static void
check_pow_si (void)
{
mpfr_t x;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MAX, GMP_RNDN); /* 2^LONG_MAX */
if (LONG_MAX > mpfr_get_emax () - 1) /* LONG_MAX + 1 > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MAX));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^LONG_MIN */
if (LONG_MIN + 1 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN + 1, GMP_RNDN); /* 2^(LONG_MIN+1) */
if (mpfr_nan_p (x))
{
printf ("Error in pow_si(2, LONG_MIN+1): got NaN\n");
exit (1);
}
if (LONG_MIN + 2 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN + 1));
}
mpfr_set_si_2exp (x, 1, -1, GMP_RNDN); /* 0.5 */
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^(-LONG_MIN) */
if (LONG_MIN < 1 - mpfr_get_emax ()) /* 1 - LONG_MIN > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 2, - (LONG_MIN + 1)));
}
mpfr_clear (x);
}
/* Implements asymptotic expansion for jn or yn (formulae 9.2.5 and 9.2.6
from Abramowitz & Stegun).
Assumes |z| > p log(2)/2, where p is the target precision
(z can be negative only for jn).
Return 0 if the expansion does not converge enough (the value 0 as inexact
flag should not happen for normal input).
*/
static int
FUNCTION (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
{
mpfr_t s, c, P, Q, t, iz, err_t, err_s, err_u;
mpfr_prec_t w;
long k;
int inex, stop, diverge = 0;
mpfr_exp_t err2, err;
MPFR_ZIV_DECL (loop);
mpfr_init (c);
w = MPFR_PREC(res) + MPFR_INT_CEIL_LOG2(MPFR_PREC(res)) + 4;
MPFR_ZIV_INIT (loop, w);
for (;;)
{
mpfr_set_prec (c, w);
mpfr_init2 (s, w);
mpfr_init2 (P, w);
mpfr_init2 (Q, w);
mpfr_init2 (t, w);
mpfr_init2 (iz, w);
mpfr_init2 (err_t, 31);
mpfr_init2 (err_s, 31);
mpfr_init2 (err_u, 31);
/* Approximate sin(z) and cos(z). In the following, err <= k means that
the approximate value y and the true value x are related by
y = x * (1 + u)^k with |u| <= 2^(-w), following Higham's method. */
mpfr_sin_cos (s, c, z, MPFR_RNDN);
if (MPFR_IS_NEG(z))
mpfr_neg (s, s, MPFR_RNDN); /* compute jn/yn(|z|), fix sign later */
/* The absolute error on s/c is bounded by 1/2 ulp(1/2) <= 2^(-w-1). */
mpfr_add (t, s, c, MPFR_RNDN);
mpfr_sub (c, s, c, MPFR_RNDN);
mpfr_swap (s, t);
/* now s approximates sin(z)+cos(z), and c approximates sin(z)-cos(z),
with total absolute error bounded by 2^(1-w). */
/* precompute 1/(8|z|) */
mpfr_si_div (iz, MPFR_IS_POS(z) ? 1 : -1, z, MPFR_RNDN); /* err <= 1 */
mpfr_div_2ui (iz, iz, 3, MPFR_RNDN);
/* compute P and Q */
mpfr_set_ui (P, 1, MPFR_RNDN);
mpfr_set_ui (Q, 0, MPFR_RNDN);
mpfr_set_ui (t, 1, MPFR_RNDN); /* current term */
mpfr_set_ui (err_t, 0, MPFR_RNDN); /* error on t */
mpfr_set_ui (err_s, 0, MPFR_RNDN); /* error on P and Q (sum of errors) */
for (k = 1, stop = 0; stop < 4; k++)
{
/* compute next term: t(k)/t(k-1) = (2n+2k-1)(2n-2k+1)/(8kz) */
mpfr_mul_si (t, t, 2 * (n + k) - 1, MPFR_RNDN); /* err <= err_k + 1 */
mpfr_mul_si (t, t, 2 * (n - k) + 1, MPFR_RNDN); /* err <= err_k + 2 */
mpfr_div_ui (t, t, k, MPFR_RNDN); /* err <= err_k + 3 */
mpfr_mul (t, t, iz, MPFR_RNDN); /* err <= err_k + 5 */
/* the relative error on t is bounded by (1+u)^(5k)-1, which is
bounded by 6ku for 6ku <= 0.02: first |5 log(1+u)| <= |5.5u|
for |u| <= 0.15, then |exp(5.5u)-1| <= 6u for |u| <= 0.02. */
mpfr_mul_ui (err_t, t, 6 * k, MPFR_IS_POS(t) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDN); /* exact */
/* the absolute error on t is bounded by err_t * 2^(-w) */
mpfr_abs (err_u, t, MPFR_RNDU);
mpfr_mul_2ui (err_u, err_u, w, MPFR_RNDU); /* t * 2^w */
mpfr_add (err_u, err_u, err_t, MPFR_RNDU); /* max|t| * 2^w */
if (stop >= 2)
{
/* take into account the neglected terms: t * 2^w */
mpfr_div_2ui (err_s, err_s, w, MPFR_RNDU);
if (MPFR_IS_POS(t))
mpfr_add (err_s, err_s, t, MPFR_RNDU);
else
mpfr_sub (err_s, err_s, t, MPFR_RNDU);
mpfr_mul_2ui (err_s, err_s, w, MPFR_RNDU);
stop ++;
}
/* if k is odd, add to Q, otherwise to P */
else if (k & 1)
{
/* if k = 1 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (Q, Q, t, MPFR_RNDN);
else
mpfr_sub (Q, Q, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(Q): if EXP(err_u)
<= EXP(Q), since the current term is bounded by
err_u * 2^(-w), it is bounded by ulp(Q) */
if (MPFR_EXP(err_u) <= MPFR_EXP(Q))
stop ++;
else
stop = 0;
}
else
{
/* if k = 0 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (P, P, t, MPFR_RNDN);
else
mpfr_sub (P, P, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(P) */
if (MPFR_EXP(err_u) <= MPFR_EXP(P))
stop ++;
else
stop = 0;
}
mpfr_add (err_s, err_s, err_t, MPFR_RNDU);
/* the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w) */
/* stop when start to diverge */
if (stop < 2 &&
((MPFR_IS_POS(z) && mpfr_cmp_ui (z, (k + 1) / 2) < 0) ||
(MPFR_IS_NEG(z) && mpfr_cmp_si (z, - ((k + 1) / 2)) > 0)))
{
/* if we have to stop the series because it diverges, then
increasing the precision will most probably fail, since
we will stop to the same point, and thus compute a very
similar approximation */
diverge = 1;
stop = 2; /* force stop */
}
}
/* the sum of the total errors on P and Q is bounded by err_s * 2^(-w) */
/* Now combine: the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w), and the absolute error on s/c is bounded by 2^(1-w) */
if ((n & 1) == 0) /* n even: P * (sin + cos) + Q (cos - sin) for jn
Q * (sin + cos) + P (sin - cos) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#else
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_sub (s, s, c, MPFR_RNDN);
#else
mpfr_add (s, s, c, MPFR_RNDN);
#endif
}
else /* n odd: P * (sin - cos) + Q (cos + sin) for jn,
Q * (sin - cos) - P (cos + sin) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#else
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_add (s, s, c, MPFR_RNDN);
#else
mpfr_sub (s, c, s, MPFR_RNDN);
#endif
}
if ((n & 2) != 0)
mpfr_neg (s, s, MPFR_RNDN);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
/* the absolute error on s is bounded by P*err(s/c) + Q*err(s/c)
+ err(P)*(s/c) + err(Q)*(s/c) + 3 * 2^(err - w - 1)
<= (|P|+|Q|) * 2^(1-w) + err_s * 2^(1-w) + 2^err * 2^(1-w),
since |c|, |old_s| <= 2. */
err2 = (MPFR_EXP(P) >= MPFR_EXP(Q)) ? MPFR_EXP(P) + 2 : MPFR_EXP(Q) + 2;
/* (|P| + |Q|) * 2^(1 - w) <= 2^(err2 - w) */
err = MPFR_EXP(err_s) >= err ? MPFR_EXP(err_s) + 2 : err + 2;
/* err_s * 2^(1-w) + 2^old_err * 2^(1-w) <= 2^err * 2^(-w) */
err2 = (err >= err2) ? err + 1 : err2 + 1;
/* now the absolute error on s is bounded by 2^(err2 - w) */
/* multiply by sqrt(1/(Pi*z)) */
mpfr_const_pi (c, MPFR_RNDN); /* Pi, err <= 1 */
mpfr_mul (c, c, z, MPFR_RNDN); /* err <= 2 */
mpfr_si_div (c, MPFR_IS_POS(z) ? 1 : -1, c, MPFR_RNDN); /* err <= 3 */
mpfr_sqrt (c, c, MPFR_RNDN); /* err<=5/2, thus the absolute error is
bounded by 3*u*|c| for |u| <= 0.25 */
mpfr_mul (err_t, c, s, MPFR_SIGN(c)==MPFR_SIGN(s) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDU);
mpfr_mul_ui (err_t, err_t, 3, MPFR_RNDU);
/* 3*2^(-w)*|old_c|*|s| [see below] is bounded by err_t * 2^(-w) */
err2 += MPFR_EXP(c);
/* |old_c| * 2^(err2 - w) [see below] is bounded by 2^(err2-w) */
mpfr_mul (c, c, s, MPFR_RNDN); /* the absolute error on c is bounded by
1/2 ulp(c) + 3*2^(-w)*|old_c|*|s|
+ |old_c| * 2^(err2 - w) */
/* compute err_t * 2^(-w) + 1/2 ulp(c) = (err_t + 2^EXP(c)) * 2^(-w) */
err = (MPFR_EXP(err_t) > MPFR_EXP(c)) ? MPFR_EXP(err_t) + 1 : MPFR_EXP(c) + 1;
/* err_t * 2^(-w) + 1/2 ulp(c) <= 2^(err - w) */
/* now err_t * 2^(-w) bounds 1/2 ulp(c) + 3*2^(-w)*|old_c|*|s| */
err = (err >= err2) ? err + 1 : err2 + 1;
/* the absolute error on c is bounded by 2^(err - w) */
mpfr_clear (s);
mpfr_clear (P);
mpfr_clear (Q);
mpfr_clear (t);
mpfr_clear (iz);
mpfr_clear (err_t);
mpfr_clear (err_s);
mpfr_clear (err_u);
err -= MPFR_EXP(c);
if (MPFR_LIKELY (MPFR_CAN_ROUND (c, w - err, MPFR_PREC(res), r)))
break;
if (diverge != 0)
{
mpfr_set (c, z, r); /* will force inex=0 below, which means the
asymptotic expansion failed */
break;
}
MPFR_ZIV_NEXT (loop, w);
}
MPFR_ZIV_FREE (loop);
inex = (MPFR_IS_POS(z) || ((n & 1) == 0)) ? mpfr_set (res, c, r)
: mpfr_neg (res, c, r);
mpfr_clear (c);
return inex;
}
/* (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, mp_rnd_t rnd_mode)
{
mp_prec_t prec, m;
int neg, reduce;
mpfr_t c, xr;
mpfr_srcptr xx;
mp_exp_t err, expx;
MPFR_ZIV_DECL (loop);
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 */
return mpfr_set_ui (z, 1, rnd_mode);
}
}
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("sin[%#R]=%R cos[%#R]=%R", y, y, z, z));
prec = MAX (MPFR_PREC (y), MPFR_PREC (z));
m = prec + MPFR_INT_CEIL_LOG2 (prec) + 13;
expx = MPFR_GET_EXP (x);
mpfr_init (c);
mpfr_init (xr);
MPFR_ZIV_INIT (loop, m);
for (;;)
{
/* the following is copied from sin.c */
if (expx >= 2) /* reduce the argument */
{
reduce = 1;
mpfr_set_prec (c, expx + m - 1);
mpfr_set_prec (xr, m);
mpfr_const_pi (c, GMP_RNDN);
mpfr_mul_2ui (c, c, 1, GMP_RNDN);
mpfr_remainder (xr, x, c, GMP_RNDN);
mpfr_div_2ui (c, c, 1, GMP_RNDN);
if (MPFR_SIGN (xr) > 0)
mpfr_sub (c, c, xr, GMP_RNDZ);
else
mpfr_add (c, c, xr, GMP_RNDZ);
if (MPFR_IS_ZERO(xr) || MPFR_EXP(xr) < (mp_exp_t) 3 - (mp_exp_t) m
|| MPFR_EXP(c) < (mp_exp_t) 3 - (mp_exp_t) m)
goto next_step;
xx = xr;
}
else /* the input argument is already reduced */
{
reduce = 0;
xx = x;
}
neg = MPFR_IS_NEG (xx); /* gives sign of sin(x) */
mpfr_set_prec (c, m);
mpfr_cos (c, xx, GMP_RNDZ);
/* If no argument reduction was performed, the error is at most ulp(c),
