater;
else
{
MPFR_ASSERTD(bp[k]<cp[k]);
goto CGreater;
}
}
else if (MPFR_UNLIKELY(bx < cx))
{
/* Swap b and c and set sign */
mpfr_srcptr t;
mpfr_exp_t tx;
CGreater:
MPFR_SET_OPPOSITE_SIGN(a,b);
t = b; b = c; c = t;
tx = bx; bx = cx; cx = tx;
}
else
{
/* b > c */
BGreater:
MPFR_SET_SAME_SIGN(a,b);
}
/* Now b > c */
MPFR_ASSERTD(bx >= cx);
d = (mpfr_uexp_t) bx - cx;
DEBUG (printf ("New with diff=%lu\n", (unsigned long) d));
if (MPFR_UNLIKELY(d <= 1))
{
if (MPFR_LIKELY(d < 1))
{
/* <-- b -->
<-- c --> : exact sub */
ap = MPFR_MANT(a);
mpn_sub_n (ap, MPFR_MANT(b), MPFR_MANT(c), n);
/* Normalize */
ExactNormalize:
limb = ap[n-1];
if (MPFR_LIKELY(limb))
{
/* First limb is not zero. */
count_leading_zeros(cnt, limb);
/* cnt could be == 0 <= SubD1Lose */
if (MPFR_LIKELY(cnt))
{
mpn_lshift(ap, ap, n, cnt); /* Normalize number */
bx -= cnt; /* Update final expo */
}
/* Last limb should be ok */
MPFR_ASSERTD(!(ap[0] & MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
else
{
/* First limb is zero */
mp_size_t k = n-1, len;
/* Find the first limb not equal to zero.
FIXME:It is assume it exists (since |b| > |c| and same prec)*/
do
{
MPFR_ASSERTD( k > 0 );
limb = ap[--k];
}
while (limb == 0);
MPFR_ASSERTD(limb != 0);
count_leading_zeros(cnt, limb);
k++;
len = n - k; /* Number of last limb */
MPFR_ASSERTD(k >= 0);
if (MPFR_LIKELY(cnt))
mpn_lshift(ap+len, ap, k, cnt); /* Normalize the High Limb*/
else
{
/* Must use DECR since src and dest may overlap & dest>=src*/
MPN_COPY_DECR(ap+len, ap, k);
}
MPN_ZERO(ap, len); /* Zeroing the last limbs */
bx -= cnt + len*GMP_NUMB_BITS; /* Update Expo */
/* Last limb should be ok */
MPFR_ASSERTD(!(ap[len]&MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
/* Check expo underflow */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
MPFR_TMP_FREE(marker);
/* inexact=0 */
DEBUG( printf("(D==0 Underflow)\n") );
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(/*inexact >= 0 &&*/ mpfr_powerof2_raw (a))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
/* No rounding is necessary since the result is exact */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
MPFR_TMP_FREE(marker);
return 0;
}
else /* if (d == 1) */
{
/* | <-- b -->
| <-- c --> */
mp_limb_t c0, mask;
mp_size_t k;
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* If we lose at least one bit, compute 2*b-c (Exact)
* else compute b-c/2 */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
k = n-1;
limb = bp[k] - cp[k]/2;
if (limb > MPFR_LIMB_HIGHBIT)
{
/* We can't lose precision: compute b-c/2 */
/* Shift c in the allocated temporary block */
SubD1NoLose:
c0 = cp[0] & (MPFR_LIMB_ONE<<sh);
cp = MPFR_TMP_LIMBS_ALLOC (n);
mpn_rshift(cp, MPFR_MANT(c), n, 1);
if (MPFR_LIKELY(c0 == 0))
{
/* Result is exact: no need of rounding! */
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
MPFR_SET_EXP(a, bx); /* No expo overflow! */
/* No truncate or normalize is needed */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
/* No rounding is necessary since the result is exact */
MPFR_TMP_FREE(marker);
return 0;
}
ap = MPFR_MANT(a);
mask = ~MPFR_LIMB_MASK(sh);
cp[0] &= mask; /* Delete last bit of c */
mpn_sub_n (ap, bp, cp, n);
MPFR_SET_EXP(a, bx); /* No expo overflow! */
MPFR_ASSERTD( !(ap[0] & ~mask) ); /* Check last bits */
/* No normalize is needed */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
/* Rounding is necessary since c0 = 1*/
/* Cp =-1 and C'p+1=0 */
bcp = 1; bcp1 = 0;
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
/* Even Rule apply: Check Ap-1 */
if (MPFR_LIKELY( (ap[0] & (MPFR_LIMB_ONE<<sh)) == 0) )
goto truncate;
else
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else
goto truncate;
}
else if (MPFR_LIKELY(limb < MPFR_LIMB_HIGHBIT))
{
/* We lose at least one bit of prec */
/* Calcul of 2*b-c (Exact) */
/* Shift b in the allocated temporary block */
SubD1Lose:
bp = MPFR_TMP_LIMBS_ALLOC (n);
mpn_lshift (bp, MPFR_MANT(b), n, 1);
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
bx--;
goto ExactNormalize;
}
else
{
/* Case: limb = 100000000000 */
/* Check while b[k] == c'[k] (C' is C shifted by 1) */
/* If b[k]<c'[k] => We lose at least one bit*/
/* If b[k]>c'[k] => We don't lose any bit */
/* If k==-1 => We don't lose any bit
AND the result is 100000000000 0000000000 00000000000 */
mp_limb_t carry;
do {
carry = cp[k]&MPFR_LIMB_ONE;
k--;
} while (k>=0 &&
bp[k]==(carry=cp[k]/2+(carry<<(GMP_NUMB_BITS-1))));
if (MPFR_UNLIKELY(k<0))
{
/*If carry then (sh==0 and Virtual c'[-1] > Virtual b[-1]) */
if (MPFR_UNLIKELY(carry)) /* carry = cp[0]&MPFR_LIMB_ONE */
{
/* FIXME: Can be faster? */
MPFR_ASSERTD(sh == 0);
goto SubD1Lose;
}
/* Result is a power of 2 */
ap = MPFR_MANT (a);
MPN_ZERO (ap, n);
ap[n-1] = MPFR_LIMB_HIGHBIT;
MPFR_SET_EXP (a, bx); /* No expo overflow! */
/* No Normalize is needed*/
/* No Rounding is needed */
MPFR_TMP_FREE (marker);
return 0;
}
/* carry = cp[k]/2+(cp[k-1]&1)<<(GMP_NUMB_BITS-1) = c'[k]*/
else if (bp[k] > carry)
goto SubD1NoLose;
else
{
MPFR_ASSERTD(bp[k]<carry);
goto SubD1Lose;
}
}
}
}
else if (MPFR_UNLIKELY(d >= p))
{
ap = MPFR_MANT(a);
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* We can't set A before since we use cp for rounding... */
/* Perform rounding: check if a=b or a=b-ulp(b) */
if (MPFR_UNLIKELY(d == p))
{
/* cp == -1 and c'p+1 = ? */
bcp = 1;
/* We need Cp+1 later for a very improbable case. */
bbcp = (MPFR_MANT(c)[n-1] & (MPFR_LIMB_ONE<<(GMP_NUMB_BITS-2)));
/* We need also C'p+1 for an even more unprobable case... */
