int
mpfr_check_range (mpfr_ptr x, mp_rnd_t rnd_mode)
{
if (MPFR_IS_FP(x) && MPFR_NOTZERO(x))
{ /* x is a non-zero FP */
mp_exp_t exp = MPFR_EXP(x);
if (exp < __mpfr_emin)
return mpfr_set_underflow(x, rnd_mode, MPFR_SIGN(x));
if (exp > __mpfr_emax)
return mpfr_set_overflow(x, rnd_mode, MPFR_SIGN(x));
}
return 0;
}
int
mpfr_get_z (mpz_ptr z, mpfr_srcptr f, mpfr_rnd_t rnd)
{
int inex;
mpfr_t r;
mpfr_exp_t exp;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (f)))
{
if (MPFR_UNLIKELY (MPFR_NOTZERO (f)))
MPFR_SET_ERANGEFLAG ();
mpz_set_ui (z, 0);
/* The ternary value is 0 even for infinity. Giving the rounding
direction in this case would not make much sense anyway, and
the direction would not necessarily match rnd. */
return 0;
}
MPFR_SAVE_EXPO_MARK (expo);
exp = MPFR_GET_EXP (f);
/* if exp <= 0, then |f|<1, thus |o(f)|<=1 */
MPFR_ASSERTN (exp < 0 || exp <= MPFR_PREC_MAX);
mpfr_init2 (r, (exp < (mpfr_exp_t) MPFR_PREC_MIN ?
MPFR_PREC_MIN : (mpfr_prec_t) exp));
inex = mpfr_rint (r, f, rnd);
MPFR_ASSERTN (inex != 1 && inex != -1); /* integral part of f is
representable in r */
MPFR_ASSERTN (MPFR_IS_FP (r));
/* The flags from mpfr_rint are the wanted ones. In particular,
it sets the inexact flag when necessary. */
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
exp = mpfr_get_z_2exp (z, r);
if (exp >= 0)
mpz_mul_2exp (z, z, exp);
else
mpz_fdiv_q_2exp (z, z, -exp);
mpfr_clear (r);
MPFR_SAVE_EXPO_FREE (expo);
return inex;
}
/* bug reported by Joseph S. Myers on 2013-10-27
https://sympa.inria.fr/sympa/arc/mpfr/2013-10/msg00015.html */
static void
bug20131027 (void)
{
mpfr_t sum, t[4];
mpfr_ptr p[4];
char *s[4] = {
"0x1p1000",
"-0x0.fffffffffffff80000000000000001p1000",
"-0x1p947",
"0x1p880"
};
int i, r;
mpfr_init2 (sum, 53);
for (i = 0; i < 4; i++)
{
mpfr_init2 (t[i], i == 0 ? 53 : 1000);
mpfr_set_str (t[i], s[i], 0, MPFR_RNDN);
p[i] = t[i];
}
RND_LOOP(r)
{
int expected_sign = (mpfr_rnd_t) r == MPFR_RNDD ? -1 : 1;
int inex;
inex = mpfr_sum (sum, p, 4, (mpfr_rnd_t) r);
if (MPFR_NOTZERO (sum) || MPFR_SIGN (sum) != expected_sign || inex != 0)
{
printf ("mpfr_sum incorrect in bug20131027 for %s:\n"
"expected %c0 with inex = 0, got ",
mpfr_print_rnd_mode ((mpfr_rnd_t) r),
expected_sign > 0 ? '+' : '-');
mpfr_dump (sum);
printf ("with inex = %d\n", inex);
exit (1);
}
}
for (i = 0; i < 4; i++)
mpfr_clear (t[i]);
mpfr_clear (sum);
}
int
mpfr_div_2si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd_mode)
{
int inexact;
inexact = y != x ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_IS_FP(y) && MPFR_NOTZERO(y))
{
if (n > 0 && (__mpfr_emin > MPFR_EMAX_MAX - n ||
MPFR_EXP(y) < __mpfr_emin + n))
return mpfr_set_underflow (y, rnd_mode, MPFR_SIGN(y));
if (n < 0 && (__mpfr_emax < MPFR_EMIN_MIN - n ||
MPFR_EXP(y) > __mpfr_emax + n))
return mpfr_set_overflow (y, rnd_mode, MPFR_SIGN(y));
MPFR_EXP(y) -= n;
}
return inexact;
}
/* 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;
}
/* Exact product. The number a is assumed to have enough allocated memory,
where the trailing bits are regarded as being part of the input numbers
(no reallocation is attempted and no check is performed as MPFR_TMP_INIT
could have been used). The arguments b and c may actually be UBF numbers
(mpfr_srcptr can be seen a bit like void *, but is stronger).
This function does not change the flags, except in case of NaN. */
void
mpfr_ubf_mul_exact (mpfr_ubf_ptr a, mpfr_srcptr b, mpfr_srcptr c)
{
MPFR_LOG_FUNC
(("b[%Pu]=%.*Rg c[%Pu]=%.*Rg",
mpfr_get_prec (b), mpfr_log_prec, b,
mpfr_get_prec (c), mpfr_log_prec, c),
("a[%Pu]=%.*Rg",
mpfr_get_prec (a), mpfr_log_prec, a));
MPFR_ASSERTD ((mpfr_ptr) a != b);
MPFR_ASSERTD ((mpfr_ptr) a != c);
MPFR_SIGN (a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_ARE_SINGULAR (b, c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
MPFR_SET_NAN (a);
else if (MPFR_IS_INF (b))
{
if (MPFR_NOTZERO (c))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_ZERO (a);
}
}
else
{
mpfr_exp_t e;
mp_size_t bn, cn;
mpfr_limb_ptr ap;
mp_limb_t u, v;
int m;
/* Note about the code below: For the choice of the precision of
* the result a, one could choose PREC(b) + PREC(c), instead of
* taking whole limbs into account, but in most cases where one
* would gain one limb, one would need to copy the significand
* instead of a no-op (see the mul.c code).
* But in the case MPFR_LIMB_MSB (u) == 0, if the result fits in
* an-1 limbs, one could actually do
* mpn_rshift (ap, ap, k, GMP_NUMB_BITS - 1)
* instead of
* mpn_lshift (ap, ap, k, 1)
* to gain one limb (and reduce the precision), replacing a shift
* by another one. Would this be interesting?