otherwise it is at most ulp(c) + 2^(2-m). Since |c| < 1, we have
ulp(c) <= 2^(-m), thus the error is bounded by 2^(3-m) in that later
case. */
if (reduce == 0)
err = m;
else
err = MPFR_GET_EXP (c) + (mp_exp_t) (m - 3);
if (!mpfr_can_round (c, err, GMP_RNDN, rnd_mode,
MPFR_PREC (z) + (rnd_mode == GMP_RNDN)))
goto next_step;
mpfr_set (z, c, rnd_mode);
mpfr_sqr (c, c, GMP_RNDU);
mpfr_ui_sub (c, 1, c, GMP_RNDN);
err = 2 + (- MPFR_GET_EXP (c)) / 2;
mpfr_sqrt (c, c, GMP_RNDN);
if (neg)
MPFR_CHANGE_SIGN (c);
/* the absolute error on c is at most 2^(err-m), which we must put
in the form 2^(EXP(c)-err). If there was an argument reduction,
we need to add 2^(2-m); since err >= 2, the error is bounded by
2^(err+1-m) in that case. */
err = MPFR_GET_EXP (c) + (mp_exp_t) m - (err + reduce);
if (mpfr_can_round (c, err, GMP_RNDN, rnd_mode,
MPFR_PREC (y) + (rnd_mode == GMP_RNDN)))
break;
/* check for huge cancellation */
if (err < (mp_exp_t) MPFR_PREC (y))
m += MPFR_PREC (y) - err;
/* Check if near 1 */
if (MPFR_GET_EXP (c) == 1
&& MPFR_MANT (c)[MPFR_LIMB_SIZE (c)-1] == MPFR_LIMB_HIGHBIT)
m += m;
next_step:
MPFR_ZIV_NEXT (loop, m);
mpfr_set_prec (c, m);
}
MPFR_ZIV_FREE (loop);
mpfr_set (y, c, rnd_mode);
mpfr_clear (c);
mpfr_clear (xr);
MPFR_RET (1); /* Always inexact */
}
static void
special (void)
{
mpfr_t x, y;
int inex;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(NaN)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-Inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lngamma(+Inf)\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lngamma(+0)\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-0)\n");
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
{
printf ("Error for lngamma(1)\n");
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-1)\n");
exit (1);
}
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
{
printf ("Error for lngamma(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, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str (x, CHECK_Y1, 10, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp (y, x))
{
printf ("mpfr_lngamma("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, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str (x, CHECK_Y2, 10, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp (y, x))
{
printf ("mpfr_lngamma("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, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDU);
mpfr_set_prec (x, 175);
mpfr_set_str_binary (x, "0.1010001100011101101011001101110010100001000001000001110011000001101100001111001001000101011011100100010101011110100111110101010100010011010010000101010111001100011000101111E7");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (1)\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 8);
mpfr_set_ui (y, 120, MPFR_RNDN);
mpfr_lngamma (x, y, MPFR_RNDZ);
mpfr_set_prec (y, 21);
mpfr_set_str_binary (y, "0.111000101000001100101E9");
if (MPFR_IS_NAN (x) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (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");
inex = mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_prec (x, 206);
mpfr_set_str_binary (x, "0.10000111011000000011100010101001100110001110000111100011000100100110110010001011011110101001111011110110000001010100111011010000000011100110110101100111000111010011110010000100010111101010001101000110101001E13");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (768)\n");
exit (1);
}
if (inex >= 0)
{
printf ("Wrong flag for mpfr_lngamma (768)\n");
exit (1);
}
mpfr_set_prec (x, 4);
mpfr_set_prec (y, 4);
mpfr_set_str_binary (x, "0.1100E-66");
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100E6");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error for lngamma(0.1100E-66)\n");
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error for lngamma(-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, MPFR_RNDN);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-2^199-0.5)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
static void
check_overflow (void)
{
mpfr_t x;
char *s;
mpfr_init (x);
/* Huge overflow */
mpfr_strtofr (x, "123456789E2147483646", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x) )
{
printf ("Check overflow failed (1) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "123456789E9223372036854775807", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x) )
{
printf ("Check overflow failed (2) with:\n s='%s'\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "123456789E170141183460469231731687303715884105728",
&s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x) )
{
printf ("Check overflow failed (3) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
/* Limit overflow */
mpfr_strtofr (x, "12E2147483646", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x) )
{
printf ("Check overflow failed (4) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "12E2147483645", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x))
{
printf ("Check overflow failed (5) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "0123456789ABCDEF@2147483640", &s, 16, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x))
{
printf ("Check overflow failed (6) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "0123456789ABCDEF@540000000", &s, 16, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_INF (x) || !MPFR_IS_POS (x))
{
printf ("Check overflow failed (7) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
/* Check underflow */
mpfr_strtofr (x, "123456789E-2147483646", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_ZERO (x) || !MPFR_IS_POS (x) )
{
printf ("Check underflow failed (1) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "123456789E-9223372036854775807", &s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_ZERO (x) || !MPFR_IS_POS (x) )
{
printf ("Check underflow failed (2) with:\n s='%s'\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "-123456789E-170141183460469231731687303715884105728",
&s, 0, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_ZERO (x) || !MPFR_IS_NEG (x) )
{
printf ("Check underflow failed (3) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_strtofr (x, "0123456789ABCDEF@-540000000", &s, 16, MPFR_RNDN);
if (s[0] != 0 || !MPFR_IS_ZERO (x) || !MPFR_IS_POS (x))
{
printf ("Check overflow failed (7) with:\n s=%s\n x=", s);
mpfr_dump (x);
exit (1);
}
mpfr_clear (x);
}
/* Assumes that the exponent range has already been extended and if y is
an integer, then the result is not exact in unbounded exponent range. */
int
mpfr_pow_general (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y,
mpfr_rnd_t rnd_mode, int y_is_integer, mpfr_save_expo_t *expo)
{
mpfr_t t, u, k, absx;
int neg_result = 0;
int k_non_zero = 0;
int check_exact_case = 0;
int inexact;
/* Declaration of the size variable */
mpfr_prec_t Nz = MPFR_PREC(z); /* target precision */
mpfr_prec_t Nt; /* working precision */
mpfr_exp_t err; /* error */
MPFR_ZIV_DECL (ziv_loop);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg y[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (x), mpfr_log_prec, x,
mpfr_get_prec (y), mpfr_log_prec, y, rnd_mode),
("z[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (z), mpfr_log_prec, z, inexact));
/* We put the absolute value of x in absx, pointing to the significand
of x to avoid allocating memory for the significand of absx. */
MPFR_ALIAS(absx, x, /*sign=*/ 1, /*EXP=*/ MPFR_EXP(x));
/* We will compute the absolute value of the result. So, let's
invert the rounding mode if the result is negative. */
if (MPFR_IS_NEG (x) && is_odd (y))
{
neg_result = 1;
rnd_mode = MPFR_INVERT_RND (rnd_mode);
}
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Nz + 5 + MPFR_INT_CEIL_LOG2 (Nz);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
MPFR_ZIV_INIT (ziv_loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags1);
/* compute exp(y*ln|x|), using MPFR_RNDU to get an upper bound, so
that we can detect underflows. */
mpfr_log (t, absx, MPFR_IS_NEG (y) ? MPFR_RNDD : MPFR_RNDU); /* ln|x| */
mpfr_mul (t, y, t, MPFR_RNDU); /* y*ln|x| */
if (k_non_zero)
{
MPFR_LOG_MSG (("subtract k * ln(2)\n", 0));
mpfr_const_log2 (u, MPFR_RNDD);
mpfr_mul (u, u, k, MPFR_RNDD);
/* Error on u = k * log(2): < k * 2^(-Nt) < 1. */
mpfr_sub (t, t, u, MPFR_RNDU);
MPFR_LOG_MSG (("t = y * ln|x| - k * ln(2)\n", 0));
MPFR_LOG_VAR (t);
}
/* estimate of the error -- see pow function in algorithms.tex.
The error on t is at most 1/2 + 3*2^(EXP(t)+1) ulps, which is
<= 2^(EXP(t)+3) for EXP(t) >= -1, and <= 2 ulps for EXP(t) <= -2.
Additional error if k_no_zero: treal = t * errk, with
1 - |k| * 2^(-Nt) <= exp(-|k| * 2^(-Nt)) <= errk <= 1,
i.e., additional absolute error <= 2^(EXP(k)+EXP(t)-Nt).
Total error <= 2^err1 + 2^err2 <= 2^(max(err1,err2)+1). */
err = MPFR_NOTZERO (t) && MPFR_GET_EXP (t) >= -1 ?
MPFR_GET_EXP (t) + 3 : 1;
if (k_non_zero)
{
if (MPFR_GET_EXP (k) > err)
err = MPFR_GET_EXP (k);
err++;
}
MPFR_BLOCK (flags1, mpfr_exp (t, t, MPFR_RNDN)); /* exp(y*ln|x|)*/
/* We need to test */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (t) || MPFR_UNDERFLOW (flags1)))
{
mpfr_prec_t Ntmin;
MPFR_BLOCK_DECL (flags2);
MPFR_ASSERTN (!k_non_zero);
MPFR_ASSERTN (!MPFR_IS_NAN (t));
/* Real underflow? */
if (MPFR_IS_ZERO (t))
{
/* Underflow. We computed rndn(exp(t)), where t >= y*ln|x|.