if (MPFR_LIKELY( bbcp ))
bcp1 = 1;
else
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && cp[k]==0);
bcp1 = (k>=0);
}
else
bcp1 = 1;
}
DEBUG( printf("(D=P) Cp=-1 Cp+1=%d C'p+1=%d \n", bbcp!=0, bcp1!=0) );
bp = MPFR_MANT (b);
/* Even if src and dest overlap, it is ok using MPN_COPY */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_UNLIKELY( bcp && bcp1==0 ))
/* Cp=-1 and C'p+1=0: Even rule Apply! */
/* Check Ap-1 = Bp-1 */
if ((bp[0] & (MPFR_LIMB_ONE<<sh)) == 0)
{
MPN_COPY(ap, bp, n);
goto truncate;
}
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
{
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
else
{
MPN_COPY(ap, bp, n);
goto truncate;
}
}
else
{
/* Cp=0, Cp+1=-1 if d==p+1, C'p+1=-1 */
bcp = 0; bbcp = (d==p+1); bcp1 = 1;
DEBUG( printf("(D>P) Cp=%d Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0) );
/* Need to compute C'p+2 if d==p+1 and if rnd_mode=NEAREST
(Because of a very improbable case) */
if (MPFR_UNLIKELY(d==p+1 && rnd_mode==MPFR_RNDN))
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && cp[k]==0);
bbcp1 = (k>=0);
}
else
bbcp1 = 1;
DEBUG( printf("(D>P) C'p+2=%d\n", bbcp1!=0) );
}
/* Copy mantissa B in A */
MPN_COPY(ap, MPFR_MANT(b), n);
/* Round */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
goto truncate;
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else /* rnd_mode = AWAY */
goto truncate;
}
}
else
{
mpfr_uexp_t dm;
mp_size_t m;
mp_limb_t mask;
/* General case: 2 <= d < p */
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift c in temporary allocated place */
dm = d % GMP_NUMB_BITS;
m = d / GMP_NUMB_BITS;
if (MPFR_UNLIKELY(dm == 0))
{
/* dm = 0 and m > 0: Just copy */
MPFR_ASSERTD(m!=0);
MPN_COPY(cp, MPFR_MANT(c)+m, n-m);
MPN_ZERO(cp+n-m, m);
}
else if (MPFR_LIKELY(m == 0))
{
/* dm >=2 and m == 0: just shift */
MPFR_ASSERTD(dm >= 2);
mpn_rshift(cp, MPFR_MANT(c), n, dm);
}
else
{
/* dm > 0 and m > 0: shift and zero */
mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm);
MPN_ZERO(cp+n-m, m);
}
DEBUG( mpfr_print_mant_binary("Before", MPFR_MANT(c), p) );
DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) );
DEBUG( mpfr_print_mant_binary("After ", cp, p) );
/* Compute bcp=Cp and bcp1=C'p+1 */
if (MPFR_LIKELY(sh))
{
/* Try to compute them from C' rather than C (FIXME: Faster?) */
bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ;
if (MPFR_LIKELY( cp[0] & MPFR_LIMB_MASK(sh-1) ))
bcp1 = 1;
else
{
/* We can't compute C'p+1 from C'. Compute it from C */
/* Start from bit x=p-d+sh in mantissa C
(+sh since we have already looked sh bits in C'!) */
mpfr_prec_t x = p-d+sh-1;
if (MPFR_LIKELY(x>p))
/* We are already looked at all the bits of c, so C'p+1 = 0*/
bcp1 = 0;
else
{
mp_limb_t *tp = MPFR_MANT(c);
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
DEBUG (printf ("(First) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx,
(unsigned long) sx));
/* Looks at the last bits of limb kx (if sx=0 does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/
/*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx >= 0);
}
}
}
}
else
{
/* Compute Cp and C'p+1 from C with sh=0 */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=p-d in mantissa C */
mpfr_prec_t x = p-d;
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p >= d);
bcp = (tp[kx] & (MPFR_LIMB_ONE<<sx));
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx>=0);
}
}
DEBUG( printf("sh=%lu Cp=%d C'p+1=%d\n", sh, bcp!=0, bcp1!=0) );
/* Check if we can lose a bit, and if so compute Cp+1 and C'p+2 */
bp = MPFR_MANT(b);
if (MPFR_UNLIKELY((bp[n-1]-cp[n-1]) <= MPFR_LIMB_HIGHBIT))
{
/* We can lose a bit so we precompute Cp+1 and C'p+2 */
/* Test for trivial case: since C'p+1=0, Cp+1=0 and C'p+2 =0 */
if (MPFR_LIKELY(bcp1 == 0))
{
bbcp = 0;
bbcp1 = 0;
}
else /* bcp1 != 0 */
{
/* We can lose a bit:
compute Cp+1 and C'p+2 from mantissa C */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=(p+1)-d in mantissa C */
mpfr_prec_t x = p+1-d;
mp_size_t kx = n-1 - (x/GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p > d);
DEBUG (printf ("(pre) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx,
(unsigned long) sx));
bbcp = (tp[kx] & (MPFR_LIMB_ONE<<sx)) ;
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
/* If Cp+1=0, since C'p+1!=0, C'p+2=1 ! */
if (MPFR_LIKELY(bbcp==0 || (tp[kx]&MPFR_LIMB_MASK(sx))))
bbcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bbcp1 = (kx>=0);
DEBUG (printf ("(Pre) Scan done for %ld\n", (long) kx));
}
} /*End of Bcp1 != 0*/
DEBUG( printf("(Pre) Cp+1=%d C'p+2=%d\n", bbcp!=0, bbcp1!=0) );
} /* End of "can lose a bit" */
/* Clean shifted C' */
mask = ~MPFR_LIMB_MASK (sh);
cp[0] &= mask;
/* Subtract the mantissa c from b in a */
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
DEBUG( mpfr_print_mant_binary("Sub= ", ap, p) );
/* Normalize: we lose at max one bit*/
if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
{
/* High bit is not set and we have to fix it! */
/* Ap >= 010000xxx001 */
mpn_lshift(ap, ap, n, 1);
/* Ap >= 100000xxx010 */
if (MPFR_UNLIKELY(bcp!=0)) /* Check if Cp = -1 */
/* Since Cp == -1, we have to substract one more */
{
mpn_sub_1(ap, ap, n, MPFR_LIMB_ONE<<sh);
MPFR_ASSERTD(MPFR_LIMB_MSB(ap[n-1]) != 0);
}
/* Ap >= 10000xxx001 */
/* Final exponent -1 since we have shifted the mantissa */
bx--;
/* Update bcp and bcp1 */
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
MPFR_ASSERTN(bbcp1 != (mp_limb_t) -1);
bcp = bbcp;
bcp1 = bbcp1;
/* We dont't have anymore a valid Cp+1!