*/
bn = MPFR_LIMB_SIZE (b);
cn = MPFR_LIMB_SIZE (c);
ap = MPFR_MANT (a);
u = (bn >= cn) ?
mpn_mul (ap, MPFR_MANT (b), bn, MPFR_MANT (c), cn) :
mpn_mul (ap, MPFR_MANT (c), cn, MPFR_MANT (b), bn);
if (MPFR_UNLIKELY (MPFR_LIMB_MSB (u) == 0))
{
m = 1;
MPFR_DBGRES (v = mpn_lshift (ap, ap, bn + cn, 1));
MPFR_ASSERTD (v == 0);
}
else
m = 0;
if (! MPFR_IS_UBF (b) && ! MPFR_IS_UBF (c) &&
(e = MPFR_GET_EXP (b) + MPFR_GET_EXP (c) - m,
MPFR_EXP_IN_RANGE (e)))
{
MPFR_SET_EXP (a, e);
}
else
{
mpz_t be, ce;
mpz_init (MPFR_ZEXP (a));
/* This may involve copies of mpz_t, but exponents should not be
very large integers anyway. */
mpfr_get_zexp (be, b);
mpfr_get_zexp (ce, c);
mpz_add (MPFR_ZEXP (a), be, ce);
mpz_clear (be);
mpz_clear (ce);
mpz_sub_ui (MPFR_ZEXP (a), MPFR_ZEXP (a), m);
MPFR_SET_UBF (a);
}
}
}
static void
underflows (void)
{
mpfr_t x, y, z;
int err = 0;
int inexact;
int i;
mp_exp_t emin;
mpfr_init2 (x, 64);
mpfr_init2 (y, 64);
mpfr_set_ui (x, 1, GMP_RNDN);
mpfr_set_exp (x, mpfr_get_emin());
for (i = 3; i < 10; i++)
{
mpfr_set_ui (y, i, GMP_RNDN);
mpfr_div_2ui (y, y, 1, GMP_RNDN);
test_pow (y, x, y, GMP_RNDN);
if (!MPFR_IS_FP(y) || mpfr_cmp_ui (y, 0))
{
printf ("Error in mpfr_pow for ");
mpfr_out_str (stdout, 2, 0, x, GMP_RNDN);
printf (" ^ (%d/2)\nGot ", i);
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf (" instead of 0.\n");
exit (1);
}
}
mpfr_init2 (z, 55);
mpfr_set_str (x, "0.110011010011101001110001110100010000110111101E0",
2, GMP_RNDN);
mpfr_set_str (y, "0.101110010011111001011010100011011100111110011E40",
2, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDU);
if (!mpfr_underflow_p ())
{
printf ("Underflow flag is not set for special underflow test.\n");
err = 1;
}
if (inexact <= 0)
{
printf ("Ternary value is wrong for special underflow test.\n");
err = 1;
}
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_nextabove (x);
if (mpfr_cmp (x, z) != 0)
{
printf ("Wrong value for special underflow test.\nGot ");
mpfr_out_str (stdout, 2, 0, z, GMP_RNDN);
printf ("\ninstead of ");
mpfr_out_str (stdout, 2, 2, x, GMP_RNDN);
printf ("\n");
err = 1;
}
if (err)
exit (1);
/* MPFR currently (2006-08-19) segfaults on the following code (and
possibly makes other programs crash due to the lack of memory),
because y is converted into an mpz_t, and the required precision
is too high. */
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -2, GMP_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emax () - 1, GMP_RNDN);
mpfr_clear_flags ();
mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z))
{
printf ("Underflow test with large y fails.\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_emin (-256);
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -2, GMP_RNDN);
mpfr_set_ui_2exp (y, 1, 38, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z) || inexact >= 0)
{
printf ("Bad underflow detection for 0.75^(2^38). Obtained:\n"
"Underflow flag... %-3s (should be 'yes')\n"
"Zero result...... %-3s (should be 'yes')\n"
"Inexact value.... %-3d (should be negative)\n",
mpfr_underflow_p () ? "yes" : "no",
MPFR_IS_ZERO (z) ? "yes" : "no", inexact);
exit (1);
}
mpfr_set_emin (emin);
emin = mpfr_get_emin ();
mpfr_set_emin (-256);
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 40);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -1, GMP_RNDN);
mpfr_set_si_2exp (y, -1, 38, GMP_RNDN);
for (i = 0; i < 4; i++)
{
if (i == 2)
mpfr_neg (x, x, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z) ||
(i == 3 ? (inexact <= 0) : (inexact >= 0)))
{
printf ("Bad underflow detection for (");
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
printf (")^(-2^38-%d). Obtained:\n"
"Overflow flag.... %-3s (should be 'no')\n"
"Underflow flag... %-3s (should be 'yes')\n"
"Zero result...... %-3s (should be 'yes')\n"
"Inexact value.... %-3d (should be %s)\n", i,
mpfr_overflow_p () ? "yes" : "no",
mpfr_underflow_p () ? "yes" : "no",
MPFR_IS_ZERO (z) ? "yes" : "no", inexact,
i == 3 ? "positive" : "negative");
exit (1);
}
inexact = mpfr_sub_ui (y, y, 1, GMP_RNDN);
MPFR_ASSERTN (inexact == 0);
}
mpfr_set_emin (emin);
mpfr_clears (x, y, z, (void *) 0);
}
static int
mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
/* Old implementation */
int sign_product, cc, inexact;
mpfr_exp_t ax;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq, cq;
mp_size_t bn, cn, tn, k;
MPFR_TMP_DECL(marker);
/* deal with special cases */
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
if (MPFR_IS_INF(b))
{
if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
{
MPFR_SET_SIGN(a,sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
if (MPFR_NOTZERO(b))
{
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 * 0 is exact */
}
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
bq = MPFR_PREC(b);
cq = MPFR_PREC(c);
MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */
cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
/* <= k, thus no int overflow */
MPFR_ASSERTD(tn <= k);
/* Check for no size_t overflow*/
MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
MPFR_TMP_MARK(marker);
tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
/* multiplies two mantissa in temporary allocated space */
b1 = (MPFR_LIKELY(bn >= cn)) ?
mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
: mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);
/* now tmp[0]..tmp[k-1] contains the product of both mantissa,
with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */
b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */
/* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
tmp += k - tn;
if (MPFR_UNLIKELY(b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq,
MPFR_IS_NEG_SIGN(sign_product),
MPFR_PREC (a), rnd_mode, &inexact);
/* cc = 1 ==> result is a power of two */
if (MPFR_UNLIKELY(cc))
MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;
MPFR_TMP_FREE(marker);
{
mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
return mpfr_overflow (a, rnd_mode, sign_product);
if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
{
/* In the rounding to the nearest mode, if the exponent of the exact
result (i.e. before rounding, i.e. without taking cc into account)
is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
both arguments are powers of 2), then round to zero. */
if (rnd_mode == MPFR_RNDN &&
(ax + (mpfr_exp_t) b1 < __gmpfr_emin ||
(mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, sign_product);
}
MPFR_SET_EXP (a, ax2);
MPFR_SET_SIGN(a, sign_product);
}
MPFR_RET (inexact);
}
int
main (void)
{
mpfr_t x, y;
int i, r;
tests_start_mpfr ();
mpfr_init2 (x, 256);
mpfr_init2 (y, 8);
RND_LOOP (r)
{
/* Check NAN */
mpfr_set_nan (x);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (1);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (2);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (3);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (4);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (5);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (6);
/* Check INF */
mpfr_set_inf (x, 1);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (7);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (8);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (9);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (10);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (11);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (12);
/* Check Zero */
MPFR_SET_ZERO (x);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (13);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (14);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (15);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (16);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (17);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (18);
/* Check small positive op */
mpfr_set_str1 (x, "1@-1");
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (19);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (20);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (21);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (22);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (23);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (24);
/* Check 17 */
mpfr_set_ui (x, 17, MPFR_RNDN);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (25);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (26);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (27);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (28);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (29);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (30);
/* Check all other values */
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (31);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (32);
mpfr_mul_2exp (x, x, 40, MPFR_RNDN);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (33);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (34);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (35);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (36);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (37);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (38);
mpfr_set_ui (x, LONG_MAX, MPFR_RNDN);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (39);
mpfr_set_ui (x, UINT_MAX, MPFR_RNDN);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (40);
mpfr_set_ui (x, INT_MAX, MPFR_RNDN);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (41);
mpfr_set_ui (x, USHRT_MAX, MPFR_RNDN);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (42);
mpfr_set_ui (x, SHRT_MAX, MPFR_RNDN);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (43);
mpfr_set_si (x, 1, MPFR_RNDN);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (44);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (45);
/* Check negative op */
for (i = 1; i <= 4; i++)
{
int inv;
mpfr_set_si_2exp (x, -i, -2, MPFR_RNDN);
mpfr_rint (y, x, (mpfr_rnd_t) r);
inv = MPFR_NOTZERO (y);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (46);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (47);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (48);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (49);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (50);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (51);
}
}
mpfr_clear (x);
mpfr_clear (y);
check_intmax ();
tests_end_mpfr ();
return 0;
}
static void
underflow_up (int extended_emin)
{
mpfr_t minpos, x, y, t, t2;
int precx, precy;
int inex;
int rnd;
int e3;
int i, j;
mpfr_init2 (minpos, 2);
mpfr_set_ui (minpos, 0, MPFR_RNDN);
mpfr_nextabove (minpos);
/* Let's test values near the underflow boundary.
*
* Minimum representable positive number: minpos = 2^(emin - 1).
* Let's choose an MPFR number x = log(minpos) + eps, with |eps| small
* (note: eps cannot be 0, and cannot be a rational number either).
* Then exp(x) = minpos * exp(eps) ~= minpos * (1 + eps + eps^2).
* We will compute y = rnd(exp(x)) in some rounding mode, precision p.
* 1. If eps > 0, then in any rounding mode:
* rnd(exp(x)) >= minpos and no underflow.
* So, let's take x1 = rndu(log(minpos)) in some precision.
* 2. If eps < 0, then exp(x) < minpos and the result will be either 0
* or minpos. An underflow always occurs in MPFR_RNDZ and MPFR_RNDD,
* but not necessarily in MPFR_RNDN and MPFR_RNDU (this is underflow
* after rounding in an unbounded exponent range). If -a < eps < -b,
* minpos * (1 - a) < exp(x) < minpos * (1 - b + b^2).
* - If eps > -2^(-p), no underflow in MPFR_RNDU.
* - If eps > -2^(-p-1), no underflow in MPFR_RNDN.
* - If eps < - (2^(-p-1) + 2^(-2p-1)), underflow in MPFR_RNDN.
* - If eps < - (2^(-p) + 2^(-2p+1)), underflow in MPFR_RNDU.
* - In MPFR_RNDN, result is minpos iff exp(eps) > 1/2, i.e.
* - log(2) < eps < ...
*
* Moreover, since precy < MPFR_EXP_THRESHOLD (to avoid tests that take
* too much time), mpfr_exp() always selects mpfr_exp_2(); so, we need
* to test mpfr_exp_3() too. This will be done via the e3 variable:
* e3 = 0: mpfr_exp(), thus mpfr_exp_2().
* e3 = 1: mpfr_exp_3(), via the exp_3() wrapper.
* i.e.: inex = e3 ? exp_3 (y, x, rnd) : mpfr_exp (y, x, rnd);
*/
/* Case eps > 0. In revision 5461 (trunk) on a 64-bit Linux machine:
* Incorrect flags in underflow_up, eps > 0, MPFR_RNDN and extended emin
* for precx = 96, precy = 16, mpfr_exp_3
* Got 9 instead of 8.
* Note: testing this case in several precisions for x and y introduces
* some useful random. Indeed, the bug is not always triggered.
* Fixed in r5469.
*/
for (precx = 16; precx <= 128; precx += 16)
{
mpfr_init2 (x, precx);
mpfr_log (x, minpos, MPFR_RNDU);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
for (e3 = 0; e3 <= 1; e3++)
{
RND_LOOP (rnd)
{
int err = 0;
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, (mpfr_rnd_t) rnd)
: mpfr_exp (y, x, (mpfr_rnd_t) rnd);
if (__gmpfr_flags != MPFR_FLAGS_INEXACT)
{
printf ("Incorrect flags in underflow_up, eps > 0, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, %s\n",
precx, precy, e3 ? "mpfr_exp_3" : "mpfr_exp");
printf ("Got %u instead of %u.\n", __gmpfr_flags,
(unsigned int) MPFR_FLAGS_INEXACT);
err = 1;
}
if (mpfr_cmp0 (y, minpos) < 0)
{
printf ("Incorrect result in underflow_up, eps > 0, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, %s\n",
precx, precy, e3 ? "mpfr_exp_3" : "mpfr_exp");
mpfr_dump (y);
err = 1;
}
MPFR_ASSERTN (inex != 0);
if (rnd == MPFR_RNDD || rnd == MPFR_RNDZ)
MPFR_ASSERTN (inex < 0);
if (rnd == MPFR_RNDU)
MPFR_ASSERTN (inex > 0);
if (err)
exit (1);
}
}
mpfr_clear (y);
}
mpfr_clear (x);
}
/* Case - log(2) < eps < 0 in MPFR_RNDN, starting with small-precision x;
* only check the result and the ternary value.
* Previous to r5453 (trunk), on 32-bit and 64-bit machines, this fails
* for precx = 65 and precy = 16, e.g.:
* exp_2.c:264: assertion failed: ...
* because mpfr_sub (r, x, r, MPFR_RNDU); yields a null value. This is
* fixed in r5453 by going to next Ziv's iteration.
*/
for (precx = sizeof(mpfr_exp_t) * CHAR_BIT + 1; precx <= 81; precx += 8)
{
mpfr_init2 (x, precx);
mpfr_log (x, minpos, MPFR_RNDD); /* |ulp| <= 1/2 */
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
inex = mpfr_exp (y, x, MPFR_RNDN);
if (inex <= 0 || mpfr_cmp0 (y, minpos) != 0)
{
printf ("Error in underflow_up, - log(2) < eps < 0");
if (extended_emin)
printf (" and extended emin");
printf (" for prec = %d\nExpected ", precy);
mpfr_out_str (stdout, 16, 0, minpos, MPFR_RNDN);
printf (" (minimum positive MPFR number) and inex > 0\nGot ");
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\nwith inex = %d\n", inex);
exit (1);
}
mpfr_clear (y);
}
mpfr_clear (x);
}
/* Cases eps ~ -2^(-p) and eps ~ -2^(-p-1). More precisely,
* _ for j = 0, eps > -2^(-(p+i)),
* _ for j = 1, eps < - (2^(-(p+i)) + 2^(1-2(p+i))),
* where i = 0 or 1.