Therefore rndn(|x|^y) = 0, and we have a real underflow on
|x|^y. */
inexact = mpfr_underflow (z, rnd_mode == MPFR_RNDN ? MPFR_RNDZ
: rnd_mode, MPFR_SIGN_POS);
if (expo != NULL)
MPFR_SAVE_EXPO_UPDATE_FLAGS (*expo, MPFR_FLAGS_INEXACT
| MPFR_FLAGS_UNDERFLOW);
break;
}
/* Real overflow? */
if (MPFR_IS_INF (t))
{
/* Note: we can probably use a low precision for this test. */
mpfr_log (t, absx, MPFR_IS_NEG (y) ? MPFR_RNDU : MPFR_RNDD);
mpfr_mul (t, y, t, MPFR_RNDD); /* y * ln|x| */
MPFR_BLOCK (flags2, mpfr_exp (t, t, MPFR_RNDD));
/* t = lower bound on exp(y * ln|x|) */
if (MPFR_OVERFLOW (flags2))
{
/* We have computed a lower bound on |x|^y, and it
overflowed. Therefore we have a real overflow
on |x|^y. */
inexact = mpfr_overflow (z, rnd_mode, MPFR_SIGN_POS);
if (expo != NULL)
MPFR_SAVE_EXPO_UPDATE_FLAGS (*expo, MPFR_FLAGS_INEXACT
| MPFR_FLAGS_OVERFLOW);
break;
}
}
k_non_zero = 1;
Ntmin = sizeof(mpfr_exp_t) * CHAR_BIT;
if (Ntmin > Nt)
{
Nt = Ntmin;
mpfr_set_prec (t, Nt);
}
mpfr_init2 (u, Nt);
mpfr_init2 (k, Ntmin);
mpfr_log2 (k, absx, MPFR_RNDN);
mpfr_mul (k, y, k, MPFR_RNDN);
mpfr_round (k, k);
MPFR_LOG_VAR (k);
/* |y| < 2^Ntmin, therefore |k| < 2^Nt. */
continue;
}
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Nz, rnd_mode)))
{
inexact = mpfr_set (z, t, rnd_mode);
break;
}
/* check exact power, except when y is an integer (since the
exact cases for y integer have already been filtered out) */
if (check_exact_case == 0 && ! y_is_integer)
{
if (mpfr_pow_is_exact (z, absx, y, rnd_mode, &inexact))
break;
check_exact_case = 1;
}
/* reactualisation of the precision */
MPFR_ZIV_NEXT (ziv_loop, Nt);
mpfr_set_prec (t, Nt);
if (k_non_zero)
mpfr_set_prec (u, Nt);
}
MPFR_ZIV_FREE (ziv_loop);
if (k_non_zero)
{
int inex2;
long lk;
/* The rounded result in an unbounded exponent range is z * 2^k. As
* MPFR chooses underflow after rounding, the mpfr_mul_2si below will
* correctly detect underflows and overflows. However, in rounding to
* nearest, if z * 2^k = 2^(emin - 2), then the double rounding may
* affect the result. We need to cope with that before overwriting z.
* This can occur only if k < 0 (this test is necessary to avoid a
* potential integer overflow).
* If inexact >= 0, then the real result is <= 2^(emin - 2), so that
* o(2^(emin - 2)) = +0 is correct. If inexact < 0, then the real
* result is > 2^(emin - 2) and we need to round to 2^(emin - 1).
*/
MPFR_ASSERTN (MPFR_EXP_MAX <= LONG_MAX);
lk = mpfr_get_si (k, MPFR_RNDN);
/* Due to early overflow detection, |k| should not be much larger than
* MPFR_EMAX_MAX, and as MPFR_EMAX_MAX <= MPFR_EXP_MAX/2 <= LONG_MAX/2,
* an overflow should not be possible in mpfr_get_si (and lk is exact).
* And one even has the following assertion. TODO: complete proof.
*/
MPFR_ASSERTD (lk > LONG_MIN && lk < LONG_MAX);
/* Note: even in case of overflow (lk inexact), the code is correct.
* Indeed, for the 3 occurrences of lk:
* - The test lk < 0 is correct as sign(lk) = sign(k).
* - In the test MPFR_GET_EXP (z) == __gmpfr_emin - 1 - lk,
* if lk is inexact, then lk = LONG_MIN <= MPFR_EXP_MIN
* (the minimum value of the mpfr_exp_t type), and
* __gmpfr_emin - 1 - lk >= MPFR_EMIN_MIN - 1 - 2 * MPFR_EMIN_MIN
* >= - MPFR_EMIN_MIN - 1 = MPFR_EMAX_MAX - 1. However, from the
* choice of k, z has been chosen to be around 1, so that the
* result of the test is false, as if lk were exact.
* - In the mpfr_mul_2si (z, z, lk, rnd_mode), if lk is inexact,
* then |lk| >= LONG_MAX >= MPFR_EXP_MAX, and as z is around 1,
* mpfr_mul_2si underflows or overflows in the same way as if
* lk were exact.
* TODO: give a bound on |t|, then on |EXP(z)|.
*/
if (rnd_mode == MPFR_RNDN && inexact < 0 && lk < 0 &&
MPFR_GET_EXP (z) == __gmpfr_emin - 1 - lk && mpfr_powerof2_raw (z))
{
/* Rounding to nearest, real result > z * 2^k = 2^(emin - 2),
* underflow case: as the minimum precision is > 1, we will
* obtain the correct result and exceptions by replacing z by
* nextabove(z).
*/
MPFR_ASSERTN (MPFR_PREC_MIN > 1);
mpfr_nextabove (z);
}
MPFR_CLEAR_FLAGS ();
inex2 = mpfr_mul_2si (z, z, lk, rnd_mode);
if (inex2) /* underflow or overflow */
{
inexact = inex2;
if (expo != NULL)
MPFR_SAVE_EXPO_UPDATE_FLAGS (*expo, __gmpfr_flags);
}
mpfr_clears (u, k, (mpfr_ptr) 0);
}
mpfr_clear (t);
/* update the sign of the result if x was negative */
if (neg_result)
{
MPFR_SET_NEG(z);
inexact = -inexact;
}
return inexact;
}
/* The computation of z = pow(x,y) is done by
z = exp(y * log(x)) = x^y
For the special cases, see Section F.9.4.4 of the C standard:
_ pow(±0, y) = ±inf for y an odd integer < 0.
_ pow(±0, y) = +inf for y < 0 and not an odd integer.
_ pow(±0, y) = ±0 for y an odd integer > 0.
_ pow(±0, y) = +0 for y > 0 and not an odd integer.
_ pow(-1, ±inf) = 1.
_ pow(+1, y) = 1 for any y, even a NaN.
_ pow(x, ±0) = 1 for any x, even a NaN.
_ pow(x, y) = NaN for finite x < 0 and finite non-integer y.
_ pow(x, -inf) = +inf for |x| < 1.
_ pow(x, -inf) = +0 for |x| > 1.
_ pow(x, +inf) = +0 for |x| < 1.
_ pow(x, +inf) = +inf for |x| > 1.
_ pow(-inf, y) = -0 for y an odd integer < 0.
_ pow(-inf, y) = +0 for y < 0 and not an odd integer.
_ pow(-inf, y) = -inf for y an odd integer > 0.
_ pow(-inf, y) = +inf for y > 0 and not an odd integer.
_ pow(+inf, y) = +0 for y < 0.
_ pow(+inf, y) = +inf for y > 0. */
int
mpfr_pow (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode)
{
int inexact;
int cmp_x_1;
int y_is_integer;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg y[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (x), mpfr_log_prec, x,
mpfr_get_prec (y), mpfr_log_prec, y, rnd_mode),
("z[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (z), mpfr_log_prec, z, inexact));
if (MPFR_ARE_SINGULAR (x, y))
{
/* pow(x, 0) returns 1 for any x, even a NaN. */
if (MPFR_UNLIKELY (MPFR_IS_ZERO (y)))
return mpfr_set_ui (z, 1, rnd_mode);
else if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
else if (MPFR_IS_NAN (y))
{
/* pow(+1, NaN) returns 1. */
if (mpfr_cmp_ui (x, 1) == 0)
return mpfr_set_ui (z, 1, rnd_mode);
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (y))
{
if (MPFR_IS_INF (x))
{
if (MPFR_IS_POS (y))
MPFR_SET_INF (z);
else
MPFR_SET_ZERO (z);
MPFR_SET_POS (z);
MPFR_RET (0);
}
else
{
int cmp;
cmp = mpfr_cmpabs (x, __gmpfr_one) * MPFR_INT_SIGN (y);
MPFR_SET_POS (z);
if (cmp > 0)
{
/* Return +inf. */
MPFR_SET_INF (z);
MPFR_RET (0);
}
else if (cmp < 0)
{
/* Return +0. */
MPFR_SET_ZERO (z);
MPFR_RET (0);
}
else
{
/* Return 1. */
return mpfr_set_ui (z, 1, rnd_mode);
}
}
}
else if (MPFR_IS_INF (x))
{
int negative;
/* Determine the sign now, in case y and z are the same object */
negative = MPFR_IS_NEG (x) && is_odd (y);
if (MPFR_IS_POS (y))
MPFR_SET_INF (z);
else
MPFR_SET_ZERO (z);
if (negative)
MPFR_SET_NEG (z);
else
MPFR_SET_POS (z);
MPFR_RET (0);
}
else
{
int negative;
MPFR_ASSERTD (MPFR_IS_ZERO (x));
/* Determine the sign now, in case y and z are the same object */
negative = MPFR_IS_NEG(x) && is_odd (y);
if (MPFR_IS_NEG (y))
{
MPFR_ASSERTD (! MPFR_IS_INF (y));
MPFR_SET_INF (z);
mpfr_set_divby0 ();
}
else
MPFR_SET_ZERO (z);
if (negative)
MPFR_SET_NEG (z);
else
MPFR_SET_POS (z);
MPFR_RET (0);
}
}
/* x^y for x < 0 and y not an integer is not defined */
y_is_integer = mpfr_integer_p (y);
if (MPFR_IS_NEG (x) && ! y_is_integer)
{
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
/* now the result cannot be NaN:
(1) either x > 0
(2) or x < 0 and y is an integer */
cmp_x_1 = mpfr_cmpabs (x, __gmpfr_one);
if (cmp_x_1 == 0)
return mpfr_set_si (z, MPFR_IS_NEG (x) && is_odd (y) ? -1 : 1, rnd_mode);
/* now we have:
(1) either x > 0
(2) or x < 0 and y is an integer
and in addition |x| <> 1.
*/
/* detect overflow: an overflow is possible if
(a) |x| > 1 and y > 0
(b) |x| < 1 and y < 0.
FIXME: this assumes 1 is always representable.
FIXME2: maybe we can test overflow and underflow simultaneously.
The idea is the following: first compute an approximation to
y * log2|x|, using rounding to nearest. If |x| is not too near from 1,
this approximation should be accurate enough, and in most cases enable
one to prove that there is no underflow nor overflow.
Otherwise, it should enable one to check only underflow or overflow,
instead of both cases as in the present case.
*/
if (cmp_x_1 * MPFR_SIGN (y) > 0)
{
mpfr_t t;
int negative, overflow;
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (t, 53);
/* we want a lower bound on y*log2|x|:
(i) if x > 0, it suffices to round log2(x) toward zero, and
to round y*o(log2(x)) toward zero too;
(ii) if x < 0, we first compute t = o(-x), with rounding toward 1,
and then follow as in case (1). */
if (MPFR_SIGN (x) > 0)
mpfr_log2 (t, x, MPFR_RNDZ);
else
{
mpfr_neg (t, x, (cmp_x_1 > 0) ? MPFR_RNDZ : MPFR_RNDU);
mpfr_log2 (t, t, MPFR_RNDZ);
}
mpfr_mul (t, t, y, MPFR_RNDZ);
overflow = mpfr_cmp_si (t, __gmpfr_emax) > 0;
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
if (overflow)
{
MPFR_LOG_MSG (("early overflow detection\n", 0));
negative = MPFR_SIGN(x) < 0 && is_odd (y);
return mpfr_overflow (z, rnd_mode, negative ? -1 : 1);
}
}
/* Basic underflow checking. One has:
* - if y > 0, |x^y| < 2^(EXP(x) * y);
* - if y < 0, |x^y| <= 2^((EXP(x) - 1) * y);
* so that one can compute a value ebound such that |x^y| < 2^ebound.
* If we have ebound <= emin - 2 (emin - 1 in directed rounding modes),
* then there is an underflow and we can decide the return value.
