static void
special (void)
{
mpfr_t x;
int inex;
mpfr_init (x);
mpfr_set_nan (x);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (x) && inex == 0);
mpfr_set_inf (x, -1);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (x) && inex == 0);
mpfr_set_inf (x, 1);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (x) && mpfr_sgn (x) > 0 && inex == 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS (x) && inex == 0);
mpfr_neg (x, x, MPFR_RNDN);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG (x) && inex == 0);
mpfr_set_si (x, -1, MPFR_RNDN);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (x) && mpfr_sgn (x) < 0 && inex == 0);
mpfr_set_si (x, -2, MPFR_RNDN);
inex = test_log1p (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (x) && inex == 0);
mpfr_clear (x);
}
static void
special (void)
{
mpfr_t x, y, z;
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
mpfr_set_nan (x);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_hypot (z, x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (z));
mpfr_hypot (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (z));
mpfr_hypot (z, y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (z));
mpfr_set_inf (x, 1);
mpfr_set_inf (y, -1);
mpfr_hypot (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && mpfr_sgn (z) > 0);
mpfr_set_inf (x, -1);
mpfr_set_nan (y);
mpfr_hypot (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && mpfr_sgn (z) > 0);
mpfr_set_nan (x);
mpfr_set_inf (y, -1);
mpfr_hypot (z, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && mpfr_sgn (z) > 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_special (void)
{
mpfr_t x, y;
mpfr_exp_t emin;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_sqr (y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (y));
mpfr_set_inf (x, 1);
mpfr_sqr (y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (y) && mpfr_sgn (y) > 0);
mpfr_set_inf (x, -1);
mpfr_sqr (y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (y) && mpfr_sgn (y) > 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_sqr (y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_zero_p (y));
emin = mpfr_get_emin ();
mpfr_set_emin (0);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
MPFR_ASSERTN (!mpfr_zero_p (x));
mpfr_sqr (y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_zero_p (y));
mpfr_set_emin (emin);
mpfr_clear (y);
mpfr_clear (x);
}
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));
}
/* (y, z) <- (sin(x), cos(x)), return value is 0 iff both results are exact
ie, iff x = 0 */
int
mpfr_sin_cos (mpfr_ptr y, mpfr_ptr z, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_prec_t prec, m;
int neg, reduce;
mpfr_t c, xr;
mpfr_srcptr xx;
mpfr_exp_t err, expx;
int inexy, inexz;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ASSERTN (y != z);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
MPFR_SET_NAN (y);
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
/* y = 0, thus exact, but z is inexact in case of underflow
or overflow */
inexy = 0; /* y is exact */
inexz = mpfr_set_ui (z, 1, rnd_mode);
return INEX(inexy,inexz);
}
}
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("sin[%Pu]=%.*Rg cos[%Pu]=%.*Rg", mpfr_get_prec(y), mpfr_log_prec, y,
mpfr_get_prec (z), mpfr_log_prec, z));
MPFR_SAVE_EXPO_MARK (expo);
prec = MAX (MPFR_PREC (y), MPFR_PREC (z));
m = prec + MPFR_INT_CEIL_LOG2 (prec) + 13;
expx = MPFR_GET_EXP (x);
/* When x is close to 0, say 2^(-k), then there is a cancellation of about
2k bits in 1-cos(x)^2. FIXME: in that case, it would be more efficient
to compute sin(x) directly. VL: This is partly done by using
MPFR_FAST_COMPUTE_IF_SMALL_INPUT from the mpfr_sin and mpfr_cos
functions. Moreover, any overflow on m is avoided. */
if (expx < 0)
{
/* Warning: in case y = x, and the first call to
MPFR_FAST_COMPUTE_IF_SMALL_INPUT succeeds but the second fails,
we will have clobbered the original value of x.
The workaround is to first compute z = cos(x) in that case, since
y and z are different. */
if (y != x)
/* y and x differ, thus we can safely try to compute y first */
{
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (
y, x, -2 * expx, 2, 0, rnd_mode,
{ inexy = _inexact;
goto small_input; });
static void
special (void)
{
mpfr_t x;
int i;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_inf (x, -1);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "-0.1001011001");
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_si_2exp (x, -159, -8) == 0);
/* corner case */
mpfr_set_prec (x, 2);
mpfr_set_str_binary (x, "1E-6");
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (x, 1, -6) == 0);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) > 0);
MPFR_ASSERTN (mpfr_overflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDD);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDU);
MPFR_ASSERTN (!MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear (x);
}
static void
check_parse (void)
{
mpfr_t x;
char *s;
int res;
mpfr_init (x);
/* Invalid data */
mpfr_set_si (x, -1, MPFR_RNDN);
res = mpfr_strtofr (x, " invalid", NULL, 10, MPFR_RNDN);
if (MPFR_NOTZERO (x) || MPFR_IS_NEG (x))
{
printf ("Failed parsing ' invalid' (1)\n X=");
mpfr_dump (x);
exit (1);
}
MPFR_ASSERTN (res == 0);
mpfr_set_si (x, -1, MPFR_RNDN);
res = mpfr_strtofr (x, " invalid", &s, 0, MPFR_RNDN);
if (MPFR_NOTZERO (x) || MPFR_IS_NEG (x) || strcmp (s, " invalid"))
{
printf ("Failed parsing ' invalid' (2)\n S=%s\n X=", s);
mpfr_dump (x);
exit (1);
}
MPFR_ASSERTN (res == 0);
/* Check if it stops correctly */
mpfr_strtofr (x, "15*x", &s, 10, MPFR_RNDN);
if (mpfr_cmp_ui (x, 15) || strcmp (s, "*x"))
{
printf ("Failed parsing '15*x'\n S=%s\n X=", s);
mpfr_dump (x);
exit (1);
}
/* Check for leading spaces */
mpfr_strtofr (x, " 1.5E-10 *x^2", &s, 10, MPFR_RNDN);
if (mpfr_cmp_str1 (x, "1.5E-10") || strcmp (s, " *x^2"))
{
printf ("Failed parsing '1.5E-10*x^2'\n S=%s\n X=", s);
mpfr_dump (x);
exit (1);
}
/* Check for leading sign */
mpfr_strtofr (x, " +17.5E-42E ", &s, 10, MPFR_RNDN);
if (mpfr_cmp_str1 (x, "17.5E-42") || strcmp (s, "E "))
{
printf ("Failed parsing '+17.5E-42E '\n S=%s\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-17.5E+42E\n", &s, 10, MPFR_RNDN);
if (mpfr_cmp_str1 (x, "-17.5E42") || strcmp (s, "E\n"))
{
printf ("Failed parsing '-17.5E+42\\n'\n S=%s\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* P form */
mpfr_strtofr (x, "0x42P17", &s, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "8650752", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '0x42P17' (base = 16)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-0X42p17", &s, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "-8650752", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '-0x42p17' (base = 16)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "42p17", &s, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "8650752", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '42p17' (base = 16)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-42P17", &s, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "-8650752", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '-42P17' (base = 16)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "0b1001P17", &s, 2, MPFR_RNDN);
if (mpfr_cmp_str (x, "1179648", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '0b1001P17' (base = 2)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-0B1001p17", &s, 2, MPFR_RNDN);
if (mpfr_cmp_str (x, "-1179648", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '-0B1001p17' (base = 2)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "1001p17", &s, 2, MPFR_RNDN);
if (mpfr_cmp_str (x, "1179648", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '1001p17' (base = 2)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-1001P17", &s, 2, MPFR_RNDN);
if (mpfr_cmp_str (x, "-1179648", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '-1001P17' (base = 2)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Check for auto-detection of the base */
mpfr_strtofr (x, "+0x42P17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "42P17", 16, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '+0x42P17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-42E17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "-42E17", 10, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '-42E17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-42P17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "-42", 10, MPFR_RNDN) || strcmp (s, "P17"))
{
printf ("Failed parsing '-42P17' (base = 0)\n S='%s'\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, " 0b0101.011@42", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "0101.011@42", 2, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '0101.011@42'\n S=%s\n X=", s);
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, " 0b0101.011P42", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "0101.011@42", 2, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '0101.011@42'\n S=%s\n X=", s);
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "+0x42@17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str (x, "4.2@18", 16, MPFR_RNDN) || *s != 0)
{
printf ("Failed parsing '+0x42P17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Check for space inside the mantissa */
mpfr_strtofr (x, "+0x4 2@17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_ui (x, 4) || strcmp(s," 2@17"))
{
printf ("Failed parsing '+0x4 2@17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "+0x42 P17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_ui (x, 0x42) || strcmp(s," P17"))
{
printf ("Failed parsing '+0x42 P17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Space between mantissa and exponent */
mpfr_strtofr (x, " -0b0101P 17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_si (x, -5) || strcmp(s,"P 17"))
{
printf ("Failed parsing '-0b0101P 17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Check for Invalid exponent. */
mpfr_strtofr (x, " -0b0101PF17", &s, 0, MPFR_RNDN);
if (mpfr_cmp_si (x, -5) || strcmp(s,"PF17"))
{
printf ("Failed parsing '-0b0101PF17'\n S=%s\n X=", s);
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* At least one digit in the mantissa. */
mpfr_strtofr (x, " .E10", &s, 0, MPFR_RNDN);
if (strcmp(s," .E10"))
{
printf ("Failed parsing ' .E10'\n S=%s\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Check 2 '.': 2.3.4 */
mpfr_strtofr (x, "-1.2.3E4", &s, 0, MPFR_RNDN);
if (mpfr_cmp_str1 (x, "-1.2") || strcmp(s,".3E4"))
{
printf ("Failed parsing '-1.2.3E4'\n S=%s\n X=", s);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
/* Check for 0x and 0b */
mpfr_strtofr (x, " 0xG", &s, 0, MPFR_RNDN);
if (mpfr_cmp_ui (x, 0) || strcmp(s,"xG"))
{
printf ("Failed parsing ' 0xG'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, " 0b2", &s, 0, MPFR_RNDN);
if (mpfr_cmp_ui (x, 0) || strcmp(s,"b2"))
{
printf ("Failed parsing ' 0b2'\n S=%s\n X=", s);
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, "-0x.23@2Z33", &s, 0, MPFR_RNDN);
if (mpfr_cmp_si (x, -0x23) || strcmp(s,"Z33"))
{
printf ("Failed parsing '-0x.23@2Z33'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_strtofr (x, " 0x", &s, 0, MPFR_RNDN);
if (mpfr_cmp_ui (x, 0) || strcmp(s,"x"))
{
printf ("Failed parsing ' 0x'\n S=%s\n X=", s);
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
exit (1);
}
mpfr_clear (x);
}
static void
check_nans (void)
{
mpfr_t x, y;
int inexact;
mpfr_init2 (x, 123);
mpfr_init2 (y, 123);
/* 1.0 - nan is nan */
mpfr_set_nan (x);
mpfr_clear_flags ();
inexact = mpfr_d_sub (y, 1.0, x, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN ((__gmpfr_flags ^ MPFR_FLAGS_NAN) == 0);
MPFR_ASSERTN (mpfr_nan_p (y));
/* 1.0 - +inf == -inf */
mpfr_set_inf (x, 1);
mpfr_clear_flags ();
inexact = mpfr_d_sub (y, 1.0, x, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_NEG (y));
/* 1.0 - -inf == +inf */
mpfr_set_inf (x, -1);
mpfr_clear_flags ();
inexact = mpfr_d_sub (y, 1.0, x, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_POS (y));
mpfr_clear (x);
mpfr_clear (y);
}
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
main (void)
{
mpfr_t x;
mpfr_exp_t emax;
tests_start_mpfr ();
mpfr_init (x);
mpfr_set_nan (x);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_inf (x, -1);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG(x));
emax = mpfr_get_emax ();
set_emax (0);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "0.111");
