int
mpfi_is_inside_si (const long a, mpfi_srcptr b)
{
/* Returns 0 if one of the operands is a NaN */
if (MPFI_NAN_P (b))
return 0;
return mpfr_cmp_si (&(b->left), a) <= 0
&& mpfr_cmp_si (&(b->right), a) >= 0;
}
int mp_isZeroContained (mp_interval_t op2) {
/* CHECKS WHETHER ZERO IS CONTAINED IN INTERVAL op2*/
// CHECKS IF ZERO IS LOWER THAN LEFT BOUND
if (mpfr_cmp_si (op2.a, 0L) > 0) return 0;
// CHECKS IF ZERO IS GREATER THAN RIGHT BOUND
if (mpfr_cmp_si (op2.b, 0L) < 0) return 0;
// OTHERWISE IS INSIDE
return 1;
}
int
restrict_domain (mpfi_ptr a)
{
/* speedup some tests restricting the possible random values */
if (mpfr_cmp_si (&(a->left), -7) < 0 || mpfr_cmp_si (&(a->left), +7) > 0) {
mpfr_set_si (&(a->left), -7, MPFI_RNDD);
}
if (mpfr_cmp_si (&(a->right), -7) < 0
|| mpfr_cmp_si (&(a->right), +7) > 0) {
mpfr_set_si (&(a->right), 7, MPFI_RNDU);
}
return 0;
}
/* try asymptotic expansion when x is large and negative:
Li2(x) = -log(-x)^2/2 - Pi^2/6 - 1/x + O(1/x^2).
More precisely for x <= -2 we have for g(x) = -log(-x)^2/2 - Pi^2/6:
|Li2(x) - g(x)| <= 1/|x|.
Assumes x <= -7, which ensures |log(-x)^2/2| >= Pi^2/6, and g(x) <= -3.5.
Return 0 if asymptotic expansion failed (unable to round), otherwise
returns correct ternary value.
*/
static int
mpfr_li2_asympt_neg (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t g, h;
mp_prec_t w = MPFR_PREC (y) + 20;
int inex = 0;
MPFR_ASSERTN (mpfr_cmp_si (x, -7) <= 0);
mpfr_init2 (g, w);
mpfr_init2 (h, w);
mpfr_neg (g, x, GMP_RNDN);
mpfr_log (g, g, GMP_RNDN); /* rel. error <= |(1 + theta) - 1| */
mpfr_sqr (g, g, GMP_RNDN); /* rel. error <= |(1 + theta)^3 - 1| <= 2^(2-w) */
mpfr_div_2ui (g, g, 1, GMP_RNDN); /* rel. error <= 2^(2-w) */
mpfr_const_pi (h, GMP_RNDN); /* error <= 2^(1-w) */
mpfr_sqr (h, h, GMP_RNDN); /* rel. error <= 2^(2-w) */
mpfr_div_ui (h, h, 6, GMP_RNDN); /* rel. error <= |(1 + theta)^4 - 1|
<= 5 * 2^(-w) */
MPFR_ASSERTN (MPFR_EXP (g) >= MPFR_EXP (h));
mpfr_add (g, g, h, GMP_RNDN); /* err <= ulp(g)/2 + g*2^(2-w) + g*5*2^(-w)
<= ulp(g) * (1/2 + 4 + 5) < 10 ulp(g).
If in addition |1/x| <= 4 ulp(g), then the
total error is bounded by 16 ulp(g). */
if ((MPFR_EXP (x) >= (mp_exp_t) (w - 2) - MPFR_EXP (g)) &&
MPFR_CAN_ROUND (g, w - 4, MPFR_PREC (y), rnd_mode))
inex = mpfr_neg (y, g, rnd_mode);
mpfr_clear (g);
mpfr_clear (h);
return inex;
}
void abs(ElementType& result, const ElementType& a) const
{
if (mpfr_cmp_si(&a, 0) < 0)
negate(result, a);
else
set(result, a);
}
static void
special (void)
{
mpfr_t x;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_tanh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_tanh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_inf (x, -1);
mpfr_tanh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_si (x, -1) == 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "-0.1001011001");
mpfr_tanh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_si_2exp (x, -135, -8) == 0);
mpfr_clear (x);
}
static void
check_special (void)
{
mpc_t z[3], res;
mpc_ptr t[3];
int i, inex;
/* z[0] = (1,2), z[1] = (2,3), z[2] = (3,4) */
for (i = 0; i < 3; i++)
{
mpc_init2 (z[i], 17);
mpc_set_ui_ui (z[i], i+1, i+2, MPC_RNDNN);
t[i] = z[i];
}
mpc_init2 (res, 17);
/* dot product of empty vectors is 0 */
inex = mpc_dot (res, t, t, 0, MPC_RNDNN);
MPC_ASSERT (inex == 0);
MPC_ASSERT (mpfr_zero_p (mpc_realref (res)));
MPC_ASSERT (mpfr_zero_p (mpc_imagref (res)));
MPC_ASSERT (mpfr_signbit (mpc_realref (res)) == 0);
MPC_ASSERT (mpfr_signbit (mpc_imagref (res)) == 0);
/* (1,2)*(1,2) = (-3,4) */
inex = mpc_dot (res, t, t, 1, MPC_RNDNN);
MPC_ASSERT (inex == 0);
MPC_ASSERT (mpfr_regular_p (mpc_realref (res)));
MPC_ASSERT (mpfr_regular_p (mpc_imagref (res)));
MPC_ASSERT (mpfr_cmp_si (mpc_realref (res), -3) == 0);
MPC_ASSERT (mpfr_cmp_ui (mpc_imagref (res), 4) == 0);
/* (1,2)*(1,2) + (2,3)*(2,3) = (-8,16) */
inex = mpc_dot (res, t, t, 2, MPC_RNDNN);
MPC_ASSERT (inex == 0);
MPC_ASSERT (mpfr_regular_p (mpc_realref (res)));
MPC_ASSERT (mpfr_regular_p (mpc_imagref (res)));
MPC_ASSERT (mpfr_cmp_si (mpc_realref (res), -8) == 0);
MPC_ASSERT (mpfr_cmp_ui (mpc_imagref (res), 16) == 0);
/* (1,2)*(1,2) + (2,3)*(2,3) + (3,4)*(3,4) = (-15,40) */
inex = mpc_dot (res, t, t, 3, MPC_RNDNN);
MPC_ASSERT (inex == 0);
MPC_ASSERT (mpfr_regular_p (mpc_realref (res)));
MPC_ASSERT (mpfr_regular_p (mpc_imagref (res)));
MPC_ASSERT (mpfr_cmp_si (mpc_realref (res), -15) == 0);
MPC_ASSERT (mpfr_cmp_ui (mpc_imagref (res), 40) == 0);
for (i = 0; i < 3; i++)
mpc_clear (z[i]);
mpc_clear (res);
}
static void
check (long int n, long int d, mpfr_rnd_t rnd, const char *ys)
{
mpq_t q;
mpfr_t x, t;
int inexact, compare;
unsigned int flags, ex_flags;
mpfr_init2 (x, 53);
mpfr_init2 (t, mpfr_get_prec (x) + mp_bits_per_limb);
mpq_init (q);
mpq_set_si (q, n, d);
mpfr_clear_flags ();
inexact = mpfr_set_q (x, q, rnd);
flags = __gmpfr_flags;
/* check values */
if (mpfr_cmp_str1 (x, ys))
{
printf ("Error for q = %ld/%ld and rnd = %s\n", n, d,
mpfr_print_rnd_mode (rnd));
printf ("correct result is %s, mpfr_set_q gives ", ys);
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
putchar ('\n');
exit (1);
}
/* check inexact flag */
if (mpfr_mul_ui (t, x, (d < 0) ? (-d) : d, rnd))
{
printf ("t <- x * d should be exact\n");
exit (1);
}
compare = mpfr_cmp_si (t, n);
if (! SAME_SIGN (inexact, compare))
{
printf ("Wrong ternary value for q = %ld/%ld and rnd = %s:\n"
"expected %d or equivalent, got %d\n",
n, d, mpfr_print_rnd_mode (rnd), compare, inexact);
exit (1);
}
ex_flags = compare == 0 ? 0 : MPFR_FLAGS_INEXACT;
if (flags != ex_flags)
{
printf ("Wrong flags for q = %ld/%ld and rnd = %s:\n",
n, d, mpfr_print_rnd_mode (rnd));
printf ("Expected flags:");
flags_out (ex_flags);
printf ("Got flags: ");
flags_out (flags);
exit (1);
}
mpfr_clear (x);
mpfr_clear (t);
mpq_clear (q);
}
void mp_IinvC (mp_interval_t *rop, mpfr_t op) {
// CHECKS WHETHER op is 0
if (mpfr_cmp_si (op, 0) == 0) {
mpfr_set_str (rop->a, "nan", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "nan", 10, MPFR_RNDU);
return;
}
// UP TO HERE, op is NOT ZERO
mpfr_si_div (rop->a, 1, op, MPFR_RNDD);
mpfr_si_div (rop->b, 1, op, MPFR_RNDU);
}
static void
check_invert (void)
{
mpfr_t x;
mpfr_init2 (x, MPFR_PREC_MIN);
mpfr_set_ui (x, 0xC, MPFR_RNDN);
mpfr_si_sub (x, -1, x, MPFR_RNDD); /* -0001 - 1100 = - 1101 --> -1 0000 */
/* If MPFR_PREC_MIN = 2, then x is first set to 12 exactly, then we get
-13 which is rounded down to -16.