*/
if (MPFR_IS_NEG (y) ? (MPFR_GET_EXP (x) > 1) : (MPFR_GET_EXP (x) < 0))
{
mpfr_t tmp;
mpfr_eexp_t ebound;
int inex2;
/* We must restore the flags. */
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (tmp, sizeof (mpfr_exp_t) * CHAR_BIT);
inex2 = mpfr_set_exp_t (tmp, MPFR_GET_EXP (x), MPFR_RNDN);
MPFR_ASSERTN (inex2 == 0);
if (MPFR_IS_NEG (y))
{
inex2 = mpfr_sub_ui (tmp, tmp, 1, MPFR_RNDN);
MPFR_ASSERTN (inex2 == 0);
}
mpfr_mul (tmp, tmp, y, MPFR_RNDU);
if (MPFR_IS_NEG (y))
mpfr_nextabove (tmp);
/* tmp doesn't necessarily fit in ebound, but that doesn't matter
since we get the minimum value in such a case. */
ebound = mpfr_get_exp_t (tmp, MPFR_RNDU);
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
if (MPFR_UNLIKELY (ebound <=
__gmpfr_emin - (rnd_mode == MPFR_RNDN ? 2 : 1)))
{
/* warning: mpfr_underflow rounds away from 0 for MPFR_RNDN */
MPFR_LOG_MSG (("early underflow detection\n", 0));
return mpfr_underflow (z,
rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
MPFR_SIGN (x) < 0 && is_odd (y) ? -1 : 1);
}
}
/* If y is an integer, we can use mpfr_pow_z (based on multiplications),
but if y is very large (I'm not sure about the best threshold -- VL),
we shouldn't use it, as it can be very slow and take a lot of memory
(and even crash or make other programs crash, as several hundred of
MBs may be necessary). Note that in such a case, either x = +/-2^b
(this case is handled below) or x^y cannot be represented exactly in
any precision supported by MPFR (the general case uses this property).
*/
if (y_is_integer && (MPFR_GET_EXP (y) <= 256))
{
mpz_t zi;
MPFR_LOG_MSG (("special code for y not too large integer\n", 0));
mpz_init (zi);
mpfr_get_z (zi, y, MPFR_RNDN);
inexact = mpfr_pow_z (z, x, zi, rnd_mode);
mpz_clear (zi);
return inexact;
}
/* Special case (+/-2^b)^Y which could be exact. If x is negative, then
necessarily y is a large integer. */
{
mpfr_exp_t b = MPFR_GET_EXP (x) - 1;
MPFR_ASSERTN (b >= LONG_MIN && b <= LONG_MAX); /* FIXME... */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), b) == 0)
{
mpfr_t tmp;
int sgnx = MPFR_SIGN (x);
MPFR_LOG_MSG (("special case (+/-2^b)^Y\n", 0));
/* now x = +/-2^b, so x^y = (+/-1)^y*2^(b*y) is exact whenever b*y is
an integer */
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (tmp, MPFR_PREC (y) + sizeof (long) * CHAR_BIT);
inexact = mpfr_mul_si (tmp, y, b, MPFR_RNDN); /* exact */
MPFR_ASSERTN (inexact == 0);
/* Note: as the exponent range has been extended, an overflow is not
possible (due to basic overflow and underflow checking above, as
the result is ~ 2^tmp), and an underflow is not possible either
because b is an integer (thus either 0 or >= 1). */
MPFR_CLEAR_FLAGS ();
inexact = mpfr_exp2 (z, tmp, rnd_mode);
mpfr_clear (tmp);
if (sgnx < 0 && is_odd (y))
{
mpfr_neg (z, z, rnd_mode);
inexact = -inexact;
}
/* Without the following, the overflows3 test in tpow.c fails. */
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (z, inexact, rnd_mode);
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* Case where |y * log(x)| is very small. Warning: x can be negative, in
that case y is a large integer. */
{
mpfr_t t;
mpfr_exp_t err;
/* We need an upper bound on the exponent of y * log(x). */
mpfr_init2 (t, 16);
if (MPFR_IS_POS(x))
mpfr_log (t, x, cmp_x_1 < 0 ? MPFR_RNDD : MPFR_RNDU); /* away from 0 */
else
{
/* if x < -1, round to +Inf, else round to zero */
mpfr_neg (t, x, (mpfr_cmp_si (x, -1) < 0) ? MPFR_RNDU : MPFR_RNDD);
mpfr_log (t, t, (mpfr_cmp_ui (t, 1) < 0) ? MPFR_RNDD : MPFR_RNDU);
}
MPFR_ASSERTN (MPFR_IS_PURE_FP (t));
err = MPFR_GET_EXP (y) + MPFR_GET_EXP (t);
mpfr_clear (t);
MPFR_CLEAR_FLAGS ();
MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (z, __gmpfr_one, - err, 0,
(MPFR_SIGN (y) > 0) ^ (cmp_x_1 < 0),
rnd_mode, expo, {});
}
/* General case */
inexact = mpfr_pow_general (z, x, y, rnd_mode, y_is_integer, &expo);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (z, inexact, rnd_mode);
}
static void
test_2exp (void)
{
mpfr_t x;
int res;
mpfr_init2 (x, 32);
mpfr_set_ui_2exp (x, 1, 0, GMP_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1U,0)");
mpfr_set_ui_2exp (x, 1024, -10, GMP_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1024U,-10)");
mpfr_set_ui_2exp (x, 1024, 10, GMP_RNDN);
if (mpfr_cmp_ui(x, 1024*1024))
ERROR("(1024U,+10)");
mpfr_set_si_2exp (x, -1024L * 1024L, -10, GMP_RNDN);
if (mpfr_cmp_si(x, -1024))
ERROR("(1M,-10)");
mpfr_set_ui_2exp (x, 0x92345678, 16, GMP_RNDN);
if (mpfr_cmp_str (x, "92345678@4", 16, GMP_RNDN))
ERROR("(x92345678U,+16)");
mpfr_set_si_2exp (x, -0x1ABCDEF0, -256, GMP_RNDN);
if (mpfr_cmp_str (x, "-1ABCDEF0@-64", 16, GMP_RNDN))
ERROR("(-x1ABCDEF0,-256)");
mpfr_set_prec (x, 2);
res = mpfr_set_si_2exp (x, 7, 10, GMP_RNDU);
if (mpfr_cmp_ui (x, 1<<13) || res <= 0)
ERROR ("Prec 2 + si_2exp");
res = mpfr_set_ui_2exp (x, 7, 10, GMP_RNDU);
if (mpfr_cmp_ui (x, 1<<13) || res <= 0)
ERROR ("Prec 2 + ui_2exp");
mpfr_clear_flags ();
mpfr_set_ui_2exp (x, 17, MPFR_EMAX_MAX, GMP_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_NEG (x))
ERROR ("mpfr_set_ui_2exp and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_ui_2exp and overflow (overflow flag not set)");
mpfr_clear_flags ();
mpfr_set_si_2exp (x, 17, MPFR_EMAX_MAX, GMP_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_NEG (x))
ERROR ("mpfr_set_si_2exp (pos) and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_si_2exp (pos) and overflow (overflow flag not set)");
mpfr_clear_flags ();
mpfr_set_si_2exp (x, -17, MPFR_EMAX_MAX, GMP_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_POS (x))
ERROR ("mpfr_set_si_2exp (neg) and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_si_2exp (neg) and overflow (overflow flag not set)");
mpfr_clear (x);
}
int
mpfr_digamma (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inex;
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, inex));
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)) /* Digamma(+Inf) = +Inf */
{
MPFR_SET_SAME_SIGN(y, x);
MPFR_SET_INF(y);
MPFR_RET(0);
}
else /* Digamma(-Inf) = NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
else /* Zero case */
{
/* the following works also in case of overlap */
MPFR_SET_INF(y);
MPFR_SET_OPPOSITE_SIGN(y, x);
mpfr_set_divby0 ();
MPFR_RET(0);
}
}
/* Digamma is undefined for negative integers */
if (MPFR_IS_NEG(x) && mpfr_integer_p (x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
/* now x is a normal number */
MPFR_SAVE_EXPO_MARK (expo);
/* for x very small, we have Digamma(x) = -1/x - gamma + O(x), more precisely
-1 < Digamma(x) + 1/x < 0 for -0.2 < x < 0.2, thus:
(i) either x is a power of two, then 1/x is exactly representable, and
as long as 1/2*ulp(1/x) > 1, we can conclude;
(ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then
|y + 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place.
Since |Digamma(x) + 1/x| <= 1, if 2^(-2n) ufp(y) >= 2, then
|y - Digamma(x)| >= 2^(-2n-1)ufp(y), and rounding -1/x 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 MAX(PREC(x),PREC(Y)). */
if (MPFR_EXP(x) < -2)
{
if (MPFR_EXP(x) <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y)))
{
int signx = MPFR_SIGN(x);
inex = mpfr_si_div (y, -1, x, rnd_mode);
if (inex == 0) /* x is a power of two */
{ /* result always -1/x, except when rounding down */
if (rnd_mode == MPFR_RNDA)
rnd_mode = (signx > 0) ? MPFR_RNDD : MPFR_RNDU;
if (rnd_mode == MPFR_RNDZ)
rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD;
if (rnd_mode == MPFR_RNDU)
inex = 1;
else if (rnd_mode == MPFR_RNDD)
{
mpfr_nextbelow (y);
inex = -1;
}
else /* nearest */
inex = 1;
}
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
goto end;
}
}
if (MPFR_IS_NEG(x))
inex = mpfr_digamma_reflection (y, x, rnd_mode);
/* if x < 1/2 we use the reflection formula */
else if (MPFR_EXP(x) < 0)
inex = mpfr_digamma_reflection (y, x, rnd_mode);
else
inex = mpfr_digamma_positive (y, x, rnd_mode);
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inex, rnd_mode);
}
static void
special (void)
{
mpfr_t x, y;
mpq_t q;
mpz_t z;
int res = 0;
mpfr_init (x);
mpfr_init (y);
mpq_init (q);
mpz_init (z);
/* cancellation in mpfr_add_q */
mpfr_set_prec (x, 60);
mpfr_set_prec (y, 20);
mpz_set_str (mpq_numref (q), "-187207494", 10);
mpz_set_str (mpq_denref (q), "5721", 10);
mpfr_set_str_binary (x, "11111111101001011011100101100011011110010011100010000100001E-44");
mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("cancelation in add_q", mpfr_cmp_ui_2exp (y, 256783, -64) == 0);
mpfr_set_prec (x, 19);
mpfr_set_str_binary (x, "0.1011110101110011100E0");
mpz_set_str (mpq_numref (q), "187207494", 10);
mpz_set_str (mpq_denref (q), "5721", 10);
mpfr_set_prec (y, 29);
mpfr_add_q (y, x, q, MPFR_RNDD);
mpfr_set_prec (x, 29);
mpfr_set_str_binary (x, "11111111101001110011010001001E-14");
CHECK_FOR ("cancelation in add_q", mpfr_cmp (x,y) == 0);
/* Inf */
mpfr_set_inf (x, 1);
mpz_set_str (mpq_numref (q), "395877315", 10);
mpz_set_str (mpq_denref (q), "3508975966", 10);
mpfr_set_prec (y, 118);
mpfr_add_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("inf", mpfr_inf_p (y) && mpfr_sgn (y) > 0);
mpfr_sub_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("inf", mpfr_inf_p (y) && mpfr_sgn (y) > 0);
/* Nan */
MPFR_SET_NAN (x);
mpfr_add_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("nan", mpfr_nan_p (y));
mpfr_sub_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("nan", mpfr_nan_p (y));
/* Exact value */
mpfr_set_prec (x, 60);
mpfr_set_prec (y, 60);
mpfr_set_str1 (x, "0.5");
mpz_set_str (mpq_numref (q), "3", 10);
mpz_set_str (mpq_denref (q), "2", 10);
res = mpfr_add_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("0.5+3/2", mpfr_cmp_ui(y, 2)==0 && res==0);
res = mpfr_sub_q (y, x, q, MPFR_RNDU);
CHECK_FOR ("0.5-3/2", mpfr_cmp_si(y, -1)==0 && res==0);
/* Inf Rationnal */
mpq_set_ui (q, 1, 0);
mpfr_set_str1 (x, "0.5");
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("0.5+1/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("0.5-1/0", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
mpq_set_si (q, -1, 0);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("0.5+ -1/0", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("0.5- -1/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
res = mpfr_div_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("0.5 / (-1/0)", mpfr_zero_p (y) && MPFR_IS_NEG (y) && res == 0);
mpq_set_ui (q, 1, 0);
mpfr_set_inf (x, 1);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("+Inf + +Inf", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("+Inf - +Inf", MPFR_IS_NAN (y) && res == 0);
mpfr_set_inf (x, -1);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("-Inf + +Inf", MPFR_IS_NAN (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("-Inf - +Inf", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
mpq_set_si (q, -1, 0);
mpfr_set_inf (x, 1);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("+Inf + -Inf", MPFR_IS_NAN (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("+Inf - -Inf", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
mpfr_set_inf (x, -1);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("-Inf + -Inf", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("-Inf - -Inf", MPFR_IS_NAN (y) && res == 0);
/* 0 */
mpq_set_ui (q, 0, 1);