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_prec (x, mp_bits_per_limb + 2);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
if (mpfr_cmp_ui(x, 4))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 4\n");
exit (1);
}
/* check case when reallocation is needed */
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
mpfr_init2 (x, 3);
mpfr_set_si (x, -5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
if (mpfr_cmp_si(x, -5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of -5\n");
exit (1);
}
/* check case when new precision needs less limbs */
mpfr_set_prec (x, mp_bits_per_limb + 1);
mpfr_set_ui (x, 5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, 3, MPFR_RNDN); /* exact */
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
tests_end_mpfr ();
return 0;
}
static void
check_special (void)
{
mpfr_t x, y, m;
mpfr_init2 (x, 123L);
mpfr_init2 (y, 123L);
mpfr_init2 (m, 123L);
/* agm(1,nan) is NaN */
mpfr_set_ui (x, 1L, MPFR_RNDN);
mpfr_set_nan (y);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(1,+inf) == +inf */
mpfr_set_ui (x, 1L, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (m));
MPFR_ASSERTN (mpfr_sgn (m) > 0);
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (m));
MPFR_ASSERTN (mpfr_sgn (m) > 0);
/* agm(+inf,+inf) == +inf */
mpfr_set_inf (x, 1);
mpfr_set_inf (y, 1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (m));
MPFR_ASSERTN (mpfr_sgn (m) > 0);
/* agm(-inf,+inf) is NaN */
mpfr_set_inf (x, -1);
mpfr_set_inf (y, 1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(+0,+inf) is NaN */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(-0,+inf) is NaN */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(+0,-inf) is NaN */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_inf (y, -1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(-0,-inf) is NaN */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_inf (y, -1);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
/* agm(+0,1) == +0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
/* agm(-0,1) == +0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
/* agm(+0,-1) == +0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
/* agm(-0,-1) == +0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
/* agm(-0,+0) == +0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (m) && MPFR_IS_POS(m));
/* agm(1,1) == 1 */
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (m ,1) == 0);
/* agm(-1,-2) is NaN */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_si (y, -2, MPFR_RNDN);
mpfr_agm (m, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_agm (m, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (m));
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (m);
}
static void
check_special (void)
{
mpfr_t a, d, q;
mpfr_exp_t emax, emin;
int i;
mpfr_init2 (a, 100L);
mpfr_init2 (d, 100L);
mpfr_init2 (q, 100L);
/* 1/nan == nan */
mpfr_set_ui (a, 1L, MPFR_RNDN);
MPFR_SET_NAN (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);
/* nan/1 == nan */
MPFR_SET_NAN (a);
mpfr_set_ui (d, 1L, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);
/* +inf/1 == +inf */
MPFR_SET_INF (a);
MPFR_SET_POS (a);
mpfr_set_ui (d, 1L, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q));
MPFR_ASSERTN (mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* +inf/-1 == -inf */
MPFR_SET_INF (a);
MPFR_SET_POS (a);
mpfr_set_si (d, -1, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q));
MPFR_ASSERTN (mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -inf/1 == -inf */
MPFR_SET_INF (a);
MPFR_SET_NEG (a);
mpfr_set_ui (d, 1L, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q));
MPFR_ASSERTN (mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -inf/-1 == +inf */
MPFR_SET_INF (a);
MPFR_SET_NEG (a);
mpfr_set_si (d, -1, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q));
MPFR_ASSERTN (mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* 1/+inf == +0 */
mpfr_set_ui (a, 1L, MPFR_RNDN);
MPFR_SET_INF (d);
MPFR_SET_POS (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (q));
MPFR_ASSERTN (mpfr_sgn (q) == 0);
MPFR_ASSERTN (MPFR_IS_POS (q));
MPFR_ASSERTN (__gmpfr_flags == 0);
/* 1/-inf == -0 */
mpfr_set_ui (a, 1L, MPFR_RNDN);
MPFR_SET_INF (d);
MPFR_SET_NEG (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (q));
MPFR_ASSERTN (mpfr_sgn (q) == 0);
MPFR_ASSERTN (MPFR_IS_NEG (q));
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -1/+inf == -0 */
mpfr_set_si (a, -1, MPFR_RNDN);
MPFR_SET_INF (d);
MPFR_SET_POS (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (q));
MPFR_ASSERTN (mpfr_sgn (q) == 0);
MPFR_ASSERTN (MPFR_IS_NEG (q));
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -1/-inf == +0 */
mpfr_set_si (a, -1, MPFR_RNDN);
MPFR_SET_INF (d);
MPFR_SET_NEG (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_number_p (q));
MPFR_ASSERTN (mpfr_sgn (q) == 0);
MPFR_ASSERTN (MPFR_IS_POS (q));
MPFR_ASSERTN (__gmpfr_flags == 0);
/* 0/0 == nan */
mpfr_set_ui (a, 0L, MPFR_RNDN);
mpfr_set_ui (d, 0L, MPFR_RNDN);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);
/* +inf/+inf == nan */
MPFR_SET_INF (a);
MPFR_SET_POS (a);
MPFR_SET_INF (d);
MPFR_SET_POS (d);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);
/* 1/+0 = +inf */
mpfr_set_ui (a, 1, MPFR_RNDZ);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
/* 1/-0 = -inf */
mpfr_set_ui (a, 1, MPFR_RNDZ);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_neg (d, d, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
/* -1/+0 = -inf */
mpfr_set_si (a, -1, MPFR_RNDZ);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
/* -1/-0 = +inf */
mpfr_set_si (a, -1, MPFR_RNDZ);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_neg (d, d, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
/* +inf/+0 = +inf */
MPFR_SET_INF (a);
MPFR_SET_POS (a);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* +inf/-0 = -inf */
MPFR_SET_INF (a);
MPFR_SET_POS (a);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_neg (d, d, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -inf/+0 = -inf */
MPFR_SET_INF (a);
MPFR_SET_NEG (a);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* -inf/-0 = +inf */
MPFR_SET_INF (a);
MPFR_SET_NEG (a);
mpfr_set_ui (d, 0, MPFR_RNDZ);
mpfr_neg (d, d, MPFR_RNDZ);
mpfr_clear_flags ();
MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
/* check overflow */
emax = mpfr_get_emax ();
set_emax (1);
mpfr_set_ui (a, 1, MPFR_RNDZ);
mpfr_set_ui (d, 1, MPFR_RNDZ);
mpfr_div_2exp (d, d, 1, MPFR_RNDZ);
mpfr_clear_flags ();
test_div (q, a, d, MPFR_RNDU); /* 1 / 0.5 = 2 -> overflow */
MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT));
set_emax (emax);
/* check underflow */
emin = mpfr_get_emin ();
set_emin (-1);
mpfr_set_ui (a, 1, MPFR_RNDZ);
mpfr_div_2exp (a, a, 2, MPFR_RNDZ);
mpfr_set_prec (d, mpfr_get_prec (q) + 8);
for (i = -1; i <= 1; i++)
{
int sign;
/* Test 2^(-2) / (+/- (2 + eps)), with eps < 0, eps = 0, eps > 0.
-> underflow.
With div.c r5513, this test fails for eps > 0 in MPFR_RNDN. */
mpfr_set_ui (d, 2, MPFR_RNDZ);
if (i < 0)
mpfr_nextbelow (d);
if (i > 0)
mpfr_nextabove (d);
for (sign = 0; sign <= 1; sign++)
{
mpfr_clear_flags ();
test_div (q, a, d, MPFR_RNDZ); /* result = 0 */
MPFR_ASSERTN (__gmpfr_flags ==
(MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT));
MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q));
MPFR_ASSERTN (MPFR_IS_ZERO (q));
mpfr_clear_flags ();
test_div (q, a, d, MPFR_RNDN); /* result = 0 iff eps >= 0 */
MPFR_ASSERTN (__gmpfr_flags ==
(MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT));
MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q));
if (i < 0)
mpfr_nexttozero (q);
MPFR_ASSERTN (MPFR_IS_ZERO (q));
mpfr_neg (d, d, MPFR_RNDN);
}
}
set_emin (emin);
mpfr_clear (a);
mpfr_clear (d);
mpfr_clear (q);
}
static int
mpfr_all_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r)
{
mpfr_t a2;
unsigned int oldflags, newflags;
int inex, inex2;
oldflags = __gmpfr_flags;
inex = mpfr_div (a, b, c, r);
if (a == b || a == c)
return inex;
newflags = __gmpfr_flags;
mpfr_init2 (a2, MPFR_PREC (a));
if (mpfr_integer_p (b) && ! (MPFR_IS_ZERO (b) && MPFR_IS_NEG (b)))
{
/* b is an integer, but not -0 (-0 is rejected as
it becomes +0 when converted to an integer). */
if (mpfr_fits_ulong_p (b, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_ui_div (a2, mpfr_get_ui (b, MPFR_RNDN), c, r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_ui_div", b, c, r);
}
if (mpfr_fits_slong_p (b, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_si_div (a2, mpfr_get_si (b, MPFR_RNDN), c, r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_si_div", b, c, r);
}
}
if (mpfr_integer_p (c) && ! (MPFR_IS_ZERO (c) && MPFR_IS_NEG (c)))
{
/* c is an integer, but not -0 (-0 is rejected as
it becomes +0 when converted to an integer). */
if (mpfr_fits_ulong_p (c, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_div_ui (a2, b, mpfr_get_ui (c, MPFR_RNDN), r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_div_ui", b, c, r);
}
if (mpfr_fits_slong_p (c, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_div_si (a2, b, mpfr_get_si (c, MPFR_RNDN), r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_div_si", b, c, r);
}
}
mpfr_clear (a2);
return inex;
}
/* check concordance between mpfr_asprintf result with a regular mpfr float
and with a regular double float */
static int
random_double (void)
{
mpfr_t x; /* random regular mpfr float */
double y; /* regular double float (equal to x) */
char flag[] =
{
'-',
'+',
' ',
'#',
'0', /* no ambiguity: first zeros are flag zero*/
'\''
};
/* no 'a': mpfr and glibc do not have the same semantic */
char specifier[] =
{
'e',
'f',
'g',
'E',
'f', /* SUSv2 doesn't accept %F, but %F and %f are the same for
regular numbers */
'G',
};
int spec; /* random index in specifier[] */
int prec; /* random value for precision field */
/* in the format string for mpfr_t variable, the maximum length is
reached by something like "%-+ #0'.*Rf", that is 12 characters. */
#define FMT_MPFR_SIZE 12
char fmt_mpfr[FMT_MPFR_SIZE];
char *ptr_mpfr;
/* in the format string for double variable, the maximum length is
reached by something like "%-+ #0'.*f", that is 11 characters. */
#define FMT_SIZE 11
char fmt[FMT_SIZE];
char *ptr;
int xi;
char *xs;
int yi;
char *ys;
int i, j, jmax;
mpfr_init2 (x, MPFR_LDBL_MANT_DIG);
for (i = 0; i < 1000; ++i)
{
/* 1. random double */
do
{
y = DBL_RAND ();
}
#ifdef HAVE_DENORMS
while (0);
#else
while (ABS(y) < DBL_MIN);
#endif
if (randlimb () % 2 == 0)
y = -y;
mpfr_set_d (x, y, MPFR_RNDN);
if (y != mpfr_get_d (x, MPFR_RNDN))
/* conversion error: skip this one */
continue;
/* 2. build random format strings fmt_mpfr and fmt */
ptr_mpfr = fmt_mpfr;
ptr = fmt;
*ptr_mpfr++ = *ptr++ = '%';
/* random specifier 'e', 'f', 'g', 'E', 'F', or 'G' */
spec = (int) (randlimb() % 6);
/* random flags, but no ' flag with %e */
jmax = (spec == 0 || spec == 3) ? 5 : 6;
for (j = 0; j < jmax; j++)
{
if (randlimb() % 3 == 0)
*ptr_mpfr++ = *ptr++ = flag[j];
}
*ptr_mpfr++ = *ptr++ = '.';
*ptr_mpfr++ = *ptr++ = '*';
*ptr_mpfr++ = 'R';
*ptr_mpfr++ = *ptr++ = specifier[spec];
*ptr_mpfr = *ptr = '\0';
MPFR_ASSERTN (ptr - fmt < FMT_SIZE);
MPFR_ASSERTN (ptr_mpfr - fmt_mpfr < FMT_MPFR_SIZE);
/* advantage small precision */
if (randlimb() % 2 == 0)
prec = (int) (randlimb() % 10);
else
prec = (int) (randlimb() % prec_max_printf);
/* 3. calls and checks */
/* the double float case is handled by the libc asprintf through
gmp_asprintf */
xi = mpfr_asprintf (&xs, fmt_mpfr, prec, x);
yi = mpfr_asprintf (&ys, fmt, prec, y);
/* test if XS and YS differ, beware that ISO C99 doesn't specify
the sign of a zero exponent (the C99 rationale says: "The sign
of a zero exponent in %e format is unspecified. The committee
knows of different implementations and choose not to require
implementations to document their behaviour in this case
(by making this be implementation defined behaviour). Most
implementations use a "+" sign, e.g., 1.2e+00; but there is at
least one implementation that uses the sign of the unlimited
precision result, e.g., the 0.987 would be 9.87e-01, so could
end up as 1e-00 after rounding to one digit of precision."),
while mpfr always uses '+' */
if (xi != yi
|| ((strcmp (xs, ys) != 0)
&& (spec == 1 || spec == 4
|| ((strstr (xs, "e+00") == NULL
|| strstr (ys, "e-00") == NULL)
&& (strstr (xs, "E+00") == NULL
|| strstr (ys, "E-00") == NULL)))))
{
mpfr_printf ("Error in mpfr_asprintf(\"%s\", %d, %Re)\n",