If MPFR_PREC_MIN = 1, then x is first set to 16 exactly, then we get
-17 which is rounded down to -32. */
if ((MPFR_PREC_MIN == 2 && mpfr_cmp_si (x, -0x10)) ||
(MPFR_PREC_MIN == 1 && mpfr_cmp_si (x, -0x20)))
{
printf ("Special rounding error\n");
exit (1);
}
mpfr_clear (x);
}
static PyObject *
_GMPy_MPFR_Acos(PyObject *x, CTXT_Object *context)
{
MPFR_Object *result;
if (!mpfr_nan_p(MPFR(x)) &&
(mpfr_cmp_si(MPFR(x), 1) > 0 || mpfr_cmp_si(MPFR(x), -1) < 0) &&
context->ctx.allow_complex
) {
return GMPy_Complex_Acos(x, context);
}
if (!(result = GMPy_MPFR_New(0, context))) {
return NULL;
}
mpfr_clear_flags();
result->rc = mpfr_acos(result->f, MPFR(x), GET_MPFR_ROUND(context));
_GMPy_MPFR_Cleanup(&result, context);
return (PyObject*)result;
}
static void
check_specials (void)
{
mpfr_t x, y;
mpfr_init2 (x, 123L);
mpfr_init2 (y, 123L);
mpfr_set_nan (x);
mpfr_coth (y, x, MPFR_RNDN);
if (! mpfr_nan_p (y))
{
printf ("Error: coth(NaN) != NaN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_coth (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 1))
{
printf ("Error: coth(Inf) != 1\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_coth (y, x, MPFR_RNDN);
if (mpfr_cmp_si (y, -1))
{
printf ("Error: coth(-Inf) != -1\n");
exit (1);
}
/* coth(+/-0) = +/-Inf */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_coth (y, x, MPFR_RNDN);
if (! (mpfr_inf_p (y) && MPFR_SIGN (y) > 0))
{
printf ("Error: coth(+0) != +Inf\n");
exit (1);
}
mpfr_neg (x, x, MPFR_RNDN);
mpfr_coth (y, x, MPFR_RNDN);
if (! (mpfr_inf_p (y) && MPFR_SIGN (y) < 0))
{
printf ("Error: coth(-0) != -Inf\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
void mp_Iinv (mp_interval_t *rop, mp_interval_t op) {
// CHECK IF OP = [0,0]
if (mpfr_cmp_si (op.a, 0) == 0 && mpfr_cmp_si (op.b, 0) == 0) {
mpfr_set_str (rop->a, "nan", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "nan", 10, MPFR_RNDU);
return;
}
// CHECKS WHETHER ZERO IS CONTAINED IN OP
if (mp_isZeroContained (op)) {
// IF ZERO IS LEFT BOUNDARY
if (mpfr_cmp_si (op.a, 0) == 0) {
mpfr_si_div (rop->a, 1, op.b, MPFR_RNDD);
mpfr_set_str (rop->b, "+inf", 10, MPFR_RNDU);
return;
}
// IF ZERO IS RIGHT BOUNDARY
if (mpfr_cmp_si (op.b, 0) == 0) {
mpfr_si_div (rop->b, 1, op.a, MPFR_RNDU);
mpfr_set_str (rop->a, "-inf", 10, MPFR_RNDD);
return;
}
// ZERO IS EXTRICTLY CONTAINED IN op
mpfr_set_str (rop->a, "-inf", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "+inf", 10, MPFR_RNDU);
return;
}
// ZERO IS NOT IN op
mpfr_t ropA; mpfr_init (ropA);
mpfr_si_div (ropA, 1, op.b, MPFR_RNDD);
mpfr_si_div (rop->b, 1, op.a, MPFR_RNDU);
mpfr_set (rop->a, ropA, MPFR_RNDD);
mpfr_clear (ropA);
}
static void
check_invert (void)
{
mpfr_t x;
mpfr_init2 (x, MPFR_PREC_MIN);
mpfr_set_ui (x, 0xC, MPFR_RNDN);
mpfr_si_sub (x, -1, x, MPFR_RNDD); /* -0001 - 1100 = - 1101 --> -1 0000 */
if (mpfr_cmp_si (x, -0x10) )
{
printf ("Special rounding error\n");
exit (1);
}
mpfr_clear (x);
}
double
virtual_timing_ai2 (struct speed_params *s)
{
double t;
unsigned i;
mpfr_t w, x;
mp_size_t size;
mpfr_t temp1, temp2;
SPEED_RESTRICT_COND (s->size >= MPFR_PREC_MIN);
SPEED_RESTRICT_COND (s->size <= MPFR_PREC_MAX);
size = (s->size-1)/GMP_NUMB_BITS+1;
s->xp[size-1] |= MPFR_LIMB_HIGHBIT;
MPFR_TMP_INIT1 (s->xp, x, s->size);
MPFR_SET_EXP (x, (mpfr_exp_t) s->r);
if (s->align_xp == 2) MPFR_SET_NEG (x);
mpfr_init2 (w, s->size);
speed_starttime ();
i = s->reps;
mpfr_init2 (temp1, MPFR_SMALL_PRECISION);
mpfr_init2 (temp2, MPFR_SMALL_PRECISION);
mpfr_set (temp1, x, MPFR_SMALL_PRECISION);
mpfr_set_si (temp2, MPFR_AI_THRESHOLD2, MPFR_RNDN);
mpfr_mul_ui (temp2, temp2, (unsigned int)MPFR_PREC (w), MPFR_RNDN);
if (MPFR_IS_NEG (x))
mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD1, MPFR_RNDN);
else
mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD3, MPFR_RNDN);
mpfr_add (temp1, temp1, temp2, MPFR_RNDN);
if (mpfr_cmp_si (temp1, MPFR_AI_SCALE) > 0)
t = 1.;
else
t = 1000.;
mpfr_clear (temp1);
mpfr_clear (temp2);
return t;
}
int
main (void)
{
mpfr_t x, y, z;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
/* case y=NaN */
mpfr_set_nan (y);
mpfr_set_ui (x, 1250, GMP_RNDN);
mpfr_copysign (z, x, y, GMP_RNDN);
if (!mpfr_nan_p (z))
{
printf ("Error in mpfr_copysign (NaN)\n");
exit (1);
}
/* case y!=NaN */
mpfr_set_ui (y, 123, GMP_RNDN);
mpfr_set_ui (x, 1250, GMP_RNDN);
mpfr_copysign (z, x, y, GMP_RNDN);
if (mpfr_cmp_ui (z, 1250))
{
printf ("Error in mpfr_copysign (1250)\n");
exit (1);
}
mpfr_set_si (y, -17, GMP_RNDN);
mpfr_set_ui (x, 42, GMP_RNDN);
mpfr_copysign (z, x, y, GMP_RNDN);
if (mpfr_cmp_si (z, -42))
{
printf ("Error in mpfr_copysign (-42)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
tests_end_mpfr ();
return 0;
}
static void
check (long int n, long int d, mpfr_rnd_t rnd, const char *ys)
{
mpq_t q;
mpfr_t x, t;
int inexact, compare;
mpfr_init2 (x, 53);
mpfr_init2 (t, mpfr_get_prec (x) + mp_bits_per_limb);
mpq_init (q);
mpq_set_si (q, n, d);
inexact = mpfr_set_q (x, q, rnd);
/* check values */
if (mpfr_cmp_str1(x, ys))
{
printf ("Error for q=%ld/%ld and rnd=%s\n", n, d,
mpfr_print_rnd_mode (rnd));
printf ("correct result is %s, mpfr_set_q gives ", ys);
mpfr_out_str(stdout, 10, 0, x, MPFR_RNDN);
putchar('\n');
exit (1);
}
/* check inexact flag */
if (mpfr_mul_ui (t, x, (d < 0) ? (-d) : d, rnd))
{
printf ("t <- x * d should be exact\n");
exit (1);
}
compare = mpfr_cmp_si (t, n);
if (((inexact == 0) && (compare != 0)) ||
((inexact < 0) && (compare >= 0)) ||
((inexact > 0) && (compare <= 0)))
{
printf ("wrong inexact flag: expected %d, got %d\n", compare,
inexact);
exit (1);
}
mpfr_clear (x);
mpfr_clear (t);
mpq_clear (q);
}
int
num_is_zero(num_t a)
{
int nz = 0;
switch (a->num_type) {
case NUM_INT:
nz = mpz_cmp_si(Z(a), 0);
break;
case NUM_FP:
nz = mpfr_cmp_si(F(a), 0);
break;
default:
yyxerror("invalid number at num_is_zero!");
exit(1);
}
return !nz;
}
/* check that -1 <= x/sqrt(x^2+s*y^2) <= 1 for rounding to nearest or up
with s = 0 and s = 1 */
static void
test_property1 (mpfr_prec_t p, mpfr_rnd_t r, int s)
{
mpfr_t x, y, z, t;
mpfr_init2 (x, p);
mpfr_init2 (y, p);
mpfr_init2 (z, p);
mpfr_init2 (t, p);
mpfr_urandomb (x, RANDS);
mpfr_mul (z, x, x, r);
if (s)
{
mpfr_urandomb (y, RANDS);
mpfr_mul (t, y, y, r);
mpfr_add (z, z, t, r);
}
mpfr_sqrt (z, z, r);
mpfr_div (z, x, z, r);
