static int
sum_tab (mpfr_ptr ret, mpfr_t *tab, unsigned long n, mpfr_rnd_t rnd)
{
mpfr_ptr *tabtmp;
unsigned long i;
int inexact;
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
tabtmp = (mpfr_ptr *) MPFR_TMP_ALLOC(n * sizeof(mpfr_srcptr));
for (i = 0; i < n; i++)
tabtmp[i] = tab[i];
inexact = mpfr_sum (ret, tabtmp, n, rnd);
MPFR_TMP_FREE(marker);
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));
}
/* agm(x,y) is between x and y, so we don't need to save exponent range */
int
mpfr_agm (mpfr_ptr r, mpfr_srcptr op2, mpfr_srcptr op1, mp_rnd_t rnd_mode)
{
int compare, inexact;
mp_size_t s;
mp_prec_t p, q;
mp_limb_t *up, *vp, *tmpp;
mpfr_t u, v, tmp;
unsigned long n; /* number of iterations */
unsigned long err = 0;
MPFR_ZIV_DECL (loop);
MPFR_TMP_DECL(marker);
MPFR_LOG_FUNC (("op2[%#R]=%R op1[%#R]=%R rnd=%d", op2,op2,op1,op1,rnd_mode),
("r[%#R]=%R inexact=%d", r, r, inexact));
/* Deal with special values */
if (MPFR_ARE_SINGULAR (op1, op2))
{
/* If a or b is NaN, the result is NaN */
if (MPFR_IS_NAN(op1) || MPFR_IS_NAN(op2))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
/* now one of a or b is Inf or 0 */
/* If a and b is +Inf, the result is +Inf.
Otherwise if a or b is -Inf or 0, the result is NaN */
else if (MPFR_IS_INF(op1) || MPFR_IS_INF(op2))
{
if (MPFR_IS_STRICTPOS(op1) && MPFR_IS_STRICTPOS(op2))
{
MPFR_SET_INF(r);
MPFR_SET_SAME_SIGN(r, op1);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
}
else /* a and b are neither NaN nor Inf, and one is zero */
{ /* If a or b is 0, the result is +0 since a sqrt is positive */
MPFR_ASSERTD (MPFR_IS_ZERO (op1) || MPFR_IS_ZERO (op2));
MPFR_SET_POS (r);
MPFR_SET_ZERO (r);
MPFR_RET (0); /* exact */
}
}
MPFR_CLEAR_FLAGS (r);
/* If a or b is negative (excluding -Infinity), the result is NaN */
if (MPFR_UNLIKELY(MPFR_IS_NEG(op1) || MPFR_IS_NEG(op2)))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
/* Precision of the following calculus */
q = MPFR_PREC(r);
p = q + MPFR_INT_CEIL_LOG2(q) + 15;
MPFR_ASSERTD (p >= 7); /* see algorithms.tex */
s = (p - 1) / BITS_PER_MP_LIMB + 1;
/* b (op2) and a (op1) are the 2 operands but we want b >= a */
compare = mpfr_cmp (op1, op2);
if (MPFR_UNLIKELY( compare == 0 ))
{
mpfr_set (r, op1, rnd_mode);
MPFR_RET (0); /* exact */
}
else if (compare > 0)
{
mpfr_srcptr t = op1;
op1 = op2;
op2 = t;
}
/* Now b(=op2) >= a (=op1) */
MPFR_TMP_MARK(marker);
/* Main loop */
MPFR_ZIV_INIT (loop, p);
for (;;)
{
mp_prec_t eq;
/* Init temporary vars */
MPFR_TMP_INIT (up, u, p, s);
MPFR_TMP_INIT (vp, v, p, s);
MPFR_TMP_INIT (tmpp, tmp, p, s);
/* Calculus of un and vn */
mpfr_mul (u, op1, op2, GMP_RNDN); /* Faster since PREC(op) < PREC(u) */
mpfr_sqrt (u, u, GMP_RNDN);
mpfr_add (v, op1, op2, GMP_RNDN); /* add with !=prec is still good*/