fmt_mpfr, prec, x);
printf ("expected: %s\n", ys);
printf (" got: %s\n", xs);
printf ("xi=%d yi=%d spec=%d\n", xi, yi, spec);
exit (1);
}
mpfr_free_str (xs);
mpfr_free_str (ys);
}
mpfr_clear (x);
return 0;
}
static void
special_atan2 (void)
{
mpfr_t x, y, z;
mpfr_inits2 (4, x, y, z, (mpfr_ptr) 0);
/* Anything with NAN should be set to NAN */
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_set_nan (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_NAN (z));
mpfr_swap (x, y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_NAN (z));
/* 0+ 0+ --> 0+ */
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
/* 0- 0+ --> 0- */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
/* 0- 0- --> -PI */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, MPFR_RNDN) == 0);
/* 0+ 0- --> +PI */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, MPFR_RNDN) == 0);
/* 0+ -1 --> PI */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, MPFR_RNDN) == 0);
/* 0- -1 --> -PI */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, MPFR_RNDN) == 0);
/* 0- +1 --> 0- */
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
/* 0+ +1 --> 0+ */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
/* +1 0+ --> PI/2 */
mpfr_swap (x, y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, MPFR_RNDN) == 0);
/* +1 0- --> PI/2 */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, MPFR_RNDN) == 0);
/* -1 0- --> -PI/2 */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, MPFR_RNDN) == 0);
/* -1 0+ --> -PI/2 */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, MPFR_RNDN) == 0);
/* -1 +INF --> -0 */
MPFR_SET_INF (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
/* +1 +INF --> +0 */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
/* +1 -INF --> +PI */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, MPFR_RNDN) == 0);
/* -1 -INF --> -PI */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, MPFR_RNDN) == 0);
/* -INF -1 --> -PI/2 */
mpfr_swap (x, y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, MPFR_RNDN) == 0);
/* +INF -1 --> PI/2 */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, MPFR_RNDN) == 0);
/* +INF -INF --> 3*PI/4 */
MPFR_SET_INF (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "2.356194490192344928", 10, MPFR_RNDN) == 0);
/* +INF +INF --> PI/4 */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "0.785375", 10, MPFR_RNDN) == 0);
/* -INF +INF --> -PI/4 */
MPFR_CHANGE_SIGN (y);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-0.785375", 10, MPFR_RNDN) == 0);
/* -INF -INF --> -3*PI/4 */
MPFR_CHANGE_SIGN (x);
mpfr_atan2 (z, y, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_str (z, "-2.356194490192344928", 10, MPFR_RNDN) == 0);
mpfr_set_prec (z, 905); /* exercises Ziv's loop */
mpfr_atan2 (z, y, x, MPFR_RNDZ);
MPFR_ASSERTN (mpfr_cmp_str (z, "-2.35619449019234492884698253745962716314787704953132936573120844423086230471465674897102611900658780098661106488496172998532038345716293667379401955609636083808771307702645389082916973346721171619778647332160823174945008459635673617534008737395340143185923642519259526145784", 10, MPFR_RNDN) == 0);
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
special (void)
{
mpfr_t x, y;
int inex;
int sign;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lgamma(NaN)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lgamma(-Inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != 1)
{
printf ("Error for lgamma(+Inf)\n");
exit (1);
}
mpfr_set_ui (x, 0, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != 1)
{
printf ("Error for lgamma(+0)\n");
exit (1);
}
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != -1)
{
printf ("Error for lgamma(-0)\n");
exit (1);
}
mpfr_set_ui (x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y) || sign != 1)
{
printf ("Error for lgamma(1)\n");
exit (1);
}
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lgamma(-1)\n");
exit (1);
}
mpfr_set_ui (x, 2, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y) || sign != 1)
{
printf ("Error for lgamma(2)\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
#define CHECK_X1 "1.0762904832837976166"
#define CHECK_Y1 "-0.039418362817587634939"
mpfr_set_str (x, CHECK_X1, 10, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str (x, CHECK_Y1, 10, GMP_RNDN);
if (mpfr_equal_p (y, x) == 0 || sign != 1)
{
printf ("mpfr_lgamma("CHECK_X1") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
#define CHECK_X2 "9.23709516716202383435e-01"
#define CHECK_Y2 "0.049010669407893718563"
mpfr_set_str (x, CHECK_X2, 10, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str (x, CHECK_Y2, 10, GMP_RNDN);
if (mpfr_equal_p (y, x) == 0 || sign != 1)
{
printf ("mpfr_lgamma("CHECK_X2") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
mpfr_set_prec (x, 8);
mpfr_set_prec (y, 175);
mpfr_set_ui (x, 33, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDU);
mpfr_set_prec (x, 175);
mpfr_set_str_binary (x, "0.1010001100011101101011001101110010100001000001000001110011000001101100001111001001000101011011100100010101011110100111110101010100010011010010000101010111001100011000101111E7");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (1)\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 8);
mpfr_set_ui (y, 120, GMP_RNDN);
sign = -17;
mpfr_lgamma (x, &sign, y, GMP_RNDZ);
mpfr_set_prec (y, 21);
mpfr_set_str_binary (y, "0.111000101000001100101E9");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (120)\n");
printf ("Expected "); mpfr_print_binary (y); puts ("");
printf ("Got "); mpfr_print_binary (x); puts ("");
exit (1);
}
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 206);
mpfr_set_str_binary (x, "0.110e10");
sign = -17;
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 206);
mpfr_set_str_binary (x, "0.10000111011000000011100010101001100110001110000111100011000100100110110010001011011110101001111011110110000001010100111011010000000011100110110101100111000111010011110010000100010111101010001101000110101001E13");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (768)\n");
exit (1);
}
if (inex >= 0)
{
printf ("Wrong flag for mpfr_lgamma (768)\n");
exit (1);
}
mpfr_set_prec (x, 4);
mpfr_set_prec (y, 4);
mpfr_set_str_binary (x, "0.1100E-66");
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "0.1100E6");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error for lgamma(0.1100E-66)\n");
printf ("Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, GMP_RNDN);
mpfr_add_ui (x, x, 1, GMP_RNDN);
mpfr_div_2ui (x, x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error for lgamma(-2^199+0.5)\n");
printf ("Got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, GMP_RNDN);
mpfr_sub_ui (x, x, 1, GMP_RNDN);
mpfr_div_2ui (x, x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (mpfr_equal_p (x, y) == 0 || sign != -1)
{
printf ("Error for lgamma(-2^199-0.5)\n");
printf ("Got ");
mpfr_dump (y);
printf ("with sign %d instead of ", sign);
mpfr_dump (x);
printf ("with sign -1.\n");
exit (1);
}
mpfr_set_prec (x, 10);
mpfr_set_prec (y, 10);
mpfr_set_str_binary (x, "-0.1101111000E-3");
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "10.01001011");
if (mpfr_equal_p (x, y) == 0 || sign != -1 || inex >= 0)
{
printf ("Error for lgamma(-0.1101111000E-3)\n");
printf ("Got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (x);
printf ("with sign %d instead of -1 (inex=%d).\n", sign, inex);
exit (1);
}
mpfr_set_prec (x, 18);
mpfr_set_prec (y, 28);
mpfr_set_str_binary (x, "-1.10001101010001101e-196");
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 28);
mpfr_set_str_binary (x, "0.100001110110101011011010011E8");
MPFR_ASSERTN (mpfr_equal_p (x, y) && inex < 0);
/* values reported by Kaveh Ghazi on 14 Jul 2007, where mpfr_lgamma()
takes forever */
#define VAL1 "-0.11100001001010110111001010001001001011110100110000110E-55"
#define OUT1 "100110.01000000010111001110110101110101001001100110111"
#define VAL2 "-0.11100001001010110111001010001001001011110011111111100E-55"
#define OUT2 "100110.0100000001011100111011010111010100100110011111"
#define VAL3 "-0.11100001001010110111001010001001001001110101101010100E-55"
#define OUT3 "100110.01000000010111001110110101110101001011110111011"
#define VAL4 "-0.10001111110110110100100100000000001111110001001001011E-57"
#define OUT4 "101000.0001010111110011101101000101111111010001100011"
#define VAL5 "-0.10001111110110110100100100000000001111011111100001000E-57"
#define OUT5 "101000.00010101111100111011010001011111110100111000001"
#define VAL6 "-0.10001111110110110100100100000000001111011101100011001E-57"
#define OUT6 "101000.0001010111110011101101000101111111010011101111"
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, VAL1);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT1);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p(x, y));
mpfr_set_str_binary (x, VAL2);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT2);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL3);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT3);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL4);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT4);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL5);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT5);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL6);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT6);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
/* further test from Kaveh Ghazi */
mpfr_set_str_binary (x, "-0.10011010101001010010001110010111010111011101010111001E-53");
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "100101.00111101101010000000101010111010001111001101111");
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_clear (x);
mpfr_clear (y);
}
static void
special (void)
{
mpfr_t x, y;
unsigned xprec, yprec;
mpfr_init (x);
mpfr_init (y);
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_div_ui (y, x, 3, MPFR_RNDN);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 100);
mpfr_urandomb (x, RANDS);
mpfr_div_ui (y, x, 123456, MPFR_RNDN);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_div_ui (y, x, 123456789, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0))
{
printf ("mpfr_div_ui gives non-zero for 0/ui\n");
exit (1);
}
/* bug found by Norbert Mueller, 21 Aug 2001 */
mpfr_set_prec (x, 110);
mpfr_set_prec (y, 60);
mpfr_set_str_binary (x, "0.110101110011111110011111001110011001110111000000111110001000111011000011E-44");
mpfr_div_ui (y, x, 17, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11001010100101100011101110000001100001010110101001010011011E-48");
if (mpfr_cmp (x, y))
{
printf ("Error in x/17 for x=1/16!\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
printf ("\n");
exit (1);
}
/* corner case */
mpfr_set_prec (x, 2 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_ui (x, 4, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_div_ui (y, x, 2, MPFR_RNDN); /* exactly in the middle */
MPFR_ASSERTN(mpfr_cmp_ui (y, 2) == 0);
mpfr_set_prec (x, 3 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_div_ui (y, x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);
mpfr_set_prec (x, 3 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_si (x, -4, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_div_ui (y, x, 2, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (y, -3) == 0);
for (xprec = 53; xprec <= 128; xprec++)
{
mpfr_set_prec (x, xprec);
mpfr_set_str_binary (x, "0.1100100100001111110011111000000011011100001100110111E2");
for (yprec = 53; yprec <= 128; yprec++)
{
mpfr_set_prec (y, yprec);
mpfr_div_ui (y, x, 1, MPFR_RNDN);
if (mpfr_cmp(x,y))
{
printf ("division by 1.0 fails for xprec=%u, yprec=%u\n", xprec, yprec);
printf ("expected "); mpfr_print_binary (x); puts ("");
printf ("got "); mpfr_print_binary (y); puts ("");
exit (1);
}
}
}
/* Bug reported by Mark Dickinson, 6 Nov 2007 */
mpfr_set_si (x, 0, MPFR_RNDN);
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_div_ui (y, x, 4, MPFR_RNDN);
MPFR_ASSERTN(MPFR_IS_ZERO(y) && MPFR_IS_POS(y));
mpfr_clear (x);
mpfr_clear (y);
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
unsigned long k, bd, nc, i;
char *str, *str2;
mp_exp_t e;
int base, logbase, prec, baseprec, ret;
tests_start_mpfr ();
if (argc >= 2) /* tset_str <string> [<prec>] [<base>] */
{
prec = (argc >= 3) ? atoi (argv[2]) : 53;
base = (argc >= 4) ? atoi (argv[3]) : 2;
mpfr_init2 (x, prec);
mpfr_set_str (x, argv[1], base, GMP_RNDN);