But since Ap >= 100000xxx001, the final sub can't unnormalize!*/
}
MPFR_ASSERTD( !(ap[0] & ~mask) );
/* Rounding */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_LIKELY(bcp==0))
goto truncate;
else if ((bcp1) || ((ap[0] & (MPFR_LIMB_ONE<<sh)) != 0))
goto sub_one_ulp;
else
goto truncate;
}
/* Update rounding mode */
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ && (MPFR_LIKELY(bcp || bcp1)))
goto sub_one_ulp;
goto truncate;
}
MPFR_RET_NEVER_GO_HERE ();
/* Sub one ulp to the result */
sub_one_ulp:
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
/* Result should be smaller than exact value: inexact=-1 */
inexact = -1;
/* Check normalisation */
if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
{
/* ap was a power of 2, and we lose a bit */
/* Now it is 0111111111111111111[00000 */
mpn_lshift(ap, ap, n, 1);
bx--;
/* And the lost bit x depends on Cp+1, and Cp */
/* Compute Cp+1 if it isn't already compute (ie d==1) */
/* FIXME: Is this case possible? */
if (MPFR_UNLIKELY(d == 1))
bbcp = 0;
DEBUG( printf("(SubOneUlp)Cp=%d, Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0));
/* Compute the last bit (Since we have shifted the mantissa)
we need one more bit!*/
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
if ( (rnd_mode == MPFR_RNDZ && bcp==0)
|| (rnd_mode==MPFR_RNDN && bbcp==0)
|| (bcp && bcp1==0) ) /*Exact result*/
{
ap[0] |= MPFR_LIMB_ONE<<sh;
if (rnd_mode == MPFR_RNDN)
inexact = 1;
DEBUG( printf("(SubOneUlp) Last bit set\n") );
}
/* Result could be exact if C'p+1 = 0 and rnd == Zero
since we have had one more bit to the result */
/* Fixme: rnd_mode == MPFR_RNDZ needed ? */
if (bcp1==0 && rnd_mode==MPFR_RNDZ)
{
DEBUG( printf("(SubOneUlp) Exact result\n") );
inexact = 0;
}
}
goto end_of_sub;
truncate:
/* Check if the result is an exact power of 2: 100000000000
in which cases, we could have to do sub_one_ulp due to some nasty reasons:
If Result is a Power of 2:
+ If rnd = AWAY,
| If Cp=-1 and C'p+1 = 0, SubOneUlp and the result is EXACT.
If Cp=-1 and C'p+1 =-1, SubOneUlp and the result is above.
Otherwise truncate
+ If rnd = NEAREST,
If Cp= 0 and Cp+1 =-1 and C'p+2=-1, SubOneUlp and the result is above
If cp=-1 and C'p+1 = 0, SubOneUlp and the result is exact.
Otherwise truncate.
X bit should always be set if SubOneUlp*/
if (MPFR_UNLIKELY(ap[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && ap[k]==0);
if (MPFR_UNLIKELY(k<0))
{
/* It is a power of 2! */
/* Compute Cp+1 if it isn't already compute (ie d==1) */
/* FIXME: Is this case possible? */
if (d == 1)
bbcp=0;
DEBUG( printf("(Truncate) Cp=%d, Cp+1=%d C'p+1=%d C'p+2=%d\n", \
bcp!=0, bbcp!=0, bcp1!=0, bbcp1!=0) );
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
MPFR_ASSERTN((rnd_mode != MPFR_RNDN) || (bcp != 0) || (bbcp == 0) || (bbcp1 != (mp_limb_t) -1));
if (((rnd_mode != MPFR_RNDZ) && bcp)
||
((rnd_mode == MPFR_RNDN) && (bcp == 0) && (bbcp) && (bbcp1)))
{
DEBUG( printf("(Truncate) Do sub\n") );
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
mpn_lshift(ap, ap, n, 1);
ap[0] |= MPFR_LIMB_ONE<<sh;
bx--;
/* FIXME: Explain why it works (or why not)... */
inexact = (bcp1 == 0) ? 0 : (rnd_mode==MPFR_RNDN) ? -1 : 1;
goto end_of_sub;
}
}
}
/* Calcul of Inexact flag.*/
inexact = MPFR_LIKELY(bcp || bcp1) ? 1 : 0;
end_of_sub:
/* Update Expo */
/* FIXME: Is this test really useful?