/* Note: if both x and y are 0, z is NAN, but the test below will
be false. So, everything is fine. */
if (mpfr_cmp_si (z, -1) < 0 || mpfr_cmp_ui (z, 1) > 0)
{
printf ("Error, -1 <= x/sqrt(x^2+y^2) <= 1 does not hold for r=%s\n",
mpfr_print_rnd_mode (r));
printf ("x="); mpfr_dump (x);
printf ("y="); mpfr_dump (y);
printf ("got "); mpfr_dump (z);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
}
static void
test_2exp (void)
{
mpfr_t x;
int res;
mpfr_init2 (x, 32);
mpfr_set_ui_2exp (x, 1, 0, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1U,0)");
mpfr_set_ui_2exp (x, 1024, -10, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1024U,-10)");
mpfr_set_ui_2exp (x, 1024, 10, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1024*1024))
ERROR("(1024U,+10)");
mpfr_set_si_2exp (x, -1024L * 1024L, -10, MPFR_RNDN);
if (mpfr_cmp_si(x, -1024))
ERROR("(1M,-10)");
mpfr_set_ui_2exp (x, 0x92345678, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "92345678@4", 16, MPFR_RNDN))
ERROR("(x92345678U,+16)");
mpfr_set_si_2exp (x, -0x1ABCDEF0, -256, MPFR_RNDN);
if (mpfr_cmp_str (x, "-1ABCDEF0@-64", 16, MPFR_RNDN))
ERROR("(-x1ABCDEF0,-256)");
mpfr_set_prec (x, 2);
res = mpfr_set_si_2exp (x, 7, 10, MPFR_RNDU);
if (mpfr_cmp_ui (x, 1<<13) || res <= 0)
ERROR ("Prec 2 + si_2exp");
res = mpfr_set_ui_2exp (x, 7, 10, MPFR_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, MPFR_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, MPFR_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, MPFR_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);
}
/* We use the reflection formula
Gamma(1+t) Gamma(1-t) = - Pi t / sin(Pi (1 + t))
in order to treat the case x <= 1,
i.e. with x = 1-t, then Gamma(x) = -Pi*(1-x)/sin(Pi*(2-x))/GAMMA(2-x)
*/
int
mpfr_gamma (mpfr_ptr gamma, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t xp, GammaTrial, tmp, tmp2;
mpz_t fact;
mpfr_prec_t realprec;
int compared, is_integer;
int inex = 0; /* 0 means: result gamma not set yet */
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("gamma[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (gamma), mpfr_log_prec, gamma, inex));
/* Trivial cases */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (MPFR_IS_NEG (x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
else
{
MPFR_SET_INF (gamma);
MPFR_SET_POS (gamma);
MPFR_RET (0); /* exact */
}
}
else /* x is zero */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
MPFR_SET_INF(gamma);
MPFR_SET_SAME_SIGN(gamma, x);
MPFR_SET_DIVBY0 ();
MPFR_RET (0); /* exact */
}
}
/* Check for tiny arguments, where gamma(x) ~ 1/x - euler + ....
We know from "Bound on Runs of Zeros and Ones for Algebraic Functions",
Proceedings of Arith15, T. Lang and J.-M. Muller, 2001, that the maximal
number of consecutive zeroes or ones after the round bit is n-1 for an
input of n bits. But we need a more precise lower bound. Assume x has
n bits, and 1/x is near a floating-point number y of n+1 bits. We can
write x = X*2^e, y = Y/2^f with X, Y integers of n and n+1 bits.
Thus X*Y^2^(e-f) is near from 1, i.e., X*Y is near from 2^(f-e).
Two cases can happen:
(i) either X*Y is exactly 2^(f-e), but this can happen only if X and Y
are themselves powers of two, i.e., x is a power of two;
(ii) or X*Y is at distance at least one from 2^(f-e), thus
|xy-1| >= 2^(e-f), or |y-1/x| >= 2^(e-f)/x = 2^(-f)/X >= 2^(-f-n).
Since ufp(y) = 2^(n-f) [ufp = unit in first place], this means
that the distance |y-1/x| >= 2^(-2n) ufp(y).
Now assuming |gamma(x)-1/x| <= 1, which is true for x <= 1,
if 2^(-2n) ufp(y) >= 2, the error is at most 2^(-2n-1) ufp(y),
and round(1/x) with precision >= 2n+2 gives the correct result.
If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
A sufficient condition is thus EXP(x) + 2 <= -2 MAX(PREC(x),PREC(Y)).
*/
if (MPFR_GET_EXP (x) + 2
<= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(gamma)))
{
int sign = MPFR_SIGN (x); /* retrieve sign before possible override */
int special;
MPFR_BLOCK_DECL (flags);
MPFR_SAVE_EXPO_MARK (expo);
/* for overflow cases, see below; this needs to be done
before x possibly gets overridden. */
special =
MPFR_GET_EXP (x) == 1 - MPFR_EMAX_MAX &&
MPFR_IS_POS_SIGN (sign) &&
MPFR_IS_LIKE_RNDD (rnd_mode, sign) &&
mpfr_powerof2_raw (x);
MPFR_BLOCK (flags, inex = mpfr_ui_div (gamma, 1, x, rnd_mode));
if (inex == 0) /* x is a power of two */
{
/* return RND(1/x - euler) = RND(+/- 2^k - eps) with eps > 0 */
if (rnd_mode == MPFR_RNDN || MPFR_IS_LIKE_RNDU (rnd_mode, sign))
inex = 1;
else
{
mpfr_nextbelow (gamma);
inex = -1;
}
}
else if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
{
/* Overflow in the division 1/x. This is a real overflow, except
in RNDZ or RNDD when 1/x = 2^emax, i.e. x = 2^(-emax): due to
the "- euler", the rounded value in unbounded exponent range
is 0.111...11 * 2^emax (not an overflow). */
if (!special)
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, flags);
}
MPFR_SAVE_EXPO_FREE (expo);
/* Note: an overflow is possible with an infinite result;
in this case, the overflow flag will automatically be
restored by mpfr_check_range. */
return mpfr_check_range (gamma, inex, rnd_mode);
}
is_integer = mpfr_integer_p (x);
/* gamma(x) for x a negative integer gives NaN */
if (is_integer && MPFR_IS_NEG(x))
{
MPFR_SET_NAN (gamma);
MPFR_RET_NAN;
}
compared = mpfr_cmp_ui (x, 1);
if (compared == 0)
return mpfr_set_ui (gamma, 1, rnd_mode);
/* if x is an integer that fits into an unsigned long, use mpfr_fac_ui
if argument is not too large.
If precision is p, fac_ui costs O(u*p), whereas gamma costs O(p*M(p)),
so for u <= M(p), fac_ui should be faster.
We approximate here M(p) by p*log(p)^2, which is not a bad guess.
Warning: since the generic code does not handle exact cases,
we want all cases where gamma(x) is exact to be treated here.
*/
if (is_integer && mpfr_fits_ulong_p (x, MPFR_RNDN))
{
unsigned long int u;
mpfr_prec_t p = MPFR_PREC(gamma);
u = mpfr_get_ui (x, MPFR_RNDN);
if (u < 44787929UL && bits_fac (u - 1) <= p + (rnd_mode == MPFR_RNDN))
/* bits_fac: lower bound on the number of bits of m,
where gamma(x) = (u-1)! = m*2^e with m odd. */
return mpfr_fac_ui (gamma, u - 1, rnd_mode);
/* if bits_fac(...) > p (resp. p+1 for rounding to nearest),
then gamma(x) cannot be exact in precision p (resp. p+1).