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
puts ("");
mpfr_clear (x);
return 0;
}
mpfr_init2 (x, 2);
nc = (argc > 1) ? atoi(argv[1]) : 53;
if (nc < 100)
nc = 100;
bd = randlimb () & 8;
str2 = str = (char*) (*__gmp_allocate_func) (nc * sizeof(char));
if (bd)
{
for(k = 1; k <= bd; k++)
*(str2++) = (randlimb () & 1) + '0';
}
else
*(str2++) = '0';
*(str2++) = '.';
for (k = 1; k < nc - 17 - bd; k++)
*(str2++) = '0' + (char) (randlimb () & 1);
*(str2++) = 'e';
sprintf (str2, "%d", (int) (randlimb () & INT_MAX) + INT_MIN/2);
mpfr_set_prec (x, nc + 10);
mpfr_set_str_binary (x, str);
mpfr_set_prec (x, 54);
mpfr_set_str_binary (x, "0.100100100110110101001010010101111000001011100100101010E-529");
mpfr_init2 (y, 54);
mpfr_set_str (y, "4.936a52bc17254@-133", 16, GMP_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1a):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str_binary (x, "0.111111101101110010111010100110000111011001010100001101E-529");
mpfr_set_str (y, "0.fedcba98765434P-529", 16, GMP_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1b):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, nc * sizeof(char));
mpfr_set_prec (x, 53);
mpfr_set_str_binary (x, "+110101100.01010000101101000000100111001000101011101110E00");
mpfr_set_str_binary (x, "1.0");
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_set_str_binary for s=1.0\n");
mpfr_clear(x);
mpfr_clear(y);
exit(1);
}
mpfr_set_str_binary (x, "+0000");
mpfr_set_str_binary (x, "+0000E0");
mpfr_set_str_binary (x, "0000E0");
if (mpfr_cmp_ui (x, 0))
{
printf ("Error in mpfr_set_str_binary for s=0.0\n");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (x, "+243495834958.53452345E1", 10, GMP_RNDN);
mpfr_set_str (x, "9007199254740993", 10, GMP_RNDN);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDU);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDD);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDZ);
/* check a random number printed and read is not modified */
prec = 53;
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
for (i=0;i<N;i++)
{
mpfr_random (x);
k = RND_RAND ();
logbase = (randlimb () % 5) + 1;
base = 1 << logbase;
/* Warning: the number of bits needed to print exactly a number of
'prec' bits in base 2^logbase may be greater than ceil(prec/logbase),
for example 0.11E-1 in base 2 cannot be written exactly with only
one digit in base 4 */
if (base == 2)
baseprec = prec;
else
baseprec = 1 + (prec - 2 + logbase) / logbase;
str = mpfr_get_str (NULL, &e, base, baseprec, x, (mp_rnd_t) k);
mpfr_set_str (y, str, base, (mp_rnd_t) k);
MPFR_EXP(y) += logbase * (e - strlen (str));
if (mpfr_cmp (x, y))
{
printf ("mpfr_set_str o mpfr_get_str <> id for rnd_mode=%s\n",
mpfr_print_rnd_mode ((mp_rnd_t) k));
printf ("x=");
mpfr_print_binary (x);
puts ("");
printf ("s=%s, exp=%d, base=%d\n", str, (int) e, base);
printf ("y=");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, strlen (str) + 1);
}
for (i = 2; i <= 36; i++)
{
if (mpfr_set_str (x, "@NaN@(garbage)", i, GMP_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on @NaN@(garbage)\n");
exit (1);
}
/*
if (mpfr_set_str (x, "@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on @Inf@garbage\n");
exit (1);
}
if (mpfr_set_str (x, "-@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on -@Inf@garbage\n");
exit (1);
}
if (mpfr_set_str (x, "+@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on +@Inf@garbage\n");
exit (1);
}
*/
if (i > 16)
continue;
if (mpfr_set_str (x, "NaN", i, GMP_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on NaN\n");
exit (1);
}
if (mpfr_set_str (x, "Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on Inf\n");
exit (1);
}
if (mpfr_set_str (x, "-Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on -Inf\n");
exit (1);
}
if (mpfr_set_str (x, "+Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on +Inf\n");
exit (1);
}
}
/* check that mpfr_set_str works for uppercase letters too */
mpfr_set_prec (x, 10);
mpfr_set_str (x, "B", 16, GMP_RNDN);
if (mpfr_cmp_ui (x, 11) != 0)
{
printf ("mpfr_set_str does not work for uppercase letters\n");
exit (1);
}
/* start of tests added by Alain Delplanque */
/* in this example an overflow can occur */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.0E-532");
mpfr_set_str (y, "0.71128279983522479470@-160", 10, GMP_RNDU);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (2):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* in this example, I think there was a pb in the old function :
result of mpfr_set_str_old for the same number , but with more
precision is: 1.111111111110000000000000000111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100111000100001100000010101100111010e184
this result is the same as mpfr_set_str */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111110000000000000000111111111111111111111111110000000001E184");
mpfr_set_str (y, "0.jo08hg31hc5mmpj5mjjmgn55p2h35g@39", 27, GMP_RNDU);
/* y = 49027884868983130654865109690613178467841148597221480052 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (3):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* not exact rounding in mpfr_set_str
same number with more precision is : 1.111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011011111101000001101110110010101101000010100110011101110010001110e195
this result is the same as mpfr_set_str */
/* problem was : can_round was call with GMP_RNDN round mode,
so can_round use an error : 1/2 * 2^err * ulp(y)
instead of 2^err * ulp(y)
I have increase err by 1 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111111111111111111111000000000000000000000000000000000001e195");
mpfr_set_str (y, "0.6e23ekb6acgh96abk10b6c9f2ka16i@45", 21, GMP_RNDU);
/* y = 100433627392042473064661483711179345482301462325708736552078 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (4):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* may be an error in mpfr_set_str_old
with more precision : 1.111111100000001111110000000000011111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111101010001110111011000010111001011100110110e180 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111100000001111110000000000011111011111111111111111111111111e180");
mpfr_set_str (y, "0.10j8j2k82ehahha56390df0a1de030@41", 23, GMP_RNDZ);
/* y = 3053110535624388280648330929253842828159081875986159414 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (5):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "0.jrchfhpp9en7hidqm9bmcofid9q3jg@39", 28, GMP_RNDU);
/* y = 196159429139499688661464718784226062699788036696626429952 */
mpfr_set_str_binary (x, "0.1111111111111111111111111111111000000000000011100000001111100001E187");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (6):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "0.h148m5ld5cf8gk1kd70b6ege92g6ba@47", 24, GMP_RNDZ);
/* y = 52652933527468502324759448399183654588831274530295083078827114496 */
mpfr_set_str_binary (x, "0.1111111111111100000000001000000000000000000011111111111111101111E215");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (7):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* worst cases for rounding to nearest in double precision */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str (y, "5e125", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10111101000101110110011000100000101001010000000111111E418");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (8):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "69e267", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10000101101111100101101100000110010011001010011011010E894");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (9):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "623e100", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10110010000001010011000101111001110101000001111011111E342");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (10):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "3571e263", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10110001001100100010011000110000111010100000110101010E886");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (11):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "75569e-254", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101101001000110001011011001000111000110101010110011E-827");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (12):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "920657e-23", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101001110101001100110000101110110111101111001101100E-56");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (13):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "9210917e80", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.11101101000100011001000110100011111100110000000110010E289");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (14):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "87575437e-309", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.11110000001110011001000000110000000100000010101101100E-1000");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (15):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "245540327e122", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E434");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (16):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "491080654e122", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E435");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (17):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "83356057653e193", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101010001001110011011011010111011100010101000011000E678");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (18):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
CHECK53(y, "83356057653e193", GMP_RNDN, x,
"0.10101010001001110011011011010111011100010101000011000E678",
18);
CHECK53(y, "619534293513e124", GMP_RNDN, x,
"0.10001000011000010000000110000001111111110000011110001e452",
19);
CHECK53(y, "3142213164987e-294", GMP_RNDN, x,
"0.11101001101000000100111011111101111001010001001101111e-935",
20);
CHECK53(y, "36167929443327e-159", GMP_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-483",
21);
CHECK53(y, "904198236083175e-161", GMP_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-485",
22);
CHECK53(y, "3743626360493413e-165", GMP_RNDN, x,
"0.11000100000100011101001010111101011011011111011111001e-496",
23);
CHECK53(y, "94080055902682397e-242", GMP_RNDN, x,
"0.10110010010011000000111100011100111100110011011001010e-747",
24);
CHECK53(y, "7e-303", GMP_RNDD, x,
"0.10011001100111001000100110001110001000110111110001011e-1003",
25);
CHECK53(y, "7e-303", GMP_RNDU, x,
"0.10011001100111001000100110001110001000110111110001100e-1003",
26);
CHECK53(y, "93e-234", GMP_RNDD, x,
"0.10010011110110010111001001111001000010000000001110101E-770",
27);
CHECK53(y, "93e-234", GMP_RNDU, x,
"0.10010011110110010111001001111001000010000000001110110E-770",
28);
CHECK53(y, "755e174", GMP_RNDD, x,
"0.10111110110010011000110010011111101111000111111000101E588",
29);
CHECK53(y, "755e174", GMP_RNDU, x,
"0.10111110110010011000110010011111101111000111111000110E588",
30);
CHECK53(y, "8699e-276", GMP_RNDD, x,
"0.10010110100101101111100100100011011101100110100101100E-903",
31);
CHECK53(y, "8699e-276", GMP_RNDU, x,
"0.10010110100101101111100100100011011101100110100101101E-903",
32);
CHECK53(y, "82081e41", GMP_RNDD, x,
"0.10111000000010000010111011111001111010100011111001011E153",
33);
CHECK53(y, "82081e41", GMP_RNDU, x,
"0.10111000000010000010111011111001111010100011111001100E153",
34);
CHECK53(y, "584169e229", GMP_RNDD, x,
"0.11101011001010111000001011001110111000111100110101010E780",
35);
CHECK53(y, "584169e229", GMP_RNDU, x,
"0.11101011001010111000001011001110111000111100110101011E780",
36);
CHECK53(y, "5783893e-128", GMP_RNDD, x,
"0.10011000111100000110011110000101100111110011101110100E-402",
37);
CHECK53(y, "5783893e-128", GMP_RNDU, x,
"0.10011000111100000110011110000101100111110011101110101E-402",
38);
CHECK53(y, "87575437e-310", GMP_RNDD, x,
"0.11000000001011100000110011110011010000000010001010110E-1003",
39);
CHECK53(y, "87575437e-310", GMP_RNDU, x,
"0.11000000001011100000110011110011010000000010001010111E-1003",
40);
CHECK53(y, "245540327e121", GMP_RNDD, x,
"0.11100010101101001111010010110100011100000100101000100E430",
41);
CHECK53(y, "245540327e121", GMP_RNDU, x,
"0.11100010101101001111010010110100011100000100101000101E430",