If d==0 : Exact case. This is never called.
if 1 < d < p : bx=MPFR_EXP(b) or MPFR_EXP(b)-1 > MPFR_EXP(c) > emin
if d == 1 : bx=MPFR_EXP(b). If we could lose any bits, the exact
normalisation is called.
if d >= p : bx=MPFR_EXP(b) >= MPFR_EXP(c) + p > emin
After SubOneUlp, we could have one bit less.
if 1 < d < p : bx >= MPFR_EXP(b)-2 >= MPFR_EXP(c) > emin
if d == 1 : bx >= MPFR_EXP(b)-1 = MPFR_EXP(c) > emin.
if d >= p : bx >= MPFR_EXP(b)-1 > emin since p>=2.
*/
MPFR_ASSERTD( bx >= __gmpfr_emin);
/*
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
DEBUG( printf("(Final Underflow)\n") );
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(inexact >= 0 && mpfr_powerof2_raw (a))))
rnd_mode = MPFR_RNDZ;
MPFR_TMP_FREE(marker);
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
*/
MPFR_SET_EXP (a, bx);
MPFR_TMP_FREE(marker);
MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
int
mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
mp_size_t rsize; /* number of limbs of r (plus 1 if exact limb multiple) */
mp_size_t rrsize;
mp_size_t usize; /* number of limbs of u */
mp_size_t tsize; /* number of limbs of the sqrtrem remainder */
mp_size_t k;
mp_size_t l;
mpfr_limb_ptr rp, rp0;
mpfr_limb_ptr up;
mpfr_limb_ptr sp;
mp_limb_t sticky0; /* truncated part of input */
mp_limb_t sticky1; /* truncated part of rp[0] */
mp_limb_t sticky;
int odd_exp;
int sh; /* number of extra bits in rp[0] */
int inexact; /* return ternary flag */
mpfr_exp_t expr;
MPFR_TMP_DECL(marker);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (u), mpfr_log_prec, u, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (r), mpfr_log_prec, r, inexact));
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u)))
{
if (MPFR_IS_NAN(u))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else if (MPFR_IS_ZERO(u))
{
/* 0+ or 0- */
MPFR_SET_SAME_SIGN(r, u);
MPFR_SET_ZERO(r);
MPFR_RET(0); /* zero is exact */
}
else
{
MPFR_ASSERTD(MPFR_IS_INF(u));
/* sqrt(-Inf) = NAN */
if (MPFR_IS_NEG(u))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
MPFR_SET_POS(r);
MPFR_SET_INF(r);
MPFR_RET(0);
}
}
if (MPFR_UNLIKELY(MPFR_IS_NEG(u)))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
MPFR_SET_POS(r);
MPFR_TMP_MARK (marker);
MPFR_UNSIGNED_MINUS_MODULO(sh,MPFR_PREC(r));
if (sh == 0 && rnd_mode == MPFR_RNDN)
sh = GMP_NUMB_BITS; /* ugly case */
rsize = MPFR_LIMB_SIZE(r) + (sh == GMP_NUMB_BITS);
/* rsize is the number of limbs of r + 1 if exact limb multiple and rounding
to nearest, this is the number of wanted limbs for the square root */
rrsize = rsize + rsize;
usize = MPFR_LIMB_SIZE(u); /* number of limbs of u */
rp0 = MPFR_MANT(r);
rp = (sh < GMP_NUMB_BITS) ? rp0 : MPFR_TMP_LIMBS_ALLOC (rsize);
up = MPFR_MANT(u);
sticky0 = MPFR_LIMB_ZERO; /* truncated part of input */
sticky1 = MPFR_LIMB_ZERO; /* truncated part of rp[0] */
odd_exp = (unsigned int) MPFR_GET_EXP (u) & 1;
inexact = -1; /* return ternary flag */
sp = MPFR_TMP_LIMBS_ALLOC (rrsize);
/* copy the most significant limbs of u to {sp, rrsize} */
if (MPFR_LIKELY(usize <= rrsize)) /* in case r and u have the same precision,
we have indeed rrsize = 2 * usize */
{
k = rrsize - usize;
if (MPFR_LIKELY(k))
MPN_ZERO (sp, k);
if (odd_exp)
{
if (MPFR_LIKELY(k))
sp[k - 1] = mpn_rshift (sp + k, up, usize, 1);
else
sticky0 = mpn_rshift (sp, up, usize, 1);
}
else
MPN_COPY (sp + rrsize - usize, up, usize);
}
else /* usize > rrsize: truncate the input */
{
k = usize - rrsize;
if (odd_exp)
sticky0 = mpn_rshift (sp, up + k, rrsize, 1);
else
MPN_COPY (sp, up + k, rrsize);
l = k;
while (sticky0 == MPFR_LIMB_ZERO && l != 0)
sticky0 = up[--l];
}
/* sticky0 is non-zero iff the truncated part of the input is non-zero */
/* mpn_rootrem with NULL 2nd argument is faster than mpn_sqrtrem, thus use
it if available and if the user asked to use GMP internal functions */
#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_ROOTREM)
tsize = __gmpn_rootrem (rp, NULL, sp, rrsize, 2);
#else
tsize = mpn_sqrtrem (rp, NULL, sp, rrsize);
#endif
/* a return value of zero in mpn_sqrtrem indicates a perfect square */
sticky = sticky0 || tsize != 0;
/* truncate low bits of rp[0] */
sticky1 = rp[0] & ((sh < GMP_NUMB_BITS) ? MPFR_LIMB_MASK(sh)
: ~MPFR_LIMB_ZERO);
rp[0] -= sticky1;
sticky = sticky || sticky1;
expr = (MPFR_GET_EXP(u) + odd_exp) / 2; /* exact */
if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD || sticky == MPFR_LIMB_ZERO)
{
inexact = (sticky == MPFR_LIMB_ZERO) ? 0 : -1;
goto truncate;
}
else if (rnd_mode == MPFR_RNDN)
{
/* if sh < GMP_NUMB_BITS, the round bit is bit (sh-1) of sticky1
and the sticky bit is formed by the low sh-1 bits from
sticky1, together with the sqrtrem remainder and sticky0. */
if (sh < GMP_NUMB_BITS)
{
if (sticky1 & (MPFR_LIMB_ONE << (sh - 1)))
{ /* round bit is set */
if (sticky1 == (MPFR_LIMB_ONE << (sh - 1)) && tsize == 0
&& sticky0 == 0)
goto even_rule;
else
goto add_one_ulp;
}
else /* round bit is zero */
goto truncate; /* with the default inexact=-1 */
}
else /* sh = GMP_NUMB_BITS: the round bit is the most significant bit
of rp[0], and the remaining GMP_NUMB_BITS-1 bits contribute to
the sticky bit */
{
if (sticky1 & MPFR_LIMB_HIGHBIT)
{ /* round bit is set */
if (sticky1 == MPFR_LIMB_HIGHBIT && tsize == 0 && sticky0 == 0)
goto even_rule;
else
goto add_one_ulp;
}
else /* round bit is zero */
goto truncate; /* with the default inexact=-1 */
}
}