FIXME: remove the test u < 44787929UL after changing bits_fac
to return a mpz_t or mpfr_t. */
}
MPFR_SAVE_EXPO_MARK (expo);
/* check for overflow: according to (6.1.37) in Abramowitz & Stegun,
gamma(x) >= exp(-x) * x^(x-1/2) * sqrt(2*Pi)
>= 2 * (x/e)^x / x for x >= 1 */
if (compared > 0)
{
mpfr_t yp;
mpfr_exp_t expxp;
MPFR_BLOCK_DECL (flags);
/* quick test for the default exponent range */
if (mpfr_get_emax () >= 1073741823UL && MPFR_GET_EXP(x) <= 25)
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_gamma_aux (gamma, x, rnd_mode);
}
/* 1/e rounded down to 53 bits */
#define EXPM1_STR "0.010111100010110101011000110110001011001110111100111"
mpfr_init2 (xp, 53);
mpfr_init2 (yp, 53);
mpfr_set_str_binary (xp, EXPM1_STR);
mpfr_mul (xp, x, xp, MPFR_RNDZ);
mpfr_sub_ui (yp, x, 2, MPFR_RNDZ);
mpfr_pow (xp, xp, yp, MPFR_RNDZ); /* (x/e)^(x-2) */
mpfr_set_str_binary (yp, EXPM1_STR);
mpfr_mul (xp, xp, yp, MPFR_RNDZ); /* x^(x-2) / e^(x-1) */
mpfr_mul (xp, xp, yp, MPFR_RNDZ); /* x^(x-2) / e^x */
mpfr_mul (xp, xp, x, MPFR_RNDZ); /* lower bound on x^(x-1) / e^x */
MPFR_BLOCK (flags, mpfr_mul_2ui (xp, xp, 1, MPFR_RNDZ));
expxp = MPFR_GET_EXP (xp);
mpfr_clear (xp);
mpfr_clear (yp);
MPFR_SAVE_EXPO_FREE (expo);
return MPFR_OVERFLOW (flags) || expxp > __gmpfr_emax ?
mpfr_overflow (gamma, rnd_mode, 1) :
mpfr_gamma_aux (gamma, x, rnd_mode);
}
/* now compared < 0 */
/* check for underflow: for x < 1,
gamma(x) = Pi*(x-1)/sin(Pi*(2-x))/gamma(2-x).
Since gamma(2-x) >= 2 * ((2-x)/e)^(2-x) / (2-x), we have
|gamma(x)| <= Pi*(1-x)*(2-x)/2/((2-x)/e)^(2-x) / |sin(Pi*(2-x))|
<= 12 * ((2-x)/e)^x / |sin(Pi*(2-x))|.
To avoid an underflow in ((2-x)/e)^x, we compute the logarithm.
*/
if (MPFR_IS_NEG(x))
{
int underflow = 0, sgn, ck;
mpfr_prec_t w;
mpfr_init2 (xp, 53);
mpfr_init2 (tmp, 53);
mpfr_init2 (tmp2, 53);
/* we want an upper bound for x * [log(2-x)-1].
since x < 0, we need a lower bound on log(2-x) */
mpfr_ui_sub (xp, 2, x, MPFR_RNDD);
mpfr_log (xp, xp, MPFR_RNDD);
mpfr_sub_ui (xp, xp, 1, MPFR_RNDD);
mpfr_mul (xp, xp, x, MPFR_RNDU);
/* we need an upper bound on 1/|sin(Pi*(2-x))|,
thus a lower bound on |sin(Pi*(2-x))|.
If 2-x is exact, then the error of Pi*(2-x) is (1+u)^2 with u = 2^(-p)
thus the error on sin(Pi*(2-x)) is less than 1/2ulp + 3Pi(2-x)u,
assuming u <= 1, thus <= u + 3Pi(2-x)u */
w = mpfr_gamma_2_minus_x_exact (x); /* 2-x is exact for prec >= w */
w += 17; /* to get tmp2 small enough */
mpfr_set_prec (tmp, w);
mpfr_set_prec (tmp2, w);
MPFR_DBGRES (ck = mpfr_ui_sub (tmp, 2, x, MPFR_RNDN));
MPFR_ASSERTD (ck == 0); /* tmp = 2-x exactly */
mpfr_const_pi (tmp2, MPFR_RNDN);
mpfr_mul (tmp2, tmp2, tmp, MPFR_RNDN); /* Pi*(2-x) */
mpfr_sin (tmp, tmp2, MPFR_RNDN); /* sin(Pi*(2-x)) */
sgn = mpfr_sgn (tmp);
mpfr_abs (tmp, tmp, MPFR_RNDN);
mpfr_mul_ui (tmp2, tmp2, 3, MPFR_RNDU); /* 3Pi(2-x) */
mpfr_add_ui (tmp2, tmp2, 1, MPFR_RNDU); /* 3Pi(2-x)+1 */
mpfr_div_2ui (tmp2, tmp2, mpfr_get_prec (tmp), MPFR_RNDU);
/* if tmp2<|tmp|, we get a lower bound */
if (mpfr_cmp (tmp2, tmp) < 0)
{
mpfr_sub (tmp, tmp, tmp2, MPFR_RNDZ); /* low bnd on |sin(Pi*(2-x))| */
mpfr_ui_div (tmp, 12, tmp, MPFR_RNDU); /* upper bound */
mpfr_log2 (tmp, tmp, MPFR_RNDU);
mpfr_add (xp, tmp, xp, MPFR_RNDU);
/* The assert below checks that expo.saved_emin - 2 always
fits in a long. FIXME if we want to allow mpfr_exp_t to
be a long long, for instance. */
MPFR_ASSERTN (MPFR_EMIN_MIN - 2 >= LONG_MIN);
underflow = mpfr_cmp_si (xp, expo.saved_emin - 2) <= 0;
}
mpfr_clear (xp);
mpfr_clear (tmp);
mpfr_clear (tmp2);
if (underflow) /* the sign is the opposite of that of sin(Pi*(2-x)) */
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (gamma, (rnd_mode == MPFR_RNDN) ? MPFR_RNDZ : rnd_mode, -sgn);
}
}
realprec = MPFR_PREC (gamma);
/* we want both 1-x and 2-x to be exact */
{
mpfr_prec_t w;
w = mpfr_gamma_1_minus_x_exact (x);
if (realprec < w)
realprec = w;
w = mpfr_gamma_2_minus_x_exact (x);
if (realprec < w)
realprec = w;
}
realprec = realprec + MPFR_INT_CEIL_LOG2 (realprec) + 20;
MPFR_ASSERTD(realprec >= 5);
MPFR_GROUP_INIT_4 (group, realprec + MPFR_INT_CEIL_LOG2 (realprec) + 20,
xp, tmp, tmp2, GammaTrial);
mpz_init (fact);
MPFR_ZIV_INIT (loop, realprec);
for (;;)
{
mpfr_exp_t err_g;
int ck;
MPFR_GROUP_REPREC_4 (group, realprec, xp, tmp, tmp2, GammaTrial);
/* reflection formula: gamma(x) = Pi*(x-1)/sin(Pi*(2-x))/gamma(2-x) */
ck = mpfr_ui_sub (xp, 2, x, MPFR_RNDN); /* 2-x, exact */
MPFR_ASSERTD(ck == 0); (void) ck; /* use ck to avoid a warning */
mpfr_gamma (tmp, xp, MPFR_RNDN); /* gamma(2-x), error (1+u) */
mpfr_const_pi (tmp2, MPFR_RNDN); /* Pi, error (1+u) */
mpfr_mul (GammaTrial, tmp2, xp, MPFR_RNDN); /* Pi*(2-x), error (1+u)^2 */
err_g = MPFR_GET_EXP(GammaTrial);
mpfr_sin (GammaTrial, GammaTrial, MPFR_RNDN); /* sin(Pi*(2-x)) */
/* If tmp is +Inf, we compute exp(lngamma(x)). */
if (mpfr_inf_p (tmp))
{
inex = mpfr_explgamma (gamma, x, &expo, tmp, tmp2, rnd_mode);
if (inex)
goto end;
else
goto ziv_next;
}
err_g = err_g + 1 - MPFR_GET_EXP(GammaTrial);
/* let g0 the true value of Pi*(2-x), g the computed value.
We have g = g0 + h with |h| <= |(1+u^2)-1|*g.
Thus sin(g) = sin(g0) + h' with |h'| <= |(1+u^2)-1|*g.
The relative error is thus bounded by |(1+u^2)-1|*g/sin(g)
<= |(1+u^2)-1|*2^err_g. <= 2.25*u*2^err_g for |u|<=1/4.