mpfr_set_ui (x, 42, MPFR_RNDN);
res = mpfr_add_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("42+0/1", mpfr_cmp_ui (y, 42) == 0 && res == 0);
res = mpfr_sub_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("42-0/1", mpfr_cmp_ui (y, 42) == 0 && res == 0);
res = mpfr_mul_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("42*0/1", mpfr_zero_p (y) && MPFR_IS_POS (y) && res == 0);
mpfr_clear_flags ();
res = mpfr_div_q (y, x, q, MPFR_RNDN);
CHECK_FOR ("42/(0/1)", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0
&& mpfr_divby0_p ());
mpz_set_ui (z, 0);
mpfr_clear_flags ();
res = mpfr_div_z (y, x, z, MPFR_RNDN);
CHECK_FORZ ("42/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0
&& mpfr_divby0_p ());
mpz_clear (z);
mpq_clear (q);
mpfr_clear (x);
mpfr_clear (y);
}
int
main (int argc, char *argv[])
{
mpfr_t x;
long k, z, d, N;
unsigned long zl, dl;
int inex;
int r;
mp_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, GMP_RNDZ);
d = mpfr_get_si (x, GMP_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, GMP_RNDZ);
dl = mpfr_get_ui (x, GMP_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, GMP_RNDZ) >= 0)
{
printf ("Wrong inexact flag for x=5, rnd=GMP_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, -5, GMP_RNDZ) <= 0)
{
printf ("Wrong inexact flag for x=-5, rnd=GMP_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 3);
inex = mpfr_set_si (x, 77617, GMP_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, GMP_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
inex = mpfr_set_ui (x, 77617, GMP_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, GMP_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
mpfr_set_prec (x, 2);
inex = mpfr_set_si (x, 33096, GMP_RNDU);
if (mpfr_get_si (x, GMP_RNDZ) != 49152 || inex <= 0)
{
printf ("Error in mpfr_set_si, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, GMP_RNDZ), inex);
exit (1);
}
inex = mpfr_set_ui (x, 33096, GMP_RNDU);
if (mpfr_get_si (x, GMP_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, GMP_RNDZ), inex);
exit (1);
}
for (r = 0 ; r < GMP_RND_MAX ; r++)
{
mpfr_set_si (x, -1, (mp_rnd_t) r);
mpfr_set_ui (x, 0, (mp_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_ui (x, (mp_rnd_t) r) != 0)
{
printf ("mpfr_set_ui (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mp_rnd_t) r));
exit (1);
}
mpfr_set_si (x, -1, (mp_rnd_t) r);
mpfr_set_si (x, 0, (mp_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_si (x, (mp_rnd_t) r) != 0)
{
printf ("mpfr_set_si (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mp_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, GMP_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, GMP_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, GMP_RNDN);
MPFR_ASSERTN(mpfr_get_ui (x, GMP_RNDN) == 0);
mpfr_set_ui (x, ULONG_MAX, GMP_RNDU);
mpfr_nextabove (x);
mpfr_get_ui (x, GMP_RNDU);
/* another test for get_ui */
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "10.101");
dl = mpfr_get_ui (x, GMP_RNDN);
MPFR_ASSERTN (dl == 3);
mpfr_set_str_binary (x, "-1.0");
mpfr_get_ui (x, GMP_RNDN);
mpfr_set_str_binary (x, "0.1");
dl = mpfr_get_ui (x, GMP_RNDN);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, GMP_RNDZ);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, GMP_RNDD);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, GMP_RNDU);
MPFR_ASSERTN (dl == 1);
/* coverage tests */
mpfr_set_prec (x, 2);
mpfr_set_si (x, -7, GMP_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (x, -8) == 0);
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 7, GMP_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui (x, 8) == 0);
emax = mpfr_get_emax ();
set_emax (3);
mpfr_set_ui (x, 7, GMP_RNDU);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (1);
MPFR_ASSERTN( mpfr_set_ui (x, 7, GMP_RNDU) );
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_ui_2exp (x, 17, -50, GMP_RNDN);
MPFR_ASSERTN (mpfr_get_ui (x, GMP_RNDD) == 0);
MPFR_ASSERTN (mpfr_get_si (x, GMP_RNDD) == 0);
/* Test for ERANGE flag + correct behaviour if overflow */
mpfr_set_prec (x, 256);
mpfr_set_ui (x, ULONG_MAX, GMP_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, GMP_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, GMP_RNDN);
dl = mpfr_get_ui (x, GMP_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, GMP_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, GMP_RNDN);
if (dl != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + -1 \n");
exit (1);
}
mpfr_set_si (x, LONG_MAX, GMP_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, GMP_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, GMP_RNDN);
d = mpfr_get_si (x, GMP_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, GMP_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, GMP_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, GMP_RNDN);
d = mpfr_get_si (x, GMP_RNDN);
if (d != LONG_MIN || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (2)\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_prec (x, 2);
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_ui (x, 7, GMP_RNDU);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_ui (x, 8) != 0)
{
printf ("Error for mpfr_set_ui (x, 7, GMP_RNDU), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_ui (x, 7, GMP_RNDU) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_si (x, -7, GMP_RNDD);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_si (x, -8) != 0)
{
printf ("Error for mpfr_set_si (x, -7, GMP_RNDD), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_si (x, -7, GMP_RNDD) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_clear (x);
test_2exp ();
test_macros ();
tests_end_mpfr ();
return 0;
}
static void
overflowed_sin_cos0 (void)
{
mpfr_t x, y, z;
int emax, inex, rnd, err = 0;
mpfr_exp_t old_emax;
old_emax = mpfr_get_emax ();
mpfr_init2 (x, 8);
mpfr_init2 (y, 8);
mpfr_init2 (z, 8);
for (emax = -1; emax <= 0; emax++)
{
mpfr_set_ui_2exp (z, 1, emax, MPFR_RNDN);
mpfr_nextbelow (z);
set_emax (emax); /* 1 is not representable. */
/* and if emax < 0, 1 - eps is not representable either. */
RND_LOOP (rnd)
{
mpfr_set_si (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_sin_cos (x, y, x, (mpfr_rnd_t) rnd);
if (! mpfr_overflow_p ())
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" The overflow flag is not set.\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! (mpfr_zero_p (x) && MPFR_IS_NEG (x)))
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" Got sin = ", mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of -0.\n");
err = 1;
}
if (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
{
if (inex == 0)
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" The inexact value must be non-zero.\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! mpfr_equal_p (y, z))
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" Got cos = ",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (y);
printf (" instead of 0.11111111E%d.\n", emax);
err = 1;
}
}
else
{
if (inex == 0)
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" The inexact value must be non-zero.\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! (mpfr_inf_p (y) && MPFR_IS_POS (y)))
{
printf ("Error in overflowed_sin_cos0 (rnd = %s):\n"
" Got cos = ",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (y);
printf (" instead of +Inf.\n");
err = 1;
}
}
}
set_emax (old_emax);
}
if (err)
exit (1);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
static void
check_pow_ui (void)
{
mpfr_t a, b;
int res;
mpfr_init2 (a, 53);
mpfr_init2 (b, 53);
/* check in-place operations */
mpfr_set_str (b, "0.6926773", 10, GMP_RNDN);
mpfr_pow_ui (a, b, 10, GMP_RNDN);
mpfr_pow_ui (b, b, 10, GMP_RNDN);
if (mpfr_cmp (a, b))
{
printf ("Error for mpfr_pow_ui (b, b, ...)\n");
exit (1);
}
/* check large exponents */
mpfr_set_ui (b, 1, GMP_RNDN);
mpfr_pow_ui (a, b, 4294967295UL, GMP_RNDN);
mpfr_set_inf (a, -1);
mpfr_pow_ui (a, a, 4049053855UL, GMP_RNDN);
if (!mpfr_inf_p (a) || (mpfr_sgn (a) >= 0))
{
printf ("Error for (-Inf)^4049053855\n");
exit (1);
}
mpfr_set_inf (a, -1);
mpfr_pow_ui (a, a, (unsigned long) 30002752, GMP_RNDN);
if (!mpfr_inf_p (a) || (mpfr_sgn (a) <= 0))
{
printf ("Error for (-Inf)^30002752\n");
exit (1);
}
/* Check underflow */
mpfr_set_str_binary (a, "1E-1");
res = mpfr_pow_ui (a, a, -mpfr_get_emin (), GMP_RNDN);
if (MPFR_GET_EXP (a) != mpfr_get_emin () + 1)
{
printf ("Error for (1e-1)^MPFR_EMAX_MAX\n");
mpfr_dump (a);
exit (1);
}
mpfr_set_str_binary (a, "1E-10");
res = mpfr_pow_ui (a, a, -mpfr_get_emin (), GMP_RNDZ);
if (!MPFR_IS_ZERO (a))
{
printf ("Error for (1e-10)^MPFR_EMAX_MAX\n");
mpfr_dump (a);
exit (1);
}
/* Check overflow */
mpfr_set_str_binary (a, "1E10");
res = mpfr_pow_ui (a, a, ULONG_MAX, GMP_RNDN);
if (!MPFR_IS_INF (a) || MPFR_SIGN (a) < 0)
{
printf ("Error for (1e10)^ULONG_MAX\n");
exit (1);
}
/* Check 0 */
MPFR_SET_ZERO (a);
MPFR_SET_POS (a);
mpfr_set_si (b, -1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 1, GMP_RNDN);
if (res != 0 || MPFR_IS_NEG (b))
{
printf ("Error for (0+)^1\n");
exit (1);
}
MPFR_SET_ZERO (a);
MPFR_SET_NEG (a);
mpfr_set_ui (b, 1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 5, GMP_RNDN);
if (res != 0 || MPFR_IS_POS (b))
{
printf ("Error for (0-)^5\n");
exit (1);
}
MPFR_SET_ZERO (a);
MPFR_SET_NEG (a);
mpfr_set_si (b, -1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 6, GMP_RNDN);
if (res != 0 || MPFR_IS_NEG (b))
{
printf ("Error for (0-)^6\n");
exit (1);
}
mpfr_set_prec (a, 122);
mpfr_set_prec (b, 122);
mpfr_set_str_binary (a, "0.10000010010000111101001110100101101010011110011100001111000001001101000110011001001001001011001011010110110110101000111011E1");
mpfr_set_str_binary (b, "0.11111111100101001001000001000001100011100000001110111111100011111000111011100111111111110100011000111011000100100011001011E51290375");
mpfr_pow_ui (a, a, 2026876995UL, GMP_RNDU);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error for x^2026876995\n");
exit (1);
}
mpfr_set_prec (a, 29);
mpfr_set_prec (b, 29);
mpfr_set_str_binary (a, "1.0000000000000000000000001111");
mpfr_set_str_binary (b, "1.1001101111001100111001010111e165");
mpfr_pow_ui (a, a, 2055225053, GMP_RNDZ);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error for x^2055225053\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
/* worst case found by Vincent Lefevre, 25 Nov 2006 */
mpfr_set_prec (a, 53);
mpfr_set_prec (b, 53);
mpfr_set_str_binary (a, "1.0000010110000100001000101101101001011101101011010111");
mpfr_set_str_binary (b, "1.0000110111101111011010110100001100010000001010110100E1");
mpfr_pow_ui (a, a, 35, GMP_RNDN);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (1)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
/* worst cases found on 2006-11-26 */
mpfr_set_str_binary (a, "1.0110100111010001101001010111001110010100111111000011");
mpfr_set_str_binary (b, "1.1111010011101110001111010110000101110000110110101100E17");
mpfr_pow_ui (a, a, 36, GMP_RNDD);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (2)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_str_binary (a, "1.1001010100001110000110111111100011011101110011000100");
mpfr_set_str_binary (b, "1.1100011101101101100010110001000001110001111110010001E23");
mpfr_pow_ui (a, a, 36, GMP_RNDU);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (3)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_clear (a);