else /* rnd_mode=GMP_RDNU, necessarily sticky <> 0, thus add 1 ulp */
goto add_one_ulp;
even_rule: /* has to set inexact */
if (sh < GMP_NUMB_BITS)
inexact = (rp[0] & (MPFR_LIMB_ONE << sh)) ? 1 : -1;
else
inexact = (rp[1] & MPFR_LIMB_ONE) ? 1 : -1;
if (inexact == -1)
goto truncate;
/* else go through add_one_ulp */
add_one_ulp:
inexact = 1; /* always here */
if (sh == GMP_NUMB_BITS)
{
rp ++;
rsize --;
sh = 0;
}
if (mpn_add_1 (rp0, rp, rsize, MPFR_LIMB_ONE << sh))
{
expr ++;
rp[rsize - 1] = MPFR_LIMB_HIGHBIT;
}
goto end;
truncate: /* inexact = 0 or -1 */
if (sh == GMP_NUMB_BITS)
MPN_COPY (rp0, rp + 1, rsize - 1);
end:
MPFR_ASSERTN (expr >= MPFR_EMIN_MIN && expr <= MPFR_EMAX_MAX);
MPFR_EXP (r) = expr;
MPFR_TMP_FREE(marker);
return mpfr_check_range (r, inexact, rnd_mode);
}
/* for k=n, we use a division with remainder (mpn_divrem),
which computes the exact quotient */
return mpn_divrem (qp, 0, np, 2 * n, dp, n);
MPFR_ASSERTD ((n+4)/2 <= k && k < n); /* bounds from [1] */
MPFR_TMP_MARK (marker);
l = n - k;
/* first divide the most significant 2k limbs from N by the most significant
k limbs of D */
qh = mpn_divrem (qp + l, 0, np + 2 * l, 2 * k, dp + l, k); /* exact */
/* it remains {np,2l+k} = {np,n+l} as remainder */
/* now we have to subtract high(Q1)*D0 where Q1=qh*B^k+{qp+l,k} and
D0={dp,l} */
tp = MPFR_TMP_LIMBS_ALLOC (2 * l);
mpfr_mulhigh_n (tp, qp + k, dp, l);
/* we are only interested in the upper l limbs from {tp,2l} */
cy = mpn_sub_n (np + n, np + n, tp + l, l);
if (qh)
cy += mpn_sub_n (np + n, np + n, dp, l);
while (cy > 0) /* Q1 was too large: subtract 1 to Q1 and add D to np+l */
{
qh -= mpn_sub_1 (qp + l, qp + l, k, MPFR_LIMB_ONE);
cy -= mpn_add_n (np + l, np + l, dp, n);
}
/* now it remains {np,n+l} to divide by D */
cy = mpfr_divhigh_n (qp, np + k, dp + k, l);
qh += mpn_add_1 (qp + l, qp + l, k, cy);
MPFR_TMP_FREE(marker);
static int
mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
/* Old implementation */
int sign_product, cc, inexact;
mpfr_exp_t ax;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq, cq;
mp_size_t bn, cn, tn, k;
MPFR_TMP_DECL(marker);
/* deal with special cases */
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
if (MPFR_IS_INF(b))
{
if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
{
MPFR_SET_SIGN(a,sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
if (MPFR_NOTZERO(b))
{
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 * 0 is exact */
}
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
bq = MPFR_PREC (b);
cq = MPFR_PREC (c);
MPFR_ASSERTN ((mpfr_uprec_t) bq + cq <= MPFR_PREC_MAX);
bn = MPFR_PREC2LIMBS (bq); /* number of limbs of b */
cn = MPFR_PREC2LIMBS (cq); /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = MPFR_PREC2LIMBS (bq + cq);
/* <= k, thus no int overflow */
MPFR_ASSERTD(tn <= k);
/* Check for no size_t overflow*/
MPFR_ASSERTD((size_t) k <= ((size_t) -1) / MPFR_BYTES_PER_MP_LIMB);
MPFR_TMP_MARK(marker);
tmp = MPFR_TMP_LIMBS_ALLOC (k);
/* multiplies two mantissa in temporary allocated space */
b1 = (MPFR_LIKELY(bn >= cn)) ?
mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
: mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);
/* now tmp[0]..tmp[k-1] contains the product of both mantissa,
with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */
b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */
/* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
tmp += k - tn;
if (MPFR_UNLIKELY(b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq,
MPFR_IS_NEG_SIGN(sign_product),
MPFR_PREC (a), rnd_mode, &inexact);
/* cc = 1 ==> result is a power of two */
if (MPFR_UNLIKELY(cc))
MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;
MPFR_TMP_FREE(marker);
{
mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
return mpfr_overflow (a, rnd_mode, sign_product);
if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
{
/* In the rounding to the nearest mode, if the exponent of the exact
result (i.e. before rounding, i.e. without taking cc into account)
is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
both arguments are powers of 2) in absolute value, then round to
zero. */
if (rnd_mode == MPFR_RNDN &&
(ax + (mpfr_exp_t) b1 < __gmpfr_emin ||
(mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, sign_product);
}
MPFR_SET_EXP (a, ax2);
MPFR_SET_SIGN(a, sign_product);
}
MPFR_RET (inexact);
}
int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
int sign, inexact;
mpfr_exp_t ax, ax2;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq, cq;
mp_size_t bn, cn, tn, k, threshold;
MPFR_TMP_DECL (marker);
MPFR_LOG_FUNC
(("b[%Pu]=%.*Rg c[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (b), mpfr_log_prec, b,
mpfr_get_prec (c), mpfr_log_prec, c, rnd_mode),
("a[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (a), mpfr_log_prec, a, inexact));
/* deal with special cases */
if (MPFR_ARE_SINGULAR (b, c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_IS_INF (b))
{
if (!MPFR_IS_ZERO (c))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET (0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN (a, sign);
MPFR_SET_ZERO (a);
MPFR_RET (0);
}
}
sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
/* Note: the exponent of the exact result will be e = bx + cx + ec with
ec in {-1,0,1} and the following assumes that e is representable. */
/* FIXME: Useful since we do an exponent check after ?