*/
mpfr_inits2 (2, t, t2, (mpfr_ptr) 0);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_set_ui_2exp (t, 1, - precy, MPFR_RNDN); /* 2^(-p) */
mpfr_set_ui_2exp (t2, 1, 1 - 2 * precy, MPFR_RNDN); /* 2^(-2p+1) */
precx = sizeof(mpfr_exp_t) * CHAR_BIT + 2 * precy + 8;
mpfr_init2 (x, precx);
mpfr_init2 (y, precy);
for (i = 0; i <= 1; i++)
{
for (j = 0; j <= 1; j++)
{
if (j == 0)
{
/* Case eps > -2^(-(p+i)). */
mpfr_log (x, minpos, MPFR_RNDU);
}
else /* j == 1 */
{
/* Case eps < - (2^(-(p+i)) + 2^(1-2(p+i))). */
mpfr_log (x, minpos, MPFR_RNDD);
inex = mpfr_sub (x, x, t2, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
}
inex = mpfr_sub (x, x, t, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
RND_LOOP (rnd)
for (e3 = 0; e3 <= 1; e3++)
{
int err = 0;
unsigned int flags;
flags = MPFR_FLAGS_INEXACT |
(((rnd == MPFR_RNDU || rnd == MPFR_RNDA)
&& (i == 1 || j == 0)) ||
(rnd == MPFR_RNDN && (i == 1 && j == 0)) ?
0 : MPFR_FLAGS_UNDERFLOW);
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, (mpfr_rnd_t) rnd)
: mpfr_exp (y, x, (mpfr_rnd_t) rnd);
if (__gmpfr_flags != flags)
{
printf ("Incorrect flags in underflow_up, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, ",
precx, precy);
if (j == 0)
printf ("eps >~ -2^(-%d)", precy + i);
else
printf ("eps <~ - (2^(-%d) + 2^(%d))",
precy + i, 1 - 2 * (precy + i));
printf (", %s\n", e3 ? "mpfr_exp_3" : "mpfr_exp");
printf ("Got %u instead of %u.\n",
__gmpfr_flags, flags);
err = 1;
}
if (rnd == MPFR_RNDU || rnd == MPFR_RNDA || rnd == MPFR_RNDN ?
mpfr_cmp0 (y, minpos) != 0 : MPFR_NOTZERO (y))
{
printf ("Incorrect result in underflow_up, %s",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precx = %d, precy = %d, ",
precx, precy);
if (j == 0)
printf ("eps >~ -2^(-%d)", precy + i);
else
printf ("eps <~ - (2^(-%d) + 2^(%d))",
precy + i, 1 - 2 * (precy + i));
printf (", %s\n", e3 ? "mpfr_exp_3" : "mpfr_exp");
mpfr_dump (y);
err = 1;
}
if (err)
exit (1);
} /* for (e3 ...) */
} /* for (j ...) */
mpfr_div_2si (t, t, 1, MPFR_RNDN);
mpfr_div_2si (t2, t2, 2, MPFR_RNDN);
} /* for (i ...) */
mpfr_clears (x, y, (mpfr_ptr) 0);
} /* for (precy ...) */
mpfr_clears (t, t2, (mpfr_ptr) 0);
/* Case exp(eps) ~= 1/2, i.e. eps ~= - log(2).
* We choose x0 and x1 with high enough precision such that:
* x0 = rndd(rndd(log(minpos)) - rndu(log(2)))
* x1 = rndu(rndu(log(minpos)) - rndd(log(2)))
* In revision 5507 (trunk) on a 64-bit Linux machine, this fails:
* Error in underflow_up, eps >~ - log(2) and extended emin
* for precy = 16, mpfr_exp
* Expected 1.0@-1152921504606846976 (minimum positive MPFR number),
* inex > 0 and flags = 9
* Got 0
* with inex = -1 and flags = 9
* due to a double-rounding problem in mpfr_mul_2si when rescaling
* the result.
*/
mpfr_inits2 (sizeof(mpfr_exp_t) * CHAR_BIT + 64, x, t, (mpfr_ptr) 0);
for (i = 0; i <= 1; i++)
{
mpfr_log (x, minpos, i ? MPFR_RNDU : MPFR_RNDD);
mpfr_const_log2 (t, i ? MPFR_RNDD : MPFR_RNDU);
mpfr_sub (x, x, t, i ? MPFR_RNDU : MPFR_RNDD);
for (precy = 16; precy <= 128; precy += 16)
{
mpfr_init2 (y, precy);
for (e3 = 0; e3 <= 1; e3++)
{
unsigned int flags, uflags =
MPFR_FLAGS_INEXACT | MPFR_FLAGS_UNDERFLOW;
mpfr_clear_flags ();
inex = e3 ? exp_3 (y, x, MPFR_RNDN) : mpfr_exp (y, x, MPFR_RNDN);
flags = __gmpfr_flags;
if (flags != uflags ||
(i ? (inex <= 0 || mpfr_cmp0 (y, minpos) != 0)
: (inex >= 0 || MPFR_NOTZERO (y))))
{
printf ("Error in underflow_up, eps %c~ - log(2)",
i ? '>' : '<');
if (extended_emin)
printf (" and extended emin");
printf ("\nfor precy = %d, %s\nExpected ", precy,
e3 ? "mpfr_exp_3" : "mpfr_exp");
if (i)
{
mpfr_out_str (stdout, 16, 0, minpos, MPFR_RNDN);
printf (" (minimum positive MPFR number),\ninex >");
}
else
{
printf ("+0, inex <");
}
printf (" 0 and flags = %u\nGot ", uflags);
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\nwith inex = %d and flags = %u\n", inex, flags);
exit (1);
}
}
mpfr_clear (y);
}
}
mpfr_clears (x, t, (mpfr_ptr) 0);
mpfr_clear (minpos);
}
int
mpfr_eq (mpfr_srcptr u, mpfr_srcptr v, unsigned long int n_bits)
{
mp_srcptr up, vp;
mp_size_t usize, vsize, size, i;
mp_exp_t uexp, vexp;
int usign, k;
uexp = MPFR_EXP(u);
vexp = MPFR_EXP(v);
usize = (MPFR_PREC(u)-1)/BITS_PER_MP_LIMB + 1;
vsize = (MPFR_PREC(v)-1)/BITS_PER_MP_LIMB + 1;
usign = MPFR_SIGN(u);
/* 1. Are the signs different? */
if (usign == MPFR_SIGN(v))
{
/* U and V are both non-negative or both negative. */
if (!MPFR_NOTZERO(u))
return !MPFR_NOTZERO(v);
if (!MPFR_NOTZERO(v))
return !MPFR_NOTZERO(u);
/* Fall out. */
}
else
{
/* Either U or V is negative, but not both. */
if (MPFR_NOTZERO(u) || MPFR_NOTZERO(v))
return 0;
else return 1; /* particular case -0 = +0 */
}
/* U and V have the same sign and are both non-zero. */
if (MPFR_IS_INF(u))
return (MPFR_IS_INF(v) && (usign == MPFR_SIGN(v)));
else if (MPFR_IS_INF(v)) return 0;
if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v)) return 0;
/* 2. Are the exponents different? */
if (uexp > vexp)
return 0; /* ??? handle (uexp = vexp + 1) */
if (vexp > uexp)
return 0; /* ??? handle (vexp = uexp + 1) */
usize = ABS (usize);
vsize = ABS (vsize);
up = MPFR_MANT(u);
vp = MPFR_MANT(v);
if (usize > vsize)
{
if (vsize * BITS_PER_MP_LIMB < n_bits)
{
k = usize - vsize - 1;
while (k >= 0 && !up[k]) --k;
if (k >= 0)
return 0; /* surely too different */
}
size = vsize;
}
else if (vsize > usize)
{
if (usize * BITS_PER_MP_LIMB < n_bits)
{