mpfr_clear (b);
}
static void
special ()
{
mpfr_t x, y, z, t;
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (z, 53);
mpfr_init2 (t, 2);
mpfr_set_ui (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, -2, GMP_RNDN);
if (mpfr_cmp_ui_2exp (x, 1, -2))
{
printf ("Error in pow_si(x,x,-2) for x=2\n");
exit (1);
}
mpfr_set_ui (x, 2, GMP_RNDN);
mpfr_set_si (y, -2, GMP_RNDN);
test_pow (x, x, y, GMP_RNDN);
if (mpfr_cmp_ui_2exp (x, 1, -2))
{
printf ("Error in pow(x,x,y) for x=2, y=-2\n");
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_str_binary (x, "1.0e-1");
mpfr_set_prec (y, 53);
mpfr_set_str_binary (y, "0.11010110011100101010110011001010100111000001000101110E-1");
mpfr_set_prec (z, 2);
test_pow (z, x, y, GMP_RNDZ);
mpfr_set_str_binary (x, "1.0e-1");
if (mpfr_cmp (x, z))
{
printf ("Error in mpfr_pow (1)\n");
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_prec (z, 64);
mpfr_set_prec (t, 64);
mpfr_set_str_binary (x, "0.111011000111100000111010000101010100110011010000011");
mpfr_set_str_binary (y, "0.111110010100110000011101100011010111000010000100101");
mpfr_set_str_binary (t, "0.1110110011110110001000110100100001001111010011111000010000011001");
test_pow (z, x, y, GMP_RNDN);
if (mpfr_cmp (z, t))
{
printf ("Error in mpfr_pow for prec=64, rnd=GMP_RNDN\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_prec (z, 53);
mpfr_set_str (x, "5.68824667828621954868e-01", 10, GMP_RNDN);
mpfr_set_str (y, "9.03327850535952658895e-01", 10, GMP_RNDN);
test_pow (z, x, y, GMP_RNDZ);
if (mpfr_cmp_str1 (z, "0.60071044650456473235"))
{
printf ("Error in mpfr_pow for prec=53, rnd=GMP_RNDZ\n");
exit (1);
}
mpfr_set_prec (t, 2);
mpfr_set_prec (x, 30);
mpfr_set_prec (y, 30);
mpfr_set_prec (z, 30);
mpfr_set_str (x, "1.00000000001010111110001111011e1", 2, GMP_RNDN);
mpfr_set_str (t, "-0.5", 10, GMP_RNDN);
test_pow (z, x, t, GMP_RNDN);
mpfr_set_str (y, "1.01101001111010101110000101111e-1", 2, GMP_RNDN);
if (mpfr_cmp (z, y))
{
printf ("Error in mpfr_pow for prec=30, rnd=GMP_RNDN\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 21);
mpfr_set_prec (z, 21);
mpfr_set_str (x, "1.11111100100001100101", 2, GMP_RNDN);
test_pow (z, x, t, GMP_RNDZ);
mpfr_set_str (y, "1.01101011010001100000e-1", 2, GMP_RNDN);
if (mpfr_cmp (z, y))
{
printf ("Error in mpfr_pow for prec=21, rnd=GMP_RNDZ\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
/* From http://www.terra.es/personal9/ismaeljc/hall.htm */
mpfr_set_prec (x, 113);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 169);
mpfr_set_str1 (x, "6078673043126084065007902175846955");
mpfr_set_ui_2exp (y, 3, -1, GMP_RNDN);
test_pow (z, x, y, GMP_RNDZ);
if (mpfr_cmp_str1 (z, "473928882491000966028828671876527456070714790264144"))
{
printf ("Error in mpfr_pow for 6078673043126084065007902175846955");
printf ("^(3/2), GMP_RNDZ\nExpected ");
printf ("4.73928882491000966028828671876527456070714790264144e50");
printf ("\nGot ");
mpfr_out_str (stdout, 10, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
test_pow (z, x, y, GMP_RNDU);
if (mpfr_cmp_str1 (z, "473928882491000966028828671876527456070714790264145"))
{
printf ("Error in mpfr_pow for 6078673043126084065007902175846955");
printf ("^(3/2), GMP_RNDU\nExpected ");
printf ("4.73928882491000966028828671876527456070714790264145e50");
printf ("\nGot ");
mpfr_out_str (stdout, 10, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_set_prec (y, 2);
mpfr_set_str_binary (y, "1E10");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_inf (x, -1);
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_prec (y, 10);
mpfr_set_str_binary (y, "1.000000001E9");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_NEG(z));
mpfr_set_str_binary (y, "1.000000001E8");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_inf (x, -1);
mpfr_set_prec (y, 2 * mp_bits_per_limb);
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_mul_2exp (y, y, mp_bits_per_limb - 1, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 1) */
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 1) + epsilon */
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_nextbelow (y);
mpfr_div_2exp (y, y, 1, GMP_RNDN);
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 2) + epsilon */
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_set_prec (y, 2);
mpfr_set_str_binary (y, "1E10");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (z, 1) == 0);
/* Check (-0)^(17.0001) */
mpfr_set_prec (x, 6);
mpfr_set_prec (y, 640);
MPFR_SET_ZERO (x);
MPFR_SET_NEG (x);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
}
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, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_y0 (y, x, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_inf (x, -1); /* -Inf */
mpfr_y0 (y, x, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_ui (x, 0, GMP_RNDN); /* +0 */
mpfr_y0 (y, x, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (y) && MPFR_IS_NEG (y)); /* y0(+0)=-Inf */
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN); /* -0 */
mpfr_y0 (y, x, GMP_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, GMP_RNDN);
mpfr_y0 (y, x, GMP_RNDN);
mpfr_set_str_binary (x, "0.00010110100110000000001000100110111100110101100011011111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_y0 for x=1, rnd=GMP_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_y0 (y, x, GMP_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error in mpfr_y0 for x=-1, rnd=GMP_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
mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
{
int inexact = 0;
mpfr_t x;
mp_prec_t Nx = MPFR_PREC(xt); /* Precision of input variable */
/* Special cases */
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(xt) ))
{
/* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
between -1 and 1 */
if (MPFR_IS_NAN(xt) || MPFR_IS_INF(xt))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else /* necessarily xt is 0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(xt));
MPFR_SET_ZERO(y); /* atanh(0) = 0 */
MPFR_SET_SAME_SIGN(y,xt);
MPFR_RET(0);
}
}
/* Useless due to final mpfr_set
MPFR_CLEAR_FLAGS(y);*/
/* atanh(x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
if (MPFR_EXP(xt) > 0)
{
if (MPFR_EXP(xt) == 1 && mpfr_powerof2_raw (xt))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y, xt);
MPFR_RET(0);
}
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
mpfr_init2 (x, Nx);
mpfr_abs (x, xt, GMP_RNDN);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te,ti;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt=Nt+4+__gmpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ti);
/* First computation of cosh */
do
{
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ti,Nt);
/* compute atanh */
mpfr_ui_sub(te,1,x,GMP_RNDU); /* (1-xt)*/
mpfr_add_ui(ti,x,1,GMP_RNDD); /* (xt+1)*/
mpfr_div(te,ti,te,GMP_RNDN); /* (1+xt)/(1-xt)*/
mpfr_log(te,te,GMP_RNDN); /* ln((1+xt)/(1-xt))*/
mpfr_div_2ui(t,te,1,GMP_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
/* error estimate see- algorithms.ps*/
/* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
/* actualisation of the precision */
Nt += 10;
}
while ((err < 0) || (!mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN))
|| MPFR_IS_ZERO(t)));
if (MPFR_IS_NEG(xt))
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear(t);
mpfr_clear(ti);
mpfr_clear(te);
}
mpfr_clear(x);
return inexact;
}
static void
check_nans (void)
{
mpfr_t x, y;
int inexact;
mpfr_init2 (x, 123);
mpfr_init2 (y, 123);
/* nan / 1.0 is nan */
mpfr_set_nan (x);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 1.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN ((__gmpfr_flags ^ MPFR_FLAGS_NAN) == 0);
MPFR_ASSERTN (mpfr_nan_p (y));
/* +inf / 1.0 == +inf */
mpfr_set_inf (x, 1);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 1.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_POS (y));
/* -inf / 1.0 == -inf */
mpfr_set_inf (x, -1);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 1.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == 0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_NEG (y));
/* 0.0 / 0.0 is nan */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 0.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);
MPFR_ASSERTN (mpfr_nan_p (y));
/* 1.0 / 0.0 == +inf */
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 0.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_POS (y));
/* -1.0 / 0.0 == -inf */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_clear_flags ();
inexact = mpfr_div_d (y, x, 0.0, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);
MPFR_ASSERTN (mpfr_inf_p (y));
MPFR_ASSERTN (MPFR_IS_NEG (y));
mpfr_clear (x);
mpfr_clear (y);
}
int
main (void)
{
mpfr_t x, y, z;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
/* case x=NaN && y=NAN */
mpfr_set_nan (x);
mpfr_set_nan (y);
mpfr_min (z, x, y, MPFR_RNDN);
if (!mpfr_nan_p (z))
{
printf ("Error in mpfr_min (NaN, NaN)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if (!mpfr_nan_p (z))
{
printf ("Error in mpfr_max (NaN, NaN)\n");
exit (1);
}
/* case x=NaN */
mpfr_set_nan (x);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_min (z, x, y, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_min (NaN, 0)\n");
exit (1);
}
mpfr_min (z, y, x, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_min (0, NaN)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_max (NaN, 0)\n");
exit (1);
}
mpfr_max (z, y, x, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_max (0, NaN)\n");
exit (1);
}
/* Case x=0+ and x=0- */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN); MPFR_SET_NEG(y);
mpfr_max (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error in mpfr_max (0+, 0-)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error in mpfr_min (0+, 0-)\n");
exit (1);
}
/* Case x=0- and y=0+ */
mpfr_set_ui (x, 0, MPFR_RNDN); MPFR_SET_NEG(x);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error in mpfr_max (0+, 0-)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error in mpfr_min (0+, 0-)\n");
exit (1);
}
/* case x=+Inf */
mpfr_set_inf (x, 1);
mpfr_set_si (y, -12, MPFR_RNDN);
mpfr_min (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_si (z, -12) )
{
printf ("Error in mpfr_min (+Inf, -12)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if ( !MPFR_IS_INF(z) || MPFR_IS_NEG(z) )
{
printf ("Error in mpfr_max (+Inf, 12)\n");
exit (1);
}
/* case x=-Inf */
mpfr_set_inf (x, -1);
mpfr_set_ui (y, 12, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 12) )
{
printf ("Error in mpfr_max (-Inf, 12)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if ( !MPFR_IS_INF(z) || MPFR_IS_POS(z) )
{
printf ("Error in mpfr_min (-Inf, 12)\n");
exit (1);
}
/* case x=17 and y=42 */
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 42) )
{
printf ("Error in mpfr_max (17, 42)\n");
exit (1);
}
mpfr_max (z, y, x, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 42) )
{
printf ("Error in mpfr_max (42, 17)\n");
exit (1);
}
mpfr_min (z, y, x, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 17) )
{
printf ("Error in mpfr_min (42, 17)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
tests_end_mpfr ();
return 0;
}
/* return non zero iff x^y is exact.