With the rounding error, this gives (0.5 + 2.25*2^err_g)*u. */
ck = mpfr_sub_ui (xp, x, 1, MPFR_RNDN); /* x-1, exact */
MPFR_ASSERTD(ck == 0); (void) ck; /* use ck to avoid a warning */
mpfr_mul (xp, tmp2, xp, MPFR_RNDN); /* Pi*(x-1), error (1+u)^2 */
mpfr_mul (GammaTrial, GammaTrial, tmp, MPFR_RNDN);
/* [1 + (0.5 + 2.25*2^err_g)*u]*(1+u)^2 = 1 + (2.5 + 2.25*2^err_g)*u
+ (0.5 + 2.25*2^err_g)*u*(2u+u^2) + u^2.
For err_g <= realprec-2, we have (0.5 + 2.25*2^err_g)*u <=
0.5*u + 2.25/4 <= 0.6875 and u^2 <= u/4, thus
(0.5 + 2.25*2^err_g)*u*(2u+u^2) + u^2 <= 0.6875*(2u+u/4) + u/4
<= 1.8*u, thus the rel. error is bounded by (4.5 + 2.25*2^err_g)*u. */
mpfr_div (GammaTrial, xp, GammaTrial, MPFR_RNDN);
/* the error is of the form (1+u)^3/[1 + (4.5 + 2.25*2^err_g)*u].
For realprec >= 5 and err_g <= realprec-2, [(4.5 + 2.25*2^err_g)*u]^2
<= 0.71, and for |y|<=0.71, 1/(1-y) can be written 1+a*y with a<=4.
(1+u)^3 * (1+4*(4.5 + 2.25*2^err_g)*u)
= 1 + (21 + 9*2^err_g)*u + (57+27*2^err_g)*u^2 + (55+27*2^err_g)*u^3
+ (18+9*2^err_g)*u^4
<= 1 + (21 + 9*2^err_g)*u + (57+27*2^err_g)*u^2 + (56+28*2^err_g)*u^3
<= 1 + (21 + 9*2^err_g)*u + (59+28*2^err_g)*u^2
<= 1 + (23 + 10*2^err_g)*u.
The final error is thus bounded by (23 + 10*2^err_g) ulps,
which is <= 2^6 for err_g<=2, and <= 2^(err_g+4) for err_g >= 2. */
err_g = (err_g <= 2) ? 6 : err_g + 4;
if (MPFR_LIKELY (MPFR_CAN_ROUND (GammaTrial, realprec - err_g,
MPFR_PREC(gamma), rnd_mode)))
break;
ziv_next:
MPFR_ZIV_NEXT (loop, realprec);
}
end:
MPFR_ZIV_FREE (loop);
if (inex == 0)
inex = mpfr_set (gamma, GammaTrial, rnd_mode);
MPFR_GROUP_CLEAR (group);
mpz_clear (fact);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (gamma, inex, rnd_mode);
}
int
main (void)
{
mpfr_t x, y;
float f, g, infp;
int i;
infp = (float) DBL_POS_INF;
if (infp * 0.5 != infp)
{
fprintf (stderr, "Error, FLT_MAX + FLT_MAX does not yield INFP\n");
fprintf (stderr, "(this is probably a compiler bug, please report)\n");
exit (1);
}
tests_start_mpfr ();
mpfr_init2 (x, 24);
mpfr_init2 (y, 24);
#if !defined(MPFR_ERRDIVZERO)
mpfr_set_nan (x);
f = mpfr_get_flt (x, MPFR_RNDN);
if (f == f)
{
printf ("Error for mpfr_get_flt(NaN)\n");
exit (1);
}
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_nan_p (x) == 0)
{
printf ("Error for mpfr_set_flt(NaN)\n");
exit (1);
}
mpfr_set_inf (x, 1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
mpfr_set_inf (x, -1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
#endif
mpfr_set_ui (x, 0, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+0))\n");
exit (1);
}
#ifdef HAVE_SIGNEDZ
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-0))\n");
exit (1);
}
#endif /* HAVE_SIGNEDZ */
mpfr_set_ui (x, 17, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_ui (x, 17) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(17))\n");
printf ("expected 17\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si (x, -42, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_si (x, -42) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-42))\n");
printf ("expected -42\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextbelow (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextabove (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_si_2exp (x, 1, -150, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -151, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -149, MPFR_RNDN);
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#if !defined(MPFR_ERRDIVZERO)
f = mpfr_get_flt (x, MPFR_RNDN); /* 2^128 rounds to itself with extended
exponent range, we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#endif
/* corner case: take x with 25 bits just below 2^128 */
mpfr_set_prec (x, 25);
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
mpfr_nextbelow (x);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDN); /* first round to 2^128 (even rule),
thus we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
tests_end_mpfr ();
return 0;
}
int
mpc_asin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
mpfr_prec_t p, p_re, p_im, incr_p = 0;
mpfr_rnd_t rnd_re, rnd_im;
mpc_t z1;
int inex;
/* special values */
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
{
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? -1 : +1);
}
else if (mpfr_zero_p (mpc_realref (op)))
{
mpfr_set (mpc_realref (rop), mpc_realref (op), GMP_RNDN);
mpfr_set_nan (mpc_imagref (rop));
}
else
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
return 0;
}
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
int inex_re;
if (mpfr_inf_p (mpc_realref (op)))
{
int inf_im = mpfr_inf_p (mpc_imagref (op));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1));
if (inf_im)
mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
}
else
{
mpfr_set_zero (mpc_realref (rop), (mpfr_signbit (mpc_realref (op)) ? -1 : 1));
inex_re = 0;
mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1));
}
return MPC_INEX (inex_re, 0);
}
/* pure real argument */
if (mpfr_zero_p (mpc_imagref (op)))
{
int inex_re;
int inex_im;
int s_im;
s_im = mpfr_signbit (mpc_imagref (op));
if (mpfr_cmp_ui (mpc_realref (op), 1) > 0)
{
if (s_im)
inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
INV_RND (MPC_RND_IM (rnd)));
else
inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
MPC_RND_IM (rnd));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
if (s_im)
mpc_conj (rop, rop, MPC_RNDNN);
}
else if (mpfr_cmp_si (mpc_realref (op), -1) < 0)
{
mpfr_t minus_op_re;
minus_op_re[0] = mpc_realref (op)[0];
MPFR_CHANGE_SIGN (minus_op_re);
if (s_im)
inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re,
INV_RND (MPC_RND_IM (rnd)));
else
inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re,
MPC_RND_IM (rnd));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
if (s_im)
mpc_conj (rop, rop, MPC_RNDNN);
}
else
{
inex_im = mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
if (s_im)
mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), GMP_RNDN);
inex_re = mpfr_asin (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
}
return MPC_INEX (inex_re, inex_im);
}
/* pure imaginary argument */
if (mpfr_zero_p (mpc_realref (op)))
{
int inex_im;
int s;
s = mpfr_signbit (mpc_realref (op));
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
if (s)
mpfr_neg (mpc_realref (rop), mpc_realref (rop), GMP_RNDN);
inex_im = mpfr_asinh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
return MPC_INEX (0, inex_im);
}
/* regular complex: asin(z) = -i*log(i*z+sqrt(1-z^2)) */
p_re = mpfr_get_prec (mpc_realref(rop));
p_im = mpfr_get_prec (mpc_imagref(rop));
rnd_re = MPC_RND_RE(rnd);
rnd_im = MPC_RND_IM(rnd);
p = p_re >= p_im ? p_re : p_im;
mpc_init2 (z1, p);
while (1)
{
mpfr_exp_t ex, ey, err;
p += mpc_ceil_log2 (p) + 3 + incr_p; /* incr_p is zero initially */
incr_p = p / 2;
mpfr_set_prec (mpc_realref(z1), p);
mpfr_set_prec (mpc_imagref(z1), p);
/* z1 <- z^2 */
mpc_sqr (z1, op, MPC_RNDNN);
/* err(x) <= 1/2 ulp(x), err(y) <= 1/2 ulp(y) */
/* z1 <- 1-z1 */
ex = mpfr_get_exp (mpc_realref(z1));
mpfr_ui_sub (mpc_realref(z1), 1, mpc_realref(z1), GMP_RNDN);
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
ex = ex - mpfr_get_exp (mpc_realref(z1));
ex = (ex <= 0) ? 0 : ex;
/* err(x) <= 2^ex * ulp(x) */
ex = ex + mpfr_get_exp (mpc_realref(z1)) - p;
/* err(x) <= 2^ex */
ey = mpfr_get_exp (mpc_imagref(z1)) - p - 1;
/* err(y) <= 2^ey */
ex = (ex >= ey) ? ex : ey; /* err(x), err(y) <= 2^ex, i.e., the norm
of the error is bounded by |h|<=2^(ex+1/2) */
/* z1 <- sqrt(z1): if z1 = z + h, then sqrt(z1) = sqrt(z) + h/2/sqrt(t) */
ey = mpfr_get_exp (mpc_realref(z1)) >= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
/* we have |z1| >= 2^(ey-1) thus 1/|z1| <= 2^(1-ey) */
mpc_sqrt (z1, z1, MPC_RNDNN);
ex = (2 * ex + 1) - 2 - (ey - 1); /* |h^2/4/|t| <= 2^ex */
ex = (ex + 1) / 2; /* ceil(ex/2) */
/* express ex in terms of ulp(z1) */
ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
ex = ex - ey + p;
/* take into account the rounding error in the mpc_sqrt call */
err = (ex <= 0) ? 1 : ex + 1;
/* err(x) <= 2^err * ulp(x), err(y) <= 2^err * ulp(y) */
/* z1 <- i*z + z1 */
ex = mpfr_get_exp (mpc_realref(z1));
ey = mpfr_get_exp (mpc_imagref(z1));
mpfr_sub (mpc_realref(z1), mpc_realref(z1), mpc_imagref(op), GMP_RNDN);
mpfr_add (mpc_imagref(z1), mpc_imagref(z1), mpc_realref(op), GMP_RNDN);
if (mpfr_cmp_ui (mpc_realref(z1), 0) == 0 || mpfr_cmp_ui (mpc_imagref(z1), 0) == 0)
continue;
ex -= mpfr_get_exp (mpc_realref(z1)); /* cancellation in x */
ey -= mpfr_get_exp (mpc_imagref(z1)); /* cancellation in y */
ex = (ex >= ey) ? ex : ey; /* maximum cancellation */
err += ex;
err = (err <= 0) ? 1 : err + 1; /* rounding error in sub/add */
/* z1 <- log(z1): if z1 = z + h, then log(z1) = log(z) + h/t with
|t| >= min(|z1|,|z|) */
ex = mpfr_get_exp (mpc_realref(z1));