k = vsize - usize - 1;
while (k >= 0 && !vp[k]) --k;
if (k >= 0)
return 0; /* surely too different */
}
size = usize;
}
else
{
size = usize;
}
if (size > (n_bits + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB)
size = (n_bits + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
up += usize - size;
vp += vsize - size;
for (i = size - 1; i > 0; i--)
{
if (up[i] != vp[i])
return 0;
}
if (n_bits & (BITS_PER_MP_LIMB - 1))
return (up[i] >> (BITS_PER_MP_LIMB - (n_bits & (BITS_PER_MP_LIMB - 1))) ==
vp[i] >> (BITS_PER_MP_LIMB - (n_bits & (BITS_PER_MP_LIMB - 1))));
else
return (up[i] == vp[i]);
static void
check_intmax (void)
{
#ifdef _MPFR_H_HAVE_INTMAX_T
mpfr_t x, y;
int i, r;
mpfr_init2 (x, sizeof (uintmax_t) * CHAR_BIT);
mpfr_init2 (y, 8);
RND_LOOP (r)
{
/* Check NAN */
mpfr_set_nan (x);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (52);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (53);
/* Check INF */
mpfr_set_inf (x, 1);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (54);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (55);
/* Check Zero */
MPFR_SET_ZERO (x);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (56);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (57);
/* Check positive small op */
mpfr_set_str1 (x, "1@-1");
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (58);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (59);
/* Check 17 */
mpfr_set_ui (x, 17, MPFR_RNDN);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (60);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (61);
/* Check hugest */
mpfr_set_ui_2exp (x, 42, sizeof (uintmax_t) * 32, MPFR_RNDN);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (62);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (63);
/* Check all other values */
mpfr_set_uj (x, MPFR_UINTMAX_MAX, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (64);
mpfr_set_uj (x, MPFR_UINTMAX_MAX, MPFR_RNDN);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (65);
mpfr_set_sj (x, MPFR_INTMAX_MAX, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (66);
mpfr_set_sj (x, MPFR_INTMAX_MAX, MPFR_RNDN);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (67);
mpfr_set_sj (x, MPFR_INTMAX_MIN, MPFR_RNDN);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (68);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (69);
/* Check negative op */
for (i = 1; i <= 4; i++)
{
int inv;
mpfr_set_si_2exp (x, -i, -2, MPFR_RNDN);
mpfr_rint (y, x, (mpfr_rnd_t) r);
inv = MPFR_NOTZERO (y);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (70);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (71);
}
}
mpfr_clear (x);
mpfr_clear (y);
#endif
}
static void
check_special_exprange (void)
{
int inexact, ov;
unsigned int eflags, gflags;
mpfr_t xi, xf, x;
mpfr_exp_t emax;
emax = mpfr_get_emax ();
mpfr_init2 (xi, 7);
mpfr_init2 (xf, 7);
mpfr_init2 (x, 8);
mpfr_set_str (x, "0.11111111", 2, MPFR_RNDN);
for (ov = 0; ov <= 1; ov++)
{
const char *s = ov ? "@Inf@" : "1";
if (ov)
set_emax (0);
mpfr_clear_flags ();
inexact = mpfr_modf (xi, xf, x, MPFR_RNDN);
gflags = __gmpfr_flags;
set_emax (emax);
if (MPFR_NOTZERO (xi) || MPFR_IS_NEG (xi) ||
mpfr_cmp_str1 (xf, s) != 0)
{
printf ("Error in check_special_exprange (ov = %d):"
" expected 0 and %s, got\n", ov, s);
mpfr_out_str (stdout, 2, 0, xi, MPFR_RNDN);
printf (" and ");
mpfr_out_str (stdout, 2, 0, xf, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (inexact != 4)
{
printf ("Bad inexact value in check_special_exprange (ov = %d):"
" expected 4, got %d\n", ov, inexact);
exit (1);
}
eflags = MPFR_FLAGS_INEXACT | (ov ? MPFR_FLAGS_OVERFLOW : 0);
if (gflags != eflags)
{
printf ("Bad flags in check_special_exprange (ov = %d):"
" expected %u, got %u\n", ov, eflags, gflags);
exit (1);
}
}
/* Test if an overflow occurs in mpfr_set for ope >= opq. */
mpfr_set_emax (MPFR_EMAX_MAX);
mpfr_set_inf (x, 1);
mpfr_nextbelow (x);
mpfr_clear_flags ();
inexact = mpfr_modf (xi, xf, x, MPFR_RNDN);
gflags = __gmpfr_flags;
if (mpfr_cmp_str1 (xi, "@Inf@") != 0 ||
MPFR_NOTZERO (xf) || MPFR_IS_NEG (xf))
{
printf ("Error in check_special_exprange:"
" expected 0 and @Inf@, got\n");
mpfr_out_str (stdout, 2, 0, xi, MPFR_RNDN);
printf (" and ");
mpfr_out_str (stdout, 2, 0, xf, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (inexact != 1)
{
printf ("Bad inexact value in check_special_exprange:"
" expected 1, got %d\n", inexact);
exit (1);
}
eflags = MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW;
if (gflags != eflags)
{
printf ("Bad flags in check_special_exprange:"
" expected %u, got %u\n", eflags, gflags);
exit (1);
}
set_emax (emax);
/* Test if an underflow occurs in the general case. TODO */
mpfr_clears (xi, xf, x, (mpfr_ptr) 0);
}
int
mpfr_atan2 (mpfr_ptr dest, mpfr_srcptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t tmp, pi;
int inexact;
mpfr_prec_t prec;
mpfr_exp_t e;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC
(("y[%Pu]=%.*Rg x[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (y), mpfr_log_prec, y,
mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("atan[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (dest), mpfr_log_prec, dest, inexact));
/* Special cases */
if (MPFR_ARE_SINGULAR (x, y))
{
/* atan2(0, 0) does not raise the "invalid" floating-point
exception, nor does atan2(y, 0) raise the "divide-by-zero"
floating-point exception.