* It is useful iff the precision is big, there is an overflow
* and we are doing further mults...*/
#ifdef HUGE
if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1))
return mpfr_overflow (a, rnd_mode, sign);
if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2))
return mpfr_underflow (a, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
sign);
#endif
bq = MPFR_PREC (b);
cq = MPFR_PREC (c);
MPFR_ASSERTN ((mpfr_uprec_t) bq + cq <= MPFR_PREC_MAX);
bn = MPFR_PREC2LIMBS (bq); /* number of limbs of b */
cn = MPFR_PREC2LIMBS (cq); /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = MPFR_PREC2LIMBS (bq + cq);
MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */
/* Check for no size_t overflow*/
MPFR_ASSERTD ((size_t) k <= ((size_t) -1) / MPFR_BYTES_PER_MP_LIMB);
MPFR_TMP_MARK (marker);
tmp = MPFR_TMP_LIMBS_ALLOC (k);
/* multiplies two mantissa in temporary allocated space */
if (MPFR_UNLIKELY (bn < cn))
{
mpfr_srcptr z = b;
mp_size_t zn = bn;
b = c;
bn = cn;
c = z;
cn = zn;
}
MPFR_ASSERTD (bn >= cn);
if (MPFR_LIKELY (bn <= 2))
{
if (bn == 1)
{
/* 1 limb * 1 limb */
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
b1 = tmp[1];
}
else if (MPFR_UNLIKELY (cn == 1))
{
/* 2 limbs * 1 limb */
mp_limb_t t;
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
umul_ppmm (tmp[2], t, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t);
b1 = tmp[2];
}
else
{
/* 2 limbs * 2 limbs */
mp_limb_t t1, t2, t3;
/* First 2 limbs * 1 limb */
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
umul_ppmm (tmp[2], t1, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t1);
/* Second, the other 2 limbs * 1 limb product */
umul_ppmm (t1, t2, MPFR_MANT (b)[0], MPFR_MANT (c)[1]);
umul_ppmm (tmp[3], t3, MPFR_MANT (b)[1], MPFR_MANT (c)[1]);
add_ssaaaa (tmp[3], t1, tmp[3], t1, 0, t3);
/* Sum those two partial products */
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], t1, t2);
tmp[3] += (tmp[2] < t1);
b1 = tmp[3];
}
b1 >>= (GMP_NUMB_BITS - 1);
tmp += k - tn;
if (MPFR_UNLIKELY (b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
}
else
/* Mulders' mulhigh. This code can also be used via mpfr_sqr,
hence the tests b != c. */
if (MPFR_UNLIKELY (bn > (threshold = b != c ?
/* compute sign(b) * (|b| + |c|)
Returns 0 iff result is exact,
a negative value when the result is less than the exact value,
a positive value otherwise. */
int
mpfr_add1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_uexp_t d;
mpfr_prec_t p;
unsigned int sh;
mp_size_t n;
mp_limb_t *ap, *cp;
mpfr_exp_t bx;
mp_limb_t limb;
int inexact;
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c));
MPFR_ASSERTD(MPFR_IS_PURE_FP(b));
MPFR_ASSERTD(MPFR_IS_PURE_FP(c));
MPFR_ASSERTD(MPFR_GET_EXP(b) >= MPFR_GET_EXP(c));
/* Read prec and num of limbs */
p = MPFR_PREC(b);
n = MPFR_PREC2LIMBS (p);
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
bx = MPFR_GET_EXP(b);
d = (mpfr_uexp_t) (bx - MPFR_GET_EXP(c));
DEBUG (printf ("New add1sp with diff=%lu\n", (unsigned long) d));
if (MPFR_UNLIKELY(d == 0))
{
/* d==0 */
DEBUG( mpfr_print_mant_binary("C= ", MPFR_MANT(c), p) );
DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) );
bx++; /* exp + 1 */
ap = MPFR_MANT(a);
limb = mpn_add_n(ap, MPFR_MANT(b), MPFR_MANT(c), n);
DEBUG( mpfr_print_mant_binary("A= ", ap, p) );
MPFR_ASSERTD(limb != 0); /* There must be a carry */
limb = ap[0]; /* Get LSB (In fact, LSW) */
mpn_rshift(ap, ap, n, 1); /* Shift mantissa A */
ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */
ap[0] &= ~MPFR_LIMB_MASK(sh); /* Clear LSB bit */
if (MPFR_LIKELY((limb&(MPFR_LIMB_ONE<<sh)) == 0)) /* Check exact case */
{ inexact = 0; goto set_exponent; }
/* Zero: Truncate
Nearest: Even Rule => truncate or add 1
Away: Add 1 */
if (MPFR_LIKELY(rnd_mode==MPFR_RNDN))
{
if (MPFR_LIKELY((ap[0]&(MPFR_LIMB_ONE<<sh))==0))
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b));
if (rnd_mode==MPFR_RNDZ)
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
else if (MPFR_UNLIKELY (d >= p))
{
if (MPFR_LIKELY (d > p))
{
/* d > p : Copy B in A */
/* Away: Add 1
Nearest: Trunc
Zero: Trunc */
if (MPFR_LIKELY (rnd_mode==MPFR_RNDN
|| MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b))))
{
copy_set_exponent:
ap = MPFR_MANT (a);
MPN_COPY (ap, MPFR_MANT(b), n);
inexact = -1;
goto set_exponent;
}
else
{
copy_add_one_ulp:
ap = MPFR_MANT(a);
MPN_COPY (ap, MPFR_MANT(b), n);
goto add_one_ulp;
}
}
else
{
/* d==p : Copy B in A */
/* Away: Add 1
Nearest: Even Rule if C is a power of 2, else Add 1
Zero: Trunc */
if (MPFR_LIKELY(rnd_mode==MPFR_RNDN))
{
/* Check if C was a power of 2 */
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && cp[k]==0);
if (MPFR_UNLIKELY(k<0))
/* Power of 2: Even rule */
if ((MPFR_MANT (b)[0]&(MPFR_LIMB_ONE<<sh))==0)