ey = mpfr_get_exp (mpc_imagref(z1));
ex = (ex >= ey) ? ex : ey;
err += ex - p; /* revert to absolute error <= 2^err */
mpc_log (z1, z1, GMP_RNDN);
err -= ex - 1; /* 1/|t| <= 1/|z| <= 2^(1-ex) */
/* express err in terms of ulp(z1) */
ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
err = err - ey + p;
/* take into account the rounding error in the mpc_log call */
err = (err <= 0) ? 1 : err + 1;
/* z1 <- -i*z1 */
mpfr_swap (mpc_realref(z1), mpc_imagref(z1));
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
if (mpfr_can_round (mpc_realref(z1), p - err, GMP_RNDN, GMP_RNDZ,
p_re + (rnd_re == GMP_RNDN)) &&
mpfr_can_round (mpc_imagref(z1), p - err, GMP_RNDN, GMP_RNDZ,
p_im + (rnd_im == GMP_RNDN)))
break;
}
inex = mpc_set (rop, z1, rnd);
mpc_clear (z1);
return inex;
}
int
main (int argc, char *argv[])
{
mpfr_t x, y, r;
long q[1];
if (argc == 3) /* usage: tremquo x y (rnd=MPFR_RNDN implicit) */
{
mpfr_init2 (x, GMP_NUMB_BITS);
mpfr_init2 (y, GMP_NUMB_BITS);
mpfr_init2 (r, GMP_NUMB_BITS);
mpfr_set_str (x, argv[1], 10, MPFR_RNDN);
mpfr_set_str (y, argv[2], 10, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
printf ("r=");
mpfr_out_str (stdout, 10, 0, r, MPFR_RNDN);
printf (" q=%ld\n", q[0]);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
return 0;
}
tests_start_mpfr ();
bug20090227 ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (r);
/* special values */
mpfr_set_nan (x);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_nan (y);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp (r, x) == 0);
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
/* check four possible sign combinations */
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-94) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-44) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-45) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-45)) = -2^(-44) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-95) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-95)) = -2^(-94) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
/* exercise large quotient */
mpfr_set_ui_2exp (x, 1, 65, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
/* quotient is 2^65 */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0);
MPFR_ASSERTN (q[0] % 1073741824L == 0L);
/* another large quotient */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_const_pi (x, MPFR_RNDN);
mpfr_mul_2exp (x, x, 63, MPFR_RNDN);
mpfr_const_log2 (y, MPFR_RNDN);
mpfr_set_prec (r, 10);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* q should be 41803643793084085130, r should be 605/2048 */
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 605, -11) == 0);
MPFR_ASSERTN ((q[0] > 0) && ((q[0] % 1073741824L) == 733836170L));
/* check cases where quotient is 1.5 +/- eps */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (r, 63);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5, quotient should be 2 (even rule), remainder should be -1 */
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_nextabove (x); /* 3 + 2^(-63) */
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 + 2^(-64), quo should be 2, r should be -1 + 2^(-63) */
MPFR_ASSERTN (mpfr_add_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -63) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_nextabove (y); /* 2 + 2^(-63) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 - eps, quo should be 1, r should be 1 - 2^(-63) */
MPFR_ASSERTN (mpfr_sub_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -63) == 0);
MPFR_ASSERTN (q[0] == 1L);
/* bug founds by Kaveh Ghazi, 3 May 2007 */
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_set_ui (y, 3, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0 && MPFR_SIGN (r) < 0);
/* check argument reuse */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (x, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (x, 0) == 0 && MPFR_SIGN (x) < 0);
mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, MPFR_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emin (), MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_zero_p (r) && MPFR_SIGN (r) > 0);
MPFR_ASSERTN (q[0] == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
tests_end_mpfr ();
return 0;
}
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);
}
int
mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inexact;
long xint;
mpfr_t xfrac;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(y), mpfr_log_prec, y,
inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (MPFR_IS_POS (x))
MPFR_SET_INF (y);
else
MPFR_SET_ZERO (y);
MPFR_SET_POS (y);
MPFR_RET (0);
}
else /* 2^0 = 1 */
{
MPFR_ASSERTD (MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
/* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
MPFR_ASSERTN (MPFR_EMIN_MIN >= LONG_MIN + 2);
if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emin - 1) < 0))
{
mpfr_rnd_t rnd2 = rnd_mode;
/* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
if (rnd_mode == MPFR_RNDN &&
mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
rnd2 = MPFR_RNDZ;
return mpfr_underflow (y, rnd2, 1);
}
MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax) >= 0))
return mpfr_overflow (y, rnd_mode, 1);
/* We now know that emin - 1 <= x < emax. */
MPFR_SAVE_EXPO_MARK (expo);
/* 2^x = 1 + x*log(2) + O(x^2) for x near zero, and for |x| <= 1 we have
|2^x - 1| <= x < 2^EXP(x). If x > 0 we must round away from 0 (dir=1);
if x < 0 we must round toward 0 (dir=0). */
MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, - MPFR_GET_EXP (x), 0,
MPFR_IS_POS (x), rnd_mode, expo, {});
xint = mpfr_get_si (x, MPFR_RNDZ);
mpfr_init2 (xfrac, MPFR_PREC (x));
mpfr_sub_si (xfrac, x, xint, MPFR_RNDN); /* exact */
if (MPFR_IS_ZERO (xfrac))
{
mpfr_set_ui (y, 1, MPFR_RNDN);
inexact = 0;
}
else
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
mpfr_prec_t Nt; /* working precision */
mpfr_exp_t err; /* error */
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialize of intermediary variable */
mpfr_init2 (t, Nt);
/* First computation */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute exp(x*ln(2))*/
mpfr_const_log2 (t, MPFR_RNDU); /* ln(2) */
mpfr_mul (t, xfrac, t, MPFR_RNDU); /* xfrac * ln(2) */
err = Nt - (MPFR_GET_EXP (t) + 2); /* Estimate of the error */
mpfr_exp (t, t, MPFR_RNDN); /* exp(xfrac * ln(2)) */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
}
mpfr_clear (xfrac);
MPFR_CLEAR_FLAGS ();
mpfr_mul_2si (y, y, xint, MPFR_RNDN); /* exact or overflow */
/* Note: We can have an overflow only when t was rounded up to 2. */
MPFR_ASSERTD (MPFR_IS_PURE_FP (y) || inexact > 0);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
static void
special (void)
{
mpfr_t x, y;
unsigned xprec, yprec;
mpfr_init (x);
mpfr_init (y);
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_div_ui (y, x, 3, MPFR_RNDN);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 100);
mpfr_urandomb (x, RANDS);
mpfr_div_ui (y, x, 123456, MPFR_RNDN);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_div_ui (y, x, 123456789, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0))
{
printf ("mpfr_div_ui gives non-zero for 0/ui\n");
exit (1);
}
/* bug found by Norbert Mueller, 21 Aug 2001 */
mpfr_set_prec (x, 110);
mpfr_set_prec (y, 60);
mpfr_set_str_binary (x, "0.110101110011111110011111001110011001110111000000111110001000111011000011E-44");
mpfr_div_ui (y, x, 17, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11001010100101100011101110000001100001010110101001010011011E-48");
if (mpfr_cmp (x, y))
{
printf ("Error in x/17 for x=1/16!\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
printf ("\n");
exit (1);
}
/* corner case */
mpfr_set_prec (x, 2 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_ui (x, 4, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_div_ui (y, x, 2, MPFR_RNDN); /* exactly in the middle */
MPFR_ASSERTN(mpfr_cmp_ui (y, 2) == 0);
mpfr_set_prec (x, 3 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_div_ui (y, x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);
mpfr_set_prec (x, 3 * mp_bits_per_limb);
mpfr_set_prec (y, 2);
mpfr_set_si (x, -4, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_div_ui (y, x, 2, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (y, -3) == 0);
for (xprec = 53; xprec <= 128; xprec++)
{
mpfr_set_prec (x, xprec);
mpfr_set_str_binary (x, "0.1100100100001111110011111000000011011100001100110111E2");
for (yprec = 53; yprec <= 128; yprec++)
{
mpfr_set_prec (y, yprec);
mpfr_div_ui (y, x, 1, MPFR_RNDN);
if (mpfr_cmp(x,y))
{
printf ("division by 1.0 fails for xprec=%u, yprec=%u\n", xprec, yprec);
printf ("expected "); mpfr_print_binary (x); puts ("");
printf ("got "); mpfr_print_binary (y); puts ("");
exit (1);
}
}
}
/* Bug reported by Mark Dickinson, 6 Nov 2007 */
mpfr_set_si (x, 0, MPFR_RNDN);