-- atan2(±0, -0) returns ±pi.313)
-- atan2(±0, +0) returns ±0.
-- atan2(±0, x) returns ±pi, for x < 0.
-- atan2(±0, x) returns ±0, for x > 0.
-- atan2(y, ±0) returns -pi/2 for y < 0.
-- atan2(y, ±0) returns pi/2 for y > 0.
-- atan2(±oo, -oo) returns ±3pi/4.
-- atan2(±oo, +oo) returns ±pi/4.
-- atan2(±oo, x) returns ±pi/2, for finite x.
-- atan2(±y, -oo) returns ±pi, for finite y > 0.
-- atan2(±y, +oo) returns ±0, for finite y > 0.
*/
if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
{
MPFR_SET_NAN (dest);
MPFR_RET_NAN;
}
if (MPFR_IS_ZERO (y))
{
if (MPFR_IS_NEG (x)) /* +/- PI */
{
set_pi:
if (MPFR_IS_NEG (y))
{
inexact = mpfr_const_pi (dest, MPFR_INVERT_RND (rnd_mode));
MPFR_CHANGE_SIGN (dest);
return -inexact;
}
else
return mpfr_const_pi (dest, rnd_mode);
}
else /* +/- 0 */
{
set_zero:
MPFR_SET_ZERO (dest);
MPFR_SET_SAME_SIGN (dest, y);
return 0;
}
}
if (MPFR_IS_ZERO (x))
{
return pi_div_2ui (dest, 1, MPFR_IS_NEG (y), rnd_mode);
}
if (MPFR_IS_INF (y))
{
if (!MPFR_IS_INF (x)) /* +/- PI/2 */
return pi_div_2ui (dest, 1, MPFR_IS_NEG (y), rnd_mode);
else if (MPFR_IS_POS (x)) /* +/- PI/4 */
return pi_div_2ui (dest, 2, MPFR_IS_NEG (y), rnd_mode);
else /* +/- 3*PI/4: Ugly since we have to round properly */
{
mpfr_t tmp2;
MPFR_ZIV_DECL (loop2);
mpfr_prec_t prec2 = MPFR_PREC (dest) + 10;
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (tmp2, prec2);
MPFR_ZIV_INIT (loop2, prec2);
for (;;)
{
mpfr_const_pi (tmp2, MPFR_RNDN);
mpfr_mul_ui (tmp2, tmp2, 3, MPFR_RNDN); /* Error <= 2 */
mpfr_div_2ui (tmp2, tmp2, 2, MPFR_RNDN);
if (mpfr_round_p (MPFR_MANT (tmp2), MPFR_LIMB_SIZE (tmp2),
MPFR_PREC (tmp2) - 2,
MPFR_PREC (dest) + (rnd_mode == MPFR_RNDN)))
break;
MPFR_ZIV_NEXT (loop2, prec2);
mpfr_set_prec (tmp2, prec2);
}
MPFR_ZIV_FREE (loop2);
if (MPFR_IS_NEG (y))
MPFR_CHANGE_SIGN (tmp2);
inexact = mpfr_set (dest, tmp2, rnd_mode);
mpfr_clear (tmp2);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (dest, inexact, rnd_mode);
}
}
MPFR_ASSERTD (MPFR_IS_INF (x));
if (MPFR_IS_NEG (x))
goto set_pi;
else
goto set_zero;
}
/* When x is a power of two, we call directly atan(y/x) since y/x is
exact. */
if (MPFR_UNLIKELY (MPFR_IS_POWER_OF_2 (x)))
{
int r;
mpfr_t yoverx;
unsigned int saved_flags = __gmpfr_flags;
mpfr_init2 (yoverx, MPFR_PREC (y));
if (MPFR_LIKELY (mpfr_div_2si (yoverx, y, MPFR_GET_EXP (x) - 1,
MPFR_RNDN) == 0))
{
/* Here the flags have not changed due to mpfr_div_2si. */
r = mpfr_atan (dest, yoverx, rnd_mode);
mpfr_clear (yoverx);
return r;
}
else
{
/* Division is inexact because of a small exponent range */
mpfr_clear (yoverx);
__gmpfr_flags = saved_flags;
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* Set up initial prec */
prec = MPFR_PREC (dest) + 3 + MPFR_INT_CEIL_LOG2 (MPFR_PREC (dest));
mpfr_init2 (tmp, prec);
MPFR_ZIV_INIT (loop, prec);
if (MPFR_IS_POS (x))
/* use atan2(y,x) = atan(y/x) */
for (;;)
{
int div_inex;
MPFR_BLOCK_DECL (flags);
MPFR_BLOCK (flags, div_inex = mpfr_div (tmp, y, x, MPFR_RNDN));
if (div_inex == 0)
{
/* Result is exact. */
inexact = mpfr_atan (dest, tmp, rnd_mode);
goto end;
}
/* Error <= ulp (tmp) except in case of underflow or overflow. */
/* If the division underflowed, since |atan(z)/z| < 1, we have
an underflow. */
if (MPFR_UNDERFLOW (flags))
{
int sign;
/* In the case MPFR_RNDN with 2^(emin-2) < |y/x| < 2^(emin-1):
The smallest significand value S > 1 of |y/x| is:
* 1 / (1 - 2^(-px)) if py <= px,
* (1 - 2^(-px) + 2^(-py)) / (1 - 2^(-px)) if py >= px.
Therefore S - 1 > 2^(-pz), where pz = max(px,py). We have:
atan(|y/x|) > atan(z), where z = 2^(emin-2) * (1 + 2^(-pz)).
> z - z^3 / 3.
> 2^(emin-2) * (1 + 2^(-pz) - 2^(2 emin - 5))
Assuming pz <= -2 emin + 5, we can round away from zero
(this is what mpfr_underflow always does on MPFR_RNDN).