goto copy_set_exponent;
}
/* Not a Power of 2 */
goto copy_add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b)))
goto copy_set_exponent;
else
goto copy_add_one_ulp;
}
}
else
{
mp_limb_t mask;
mp_limb_t bcp, bcp1; /* Cp and C'p+1 */
/* General case: 1 <= d < p */
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift c in temporary allocated place */
{
mpfr_uexp_t dm;
mp_size_t m;
dm = d % GMP_NUMB_BITS;
m = d / GMP_NUMB_BITS;
if (MPFR_UNLIKELY(dm == 0))
{
/* dm = 0 and m > 0: Just copy */
MPFR_ASSERTD(m!=0);
MPN_COPY(cp, MPFR_MANT(c)+m, n-m);
MPN_ZERO(cp+n-m, m);
}
else if (MPFR_LIKELY(m == 0))
{
/* dm >=1 and m == 0: just shift */
MPFR_ASSERTD(dm >= 1);
mpn_rshift(cp, MPFR_MANT(c), n, dm);
}
else
{
/* dm > 0 and m > 0: shift and zero */
mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm);
MPN_ZERO(cp+n-m, m);
}
}
DEBUG( mpfr_print_mant_binary("Before", MPFR_MANT(c), p) );
DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) );
DEBUG( mpfr_print_mant_binary("After ", cp, p) );
/* Compute bcp=Cp and bcp1=C'p+1 */
if (MPFR_LIKELY (sh > 0))
{
/* Try to compute them from C' rather than C */
bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ;
if (MPFR_LIKELY(cp[0]&MPFR_LIMB_MASK(sh-1)))
bcp1 = 1;
else
{
/* We can't compute C'p+1 from C'. Compute it from C */
/* Start from bit x=p-d+sh in mantissa C
(+sh since we have already looked sh bits in C'!) */
mpfr_prec_t x = p-d+sh-1;
if (MPFR_LIKELY(x>p))
/* We are already looked at all the bits of c, so C'p+1 = 0*/
bcp1 = 0;
else
{
mp_limb_t *tp = MPFR_MANT(c);
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
DEBUG (printf ("(First) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx,
(unsigned long) sx));
/* Looks at the last bits of limb kx (if sx=0 does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/
/*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx >= 0);
}
}
}
}
else /* sh == 0 */
{
/* Compute Cp and C'p+1 from C with sh=0 */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=p-d in mantissa C */
mpfr_prec_t x = p-d;
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p >= d);
bcp = tp[kx] & (MPFR_LIMB_ONE<<sx);
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
if (tp[kx]&MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx>=0);
}
}
DEBUG (printf("sh=%u Cp=%lu C'p+1=%lu\n", sh,
(unsigned long) bcp, (unsigned long) bcp1));
/* Clean shifted C' */
mask = ~MPFR_LIMB_MASK(sh);
cp[0] &= mask;
/* Add the mantissa c from b in a */
ap = MPFR_MANT(a);
limb = mpn_add_n (ap, MPFR_MANT(b), cp, n);
DEBUG( mpfr_print_mant_binary("Add= ", ap, p) );
/* Check for overflow */
if (MPFR_UNLIKELY (limb))
{
limb = ap[0] & (MPFR_LIMB_ONE<<sh); /* Get LSB */
mpn_rshift (ap, ap, n, 1); /* Shift mantissa*/
bx++; /* Fix exponent */
ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */
ap[0] &= mask; /* Clear LSB bit */
bcp1 |= bcp; /* Recompute C'p+1 */
bcp = limb; /* Recompute Cp */
DEBUG (printf ("(Overflow) Cp=%lu C'p+1=%lu\n",
(unsigned long) bcp, (unsigned long) bcp1));
DEBUG (mpfr_print_mant_binary ("Add= ", ap, p));
}
/* Round:
Zero: Truncate but could be exact.
Away: Add 1 if Cp or C'p+1 !=0
Nearest: Truncate but could be exact if Cp==0
Add 1 if C'p+1 !=0,
Even rule else */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_LIKELY(bcp == 0))
{ inexact = MPFR_LIKELY(bcp1) ? -1 : 0; goto set_exponent; }
else if (MPFR_UNLIKELY(bcp1==0) && (ap[0]&(MPFR_LIMB_ONE<<sh))==0)
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b));
if (rnd_mode == MPFR_RNDZ)
{
inexact = MPFR_LIKELY(bcp || bcp1) ? -1 : 0;
goto set_exponent;
}
else
{
if (MPFR_UNLIKELY(bcp==0 && bcp1==0))
{ inexact = 0; goto set_exponent; }
else
goto add_one_ulp;
}
}
MPFR_ASSERTN(0);
add_one_ulp:
/* add one unit in last place to a */
DEBUG( printf("AddOneUlp\n") );
if (MPFR_UNLIKELY( mpn_add_1(ap, ap, n, MPFR_LIMB_ONE<<sh) ))
{
/* Case 100000x0 = 0x1111x1 + 1*/
DEBUG( printf("Pow of 2\n") );
bx++;
ap[n-1] = MPFR_LIMB_HIGHBIT;
}
inexact = 1;
set_exponent:
if (MPFR_UNLIKELY(bx > __gmpfr_emax)) /* Check for overflow */
{
DEBUG( printf("Overflow\n") );
MPFR_TMP_FREE(marker);
MPFR_SET_SAME_SIGN(a,b);
return mpfr_overflow(a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
MPFR_SET_SAME_SIGN(a,b);
MPFR_TMP_FREE(marker);
MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
/* returns 0 if result exact, non-zero otherwise */
int
mpfr_div_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode)
{
long i;
int sh;
mp_size_t xn, yn, dif;
mp_limb_t *xp, *yp, *tmp, c, d;
mpfr_exp_t exp;
int inexact, middle = 1, nexttoinf;
MPFR_TMP_DECL(marker);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg u=%lu rnd=%d",