mpfr_set_si (y, -1, MPFR_RNDN);
mpfr_div_ui (y, x, 4, MPFR_RNDN);
MPFR_ASSERTN(MPFR_IS_ZERO(y) && MPFR_IS_POS(y));
mpfr_clear (x);
mpfr_clear (y);
}
int
main (int argc, char *argv[])
{
mpfr_t x;
long k, z, d, N;
unsigned long zl, dl;
int inex;
int r;
mpfr_exp_t emin, emax;
int flag;
tests_start_mpfr ();
mpfr_init2 (x, 100);
N = (argc==1) ? 100000 : atol (argv[1]);
for (k = 1; k <= N; k++)
{
z = (long) (randlimb () & LONG_MAX) + LONG_MIN / 2;
inex = mpfr_set_si (x, z, MPFR_RNDZ);
d = mpfr_get_si (x, MPFR_RNDZ);
if (d != z)
{
printf ("Error in mpfr_set_si: expected %ld got %ld\n", z, d);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_si: inex value incorrect for %ld: %d\n",
z, inex);
exit (1);
}
}
for (k = 1; k <= N; k++)
{
zl = randlimb ();
inex = mpfr_set_ui (x, zl, MPFR_RNDZ);
dl = mpfr_get_ui (x, MPFR_RNDZ);
if (dl != zl)
{
printf ("Error in mpfr_set_ui: expected %lu got %lu\n", zl, dl);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_ui: inex value incorrect for %lu: %d\n",
zl, inex);
exit (1);
}
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, 5, MPFR_RNDZ) >= 0)
{
printf ("Wrong inexact flag for x=5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, -5, MPFR_RNDZ) <= 0)
{
printf ("Wrong inexact flag for x=-5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 3);
inex = mpfr_set_si (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_si(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
inex = mpfr_set_ui (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_ui(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
mpfr_set_prec (x, 2);
inex = mpfr_set_si (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152 || inex <= 0)
{
printf ("Error in mpfr_set_si, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
inex = mpfr_set_ui (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
/* Also test the mpfr_set_ui function (instead of macro). */
inex = (mpfr_set_ui) (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui function, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
for (r = 0 ; r < MPFR_RND_MAX ; r++)
{
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_ui (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_ui (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_ui (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_si (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_si (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_si (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
}
/* check potential bug in case mp_limb_t is unsigned */
emax = mpfr_get_emax ();
set_emax (0);
mpfr_set_si (x, -1, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -1) fails\n");
exit (1);
}
set_emax (emax);
emax = mpfr_get_emax ();
set_emax (5);
mpfr_set_prec (x, 2);
mpfr_set_si (x, -31, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -31) fails\n");
exit (1);
}
set_emax (emax);
/* test for get_ui */
mpfr_set_ui (x, 0, MPFR_RNDN);
MPFR_ASSERTN(mpfr_get_ui (x, MPFR_RNDN) == 0);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDU);
mpfr_nextabove (x);
mpfr_get_ui (x, MPFR_RNDU);
/* another test for get_ui */
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "10.101");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 3);
mpfr_set_str_binary (x, "-1.0");
mpfr_get_ui (x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDZ);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDD);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDU);
MPFR_ASSERTN (dl == 1);
/* coverage tests */
mpfr_set_prec (x, 2);
mpfr_set_si (x, -7, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (x, -8) == 0);
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui (x, 8) == 0);
emax = mpfr_get_emax ();
set_emax (3);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (1);
MPFR_ASSERTN( mpfr_set_ui (x, 7, MPFR_RNDU) );
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_ui_2exp (x, 17, -50, MPFR_RNDN);
MPFR_ASSERTN (mpfr_get_ui (x, MPFR_RNDD) == 0);
MPFR_ASSERTN (mpfr_get_si (x, MPFR_RNDD) == 0);
/* Test for ERANGE flag + correct behaviour if overflow */
mpfr_set_prec (x, 256);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (1)\n");
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + -1 \n");
exit (1);
}
mpfr_set_si (x, LONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (1): %ld\n", d);
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, LONG_MIN, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (1)\n");
exit (1);
}
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (2)\n");
exit (1);
}
mpfr_set_nan (x);
mpfr_clear_erangeflag ();
d = mpfr_get_ui (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + NaN\n");
exit (1);
}
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + NaN\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_prec (x, 2);
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_ui (x, 7, MPFR_RNDU);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_ui (x, 8) != 0)
{
printf ("Error for mpfr_set_ui (x, 7, MPFR_RNDU), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_ui (x, 7, MPFR_RNDU) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_si (x, -7, MPFR_RNDD);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_si (x, -8) != 0)
{
printf ("Error for mpfr_set_si (x, -7, MPFR_RNDD), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_si (x, -7, MPFR_RNDD) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_clear (x);
test_2exp ();
test_macros ();
test_macros_keyword ();
tests_end_mpfr ();
return 0;
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
unsigned long k, bd, nc, i;
char *str, *str2;
mp_exp_t e;
int base, logbase, prec, baseprec, ret;
tests_start_mpfr ();
if (argc >= 2) /* tset_str <string> [<prec>] [<base>] */
{
prec = (argc >= 3) ? atoi (argv[2]) : 53;
base = (argc >= 4) ? atoi (argv[3]) : 2;
mpfr_init2 (x, prec);
mpfr_set_str (x, argv[1], base, GMP_RNDN);
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
puts ("");
mpfr_clear (x);
return 0;
}
mpfr_init2 (x, 2);
nc = (argc > 1) ? atoi(argv[1]) : 53;
if (nc < 100)
nc = 100;
bd = randlimb () & 8;
str2 = str = (char*) (*__gmp_allocate_func) (nc * sizeof(char));
if (bd)
{
for(k = 1; k <= bd; k++)
*(str2++) = (randlimb () & 1) + '0';
}
else
*(str2++) = '0';
*(str2++) = '.';
for (k = 1; k < nc - 17 - bd; k++)
*(str2++) = '0' + (char) (randlimb () & 1);
*(str2++) = 'e';
sprintf (str2, "%d", (int) (randlimb () & INT_MAX) + INT_MIN/2);
mpfr_set_prec (x, nc + 10);
mpfr_set_str_binary (x, str);
mpfr_set_prec (x, 54);
mpfr_set_str_binary (x, "0.100100100110110101001010010101111000001011100100101010E-529");
mpfr_init2 (y, 54);
mpfr_set_str (y, "4.936a52bc17254@-133", 16, GMP_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1a):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str_binary (x, "0.111111101101110010111010100110000111011001010100001101E-529");
mpfr_set_str (y, "0.fedcba98765434P-529", 16, GMP_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1b):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, nc * sizeof(char));
mpfr_set_prec (x, 53);
mpfr_set_str_binary (x, "+110101100.01010000101101000000100111001000101011101110E00");
mpfr_set_str_binary (x, "1.0");
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_set_str_binary for s=1.0\n");
mpfr_clear(x);
mpfr_clear(y);
exit(1);
}
mpfr_set_str_binary (x, "+0000");
mpfr_set_str_binary (x, "+0000E0");
mpfr_set_str_binary (x, "0000E0");
if (mpfr_cmp_ui (x, 0))
{
printf ("Error in mpfr_set_str_binary for s=0.0\n");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (x, "+243495834958.53452345E1", 10, GMP_RNDN);
mpfr_set_str (x, "9007199254740993", 10, GMP_RNDN);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDU);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDD);
mpfr_set_str (x, "9007199254740992", 10, GMP_RNDZ);
/* check a random number printed and read is not modified */
prec = 53;
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
for (i=0;i<N;i++)
{
mpfr_random (x);
k = RND_RAND ();
logbase = (randlimb () % 5) + 1;
base = 1 << logbase;
/* Warning: the number of bits needed to print exactly a number of
'prec' bits in base 2^logbase may be greater than ceil(prec/logbase),
for example 0.11E-1 in base 2 cannot be written exactly with only
one digit in base 4 */
if (base == 2)
baseprec = prec;
else
baseprec = 1 + (prec - 2 + logbase) / logbase;
str = mpfr_get_str (NULL, &e, base, baseprec, x, (mp_rnd_t) k);
mpfr_set_str (y, str, base, (mp_rnd_t) k);
MPFR_EXP(y) += logbase * (e - strlen (str));
if (mpfr_cmp (x, y))
{
printf ("mpfr_set_str o mpfr_get_str <> id for rnd_mode=%s\n",
mpfr_print_rnd_mode ((mp_rnd_t) k));
printf ("x=");
mpfr_print_binary (x);
puts ("");
printf ("s=%s, exp=%d, base=%d\n", str, (int) e, base);
printf ("y=");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, strlen (str) + 1);