42);
CHECK53(y, "9078555839e-109", GMP_RNDD, x,
"0.11111110001010111010110000110011100110001010011101101E-329",
43);
CHECK53(y, "9078555839e-109", GMP_RNDU, x,
"0.11111110001010111010110000110011100110001010011101110E-329",
44);
CHECK53(y, "42333842451e201", GMP_RNDD, x,
"0.10000000110001001101000100110110111110101011101011111E704",
45);
CHECK53(y, "42333842451e201", GMP_RNDU, x,
"0.10000000110001001101000100110110111110101011101100000E704",
46);
CHECK53(y, "778380362293e218", GMP_RNDD, x,
"0.11001101010111000001001100001100110010000001010010010E764",
47);
CHECK53(y, "778380362293e218", GMP_RNDU, x,
"0.11001101010111000001001100001100110010000001010010011E764",
48);
CHECK53(y, "7812878489261e-179", GMP_RNDD, x,
"0.10010011011011010111001111011101111101101101001110100E-551",
49);
CHECK53(y, "7812878489261e-179", GMP_RNDU, x,
"0.10010011011011010111001111011101111101101101001110101E-551",
50);
CHECK53(y, "77003665618895e-73", GMP_RNDD, x,
"0.11000101111110111111001111111101001101111000000101001E-196",
51);
CHECK53(y, "77003665618895e-73", GMP_RNDU, x,
"0.11000101111110111111001111111101001101111000000101010E-196",
52);
CHECK53(y, "834735494917063e-300", GMP_RNDD, x,
"0.11111110001101100001001101111100010011001110111010001E-947",
53);
CHECK53(y, "834735494917063e-300", GMP_RNDU, x,
"0.11111110001101100001001101111100010011001110111010010E-947",
54);
CHECK53(y, "6182410494241627e-119", GMP_RNDD, x,
"0.10001101110010110010001011000010001000101110100000111E-342",
55);
CHECK53(y, "6182410494241627e-119", GMP_RNDU, x,
"0.10001101110010110010001011000010001000101110100001000E-342",
56);
CHECK53(y, "26153245263757307e49", GMP_RNDD, x,
"0.10011110111100000000001011011110101100010000011011110E218",
57);
CHECK53(y, "26153245263757307e49", GMP_RNDU, x,
"0.10011110111100000000001011011110101100010000011011111E218",
58);
/* to check this problem : I convert limb (10--0 or 101--1) into base b
with more than mp_bits_per_limb digits,
so when convert into base 2 I should have
the limb that I have choose */
/* this use mpfr_get_str */
{
size_t nb_digit = mp_bits_per_limb;
mp_limb_t check_limb[2] = {MPFR_LIMB_HIGHBIT, ~(MPFR_LIMB_HIGHBIT >> 1)};
int base[3] = {10, 16, 19};
mp_rnd_t rnd[3] = {GMP_RNDU, GMP_RNDN, GMP_RNDD};
int cbase, climb, crnd;
char *str;
mpfr_set_prec (x, mp_bits_per_limb); /* x and y have only one limb */
mpfr_set_prec (y, mp_bits_per_limb);
str = (char*) (*__gmp_allocate_func) (N + 20);
mpfr_set_ui (x, 1, GMP_RNDN); /* ensures that x is not NaN or Inf */
for (; nb_digit < N; nb_digit *= 10)
for (cbase = 0; cbase < 3; cbase++)
for (climb = 0; climb < 2; climb++)
for (crnd = 0; crnd < 3; crnd++)
{
char *str1;
mp_exp_t exp;
*(MPFR_MANT(x)) = check_limb[climb];
MPFR_EXP(x) = 0;
mpfr_get_str (str + 2, &exp, base[cbase],
nb_digit, x, rnd[crnd]);
str[0] = '-';
str[(str[2] == '-')] = '0';
str[(str[2] == '-') + 1] = '.';
for (str1 = str; *str1 != 0; str1++)
;
sprintf (str1, "@%i", (int) exp);
mpfr_set_str (y, str, base[cbase], rnd[2 - crnd]);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error in mpfr_set_str for nb_digit=%u, base=%d, "
"rnd=%s:\n", (unsigned int) nb_digit, base[cbase],
mpfr_print_rnd_mode (rnd[crnd]));
printf ("instead of: ");
mpfr_print_binary (x);
puts ("");
printf ("return : ");
mpfr_print_binary (y);
puts ("");
exit (1);
}
}
(*__gmp_free_func) (str, N + 20);
}
/* end of tests added by Alain Delplanque */
/* check that flags are correctly cleared */
mpfr_set_nan (x);
mpfr_set_str (x, "+0.0", 10, GMP_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) < 0)
{
printf ("x <- +0.0 failed after x=NaN\n");
exit (1);
}
mpfr_set_str (x, "-0.0", 10, GMP_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) > 0)
{
printf ("x <- -0.0 failed after x=NaN\n");
exit (1);
}
/* check invalid input */
ret = mpfr_set_str (x, "1E10toto", 10, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1p10toto", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "+", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "-", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "this_is_an_invalid_number_in_base_36", 36, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1.2.3", 10, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
mpfr_set_prec (x, 135);
ret = mpfr_set_str (x, "thisisavalidnumberinbase36", 36, GMP_RNDN);
mpfr_set_prec (y, 135);
mpfr_set_str (y, "23833565676460972739462619524519814462546", 10, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp (x, y) == 0 && ret == 0);
/* coverage test for set_str_binary */
mpfr_set_str_binary (x, "NaN");
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_str_binary (x, "Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "+Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "-Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "0.01E2");
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_str_binary (x, "-0.01E2");
MPFR_ASSERTN(mpfr_cmp_si (x, -1) == 0);
mpfr_clear (x);
mpfr_clear (y);
check_underflow ();
tests_end_mpfr ();
return 0;
}
int
mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inexact;
long xint;
mpfr_t xfrac;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, 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))
{
if (MPFR_IS_POS (x))
MPFR_SET_INF (y);
else
MPFR_SET_ZERO (y);
MPFR_SET_POS (y);
MPFR_RET (0);
}
else /* 2^0 = 1 */
{
MPFR_ASSERTD (MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
/* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
MPFR_ASSERTN (MPFR_EMIN_MIN >= LONG_MIN + 2);
if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emin - 1) < 0))
{
mpfr_rnd_t rnd2 = rnd_mode;
/* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
if (rnd_mode == MPFR_RNDN &&
mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
rnd2 = MPFR_RNDZ;
return mpfr_underflow (y, rnd2, 1);
}
MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax) >= 0))
return mpfr_overflow (y, rnd_mode, 1);
/* We now know that emin - 1 <= x < emax. */
MPFR_SAVE_EXPO_MARK (expo);
/* 2^x = 1 + x*log(2) + O(x^2) for x near zero, and for |x| <= 1 we have
|2^x - 1| <= x < 2^EXP(x). If x > 0 we must round away from 0 (dir=1);
if x < 0 we must round toward 0 (dir=0). */
MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, - MPFR_GET_EXP (x), 0,
MPFR_IS_POS (x), rnd_mode, expo, {});
xint = mpfr_get_si (x, MPFR_RNDZ);
mpfr_init2 (xfrac, MPFR_PREC (x));
mpfr_sub_si (xfrac, x, xint, MPFR_RNDN); /* exact */
if (MPFR_IS_ZERO (xfrac))
{
mpfr_set_ui (y, 1, MPFR_RNDN);
inexact = 0;
}
else
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
mpfr_prec_t Nt; /* working precision */
mpfr_exp_t err; /* error */
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialize of intermediary variable */
mpfr_init2 (t, Nt);
/* First computation */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute exp(x*ln(2))*/
mpfr_const_log2 (t, MPFR_RNDU); /* ln(2) */
mpfr_mul (t, xfrac, t, MPFR_RNDU); /* xfrac * ln(2) */
err = Nt - (MPFR_GET_EXP (t) + 2); /* Estimate of the error */
mpfr_exp (t, t, MPFR_RNDN); /* exp(xfrac * ln(2)) */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
}
mpfr_clear (xfrac);
MPFR_CLEAR_FLAGS ();
mpfr_mul_2si (y, y, xint, MPFR_RNDN); /* exact or overflow */
/* Note: We can have an overflow only when t was rounded up to 2. */
MPFR_ASSERTD (MPFR_IS_PURE_FP (y) || inexact > 0);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
static void
special (void)
{
mpfr_t x, y, res;
int inexact;
mpfr_init (x);
mpfr_init (y);
mpfr_init (res);
mpfr_set_prec (x, 24);
mpfr_set_prec (y, 24);
mpfr_set_str_binary (y, "0.111100110001011010111");
inexact = mpfr_ui_sub (x, 1, y, GMP_RNDN);
if (inexact)
{
printf ("Wrong inexact flag: got %d, expected 0\n", inexact);
exit (1);
}
mpfr_set_prec (x, 24);
mpfr_set_prec (y, 24);
mpfr_set_str_binary (y, "0.111100110001011010111");
if ((inexact = mpfr_ui_sub (x, 38181761, y, GMP_RNDN)) >= 0)
{
printf ("Wrong inexact flag: got %d, expected -1\n", inexact);
exit (1);
}
mpfr_set_prec (x, 63);
mpfr_set_prec (y, 63);
mpfr_set_str_binary (y, "0.111110010010100100110101101010001001100101110001000101110111111E-1");
if ((inexact = mpfr_ui_sub (x, 1541116494, y, GMP_RNDN)) <= 0)
{
printf ("Wrong inexact flag: got %d, expected +1\n", inexact);
exit (1);
}
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (y, "0.11011000110111010001011100011100E-1");
if ((inexact = mpfr_ui_sub (x, 2000375416, y, GMP_RNDN)) >= 0)
{
printf ("Wrong inexact flag: got %d, expected -1\n", inexact);
exit (1);
}
mpfr_set_prec (x, 24);
mpfr_set_prec (y, 24);
mpfr_set_str_binary (y, "0.110011011001010011110111E-2");
if ((inexact = mpfr_ui_sub (x, 927694848, y, GMP_RNDN)) <= 0)
{
printf ("Wrong inexact flag: got %d, expected +1\n", inexact);
exit (1);
}
/* bug found by Mathieu Dutour, 12 Apr 2001 */
mpfr_set_prec (x, 5);
mpfr_set_prec (y, 5);
mpfr_set_prec (res, 5);
mpfr_set_str_binary (x, "1e-12");
mpfr_ui_sub (y, 1, x, GMP_RNDD);
mpfr_set_str_binary (res, "0.11111");
if (mpfr_cmp (y, res))
{
printf ("Error in mpfr_ui_sub (y, 1, x, GMP_RNDD) for x=2^(-12)\nexpected 1.1111e-1, got ");
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_ui_sub (y, 1, x, GMP_RNDU);
mpfr_set_str_binary (res, "1.0");
if (mpfr_cmp (y, res))
{
printf ("Error in mpfr_ui_sub (y, 1, x, GMP_RNDU) for x=2^(-12)\n"
"expected 1.0, got ");
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_ui_sub (y, 1, x, GMP_RNDN);
mpfr_set_str_binary (res, "1.0");
if (mpfr_cmp (y, res))
{
printf ("Error in mpfr_ui_sub (y, 1, x, GMP_RNDN) for x=2^(-12)\n"
"expected 1.0, got ");
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_prec (x, 10);
mpfr_set_prec (y, 10);
mpfr_random (x);
mpfr_ui_sub (y, 0, x, GMP_RNDN);
if (MPFR_IS_ZERO(x))
MPFR_ASSERTN(MPFR_IS_ZERO(y));
else
MPFR_ASSERTN(mpfr_cmpabs (x, y) == 0 && mpfr_sgn (x) != mpfr_sgn (y));
mpfr_set_prec (x, 73);
mpfr_set_str_binary (x, "0.1101111010101011011011100011010000000101110001011111001011011000101111101E-99");
mpfr_ui_sub (x, 1, x, GMP_RNDZ);
mpfr_nextabove (x);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (res);
}
static void
test_overflow2 (void)
{
mpfr_t x, y, z, r;
int i, inex, rnd, err = 0;
mpfr_inits2 (8, x, y, z, r, (void *) 0);
MPFR_SET_POS (x);
mpfr_setmin (x, mpfr_get_emax ()); /* x = 0.1@emax */
mpfr_set_si (y, -2, GMP_RNDN); /* y = -2 */
/* The intermediate multiplication x * y will overflow. */
for (i = -9; i <= 9; i++)
RND_LOOP (rnd)
{
int inf, overflow;
inf = rnd == GMP_RNDN || rnd == GMP_RNDD;
overflow = inf || i <= 0;
inex = mpfr_set_si_2exp (z, i, mpfr_get_emin (), GMP_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_clear_flags ();
/* One has: x * y = -1@emax exactly (but not representable). */
inex = mpfr_fma (r, x, y, z, rnd);
if (overflow ^ (mpfr_overflow_p () != 0))
{
printf ("Error in test_overflow2 (i = %d, %s): wrong overflow"
" flag (should be %d)\n", i, mpfr_print_rnd_mode (rnd),
overflow);
err = 1;
}
if (mpfr_nanflag_p ())
{
printf ("Error in test_overflow2 (i = %d, %s): NaN flag should"
" not be set\n", i, mpfr_print_rnd_mode (rnd));
err = 1;
}
if (mpfr_nan_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): got NaN\n",
i, mpfr_print_rnd_mode (rnd));
err = 1;
}
else if (MPFR_SIGN (r) >= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong sign "
"(+ instead of -)\n", i, mpfr_print_rnd_mode (rnd));
err = 1;
}
else if (inf && ! mpfr_inf_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -Inf,"
" got\n", i, mpfr_print_rnd_mode (rnd));
mpfr_dump (r);
err = 1;
}
else if (!inf && (mpfr_inf_p (r) ||
(mpfr_nextbelow (r), ! mpfr_inf_p (r))))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -MAX,"
" got\n", i, mpfr_print_rnd_mode (rnd));
mpfr_dump (r);
err = 1;
}
if (inf ? inex >= 0 : inex <= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong inexact"
" flag (got %d)\n", i, mpfr_print_rnd_mode (rnd), inex);
err = 1;
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (void *) 0);
}
int
main (int argc, char *argv[])
{
mpfr_t x;
long k, z, d, N;
unsigned long zl, dl;
int inex;
int r;
mpfr_exp_t emin, emax;
int flag;
tests_start_mpfr ();
mpfr_init2 (x, 100);
N = (argc==1) ? 100000 : atol (argv[1]);
for (k = 1; k <= N; k++)
{
z = (long) (randlimb () & LONG_MAX) + LONG_MIN / 2;
inex = mpfr_set_si (x, z, MPFR_RNDZ);
d = mpfr_get_si (x, MPFR_RNDZ);
if (d != z)
{
printf ("Error in mpfr_set_si: expected %ld got %ld\n", z, d);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_si: inex value incorrect for %ld: %d\n",
z, inex);
exit (1);
}
}