mpfr_div_2ui (v, v, 1, GMP_RNDN);
n = 1;
while (mpfr_cmp2 (u, v, &eq) != 0 && eq <= p - 2)
{
mpfr_add (tmp, u, v, GMP_RNDN);
mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN);
/* See proof in algorithms.tex */
if (4*eq > p)
{
mpfr_t w;
/* tmp = U(k) */
mpfr_init2 (w, (p + 1) / 2);
mpfr_sub (w, v, u, GMP_RNDN); /* e = V(k-1)-U(k-1) */
mpfr_sqr (w, w, GMP_RNDN); /* e = e^2 */
mpfr_div_2ui (w, w, 4, GMP_RNDN); /* e*= (1/2)^2*1/4 */
mpfr_div (w, w, tmp, GMP_RNDN); /* 1/4*e^2/U(k) */
mpfr_sub (v, tmp, w, GMP_RNDN);
err = MPFR_GET_EXP (tmp) - MPFR_GET_EXP (v); /* 0 or 1 */
mpfr_clear (w);
break;
}
mpfr_mul (u, u, v, GMP_RNDN);
mpfr_sqrt (u, u, GMP_RNDN);
mpfr_swap (v, tmp);
n ++;
}
/* the error on v is bounded by (18n+51) ulps, or twice if there
was an exponent loss in the final subtraction */
err += MPFR_INT_CEIL_LOG2(18 * n + 51); /* 18n+51 should not overflow
since n is about log(p) */
/* we should have n+2 <= 2^(p/4) [see algorithms.tex] */
if (MPFR_LIKELY (MPFR_INT_CEIL_LOG2(n + 2) <= p / 4 &&
MPFR_CAN_ROUND (v, p - err, q, rnd_mode)))
break; /* Stop the loop */
/* Next iteration */
MPFR_ZIV_NEXT (loop, p);
s = (p - 1) / BITS_PER_MP_LIMB + 1;
}
MPFR_ZIV_FREE (loop);
/* Setting of the result */
inexact = mpfr_set (r, v, rnd_mode);
/* Let's clean */
MPFR_TMP_FREE(marker);
return inexact; /* agm(u,v) can be exact for u, v rational only for u=v.
Proof (due to Nicolas Brisebarre): it suffices to consider
u=1 and v<1. Then 1/AGM(1,v) = 2F1(1/2,1/2,1;1-v^2),
and a theorem due to G.V. Chudnovsky states that for x a
non-zero algebraic number with |x|<1, then
2F1(1/2,1/2,1;x) and 2F1(-1/2,1/2,1;x) are algebraically
independent over Q. */
}
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;
}
/* Don't need to save / restore exponent range: the cache does it */
int
mpfr_const_log2_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
{
unsigned long n = MPFR_PREC (x);
mpfr_prec_t w; /* working precision */
unsigned long N;
mpz_t *T, *P, *Q;
mpfr_t t, q;
int inexact;
int ok = 1; /* ensures that the 1st try will give correct rounding */
unsigned long lgN, i;
MPFR_GROUP_DECL(group);
MPFR_TMP_DECL(marker);
MPFR_ZIV_DECL(loop);
MPFR_LOG_FUNC (
("rnd_mode=%d", rnd_mode),
("x[%Pu]=%.*Rg inex=%d", mpfr_get_prec(x), mpfr_log_prec, x, inexact));
if (n < 1253)
w = n + 10; /* ensures correct rounding for the four rounding modes,
together with N = w / 3 + 1 (see below). */
else if (n < 2571)
w = n + 11; /* idem */
else if (n < 3983)
w = n + 12;
else if (n < 4854)
w = n + 13;
else if (n < 26248)
w = n + 14;
else
{
w = n + 15;
ok = 0;
}
MPFR_TMP_MARK(marker);
MPFR_GROUP_INIT_2(group, w, t, q);
MPFR_ZIV_INIT (loop, w);
for (;;)
{
N = w / 3 + 1; /* Warning: do not change that (even increasing N!)