In the case MPFR_RNDN with |y/x| <= 2^(emin-2), we round
toward zero, as |atan(z)/z| < 1. */
MPFR_ASSERTN (MPFR_PREC_MAX <=
2 * (mpfr_uexp_t) - MPFR_EMIN_MIN + 5);
if (rnd_mode == MPFR_RNDN && MPFR_IS_ZERO (tmp))
rnd_mode = MPFR_RNDZ;
sign = MPFR_SIGN (tmp);
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (dest, rnd_mode, sign);
}
mpfr_atan (tmp, tmp, MPFR_RNDN); /* Error <= 2*ulp (tmp) since
abs(D(arctan)) <= 1 */
/* TODO: check that the error bound is correct in case of overflow. */
/* FIXME: Error <= ulp(tmp) ? */
if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - 2, MPFR_PREC (dest),
rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
}
else /* x < 0 */
/* Use sign(y)*(PI - atan (|y/x|)) */
{
mpfr_init2 (pi, prec);
for (;;)
{
mpfr_div (tmp, y, x, MPFR_RNDN); /* Error <= ulp (tmp) */
/* If tmp is 0, we have |y/x| <= 2^(-emin-2), thus
atan|y/x| < 2^(-emin-2). */
MPFR_SET_POS (tmp); /* no error */
mpfr_atan (tmp, tmp, MPFR_RNDN); /* Error <= 2*ulp (tmp) since
abs(D(arctan)) <= 1 */
mpfr_const_pi (pi, MPFR_RNDN); /* Error <= ulp(pi) /2 */
e = MPFR_NOTZERO(tmp) ? MPFR_GET_EXP (tmp) : __gmpfr_emin - 1;
mpfr_sub (tmp, pi, tmp, MPFR_RNDN); /* see above */
if (MPFR_IS_NEG (y))
MPFR_CHANGE_SIGN (tmp);
/* Error(tmp) <= (1/2+2^(EXP(pi)-EXP(tmp)-1)+2^(e-EXP(tmp)+1))*ulp
<= 2^(MAX (MAX (EXP(PI)-EXP(tmp)-1, e-EXP(tmp)+1),
-1)+2)*ulp(tmp) */
e = MAX (MAX (MPFR_GET_EXP (pi)-MPFR_GET_EXP (tmp) - 1,
e - MPFR_GET_EXP (tmp) + 1), -1) + 2;
if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - e, MPFR_PREC (dest),
rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
mpfr_set_prec (pi, prec);
}
mpfr_clear (pi);
}
inexact = mpfr_set (dest, tmp, rnd_mode);
end:
MPFR_ZIV_FREE (loop);
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (dest, inexact, rnd_mode);
}
static void
tst (void)
{
int sv = sizeof (val) / sizeof (*val);
int i, j;
int rnd;
mpfr_t x, y, z, tmp;
mpfr_inits2 (53, x, y, z, tmp, (mpfr_ptr) 0);
for (i = 0; i < sv; i++)
for (j = 0; j < sv; j++)
RND_LOOP (rnd)
{
int exact, inex;
unsigned int flags;
if (my_setstr (x, val[i]) || my_setstr (y, val[j]))
{
printf ("internal error for (%d,%d,%d)\n", i, j, rnd);
exit (1);
}
mpfr_clear_flags ();
inex = mpfr_pow (z, x, y, (mpfr_rnd_t) rnd);
flags = __gmpfr_flags;
if (! MPFR_IS_NAN (z) && mpfr_nanflag_p ())
err ("got NaN flag without NaN value", i, j, rnd, z, inex);
if (MPFR_IS_NAN (z) && ! mpfr_nanflag_p ())
err ("got NaN value without NaN flag", i, j, rnd, z, inex);
if (inex != 0 && ! mpfr_inexflag_p ())
err ("got non-zero ternary value without inexact flag",
i, j, rnd, z, inex);
if (inex == 0 && mpfr_inexflag_p ())
err ("got null ternary value with inexact flag",
i, j, rnd, z, inex);
if (i >= 3 && j >= 3)
{
if (mpfr_underflow_p ())
err ("got underflow", i, j, rnd, z, inex);
if (mpfr_overflow_p ())
err ("got overflow", i, j, rnd, z, inex);
exact = MPFR_IS_SINGULAR (z) ||
(mpfr_mul_2ui (tmp, z, 16, MPFR_RNDN), mpfr_integer_p (tmp));
if (exact && inex != 0)
err ("got exact value with ternary flag different from 0",
i, j, rnd, z, inex);
if (! exact && inex == 0)
err ("got inexact value with ternary flag equal to 0",
i, j, rnd, z, inex);
}
if (MPFR_IS_ZERO (x) && ! MPFR_IS_NAN (y) && MPFR_NOTZERO (y))
{
if (MPFR_IS_NEG (y) && ! MPFR_IS_INF (z))
err ("expected an infinity", i, j, rnd, z, inex);
if (MPFR_IS_POS (y) && ! MPFR_IS_ZERO (z))
err ("expected a zero", i, j, rnd, z, inex);
if ((MPFR_IS_NEG (x) && is_odd (y)) ^ MPFR_IS_NEG (z))
err ("wrong sign", i, j, rnd, z, inex);
}
if (! MPFR_IS_NAN (x) && mpfr_cmp_si (x, -1) == 0)
{
/* x = -1 */
if (! (MPFR_IS_INF (y) || mpfr_integer_p (y)) &&
! MPFR_IS_NAN (z))
err ("expected NaN", i, j, rnd, z, inex);
if ((MPFR_IS_INF (y) || (mpfr_integer_p (y) && ! is_odd (y)))
&& ! mpfr_equal_p (z, __gmpfr_one))
err ("expected 1", i, j, rnd, z, inex);
if (is_odd (y) &&
(MPFR_IS_NAN (z) || mpfr_cmp_si (z, -1) != 0))
err ("expected -1", i, j, rnd, z, inex);
}
if ((mpfr_equal_p (x, __gmpfr_one) || MPFR_IS_ZERO (y)) &&
! mpfr_equal_p (z, __gmpfr_one))
err ("expected 1", i, j, rnd, z, inex);
if (MPFR_IS_PURE_FP (x) && MPFR_IS_NEG (x) &&
MPFR_IS_FP (y) && ! mpfr_integer_p (y) &&
! MPFR_IS_NAN (z))
err ("expected NaN", i, j, rnd, z, inex);
if (MPFR_IS_INF (y) && MPFR_NOTZERO (x))
{
int cmpabs1 = mpfr_cmpabs (x, __gmpfr_one);
if ((MPFR_IS_NEG (y) ? (cmpabs1 < 0) : (cmpabs1 > 0)) &&
! (MPFR_IS_POS (z) && MPFR_IS_INF (z)))
err ("expected +Inf", i, j, rnd, z, inex);
if ((MPFR_IS_NEG (y) ? (cmpabs1 > 0) : (cmpabs1 < 0)) &&
! (MPFR_IS_POS (z) && MPFR_IS_ZERO (z)))
err ("expected +0", i, j, rnd, z, inex);
}
if (MPFR_IS_INF (x) && ! MPFR_IS_NAN (y) && MPFR_NOTZERO (y))
{
if (MPFR_IS_POS (y) && ! MPFR_IS_INF (z))
err ("expected an infinity", i, j, rnd, z, inex);
if (MPFR_IS_NEG (y) && ! MPFR_IS_ZERO (z))
err ("expected a zero", i, j, rnd, z, inex);
if ((MPFR_IS_NEG (x) && is_odd (y)) ^ MPFR_IS_NEG (z))