Assumes x and y are ordinary numbers,
y is not an integer, x is not a power of 2 and x is positive
If x^y is exact, it computes it and sets *inexact.
*/
static int
mpfr_pow_is_exact (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y,
mpfr_rnd_t rnd_mode, int *inexact)
{
mpz_t a, c;
mpfr_exp_t d, b;
unsigned long i;
int res;
MPFR_ASSERTD (!MPFR_IS_SINGULAR (y));
MPFR_ASSERTD (!MPFR_IS_SINGULAR (x));
MPFR_ASSERTD (!mpfr_integer_p (y));
MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_INT_SIGN (x),
MPFR_GET_EXP (x) - 1) != 0);
MPFR_ASSERTD (MPFR_IS_POS (x));
if (MPFR_IS_NEG (y))
return 0; /* x is not a power of two => x^-y is not exact */
/* compute d such that y = c*2^d with c odd integer */
mpz_init (c);
d = mpfr_get_z_2exp (c, y);
i = mpz_scan1 (c, 0);
mpz_fdiv_q_2exp (c, c, i);
d += i;
/* now y=c*2^d with c odd */
/* Since y is not an integer, d is necessarily < 0 */
MPFR_ASSERTD (d < 0);
/* Compute a,b such that x=a*2^b */
mpz_init (a);
b = mpfr_get_z_2exp (a, x);
i = mpz_scan1 (a, 0);
mpz_fdiv_q_2exp (a, a, i);
b += i;
/* now x=a*2^b with a is odd */
for (res = 1 ; d != 0 ; d++)
{
/* a*2^b is a square iff
(i) a is a square when b is even
(ii) 2*a is a square when b is odd */
if (b % 2 != 0)
{
mpz_mul_2exp (a, a, 1); /* 2*a */
b --;
}
MPFR_ASSERTD ((b % 2) == 0);
if (!mpz_perfect_square_p (a))
{
res = 0;
goto end;
}
mpz_sqrt (a, a);
b = b / 2;
}
/* Now x = (a'*2^b')^(2^-d) with d < 0
so x^y = ((a'*2^b')^(2^-d))^(c*2^d)
= ((a'*2^b')^c with c odd integer */
{
mpfr_t tmp;
mpfr_prec_t p;
MPFR_MPZ_SIZEINBASE2 (p, a);
mpfr_init2 (tmp, p); /* prec = 1 should not be possible */
res = mpfr_set_z (tmp, a, MPFR_RNDN);
MPFR_ASSERTD (res == 0);
res = mpfr_mul_2si (tmp, tmp, b, MPFR_RNDN);
MPFR_ASSERTD (res == 0);
*inexact = mpfr_pow_z (z, tmp, c, rnd_mode);
mpfr_clear (tmp);
res = 1;
}
end:
mpz_clear (a);
mpz_clear (c);
return res;
}
int
mpfr_add (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
("a[%#R]=%R", a, a));
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
/* neither b nor c is NaN here */
else if (MPFR_IS_INF(b))
{
if (!MPFR_IS_INF(c) || MPFR_SIGN(b) == MPFR_SIGN(c))
{
MPFR_SET_INF(a);
MPFR_SET_SAME_SIGN(a, b);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
MPFR_SET_INF(a);
MPFR_SET_SAME_SIGN(a, c);
MPFR_RET(0); /* exact */
}
/* now either b or c is zero */
else if (MPFR_IS_ZERO(b))
{
if (MPFR_IS_ZERO(c))
{
/* for round away, we take the same convention for 0 + 0
as for round to zero or to nearest: it always gives +0,
except (-0) + (-0) = -0. */
MPFR_SET_SIGN(a,
(rnd_mode != MPFR_RNDD ?
((MPFR_IS_NEG(b) && MPFR_IS_NEG(c)) ? -1 : 1) :
((MPFR_IS_POS(b) && MPFR_IS_POS(c)) ? 1 : -1)));
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 + 0 is exact */
}
return mpfr_set (a, c, rnd_mode);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(c));
return mpfr_set (a, b, rnd_mode);
}
}
MPFR_ASSERTD(MPFR_IS_PURE_FP(b) && MPFR_IS_PURE_FP(c));
if (MPFR_UNLIKELY(MPFR_SIGN(b) != MPFR_SIGN(c)))
{ /* signs differ, it's a subtraction */
if (MPFR_LIKELY(MPFR_PREC(a) == MPFR_PREC(b)
&& MPFR_PREC(b) == MPFR_PREC(c)))
return mpfr_sub1sp(a,b,c,rnd_mode);
else
return mpfr_sub1(a, b, c, rnd_mode);
}
else
{ /* signs are equal, it's an addition */
if (MPFR_LIKELY(MPFR_PREC(a) == MPFR_PREC(b)
&& MPFR_PREC(b) == MPFR_PREC(c)))
if (MPFR_GET_EXP(b) < MPFR_GET_EXP(c))
return mpfr_add1sp(a, c, b, rnd_mode);
else
return mpfr_add1sp(a, b, c, rnd_mode);
else
if (MPFR_GET_EXP(b) < MPFR_GET_EXP(c))
return mpfr_add1(a, c, b, rnd_mode);
else
return mpfr_add1(a, b, c, rnd_mode);
}
}
int
main (void)
{
mpfr_t x;
mp_exp_t emax;
tests_start_mpfr ();
mpfr_init (x);
mpfr_set_nan (x);
mpfr_prec_round (x, 2, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_prec_round (x, 2, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_inf (x, -1);
mpfr_prec_round (x, 2, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_prec_round (x, 2, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_prec_round (x, 2, GMP_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, GMP_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, GMP_RNDN);
mpfr_nextbelow (x);
mpfr_prec_round (x, mp_bits_per_limb + 1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, GMP_RNDN);
mpfr_prec_round (x, 2, GMP_RNDN);
if (mpfr_cmp_ui(x, 4))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
printf (" instead of 4\n");
exit (1);
}
/* check case when reallocation is needed */
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, GMP_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, GMP_RNDN);
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
mpfr_init2 (x, 3);
mpfr_set_si (x, -5, GMP_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, GMP_RNDN);
if (mpfr_cmp_si(x, -5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, GMP_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, GMP_RNDN); /* exact */
mpfr_prec_round (x, 3, GMP_RNDN); /* exact */
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
tests_end_mpfr ();
return 0;
}
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;
}
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_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);
}
float
mpfr_get_flt (mpfr_srcptr src, mpfr_rnd_t rnd_mode)
{
int negative;
mpfr_exp_t e;
float d;
/* in case of NaN, +Inf, -Inf, +0, -0, the conversion from double to float
is exact */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
return (float) mpfr_get_d (src, rnd_mode);
e = MPFR_GET_EXP (src);
negative = MPFR_IS_NEG (src);
if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA))
rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU;
/* the smallest positive normal float number is 2^(-126) = 0.5*2^(-125),
and the smallest positive subnormal number is 2^(-149) = 0.5*2^(-148) */
if (MPFR_UNLIKELY (e < -148))
{
/* |src| < 2^(-149), i.e., |src| is smaller than the smallest positive
subnormal number.
In round-to-nearest mode, 2^(-150) is rounded to zero.
*/
d = negative ?
(rnd_mode == MPFR_RNDD ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, -1, -150) < 0)
? -FLT_MIN : FLT_NEG_ZERO) :
(rnd_mode == MPFR_RNDU ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, 1, -150) > 0)
? FLT_MIN : 0.0);
if (d != 0.0) /* we multiply FLT_MIN = 2^(-126) by FLT_EPSILON = 2^(-23)
to get +-2^(-149) */
d *= FLT_EPSILON;
}
/* the largest normal number is 2^128*(1-2^(-24)) = 0.111...111e128 */
else if (MPFR_UNLIKELY (e > 128))
{
d = negative ?
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ?
-FLT_MAX : MPFR_FLT_INFM) :
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ?
FLT_MAX : MPFR_FLT_INFP);
}
else /* -148 <= e <= 127 */
{
int nbits;
mp_size_t np, i;
mp_limb_t tp[MPFR_LIMBS_PER_FLT];
int carry;
double dd;
nbits = IEEE_FLT_MANT_DIG; /* 24 */
if (MPFR_UNLIKELY (e < -125))
/*In the subnormal case, compute the exact number of significant bits*/
{
nbits += (125 + e);
MPFR_ASSERTD (nbits >= 1);
}
np = MPFR_PREC2LIMBS (nbits);
MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT);
carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
nbits, rnd_mode);
/* we perform the reconstruction using the 'double' type here,
knowing the result is exactly representable as 'float' */
if (MPFR_UNLIKELY(carry))
dd = 1.0;
else
{
/* The following computations are exact thanks to the previous
mpfr_round_raw. */
dd = (double) tp[0] / MP_BASE_AS_DOUBLE;
for (i = 1 ; i < np ; i++)
dd = (dd + tp[i]) / MP_BASE_AS_DOUBLE;
/* dd is the mantissa (between 1/2 and 1) of the argument rounded
to 24 bits */
}
dd = mpfr_scale2 (dd, e);
if (negative)
dd = -dd;
/* convert (exacly) to float */
d = (float) dd;
}
return d;
}
double
mpfr_get_d (mpfr_srcptr src, mpfr_rnd_t rnd_mode)
{
double d;
int negative;
mpfr_exp_t e;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
{
if (MPFR_IS_NAN (src))
return MPFR_DBL_NAN;
negative = MPFR_IS_NEG (src);
if (MPFR_IS_INF (src))
return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP;
MPFR_ASSERTD (MPFR_IS_ZERO(src));
return negative ? DBL_NEG_ZERO : 0.0;
}
e = MPFR_GET_EXP (src);
negative = MPFR_IS_NEG (src);
if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA))
rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU;
/* the smallest normalized number is 2^(-1022)=0.1e-1021, and the smallest
subnormal is 2^(-1074)=0.1e-1073 */
if (MPFR_UNLIKELY (e < -1073))
{
/* Note: Avoid using a constant expression DBL_MIN * DBL_EPSILON
as this gives 0 instead of the correct result with gcc on some
Alpha machines. */
d = negative ?
(rnd_mode == MPFR_RNDD ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, -1, -1075) < 0)
? -DBL_MIN : DBL_NEG_ZERO) :
(rnd_mode == MPFR_RNDU ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, 1, -1075) > 0)
? DBL_MIN : 0.0);
if (d != 0.0) /* we multiply DBL_MIN = 2^(-1022) by DBL_EPSILON = 2^(-52)
to get +-2^(-1074) */
d *= DBL_EPSILON;
}
/* the largest normalized number is 2^1024*(1-2^(-53))=0.111...111e1024 */
else if (MPFR_UNLIKELY (e > 1024))
{
d = negative ?
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ?
-DBL_MAX : MPFR_DBL_INFM) :
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ?