without checking correct rounding in the above
ranges for n. */
/* the following are needed for error analysis (see algorithms.tex) */
MPFR_ASSERTD(w >= 3 && N >= 2);
lgN = MPFR_INT_CEIL_LOG2 (N) + 1;
T = (mpz_t *) MPFR_TMP_ALLOC (3 * lgN * sizeof (mpz_t));
P = T + lgN;
Q = T + 2*lgN;
for (i = 0; i < lgN; i++)
{
mpz_init (T[i]);
mpz_init (P[i]);
mpz_init (Q[i]);
}
S (T, P, Q, 0, N, 0);
mpfr_set_z (t, T[0], MPFR_RNDN);
mpfr_set_z (q, Q[0], MPFR_RNDN);
mpfr_div (t, t, q, MPFR_RNDN);
for (i = 0; i < lgN; i++)
{
mpz_clear (T[i]);
mpz_clear (P[i]);
mpz_clear (Q[i]);
}
if (MPFR_LIKELY (ok != 0
|| mpfr_can_round (t, w - 2, MPFR_RNDN, rnd_mode, n)))
break;
MPFR_ZIV_NEXT (loop, w);
MPFR_GROUP_REPREC_2(group, w, t, q);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (x, t, rnd_mode);
MPFR_GROUP_CLEAR(group);
MPFR_TMP_FREE(marker);
return inexact;
}
int
mpfr_sqr (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
int cc, inexact;
mpfr_exp_t ax;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq;
mp_size_t bn, tn;
MPFR_TMP_DECL(marker);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", b, b, rnd_mode),
("y[%#R]=%R inexact=%d", a, a, inexact));
/* deal with special cases */
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(b)))
{
if (MPFR_IS_NAN(b))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
MPFR_SET_POS (a);
if (MPFR_IS_INF(b))
MPFR_SET_INF(a);
else
( MPFR_ASSERTD(MPFR_IS_ZERO(b)), MPFR_SET_ZERO(a) );
MPFR_RET(0);
}
ax = 2 * MPFR_GET_EXP (b);
bq = MPFR_PREC(b);
MPFR_ASSERTD (2 * bq > bq); /* PREC_MAX is /2 so no integer overflow */
bn = MPFR_LIMB_SIZE(b); /* number of limbs of b */
tn = 1 + (2 * bq - 1) / GMP_NUMB_BITS; /* number of limbs of square,
2*bn or 2*bn-1 */
MPFR_TMP_MARK(marker);
tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) 2 * bn * BYTES_PER_MP_LIMB);
/* Multiplies the mantissa in temporary allocated space */
mpn_sqr_n (tmp, MPFR_MANT(b), bn);
b1 = tmp[2 * bn - 1];
/* now tmp[0]..tmp[2*bn-1] contains the product of both mantissa,
with tmp[2*bn-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 += 2 * bn - tn; /* +0 or +1 */
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, 2 * bq, 0,
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, MPFR_SIGN_POS);
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), then round to zero. */
if (rnd_mode == MPFR_RNDN &&
(ax + (mpfr_exp_t) b1 < __gmpfr_emin || mpfr_powerof2_raw (b)))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN_POS);
}
MPFR_SET_EXP (a, ax2);
MPFR_SET_POS (a);
}
MPFR_RET (inexact);
}
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_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */
cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
/* <= k, thus no int overflow */
MPFR_ASSERTD(tn <= k);
/* Check for no size_t overflow*/
MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
MPFR_TMP_MARK(marker);
tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
/* 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), 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_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);
}
/* 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));
}
/* Compute the first 2^m terms from the hypergeometric series