for (k = 1; k <= N; k++)
{
zl = randlimb ();
inex = mpfr_set_ui (x, zl, MPFR_RNDZ);
dl = mpfr_get_ui (x, MPFR_RNDZ);
if (dl != zl)
{
printf ("Error in mpfr_set_ui: expected %lu got %lu\n", zl, dl);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_ui: inex value incorrect for %lu: %d\n",
zl, inex);
exit (1);
}
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, 5, MPFR_RNDZ) >= 0)
{
printf ("Wrong inexact flag for x=5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, -5, MPFR_RNDZ) <= 0)
{
printf ("Wrong inexact flag for x=-5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 3);
inex = mpfr_set_si (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_si(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
inex = mpfr_set_ui (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_ui(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
mpfr_set_prec (x, 2);
inex = mpfr_set_si (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152 || inex <= 0)
{
printf ("Error in mpfr_set_si, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
inex = mpfr_set_ui (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
/* Also test the mpfr_set_ui function (instead of macro). */
inex = (mpfr_set_ui) (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui function, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
for (r = 0 ; r < MPFR_RND_MAX ; r++)
{
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_ui (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_ui (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_ui (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_si (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_si (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_si (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
}
/* check potential bug in case mp_limb_t is unsigned */
emax = mpfr_get_emax ();
set_emax (0);
mpfr_set_si (x, -1, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -1) fails\n");
exit (1);
}
set_emax (emax);
emax = mpfr_get_emax ();
set_emax (5);
mpfr_set_prec (x, 2);
mpfr_set_si (x, -31, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -31) fails\n");
exit (1);
}
set_emax (emax);
/* test for get_ui */
mpfr_set_ui (x, 0, MPFR_RNDN);
MPFR_ASSERTN(mpfr_get_ui (x, MPFR_RNDN) == 0);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDU);
mpfr_nextabove (x);
mpfr_get_ui (x, MPFR_RNDU);
/* another test for get_ui */
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "10.101");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 3);
mpfr_set_str_binary (x, "-1.0");
mpfr_get_ui (x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDZ);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDD);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDU);
MPFR_ASSERTN (dl == 1);
/* coverage tests */
mpfr_set_prec (x, 2);
mpfr_set_si (x, -7, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (x, -8) == 0);
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui (x, 8) == 0);
emax = mpfr_get_emax ();
set_emax (3);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (1);
MPFR_ASSERTN( mpfr_set_ui (x, 7, MPFR_RNDU) );
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_ui_2exp (x, 17, -50, MPFR_RNDN);
MPFR_ASSERTN (mpfr_get_ui (x, MPFR_RNDD) == 0);
MPFR_ASSERTN (mpfr_get_si (x, MPFR_RNDD) == 0);
/* Test for ERANGE flag + correct behaviour if overflow */
mpfr_set_prec (x, 256);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (1)\n");
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + -1 \n");
exit (1);
}
mpfr_set_si (x, LONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (1): %ld\n", d);
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, LONG_MIN, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (1)\n");
exit (1);
}
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (2)\n");
exit (1);
}
mpfr_set_nan (x);
mpfr_clear_erangeflag ();
d = mpfr_get_ui (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + NaN\n");
exit (1);
}
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + NaN\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_prec (x, 2);
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_ui (x, 7, MPFR_RNDU);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_ui (x, 8) != 0)
{
printf ("Error for mpfr_set_ui (x, 7, MPFR_RNDU), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_ui (x, 7, MPFR_RNDU) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_si (x, -7, MPFR_RNDD);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_si (x, -8) != 0)
{
printf ("Error for mpfr_set_si (x, -7, MPFR_RNDD), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_si (x, -7, MPFR_RNDD) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_clear (x);
test_2exp ();
test_macros ();
test_macros_keyword ();
tests_end_mpfr ();
return 0;
}
int
main (int argc, char *argv[])
{
mpfr_t x, y, r;
long q[1];
if (argc == 3) /* usage: tremquo x y (rnd=MPFR_RNDN implicit) */
{
mpfr_init2 (x, GMP_NUMB_BITS);
mpfr_init2 (y, GMP_NUMB_BITS);
mpfr_init2 (r, GMP_NUMB_BITS);
mpfr_set_str (x, argv[1], 10, MPFR_RNDN);
mpfr_set_str (y, argv[2], 10, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
printf ("r=");
mpfr_out_str (stdout, 10, 0, r, MPFR_RNDN);
printf (" q=%ld\n", q[0]);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
return 0;
}
tests_start_mpfr ();
bug20090227 ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (r);
/* special values */
mpfr_set_nan (x);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_nan (y);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp (r, x) == 0);
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
/* check four possible sign combinations */
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-94) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-44) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-45) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-45)) = -2^(-44) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-95) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-95)) = -2^(-94) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
/* exercise large quotient */
mpfr_set_ui_2exp (x, 1, 65, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
/* quotient is 2^65 */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0);
MPFR_ASSERTN (q[0] % 1073741824L == 0L);
/* another large quotient */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_const_pi (x, MPFR_RNDN);
mpfr_mul_2exp (x, x, 63, MPFR_RNDN);
mpfr_const_log2 (y, MPFR_RNDN);
mpfr_set_prec (r, 10);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* q should be 41803643793084085130, r should be 605/2048 */
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 605, -11) == 0);
MPFR_ASSERTN ((q[0] > 0) && ((q[0] % 1073741824L) == 733836170L));
/* check cases where quotient is 1.5 +/- eps */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (r, 63);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5, quotient should be 2 (even rule), remainder should be -1 */
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_nextabove (x); /* 3 + 2^(-63) */
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 + 2^(-64), quo should be 2, r should be -1 + 2^(-63) */
MPFR_ASSERTN (mpfr_add_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -63) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_nextabove (y); /* 2 + 2^(-63) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 - eps, quo should be 1, r should be 1 - 2^(-63) */
MPFR_ASSERTN (mpfr_sub_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -63) == 0);
MPFR_ASSERTN (q[0] == 1L);
/* bug founds by Kaveh Ghazi, 3 May 2007 */
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_set_ui (y, 3, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0 && MPFR_SIGN (r) < 0);
/* check argument reuse */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (x, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (x, 0) == 0 && MPFR_SIGN (x) < 0);
mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, MPFR_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emin (), MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_zero_p (r) && MPFR_SIGN (r) > 0);
MPFR_ASSERTN (q[0] == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
tests_end_mpfr ();
return 0;
}
/* Don't need to save/restore exponent range: the cache does it */
int
mpfr_const_pi_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t a, A, B, D, S;
mpfr_prec_t px, p, cancel, k, kmax;
MPFR_ZIV_DECL (loop);
int inex;
MPFR_LOG_FUNC
(("rnd_mode=%d", rnd_mode),
("x[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(x), mpfr_log_prec, x, inex));
px = MPFR_PREC (x);
/* we need 9*2^kmax - 4 >= px+2*kmax+8 */
for (kmax = 2; ((px + 2 * kmax + 12) / 9) >> kmax; kmax ++);
p = px + 3 * kmax + 14; /* guarantees no recomputation for px <= 10000 */
mpfr_init2 (a, p);
mpfr_init2 (A, p);
mpfr_init2 (B, p);
mpfr_init2 (D, p);
mpfr_init2 (S, p);
MPFR_ZIV_INIT (loop, p);
for (;;) {
mpfr_set_ui (a, 1, MPFR_RNDN); /* a = 1 */
mpfr_set_ui (A, 1, MPFR_RNDN); /* A = a^2 = 1 */
mpfr_set_ui_2exp (B, 1, -1, MPFR_RNDN); /* B = b^2 = 1/2 */
mpfr_set_ui_2exp (D, 1, -2, MPFR_RNDN); /* D = 1/4 */
#define b B
#define ap a
#define Ap A
#define Bp B
for (k = 0; ; k++)
{
/* invariant: 1/2 <= B <= A <= a < 1 */
mpfr_add (S, A, B, MPFR_RNDN); /* 1 <= S <= 2 */
mpfr_div_2ui (S, S, 2, MPFR_RNDN); /* exact, 1/4 <= S <= 1/2 */
mpfr_sqrt (b, B, MPFR_RNDN); /* 1/2 <= b <= 1 */
mpfr_add (ap, a, b, MPFR_RNDN); /* 1 <= ap <= 2 */
mpfr_div_2ui (ap, ap, 1, MPFR_RNDN); /* exact, 1/2 <= ap <= 1 */
mpfr_mul (Ap, ap, ap, MPFR_RNDN); /* 1/4 <= Ap <= 1 */
mpfr_sub (Bp, Ap, S, MPFR_RNDN); /* -1/4 <= Bp <= 3/4 */
mpfr_mul_2ui (Bp, Bp, 1, MPFR_RNDN); /* -1/2 <= Bp <= 3/2 */
mpfr_sub (S, Ap, Bp, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (S, 1) < 0);
cancel = mpfr_cmp_ui (S, 0) ? (mpfr_uexp_t) -mpfr_get_exp(S) : p;
/* MPFR_ASSERTN (cancel >= px || cancel >= 9 * (1 << k) - 4); */
mpfr_mul_2ui (S, S, k, MPFR_RNDN);
mpfr_sub (D, D, S, MPFR_RNDN);
/* stop when |A_k - B_k| <= 2^(k-p) i.e. cancel >= p-k */
if (cancel + k >= p)
break;
}
#undef b
#undef ap
#undef Ap
#undef Bp
mpfr_div (A, B, D, MPFR_RNDN);
/* MPFR_ASSERTN(p >= 2 * k + 8); */
if (MPFR_LIKELY (MPFR_CAN_ROUND (A, p - 2 * k - 8, px, rnd_mode)))
break;
p += kmax;
MPFR_ZIV_NEXT (loop, p);
mpfr_set_prec (a, p);
mpfr_set_prec (A, p);
mpfr_set_prec (B, p);
mpfr_set_prec (D, p);
mpfr_set_prec (S, p);
}
MPFR_ZIV_FREE (loop);
inex = mpfr_set (x, A, rnd_mode);
mpfr_clear (a);
mpfr_clear (A);
mpfr_clear (B);
mpfr_clear (D);
mpfr_clear (S);
return inex;
}
/* We use the reflection formula
Gamma(1+t) Gamma(1-t) = - Pi t / sin(Pi (1 + t))
in order to treat the case x <= 1,
i.e. with x = 1-t, then Gamma(x) = -Pi*(1-x)/sin(Pi*(2-x))/GAMMA(2-x)
*/
int
mpfr_gamma (mpfr_ptr gamma, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t xp, GammaTrial, tmp, tmp2;
mpz_t fact;
mpfr_prec_t realprec;
int compared, is_integer;
int inex = 0; /* 0 means: result gamma not set yet */
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("gamma[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (gamma), mpfr_log_prec, gamma, inex));
/* Trivial cases */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (MPFR_IS_NEG (x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
else
{
MPFR_SET_INF (gamma);
MPFR_SET_POS (gamma);
MPFR_RET (0); /* exact */
}
}
else /* x is zero */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
MPFR_SET_INF(gamma);
MPFR_SET_SAME_SIGN(gamma, x);
MPFR_SET_DIVBY0 ();
MPFR_RET (0); /* exact */
}
}
/* Check for tiny arguments, where gamma(x) ~ 1/x - euler + ....
We know from "Bound on Runs of Zeros and Ones for Algebraic Functions",
Proceedings of Arith15, T. Lang and J.-M. Muller, 2001, that the maximal
number of consecutive zeroes or ones after the round bit is n-1 for an
input of n bits. But we need a more precise lower bound. Assume x has
n bits, and 1/x is near a floating-point number y of n+1 bits. We can
write x = X*2^e, y = Y/2^f with X, Y integers of n and n+1 bits.
Thus X*Y^2^(e-f) is near from 1, i.e., X*Y is near from 2^(f-e).
Two cases can happen:
(i) either X*Y is exactly 2^(f-e), but this can happen only if X and Y
are themselves powers of two, i.e., x is a power of two;
(ii) or X*Y is at distance at least one from 2^(f-e), thus
|xy-1| >= 2^(e-f), or |y-1/x| >= 2^(e-f)/x = 2^(-f)/X >= 2^(-f-n).
Since ufp(y) = 2^(n-f) [ufp = unit in first place], this means
that the distance |y-1/x| >= 2^(-2n) ufp(y).