DBL_MAX : MPFR_DBL_INFP);
}
else
{
int nbits;
mp_size_t np, i;
mp_limb_t tp[ MPFR_LIMBS_PER_DOUBLE ];
int carry;
nbits = IEEE_DBL_MANT_DIG; /* 53 */
if (MPFR_UNLIKELY (e < -1021))
/*In the subnormal case, compute the exact number of significant bits*/
{
nbits += (1021 + e);
MPFR_ASSERTD (nbits >= 1);
}
np = MPFR_PREC2LIMBS (nbits);
MPFR_ASSERTD ( np <= MPFR_LIMBS_PER_DOUBLE );
carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
nbits, rnd_mode);
if (MPFR_UNLIKELY(carry))
d = 1.0;
else
{
/* The following computations are exact thanks to the previous
mpfr_round_raw. */
d = (double) tp[0] / MP_BASE_AS_DOUBLE;
for (i = 1 ; i < np ; i++)
d = (d + tp[i]) / MP_BASE_AS_DOUBLE;
/* d is the mantissa (between 1/2 and 1) of the argument rounded
to 53 bits */
}
d = mpfr_scale2 (d, e);
if (negative)
d = -d;
}
return d;
}
/* We can't use fits_s.h <= mpfr_cmp_ui */
int
mpfr_fits_intmax_p (mpfr_srcptr f, mpfr_rnd_t rnd)
{
mpfr_exp_t e;
int prec;
mpfr_t x, y;
int neg;
int res;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (f)))
/* Zero always fit */
return MPFR_IS_ZERO (f) ? 1 : 0;
/* now it fits if either
(a) MINIMUM <= f <= MAXIMUM
(b) or MINIMUM <= round(f, prec(slong), rnd) <= MAXIMUM */
e = MPFR_EXP (f);
if (e < 1)
return 1; /* |f| < 1: always fits */
neg = MPFR_IS_NEG (f);
/* let EXTREMUM be MAXIMUM if f > 0, and MINIMUM if f < 0 */
/* first compute prec(EXTREMUM), this could be done at configure time,
but the result can depend on neg (the loop is moved inside the "if"
to give the compiler a better chance to compute prec statically) */
if (neg)
{
uintmax_t s;
/* In C89, the division on negative integers isn't well-defined. */
s = SAFE_ABS (uintmax_t, MPFR_INTMAX_MIN);
for (prec = 0; s != 0; s /= 2, prec ++);
}
else
{
intmax_t s;
s = MPFR_INTMAX_MAX;
for (prec = 0; s != 0; s /= 2, prec ++);
}
/* EXTREMUM needs prec bits, i.e. 2^(prec-1) <= |EXTREMUM| < 2^prec */
/* if e <= prec - 1, then f < 2^(prec-1) <= |EXTREMUM| */
if (e <= prec - 1)
return 1;
/* if e >= prec + 1, then f >= 2^prec > |EXTREMUM| */
if (e >= prec + 1)
return 0;
MPFR_ASSERTD (e == prec);
/* hard case: first round to prec bits, then check */
mpfr_init2 (x, prec);
mpfr_set (x, f, rnd);
if (neg)
{
mpfr_init2 (y, prec);
mpfr_set_sj (y, MPFR_INTMAX_MIN, MPFR_RNDN);
res = mpfr_cmp (x, y) >= 0;
mpfr_clear (y);
}
else
{
res = MPFR_GET_EXP (x) == e;
}
mpfr_clear (x);
return res;
}
int
mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
{
/* If a is NaN, the result is NaN */
if (MPFR_IS_NAN (a))
{
MPFR_SET_NAN (r);
MPFR_RET_NAN;
}
/* check for infinity before zero */
else if (MPFR_IS_INF (a))
{
if (MPFR_IS_NEG (a))
/* log(-Inf) = NaN */
{
MPFR_SET_NAN (r);
MPFR_RET_NAN;
}
else /* log(+Inf) = +Inf */
{
MPFR_SET_INF (r);
MPFR_SET_POS (r);
MPFR_RET (0);
}
}
else /* a is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (a));
MPFR_SET_INF (r);
MPFR_SET_NEG (r);
MPFR_RET (0); /* log2(0) is an exact -infinity */
}
}
/* If a is negative, the result is NaN */
if (MPFR_UNLIKELY (MPFR_IS_NEG (a)))
{
MPFR_SET_NAN (r);
MPFR_RET_NAN;
}
/* If a is 1, the result is 0 */
if (MPFR_UNLIKELY (mpfr_cmp_ui (a, 1) == 0))
{
MPFR_SET_ZERO (r);
MPFR_SET_POS (r);
MPFR_RET (0); /* only "normal" case where the result is exact */
}
/* If a is 2^N, log2(a) is exact*/
if (MPFR_UNLIKELY (mpfr_cmp_ui_2exp (a, 1, MPFR_GET_EXP (a) - 1) == 0))
return mpfr_set_si(r, MPFR_GET_EXP (a) - 1, rnd_mode);
MPFR_SAVE_EXPO_MARK (expo);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, tt;
/* Declaration of the size variable */
mpfr_prec_t Ny = MPFR_PREC(r); /* 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 + 3 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
mpfr_init2 (tt, Nt);
/* First computation of log2 */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute log2 */
mpfr_const_log2(t,MPFR_RNDD); /* log(2) */
mpfr_log(tt,a,MPFR_RNDN); /* log(a) */
mpfr_div(t,tt,t,MPFR_RNDN); /* log(a)/log(2) */
/* estimation of the error */
err = Nt-3;
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_set_prec (tt, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (r, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (tt);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (r, inexact, rnd_mode);
}
int
mpfr_sub (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
("a[%#R]=%R", a, a));
if (MPFR_ARE_SINGULAR (b,c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (b))
{
if (!MPFR_IS_INF (c) || MPFR_SIGN (b) != MPFR_SIGN(c))
{
MPFR_SET_INF (a);
MPFR_SET_SAME_SIGN (a, b);
MPFR_RET (0); /* exact */
}
else
{
MPFR_SET_NAN (a); /* Inf - Inf */
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF (c))
{
MPFR_SET_INF (a);
MPFR_SET_OPPOSITE_SIGN (a, c);
MPFR_RET (0); /* exact */
}
else if (MPFR_IS_ZERO (b))
{
if (MPFR_IS_ZERO (c))
{
int sign = rnd_mode != MPFR_RNDD
? ((MPFR_IS_NEG(b) && MPFR_IS_POS(c)) ? -1 : 1)
: ((MPFR_IS_POS(b) && MPFR_IS_NEG(c)) ? 1 : -1);
MPFR_SET_SIGN (a, sign);
MPFR_SET_ZERO (a);
MPFR_RET(0); /* 0 - 0 is exact */
}
else
return mpfr_neg (a, c, rnd_mode);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO (c));
return mpfr_set (a, b, rnd_mode);
}
}
MPFR_ASSERTD (MPFR_IS_PURE_FP (b) && MPFR_IS_PURE_FP (c));
if (MPFR_LIKELY (MPFR_SIGN (b) == MPFR_SIGN (c)))
{ /* signs are equal, it's a real subtraction */
if (MPFR_LIKELY (MPFR_PREC (a) == MPFR_PREC (b)
&& MPFR_PREC (b) == MPFR_PREC (c)))
return mpfr_sub1sp (a, b, c, rnd_mode);
else
return mpfr_sub1 (a, b, c, rnd_mode);
}
else
{ /* signs differ, it's an addition */
if (MPFR_GET_EXP (b) < MPFR_GET_EXP (c))
{ /* exchange rounding modes toward +/- infinity */
int inexact;
rnd_mode = MPFR_INVERT_RND (rnd_mode);
if (MPFR_LIKELY (MPFR_PREC (a) == MPFR_PREC (b)
&& MPFR_PREC (b) == MPFR_PREC (c)))
inexact = mpfr_add1sp (a, c, b, rnd_mode);
else
inexact = mpfr_add1 (a, c, b, rnd_mode);
MPFR_CHANGE_SIGN (a);
return -inexact;
}
else
{
if (MPFR_LIKELY (MPFR_PREC (a) == MPFR_PREC (b)
&& MPFR_PREC (b) == MPFR_PREC (c)))
return mpfr_add1sp (a, b, c, rnd_mode);
else
return mpfr_add1 (a, b, c, rnd_mode);
}
}
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
long n;
if (argc > 1)
{
mpfr_init2 (x, atoi (argv[1]));
mpfr_set_str (x, argv[3], 10, MPFR_RNDN);
mpfr_jn (x, atoi (argv[2]), x, MPFR_RNDN);
mpfr_out_str (stdout, 10, 10, x, MPFR_RNDN);
printf ("\n");
mpfr_clear (x);
return 0;
}
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
/* special values */
mpfr_set_nan (x);
mpfr_jn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (y));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_jn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_inf (x, -1); /* -Inf */
mpfr_jn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y));
mpfr_set_ui (x, 0, MPFR_RNDN); /* +0 */
mpfr_jn (y, 0, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(+0)=1 */
mpfr_jn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j17(+0)=+0 */
mpfr_jn (y, -17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG (y)); /* j-17(+0)=-0 */
mpfr_jn (y, 42, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j42(+0)=+0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_jn (y, 0, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(-0)=1 */
mpfr_jn (y, 17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG (y)); /* j17(-0)=-0 */
mpfr_jn (y, -17, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j-17(-0)=+0 */
mpfr_jn (y, 42, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j42(-0)=+0 */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_jn (y, 0, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=0, 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_jn (y, 0, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn 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_jn (y, 1, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.0111000010100111001001111011101001011100001100011011");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn 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_jn (y, 17, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100011111001010101001001001000110110000010001011E-65");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn 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_jn (y, 42, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10000111100011010100111011100111101101000100000001001E-211");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=42, 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_jn (y, -42, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10000111100011010100111011100111101101000100000001001E-211");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=-42, 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_jn (y, 42, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10000111100011010100111011100111101101000100000001001E-211");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=42, 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_jn (y, -42, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10000111100011010100111011100111101101000100000001001E-211");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=-42, 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_jn (y, 4, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.0001110001011001100010100111100111100000111110111011111");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=4, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 16, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.0011101111100111101111010100000111111001111001001010011");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=16, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 256, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11111101111100110000000010111101101011101011110001011E-894");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=256, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 65536, x, MPFR_RNDN);
mpfr_set_str_binary (x, "100010010010011010110101100001000100011100010111011E-751747");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=65536, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 131072, x, MPFR_RNDN);
mpfr_set_str_binary (x, "1000001001110011111001110110000010011010000001001101E-1634508");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=131072, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 262144, x, MPFR_RNDN);
mpfr_set_str_binary (x, "1010011011000100111011001011110001000010000010111111E-3531100");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=262144, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, 524288, x, MPFR_RNDN);
mpfr_set_str_binary (x, "110000001010001111011011000011001011010100010001011E-7586426");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=524288, x=17, rnd=MPFR_RNDN\n");
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
n = LONG_MAX;
/* ensures n is odd */
if (n % 2 == 0)
n --;
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, n, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=%ld, x=17, rnd=MPFR_RNDN\n", n);
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_si (x, -17, MPFR_RNDN);
mpfr_jn (y, n, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=%ld, x=-17, rnd=MPFR_RNDN\n", n);
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_jn (y, -n, x, MPFR_RNDN);
mpfr_set_str_binary (x, "-0.0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=%ld, x=17, rnd=MPFR_RNDN\n", -n);
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_set_si (x, -17, MPFR_RNDN);
mpfr_jn (y, -n, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_jn for n=%ld, x=-17, rnd=MPFR_RNDN\n", -n);
printf ("Expected "); mpfr_dump (x);
printf ("Got "); mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
tests_end_mpfr ();
return 0;
}