mpfr_get_prec(x), mpfr_log_prec, x, u, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec(y), mpfr_log_prec, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(x));
if (u == 0) /* 0/0 is NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET(0);
}
}
}
else if (MPFR_UNLIKELY (u <= 1))
{
if (u < 1)
{
/* x/0 is Inf since x != 0*/
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
mpfr_set_divby0 ();
MPFR_RET (0);
}
else /* y = x/1 = x */
return mpfr_set (y, x, rnd_mode);
}
else if (MPFR_UNLIKELY (IS_POW2 (u)))
return mpfr_div_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode);
MPFR_SET_SAME_SIGN (y, x);
MPFR_TMP_MARK (marker);
xn = MPFR_LIMB_SIZE (x);
yn = MPFR_LIMB_SIZE (y);
xp = MPFR_MANT (x);
yp = MPFR_MANT (y);
exp = MPFR_GET_EXP (x);
dif = yn + 1 - xn;
/* we need to store yn+1 = xn + dif limbs of the quotient */
/* don't use tmp=yp since the mpn_lshift call below requires yp >= tmp+1 */
tmp = MPFR_TMP_LIMBS_ALLOC (yn + 1);
c = (mp_limb_t) u;
MPFR_ASSERTN (u == c);
if (dif >= 0)
c = mpn_divrem_1 (tmp, dif, xp, xn, c); /* used all the dividend */
else /* dif < 0 i.e. xn > yn, don't use the (-dif) low limbs from x */
c = mpn_divrem_1 (tmp, 0, xp - dif, yn + 1, c);
inexact = (c != 0);
/* First pass in estimating next bit of the quotient, in case of RNDN *
* In case we just have the right number of bits (postpone this ?), *
* we need to check whether the remainder is more or less than half *
* the divisor. The test must be performed with a subtraction, so as *
* to prevent carries. */
if (MPFR_LIKELY (rnd_mode == MPFR_RNDN))
{
if (c < (mp_limb_t) u - c) /* We have u > c */
middle = -1;
else if (c > (mp_limb_t) u - c)
middle = 1;
else
middle = 0; /* exactly in the middle */
}
/* If we believe that we are right in the middle or exact, we should check
that we did not neglect any word of x (division large / 1 -> small). */
for (i=0; ((inexact == 0) || (middle == 0)) && (i < -dif); i++)
if (xp[i])
inexact = middle = 1; /* larger than middle */
/*
If the high limb of the result is 0 (xp[xn-1] < u), remove it.
Otherwise, compute the left shift to be performed to normalize.
In the latter case, we discard some low bits computed. They
contain information useful for the rounding, hence the updating
of middle and inexact.
*/
if (tmp[yn] == 0)
{
MPN_COPY(yp, tmp, yn);
exp -= GMP_NUMB_BITS;
}
else
{
int shlz;
count_leading_zeros (shlz, tmp[yn]);
/* shift left to normalize */
if (MPFR_LIKELY (shlz != 0))
{
mp_limb_t w = tmp[0] << shlz;
mpn_lshift (yp, tmp + 1, yn, shlz);
yp[0] += tmp[0] >> (GMP_NUMB_BITS - shlz);
if (w > (MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1)))
{ middle = 1; }
else if (w < (MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1)))
{ middle = -1; }
else
{ middle = (c != 0); }
inexact = inexact || (w != 0);
exp -= shlz;
}
else
{ /* this happens only if u == 1 and xp[xn-1] >=
int
mpfr_set_f (mpfr_ptr y, mpf_srcptr x, mpfr_rnd_t rnd_mode)
{
mp_limb_t *my, *mx, *tmp;
unsigned long cnt, sx, sy;
int inexact, carry = 0;
MPFR_TMP_DECL(marker);
sx = ABS(SIZ(x)); /* number of limbs of the mantissa of x */
if (sx == 0) /* x is zero */
{
MPFR_SET_ZERO(y);
MPFR_SET_POS(y);
return 0; /* 0 is exact */
}
if (SIZ(x) * MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(y)) < 0)
MPFR_CHANGE_SIGN (y);
sy = MPFR_LIMB_SIZE (y);
my = MPFR_MANT(y);
mx = PTR(x);
count_leading_zeros(cnt, mx[sx - 1]);
if (sy <= sx) /* we may have to round even when sy = sx */
{
unsigned long xprec = sx * GMP_NUMB_BITS;
MPFR_TMP_MARK(marker);
tmp = MPFR_TMP_LIMBS_ALLOC (sx);
if (cnt)
mpn_lshift (tmp, mx, sx, cnt);
else
/* FIXME: we may avoid the copy here, and directly call mpfr_round_raw
on mx instead of tmp */
MPN_COPY (tmp, mx, sx);
carry = mpfr_round_raw (my, tmp, xprec, (SIZ(x) < 0), MPFR_PREC(y),
rnd_mode, &inexact);
if (MPFR_UNLIKELY(carry)) /* result is a power of two */
my[sy - 1] = MPFR_LIMB_HIGHBIT;
MPFR_TMP_FREE(marker);
}
else
{
if (cnt)
mpn_lshift (my + sy - sx, mx, sx, cnt);
else
MPN_COPY (my + sy - sx, mx, sx);
MPN_ZERO(my, sy - sx);
/* no rounding necessary, since y has a larger mantissa */
inexact = 0;
}
/* warning: EXP(x) * GMP_NUMB_BITS may exceed the maximal exponent */
if (EXP(x) > 1 + (__gmpfr_emax - 1) / GMP_NUMB_BITS)
{
/* EXP(x) >= 2 + floor((__gmpfr_emax-1)/GMP_NUMB_BITS)
EXP(x) >= 2 + (__gmpfr_emax - GMP_NUMB_BITS) / GMP_NUMB_BITS
>= 1 + __gmpfr_emax / GMP_NUMB_BITS
EXP(x) * GMP_NUMB_BITS >= __gmpfr_emax + GMP_NUMB_BITS
Since 0 <= cnt <= GMP_NUMB_BITS-1, and 0 <= carry <= 1,
we have then EXP(x) * GMP_NUMB_BITS - cnt + carry > __gmpfr_emax */
return mpfr_overflow (y, rnd_mode, MPFR_SIGN (y));
}
else
{
/* Do not use MPFR_SET_EXP as the exponent may be out of range. */
MPFR_EXP (y) = EXP (x) * GMP_NUMB_BITS - (mpfr_exp_t) cnt + carry;
}
return mpfr_check_range (y, inexact, rnd_mode);
}