Now assuming |gamma(x)-1/x| <= 1, which is true for x <= 1,
if 2^(-2n) ufp(y) >= 2, the error is at most 2^(-2n-1) ufp(y),
and round(1/x) with precision >= 2n+2 gives the correct result.
If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
A sufficient condition is thus EXP(x) + 2 <= -2 MAX(PREC(x),PREC(Y)).
*/
if (MPFR_GET_EXP (x) + 2
<= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(gamma)))
{
int sign = MPFR_SIGN (x); /* retrieve sign before possible override */
int special;
MPFR_BLOCK_DECL (flags);
MPFR_SAVE_EXPO_MARK (expo);
/* for overflow cases, see below; this needs to be done
before x possibly gets overridden. */
special =
MPFR_GET_EXP (x) == 1 - MPFR_EMAX_MAX &&
MPFR_IS_POS_SIGN (sign) &&
MPFR_IS_LIKE_RNDD (rnd_mode, sign) &&
mpfr_powerof2_raw (x);
MPFR_BLOCK (flags, inex = mpfr_ui_div (gamma, 1, x, rnd_mode));
if (inex == 0) /* x is a power of two */
{
/* return RND(1/x - euler) = RND(+/- 2^k - eps) with eps > 0 */
if (rnd_mode == MPFR_RNDN || MPFR_IS_LIKE_RNDU (rnd_mode, sign))
inex = 1;
else
{
mpfr_nextbelow (gamma);
inex = -1;
}
}
else if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
{
/* Overflow in the division 1/x. This is a real overflow, except
in RNDZ or RNDD when 1/x = 2^emax, i.e. x = 2^(-emax): due to
the "- euler", the rounded value in unbounded exponent range
is 0.111...11 * 2^emax (not an overflow). */
if (!special)
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, flags);
}
MPFR_SAVE_EXPO_FREE (expo);
/* Note: an overflow is possible with an infinite result;
in this case, the overflow flag will automatically be
restored by mpfr_check_range. */
return mpfr_check_range (gamma, inex, rnd_mode);
}
is_integer = mpfr_integer_p (x);
/* gamma(x) for x a negative integer gives NaN */
if (is_integer && MPFR_IS_NEG(x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
compared = mpfr_cmp_ui (x, 1);
if (compared == 0)
return mpfr_set_ui (gamma, 1, rnd_mode);
/* if x is an integer that fits into an unsigned long, use mpfr_fac_ui
if argument is not too large.
If precision is p, fac_ui costs O(u*p), whereas gamma costs O(p*M(p)),
so for u <= M(p), fac_ui should be faster.
We approximate here M(p) by p*log(p)^2, which is not a bad guess.
Warning: since the generic code does not handle exact cases,
we want all cases where gamma(x) is exact to be treated here.
*/
if (is_integer && mpfr_fits_ulong_p (x, MPFR_RNDN))
{
unsigned long int u;
mpfr_prec_t p = MPFR_PREC(gamma);
u = mpfr_get_ui (x, MPFR_RNDN);
if (u < 44787929UL && bits_fac (u - 1) <= p + (rnd_mode == MPFR_RNDN))
/* bits_fac: lower bound on the number of bits of m,
where gamma(x) = (u-1)! = m*2^e with m odd. */
return mpfr_fac_ui (gamma, u - 1, rnd_mode);
/* if bits_fac(...) > p (resp. p+1 for rounding to nearest),
then gamma(x) cannot be exact in precision p (resp. p+1).
FIXME: remove the test u < 44787929UL after changing bits_fac
to return a mpz_t or mpfr_t. */
}
MPFR_SAVE_EXPO_MARK (expo);
/* check for overflow: according to (6.1.37) in Abramowitz & Stegun,
gamma(x) >= exp(-x) * x^(x-1/2) * sqrt(2*Pi)
>= 2 * (x/e)^x / x for x >= 1 */
if (compared > 0)
{
mpfr_t yp;
mpfr_exp_t expxp;
MPFR_BLOCK_DECL (flags);
/* quick test for the default exponent range */
if (mpfr_get_emax () >= 1073741823UL && MPFR_GET_EXP(x) <= 25)
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_gamma_aux (gamma, x, rnd_mode);
}
/* 1/e rounded down to 53 bits */
#define EXPM1_STR "0.010111100010110101011000110110001011001110111100111"
mpfr_init2 (xp, 53);
mpfr_init2 (yp, 53);
mpfr_set_str_binary (xp, EXPM1_STR);
mpfr_mul (xp, x, xp, MPFR_RNDZ);
mpfr_sub_ui (yp, x, 2, MPFR_RNDZ);
mpfr_pow (xp, xp, yp, MPFR_RNDZ); /* (x/e)^(x-2) */
mpfr_set_str_binary (yp, EXPM1_STR);
mpfr_mul (xp, xp, yp, MPFR_RNDZ); /* x^(x-2) / e^(x-1) */
mpfr_mul (xp, xp, yp, MPFR_RNDZ); /* x^(x-2) / e^x */
mpfr_mul (xp, xp, x, MPFR_RNDZ); /* lower bound on x^(x-1) / e^x */
MPFR_BLOCK (flags, mpfr_mul_2ui (xp, xp, 1, MPFR_RNDZ));
expxp = MPFR_GET_EXP (xp);
mpfr_clear (xp);
mpfr_clear (yp);
MPFR_SAVE_EXPO_FREE (expo);
return MPFR_OVERFLOW (flags) || expxp > __gmpfr_emax ?
mpfr_overflow (gamma, rnd_mode, 1) :
mpfr_gamma_aux (gamma, x, rnd_mode);
}
/* now compared < 0 */
/* check for underflow: for x < 1,
gamma(x) = Pi*(x-1)/sin(Pi*(2-x))/gamma(2-x).
Since gamma(2-x) >= 2 * ((2-x)/e)^(2-x) / (2-x), we have
|gamma(x)| <= Pi*(1-x)*(2-x)/2/((2-x)/e)^(2-x) / |sin(Pi*(2-x))|
<= 12 * ((2-x)/e)^x / |sin(Pi*(2-x))|.
To avoid an underflow in ((2-x)/e)^x, we compute the logarithm.
*/
if (MPFR_IS_NEG(x))
{
int underflow = 0, sgn, ck;
mpfr_prec_t w;
mpfr_init2 (xp, 53);
mpfr_init2 (tmp, 53);
mpfr_init2 (tmp2, 53);
/* we want an upper bound for x * [log(2-x)-1].
since x < 0, we need a lower bound on log(2-x) */
mpfr_ui_sub (xp, 2, x, MPFR_RNDD);
mpfr_log (xp, xp, MPFR_RNDD);
mpfr_sub_ui (xp, xp, 1, MPFR_RNDD);
mpfr_mul (xp, xp, x, MPFR_RNDU);
/* we need an upper bound on 1/|sin(Pi*(2-x))|,
thus a lower bound on |sin(Pi*(2-x))|.
If 2-x is exact, then the error of Pi*(2-x) is (1+u)^2 with u = 2^(-p)
thus the error on sin(Pi*(2-x)) is less than 1/2ulp + 3Pi(2-x)u,
assuming u <= 1, thus <= u + 3Pi(2-x)u */
w = mpfr_gamma_2_minus_x_exact (x); /* 2-x is exact for prec >= w */
w += 17; /* to get tmp2 small enough */
mpfr_set_prec (tmp, w);
mpfr_set_prec (tmp2, w);
MPFR_DBGRES (ck = mpfr_ui_sub (tmp, 2, x, MPFR_RNDN));
MPFR_ASSERTD (ck == 0); /* tmp = 2-x exactly */
mpfr_const_pi (tmp2, MPFR_RNDN);
mpfr_mul (tmp2, tmp2, tmp, MPFR_RNDN); /* Pi*(2-x) */
mpfr_sin (tmp, tmp2, MPFR_RNDN); /* sin(Pi*(2-x)) */
sgn = mpfr_sgn (tmp);
mpfr_abs (tmp, tmp, MPFR_RNDN);
mpfr_mul_ui (tmp2, tmp2, 3, MPFR_RNDU); /* 3Pi(2-x) */
mpfr_add_ui (tmp2, tmp2, 1, MPFR_RNDU); /* 3Pi(2-x)+1 */
mpfr_div_2ui (tmp2, tmp2, mpfr_get_prec (tmp), MPFR_RNDU);
/* if tmp2<|tmp|, we get a lower bound */
if (mpfr_cmp (tmp2, tmp) < 0)
{
mpfr_sub (tmp, tmp, tmp2, MPFR_RNDZ); /* low bnd on |sin(Pi*(2-x))| */
mpfr_ui_div (tmp, 12, tmp, MPFR_RNDU); /* upper bound */
mpfr_log2 (tmp, tmp, MPFR_RNDU);
mpfr_add (xp, tmp, xp, MPFR_RNDU);
/* The assert below checks that expo.saved_emin - 2 always
fits in a long. FIXME if we want to allow mpfr_exp_t to
be a long long, for instance. */
MPFR_ASSERTN (MPFR_EMIN_MIN - 2 >= LONG_MIN);
underflow = mpfr_cmp_si (xp, expo.saved_emin - 2) <= 0;
}
mpfr_clear (xp);
mpfr_clear (tmp);
mpfr_clear (tmp2);
if (underflow) /* the sign is the opposite of that of sin(Pi*(2-x)) */
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (gamma, (rnd_mode == MPFR_RNDN) ? MPFR_RNDZ : rnd_mode, -sgn);
}
}
realprec = MPFR_PREC (gamma);
/* we want both 1-x and 2-x to be exact */
{
mpfr_prec_t w;
w = mpfr_gamma_1_minus_x_exact (x);
if (realprec < w)
realprec = w;
w = mpfr_gamma_2_minus_x_exact (x);
if (realprec < w)
realprec = w;
}
realprec = realprec + MPFR_INT_CEIL_LOG2 (realprec) + 20;
MPFR_ASSERTD(realprec >= 5);
MPFR_GROUP_INIT_4 (group, realprec + MPFR_INT_CEIL_LOG2 (realprec) + 20,
xp, tmp, tmp2, GammaTrial);
mpz_init (fact);
MPFR_ZIV_INIT (loop, realprec);
for (;;)
{
mpfr_exp_t err_g;
int ck;
MPFR_GROUP_REPREC_4 (group, realprec, xp, tmp, tmp2, GammaTrial);
/* reflection formula: gamma(x) = Pi*(x-1)/sin(Pi*(2-x))/gamma(2-x) */
ck = mpfr_ui_sub (xp, 2, x, MPFR_RNDN); /* 2-x, exact */
MPFR_ASSERTD(ck == 0); (void) ck; /* use ck to avoid a warning */
mpfr_gamma (tmp, xp, MPFR_RNDN); /* gamma(2-x), error (1+u) */
mpfr_const_pi (tmp2, MPFR_RNDN); /* Pi, error (1+u) */
mpfr_mul (GammaTrial, tmp2, xp, MPFR_RNDN); /* Pi*(2-x), error (1+u)^2 */
err_g = MPFR_GET_EXP(GammaTrial);
mpfr_sin (GammaTrial, GammaTrial, MPFR_RNDN); /* sin(Pi*(2-x)) */
/* If tmp is +Inf, we compute exp(lngamma(x)). */
if (mpfr_inf_p (tmp))
{
inex = mpfr_explgamma (gamma, x, &expo, tmp, tmp2, rnd_mode);
if (inex)
goto end;
else
goto ziv_next;
}
err_g = err_g + 1 - MPFR_GET_EXP(GammaTrial);
/* let g0 the true value of Pi*(2-x), g the computed value.
We have g = g0 + h with |h| <= |(1+u^2)-1|*g.
Thus sin(g) = sin(g0) + h' with |h'| <= |(1+u^2)-1|*g.
The relative error is thus bounded by |(1+u^2)-1|*g/sin(g)
<= |(1+u^2)-1|*2^err_g. <= 2.25*u*2^err_g for |u|<=1/4.
With the rounding error, this gives (0.5 + 2.25*2^err_g)*u. */
ck = mpfr_sub_ui (xp, x, 1, MPFR_RNDN); /* x-1, exact */
MPFR_ASSERTD(ck == 0); (void) ck; /* use ck to avoid a warning */
mpfr_mul (xp, tmp2, xp, MPFR_RNDN); /* Pi*(x-1), error (1+u)^2 */
mpfr_mul (GammaTrial, GammaTrial, tmp, MPFR_RNDN);
/* [1 + (0.5 + 2.25*2^err_g)*u]*(1+u)^2 = 1 + (2.5 + 2.25*2^err_g)*u
+ (0.5 + 2.25*2^err_g)*u*(2u+u^2) + u^2.