err ("wrong sign", i, j, rnd, z, inex);
}
test_others (val[i], val[j], (mpfr_rnd_t) rnd, x, y, z, inex, flags,
"tst");
}
mpfr_clears (x, y, z, tmp, (mpfr_ptr) 0);
}
static void
generic_tests (void)
{
mpfr_t exact_sum, sum1, sum2;
mpfr_t *t;
mpfr_ptr *p;
mpfr_prec_t precmax = 444;
int i, m, nmax = 500;
int rnd_mode;
t = (mpfr_t *) tests_allocate (nmax * sizeof(mpfr_t));
p = (mpfr_ptr *) tests_allocate (nmax * sizeof(mpfr_ptr));
for (i = 0; i < nmax; i++)
{
mpfr_init2 (t[i], precmax);
p[i] = t[i];
}
mpfr_inits2 (precmax, exact_sum, sum1, sum2, (mpfr_ptr) 0);
for (m = 0; m < 4000; m++)
{
int non_uniform, n;
mpfr_prec_t prec;
non_uniform = randlimb () % 10;
n = (randlimb () % nmax) + 1;
prec = MPFR_PREC_MIN + (randlimb () % (precmax - MPFR_PREC_MIN + 1));
mpfr_set_prec (sum1, prec);
mpfr_set_prec (sum2, prec);
for (i = 0; i < n; i++)
{
mpfr_set_prec (t[i], MPFR_PREC_MIN +
(randlimb () % (precmax - MPFR_PREC_MIN + 1)));
mpfr_urandomb (t[i], RANDS);
if (m % 8 != 0 && (m % 8 == 1 || (randlimb () & 1)))
mpfr_neg (t[i], t[i], MPFR_RNDN);
if (non_uniform && MPFR_NOTZERO (t[i]))
mpfr_set_exp (t[i], randlimb () % 1000);
/* putchar ("-0+"[SIGN (mpfr_sgn (t[i])) + 1]); */
}
/* putchar ('\n'); */
get_exact_sum (exact_sum, t, n);
RND_LOOP (rnd_mode)
{
int inex1, inex2;
inex1 = mpfr_set (sum1, exact_sum, (mpfr_rnd_t) rnd_mode);
inex2 = mpfr_sum (sum2, p, n, (mpfr_rnd_t) rnd_mode);
if (!(mpfr_equal_p (sum1, sum2) && SAME_SIGN (inex1, inex2)))
{
printf ("generic_tests failed on m = %d, %s\n", m,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd_mode));
printf ("Expected ");
mpfr_dump (sum1);
printf ("with inex = %d\n", inex1);
printf ("Got ");
mpfr_dump (sum2);
printf ("with inex = %d\n", inex2);
exit (1);
}
}
}
for (i = 0; i < nmax; i++)
mpfr_clear (t[i]);
mpfr_clears (exact_sum, sum1, sum2, (mpfr_ptr) 0);
tests_free (t, nmax * sizeof(mpfr_t));
tests_free (p, nmax * sizeof(mpfr_ptr));
}
/* generic code */
__float128
mpfr_get_float128 (mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return (__float128) mpfr_get_d (x, rnd_mode);
else /* now x is a normal non-zero number */
{
__float128 r; /* result */
__float128 m;
double s; /* part of result */
mpfr_exp_t sh; /* exponent shift, so that x/2^sh is in the double range */
mpfr_t y, z;
int sign;
/* first round x to the target __float128 precision, so that
all subsequent operations are exact (this avoids double rounding
problems) */
mpfr_init2 (y, IEEE_FLOAT128_MANT_DIG);
mpfr_init2 (z, IEEE_FLOAT128_MANT_DIG);
mpfr_set (y, x, rnd_mode);
sh = MPFR_GET_EXP (y);
sign = MPFR_SIGN (y);
MPFR_SET_EXP (y, 0);
MPFR_SET_POS (y);
r = 0.0;
do
{
s = mpfr_get_d (y, MPFR_RNDN); /* high part of y */
r += (__float128) s;
mpfr_set_d (z, s, MPFR_RNDN); /* exact */
mpfr_sub (y, y, z, MPFR_RNDN); /* exact */
}
while (MPFR_NOTZERO (y));
mpfr_clear (z);
mpfr_clear (y);
/* we now have to multiply r by 2^sh */
MPFR_ASSERTD (r > 0);
if (sh != 0)
{
/* An overflow may occur (example: 0.5*2^1024) */
while (r < 1.0)
{
r += r;
sh--;
}
if (sh > 0)
m = 2.0;
else
{
m = 0.5;
sh = -sh;
}
for (;;)
{
if (sh % 2)
r = r * m;
sh >>= 1;
if (sh == 0)
break;
m = m * m;
}
}
if (sign < 0)
r = -r;
return r;
}
}
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
test_urandomb (long nbtests, mpfr_prec_t prec, int verbose)
{
mpfr_t x;
int *tab, size_tab, k, sh, xn;
double d, av = 0, var = 0, chi2 = 0, th;
mpfr_exp_t emin;
size_tab = (nbtests >= 1000 ? nbtests / 50 : 20);
tab = (int *) calloc (size_tab, sizeof(int));
if (tab == NULL)
{
fprintf (stderr, "trandom: can't allocate memory in test_urandomb\n");
exit (1);
}
mpfr_init2 (x, prec);
xn = 1 + (prec - 1) / mp_bits_per_limb;
sh = xn * mp_bits_per_limb - prec;
for (k = 0; k < nbtests; k++)
{
mpfr_urandomb (x, RANDS);
MPFR_ASSERTN (MPFR_IS_FP (x));
/* check that lower bits are zero */
if (MPFR_NOTZERO(x) && (MPFR_MANT(x)[0] & MPFR_LIMB_MASK(sh)))
{
printf ("Error: mpfr_urandomb() returns invalid numbers:\n");
mpfr_dump (x);
exit (1);
}
d = mpfr_get_d1 (x);
av += d;
var += d*d;
tab[(int)(size_tab * d)]++;
}
/* coverage test */
emin = mpfr_get_emin ();
set_emin (1); /* the generated number in [0,1[ is not in the exponent
range, except if it is zero */
k = mpfr_urandomb (x, RANDS);
if (MPFR_IS_ZERO(x) == 0 && (k == 0 || mpfr_nan_p (x) == 0))
{
printf ("Error in mpfr_urandomb, expected NaN, got ");
mpfr_dump (x);
exit (1);
}
set_emin (emin);
mpfr_clear (x);
if (!verbose)
{
free(tab);
return;
}
av /= nbtests;
var = (var / nbtests) - av * av;
th = (double)nbtests / size_tab;
printf("Average = %.5f\nVariance = %.5f\n", av, var);
printf("Repartition for urandomb. Each integer should be close to %d.\n",
(int)th);
for (k = 0; k < size_tab; k++)
{
chi2 += (tab[k] - th) * (tab[k] - th) / th;
printf("%d ", tab[k]);
if (((k+1) & 7) == 0)
printf("\n");
}
printf("\nChi2 statistics value (with %d degrees of freedom) : %.5f\n\n",
size_tab - 1, chi2);
free(tab);
return;
}