with x = p / 2^r */
static int
GENERIC (mpfr_ptr y, mpz_srcptr p, long r, int m)
{
unsigned long n,i,k,j,l;
int is_p_one;
mpz_t* P,*S;
#ifdef A
mpz_t *T;
#endif
mpz_t* ptoj;
#ifdef R_IS_RATIONAL
mpz_t* qtoj;
mpfr_t tmp;
#endif
mp_exp_t diff, expo;
mp_prec_t precy = MPFR_PREC(y);
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
MPFR_CLEAR_FLAGS(y);
n = 1UL << m;
P = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
S = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
ptoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */
#ifdef A
T = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
#endif
#ifdef R_IS_RATIONAL
qtoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t));
#endif
for (i = 0 ; i <= m ; i++)
{
mpz_init (P[i]);
mpz_init (S[i]);
mpz_init (ptoj[i]);
#ifdef R_IS_RATIONAL
mpz_init (qtoj[i]);
#endif
#ifdef A
mpz_init (T[i]);
#endif
}
mpz_set (ptoj[0], p);
#ifdef C
# if C2 != 1
mpz_mul_ui (ptoj[0], ptoj[0], C2);
# endif
#endif
is_p_one = mpz_cmp_ui(ptoj[0], 1) == 0;
#ifdef A
# ifdef B
mpz_set_ui (T[0], A1 * B1);
# else
mpz_set_ui (T[0], A1);
# endif
#endif
if (!is_p_one)
for (i = 1 ; i < m ; i++)
mpz_mul (ptoj[i], ptoj[i-1], ptoj[i-1]);
#ifdef R_IS_RATIONAL
mpz_set_si (qtoj[0], r);
for (i = 1 ; i <= m ; i++)
mpz_mul(qtoj[i], qtoj[i-1], qtoj[i-1]);
#endif
mpz_set_ui (P[0], 1);
mpz_set_ui (S[0], 1);
k = 0;
for (i = 1 ; i < n ; i++) {
k++;
#ifdef A
# ifdef B
mpz_set_ui (T[k], (A1 + A2*i)*(B1+B2*i));
# else
mpz_set_ui (T[k], A1 + A2*i);
# endif
#endif
#ifdef C
# ifdef NO_FACTORIAL
mpz_set_ui (P[k], (C1 + C2 * (i-1)));
mpz_set_ui (S[k], 1);
# else
mpz_set_ui (P[k], (i+1) * (C1 + C2 * (i-1)));
mpz_set_ui (S[k], i+1);
# endif
#else
# ifdef NO_FACTORIAL
mpz_set_ui (P[k], 1);
# else
mpz_set_ui (P[k], i+1);
# endif
mpz_set (S[k], P[k]);
#endif
for (j = i+1, l = 0 ; (j & 1) == 0 ; l++, j>>=1, k--) {
if (!is_p_one)
mpz_mul (S[k], S[k], ptoj[l]);
#ifdef A
# ifdef B
# if (A2*B2) != 1
mpz_mul_ui (P[k], P[k], A2*B2);
# endif
# else
# if A2 != 1
mpz_mul_ui (P[k], P[k], A2);
# endif
#endif
mpz_mul (S[k], S[k], T[k-1]);
#endif
mpz_mul (S[k-1], S[k-1], P[k]);
#ifdef R_IS_RATIONAL
mpz_mul (S[k-1], S[k-1], qtoj[l]);
#else
mpz_mul_2exp (S[k-1], S[k-1], r*(1<<l));
#endif
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (P[k-1], P[k-1], P[k]);
#ifdef A
mpz_mul (T[k-1], T[k-1], T[k]);
#endif
}
}
diff = mpz_sizeinbase(S[0],2) - 2*precy;
expo = diff;
if (diff >= 0)
mpz_div_2exp(S[0],S[0],diff);
else
mpz_mul_2exp(S[0],S[0],-diff);
diff = mpz_sizeinbase(P[0],2) - precy;
expo -= diff;
if (diff >=0)
mpz_div_2exp(P[0],P[0],diff);
else
mpz_mul_2exp(P[0],P[0],-diff);
mpz_tdiv_q(S[0], S[0], P[0]);
mpfr_set_z(y, S[0], GMP_RNDD);
MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo);
#ifdef R_IS_RATIONAL
/* exact division */
mpz_div_ui (qtoj[m], qtoj[m], r);
mpfr_init2 (tmp, MPFR_PREC(y));
mpfr_set_z (tmp, qtoj[m] , GMP_RNDD);
mpfr_div (y, y, tmp, GMP_RNDD);
mpfr_clear (tmp);
#else
mpfr_div_2ui(y, y, r*(i-1), GMP_RNDN);
#endif
for (i = 0 ; i <= m ; i++)
{
mpz_clear (P[i]);
mpz_clear (S[i]);
mpz_clear (ptoj[i]);
#ifdef R_IS_RATIONAL
mpz_clear (qtoj[i]);
#endif
#ifdef A
mpz_clear (T[i]);
#endif
}
MPFR_TMP_FREE (marker);
return 0;
}
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);
}