For err_g <= realprec-2, we have (0.5 + 2.25*2^err_g)*u <=
0.5*u + 2.25/4 <= 0.6875 and u^2 <= u/4, thus
(0.5 + 2.25*2^err_g)*u*(2u+u^2) + u^2 <= 0.6875*(2u+u/4) + u/4
<= 1.8*u, thus the rel. error is bounded by (4.5 + 2.25*2^err_g)*u. */
mpfr_div (GammaTrial, xp, GammaTrial, MPFR_RNDN);
/* the error is of the form (1+u)^3/[1 + (4.5 + 2.25*2^err_g)*u].
For realprec >= 5 and err_g <= realprec-2, [(4.5 + 2.25*2^err_g)*u]^2
<= 0.71, and for |y|<=0.71, 1/(1-y) can be written 1+a*y with a<=4.
(1+u)^3 * (1+4*(4.5 + 2.25*2^err_g)*u)
= 1 + (21 + 9*2^err_g)*u + (57+27*2^err_g)*u^2 + (55+27*2^err_g)*u^3
+ (18+9*2^err_g)*u^4
<= 1 + (21 + 9*2^err_g)*u + (57+27*2^err_g)*u^2 + (56+28*2^err_g)*u^3
<= 1 + (21 + 9*2^err_g)*u + (59+28*2^err_g)*u^2
<= 1 + (23 + 10*2^err_g)*u.
The final error is thus bounded by (23 + 10*2^err_g) ulps,
which is <= 2^6 for err_g<=2, and <= 2^(err_g+4) for err_g >= 2. */
err_g = (err_g <= 2) ? 6 : err_g + 4;
if (MPFR_LIKELY (MPFR_CAN_ROUND (GammaTrial, realprec - err_g,
MPFR_PREC(gamma), rnd_mode)))
break;
ziv_next:
MPFR_ZIV_NEXT (loop, realprec);
}
end:
MPFR_ZIV_FREE (loop);
if (inex == 0)
inex = mpfr_set (gamma, GammaTrial, rnd_mode);
MPFR_GROUP_CLEAR (group);
mpz_clear (fact);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (gamma, inex, rnd_mode);
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
/* special values */
mpfr_set_nan (x);
mpfr_y0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_y0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_inf (x, -1); /* -Inf */
mpfr_y0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_ui (x, 0, MPFR_RNDN); /* +0 */
mpfr_y0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y0(+0)=-Inf */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_y0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y0(-0)=-Inf */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_y0 (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.00010110100110000000001000100110111100110101100011011111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_y0 for x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_y0 (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error in mpfr_y0 for x=-1, rnd=MPFR_RNDN\n");
printf ("Expected NaN\n");
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
test_generic (2, 100, 1);
data_check ("data/y0", mpfr_y0, "mpfr_y0");
tests_end_mpfr ();
return 0;
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
long n;
mpfr_prec_t prec = 53;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
if (argc != 1)
{
if (argc != 4)
{
printf ("Usage: tyn n x prec\n");
exit (1);
}
n = atoi (argv[1]);
prec = atoi (argv[3]);
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
mpfr_set_str (x, argv[2], 10, MPFR_RNDN);
mpfr_yn (y, n, x, MPFR_RNDN);
printf ("Y(%ld,", n);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (")=");
mpfr_out_str (stdout, 10, 0, y, MPFR_RNDN);
printf ("\n");
goto end;
}
/* special values */
mpfr_set_nan (x);
mpfr_yn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_yn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_inf (x, -1); /* -Inf */
mpfr_yn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_ui (x, 0, MPFR_RNDN); /* +0 */
mpfr_yn (y, 0, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y0(+0)=-Inf */
mpfr_yn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y17(+0)=-Inf */
mpfr_yn (y, -17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_POS (y)); /* y(-17,+0)=+Inf */
mpfr_yn (y, -42, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y(-42,+0)=-Inf */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_yn (y, 0, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y0(-0)=-Inf */
mpfr_yn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y17(-0)=-Inf */
mpfr_yn (y, -17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_POS (y)); /* y(-17,-0)=+Inf */
mpfr_yn (y, -42, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y(-42,-0)=-Inf */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, 0, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.00010110100110000000001000100110111100110101100011011111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=0, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, 1, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.110001111111110110010000001111101011001101011100101");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=1, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, -1, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.110001111111110110010000001111101011001101011100101");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=-1, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, 2, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-1.101001101001001100100010101001000101101000010010001");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=2, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, -2, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-1.101001101001001100100010101001000101101000010010001");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=-2, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, 17, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.11000100111000100010101101011000110011001101100001011E60");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=17, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_yn (y, -17, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11000100111000100010101101011000110011001101100001011E60");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=-17, x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_yn (y, 1, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.00101010110011011111001100000001101011011001111111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_yn for n=1, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
end:
mpfr_clear (x);
mpfr_clear (y);
tests_end_mpfr ();
return 0;
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
int inex;
tests_start_mpfr ();
special_overflow ();
check_nans ();
mpfr_init (x);
mpfr_init (y);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 2);
mpfr_set_str (x, "9.81333845856942e-1", 10, MPFR_RNDN);
test_cos (y, x, MPFR_RNDN);
mpfr_set_prec (x, 30);
mpfr_set_prec (y, 30);
mpfr_set_str_binary (x, "1.00001010001101110010100010101e-1");
test_cos (y, x, MPFR_RNDU);
mpfr_set_str_binary (x, "1.10111100010101011110101010100e-1");
if (mpfr_cmp (y, x))
{
printf ("Error for prec=30, rnd=MPFR_RNDU\n");
printf ("expected "); mpfr_print_binary (x); puts ("");
printf (" got "); mpfr_print_binary (y); puts ("");
exit (1);
}
mpfr_set_prec (x, 59);
mpfr_set_prec (y, 59);
mpfr_set_str_binary (x, "1.01101011101111010011111110111111111011011101100111100011e-3");
test_cos (y, x, MPFR_RNDU);
mpfr_set_str_binary (x, "1.1111011111110010001001001011100111101110100010000010010011e-1");
if (mpfr_cmp (y, x))
{
printf ("Error for prec=59, rnd=MPFR_RNDU\n");
printf ("expected "); mpfr_print_binary (x); puts ("");
printf (" got "); mpfr_print_binary (y); puts ("");
exit (1);
}
mpfr_set_prec (x, 5);
mpfr_set_prec (y, 5);
mpfr_set_str_binary (x, "1.1100e-2");
test_cos (y, x, MPFR_RNDD);
mpfr_set_str_binary (x, "1.1100e-1");
if (mpfr_cmp (y, x))
{
printf ("Error for x=1.1100e-2, rnd=MPFR_RNDD\n");
printf ("expected 1.1100e-1, got "); mpfr_print_binary (y); puts ("");
exit (1);
}
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (x, "0.10001000001001011000100001E-6");
mpfr_set_str_binary (y, "0.1111111111111101101111001100001");
test_cos (x, x, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error for prec=32 (1)\n");
exit (1);
}
mpfr_set_str_binary (x, "-0.1101011110111100111010011001011E-1");
mpfr_set_str_binary (y, "0.11101001100110111011011010100011");
test_cos (x, x, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error for prec=32 (2)\n");
exit (1);
}
/* huge argument reduction */
mpfr_set_str_binary (x, "0.10000010000001101011101111001011E40");
mpfr_set_str_binary (y, "0.10011000001111010000101011001011E-1");
test_cos (x, x, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error for prec=32 (3)\n");
exit (1);
}
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 3);
mpfr_set_str_binary (x, "0.110E60");
inex = mpfr_cos (y, x, MPFR_RNDD);
MPFR_ASSERTN(inex < 0);
/* worst case from PhD thesis of Vincent Lefe`vre: x=8980155785351021/2^54 */
check53 ("4.984987858808754279e-1", "8.783012931285841817e-1", MPFR_RNDN);
check53 ("4.984987858808754279e-1", "8.783012931285840707e-1", MPFR_RNDD);
check53 ("4.984987858808754279e-1", "8.783012931285840707e-1", MPFR_RNDZ);
check53 ("4.984987858808754279e-1", "8.783012931285841817e-1", MPFR_RNDU);
check53 ("1.00031274099908640274", "0.540039116973283217504", MPFR_RNDN);
check53 ("1.00229256850978698523", "0.538371757797526551137", MPFR_RNDZ);
check53 ("1.00288304857059840103", "0.537874062022526966409", MPFR_RNDZ);
check53 ("1.00591265847407274059", "0.53531755997839769456", MPFR_RNDN);
check53 ("1.00591265847407274059", "0.53531755997839769456", MPFR_RNDN);
overflowed_cos0 ();
test_generic (2, 100, 15);
/* check inexact flag */
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 13);
mpfr_set_str_binary (x, "-0.100E196");
inex = mpfr_cos (y, x, MPFR_RNDU);
mpfr_set_prec (x, 13);
mpfr_set_str_binary (x, "0.1111111100101");
MPFR_ASSERTN (inex > 0 && mpfr_equal_p (x, y));
mpfr_clear (x);
mpfr_clear (y);
bug20091030 ();
data_check ("data/cos", mpfr_cos, "mpfr_cos");
bad_cases (mpfr_cos, mpfr_acos, "mpfr_cos", 256, -40, 0, 4, 128, 800, 50);
tests_end_mpfr ();
return 0;
}
/* returns 0 if result exact, non-zero otherwise */
int
mpfr_div_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mp_rnd_t rnd_mode)
{
long int xn, yn, dif, sh, i;
mp_limb_t *xp, *yp, *tmp, c, d;
mp_exp_t exp;
int inexact, middle = 1;
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))
{
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_RET(0);
}
}
}
if (MPFR_UNLIKELY(u == 0))
{
/* x/0 is Inf */
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y, x);
MPFR_RET(0);
}
MPFR_CLEAR_FLAGS(y);
MPFR_SET_SAME_SIGN(y, x);
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 = (mp_limb_t*) TMP_ALLOC((yn + 1) * BYTES_PER_MP_LIMB);
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 (rnd_mode == GMP_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 -= BITS_PER_MP_LIMB;
sh = 0;
}
else
{
count_leading_zeros (sh, tmp[yn]);
/* shift left to normalize */
if (sh)
{
mp_limb_t w = tmp[0] << sh;
mpn_lshift (yp, tmp + 1, yn, sh);
yp[0] += tmp[0] >> (BITS_PER_MP_LIMB - sh);
if (w > (MPFR_LIMB_ONE << (BITS_PER_MP_LIMB - 1)))
{ middle = 1; }
else if (w < (MPFR_LIMB_ONE << (BITS_PER_MP_LIMB - 1)))
{ middle = -1; }
else
{ middle = (c != 0); }
inexact = inexact || (w != 0);
exp -= sh;
}
else
{ /* this happens only if u == 1 and xp[xn-1] >=
1<<(BITS_PER_MP_LIMB-1). It might be better to handle the
u == 1 case seperately ?
*/
MPN_COPY (yp, tmp + 1, yn);
}
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
int inex;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
/* special values */
mpfr_set_nan (x);
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_inf (x, -1); /* -Inf */
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_ui (x, 0, MPFR_RNDN); /* +0 */
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(+0)=1 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(-0)=1 */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_j0 (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_j0 for x=1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_j0 (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_j0 for x=-1, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
/* Bug reported on 2007-07-03 by Sisyphus (assertion failed in r4619) */
mpfr_set_si (x, 70000, MPFR_RNDN);
mpfr_j0 (y, x, MPFR_RNDN);
/* Bug reported by Kevin Rauch on 27 Oct 2007 */
mpfr_set_prec (x, 7);
mpfr_set_prec (y, 7);
mpfr_set_si (x, -100, MPFR_RNDN);
mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN (! mpfr_nan_p (y) && mpfr_cmp_ui_2exp (y, 41, -11) == 0);
/* Case for which s = 0 in mpfr_jn */
mpfr_set_prec (x, 44);
mpfr_set_prec (y, 44);
mpfr_set_si (x, 2, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_j0 (y, x, MPFR_RNDN);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_INEXACT);
mpfr_set_str (x, "0x.e5439fd9267p-2", 0, MPFR_RNDN);
if (! mpfr_equal_p (y, x))
{
printf ("Error on 2:\n");
printf ("Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
if (inex >= 0)
{
printf ("Bad ternary value on 2: expected negative, got %d\n", inex);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
test_generic (2, 100, 10);
data_check ("data/j0", mpfr_j0, "mpfr_j0");
tests_end_mpfr ();
return 0;
}