}
for (i = 2; i <= 36; i++)
{
if (mpfr_set_str (x, "@NaN@(garbage)", i, GMP_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on @NaN@(garbage)\n");
exit (1);
}
/*
if (mpfr_set_str (x, "@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on @Inf@garbage\n");
exit (1);
}
if (mpfr_set_str (x, "-@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on -@Inf@garbage\n");
exit (1);
}
if (mpfr_set_str (x, "+@Inf@garbage", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on +@Inf@garbage\n");
exit (1);
}
*/
if (i > 16)
continue;
if (mpfr_set_str (x, "NaN", i, GMP_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on NaN\n");
exit (1);
}
if (mpfr_set_str (x, "Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on Inf\n");
exit (1);
}
if (mpfr_set_str (x, "-Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on -Inf\n");
exit (1);
}
if (mpfr_set_str (x, "+Inf", i, GMP_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on +Inf\n");
exit (1);
}
}
/* check that mpfr_set_str works for uppercase letters too */
mpfr_set_prec (x, 10);
mpfr_set_str (x, "B", 16, GMP_RNDN);
if (mpfr_cmp_ui (x, 11) != 0)
{
printf ("mpfr_set_str does not work for uppercase letters\n");
exit (1);
}
/* start of tests added by Alain Delplanque */
/* in this example an overflow can occur */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.0E-532");
mpfr_set_str (y, "0.71128279983522479470@-160", 10, GMP_RNDU);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (2):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* in this example, I think there was a pb in the old function :
result of mpfr_set_str_old for the same number , but with more
precision is: 1.111111111110000000000000000111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100111000100001100000010101100111010e184
this result is the same as mpfr_set_str */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111110000000000000000111111111111111111111111110000000001E184");
mpfr_set_str (y, "0.jo08hg31hc5mmpj5mjjmgn55p2h35g@39", 27, GMP_RNDU);
/* y = 49027884868983130654865109690613178467841148597221480052 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (3):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* not exact rounding in mpfr_set_str
same number with more precision is : 1.111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011011111101000001101110110010101101000010100110011101110010001110e195
this result is the same as mpfr_set_str */
/* problem was : can_round was call with GMP_RNDN round mode,
so can_round use an error : 1/2 * 2^err * ulp(y)
instead of 2^err * ulp(y)
I have increase err by 1 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111111111111111111111000000000000000000000000000000000001e195");
mpfr_set_str (y, "0.6e23ekb6acgh96abk10b6c9f2ka16i@45", 21, GMP_RNDU);
/* y = 100433627392042473064661483711179345482301462325708736552078 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (4):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* may be an error in mpfr_set_str_old
with more precision : 1.111111100000001111110000000000011111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111101010001110111011000010111001011100110110e180 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111100000001111110000000000011111011111111111111111111111111e180");
mpfr_set_str (y, "0.10j8j2k82ehahha56390df0a1de030@41", 23, GMP_RNDZ);
/* y = 3053110535624388280648330929253842828159081875986159414 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (5):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "0.jrchfhpp9en7hidqm9bmcofid9q3jg@39", 28, GMP_RNDU);
/* y = 196159429139499688661464718784226062699788036696626429952 */
mpfr_set_str_binary (x, "0.1111111111111111111111111111111000000000000011100000001111100001E187");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (6):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "0.h148m5ld5cf8gk1kd70b6ege92g6ba@47", 24, GMP_RNDZ);
/* y = 52652933527468502324759448399183654588831274530295083078827114496 */
mpfr_set_str_binary (x, "0.1111111111111100000000001000000000000000000011111111111111101111E215");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (7):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* worst cases for rounding to nearest in double precision */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str (y, "5e125", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10111101000101110110011000100000101001010000000111111E418");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (8):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "69e267", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10000101101111100101101100000110010011001010011011010E894");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (9):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "623e100", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10110010000001010011000101111001110101000001111011111E342");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (10):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "3571e263", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10110001001100100010011000110000111010100000110101010E886");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (11):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "75569e-254", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101101001000110001011011001000111000110101010110011E-827");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (12):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "920657e-23", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101001110101001100110000101110110111101111001101100E-56");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (13):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "9210917e80", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.11101101000100011001000110100011111100110000000110010E289");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (14):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "87575437e-309", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.11110000001110011001000000110000000100000010101101100E-1000");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (15):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "245540327e122", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E434");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (16):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "491080654e122", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E435");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (17):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "83356057653e193", 10, GMP_RNDN);
mpfr_set_str_binary (x, "0.10101010001001110011011011010111011100010101000011000E678");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (18):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
CHECK53(y, "83356057653e193", GMP_RNDN, x,
"0.10101010001001110011011011010111011100010101000011000E678",
18);
CHECK53(y, "619534293513e124", GMP_RNDN, x,
"0.10001000011000010000000110000001111111110000011110001e452",
19);
CHECK53(y, "3142213164987e-294", GMP_RNDN, x,
"0.11101001101000000100111011111101111001010001001101111e-935",
20);
CHECK53(y, "36167929443327e-159", GMP_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-483",
21);
CHECK53(y, "904198236083175e-161", GMP_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-485",
22);
CHECK53(y, "3743626360493413e-165", GMP_RNDN, x,
"0.11000100000100011101001010111101011011011111011111001e-496",
23);
CHECK53(y, "94080055902682397e-242", GMP_RNDN, x,
"0.10110010010011000000111100011100111100110011011001010e-747",
24);
CHECK53(y, "7e-303", GMP_RNDD, x,
"0.10011001100111001000100110001110001000110111110001011e-1003",
25);
CHECK53(y, "7e-303", GMP_RNDU, x,
"0.10011001100111001000100110001110001000110111110001100e-1003",
26);
CHECK53(y, "93e-234", GMP_RNDD, x,
"0.10010011110110010111001001111001000010000000001110101E-770",
27);
CHECK53(y, "93e-234", GMP_RNDU, x,
"0.10010011110110010111001001111001000010000000001110110E-770",
28);
CHECK53(y, "755e174", GMP_RNDD, x,
"0.10111110110010011000110010011111101111000111111000101E588",
29);
CHECK53(y, "755e174", GMP_RNDU, x,
"0.10111110110010011000110010011111101111000111111000110E588",
30);
CHECK53(y, "8699e-276", GMP_RNDD, x,
"0.10010110100101101111100100100011011101100110100101100E-903",
31);
CHECK53(y, "8699e-276", GMP_RNDU, x,
"0.10010110100101101111100100100011011101100110100101101E-903",
32);
CHECK53(y, "82081e41", GMP_RNDD, x,
"0.10111000000010000010111011111001111010100011111001011E153",
33);
CHECK53(y, "82081e41", GMP_RNDU, x,
"0.10111000000010000010111011111001111010100011111001100E153",
34);
CHECK53(y, "584169e229", GMP_RNDD, x,
"0.11101011001010111000001011001110111000111100110101010E780",
35);
CHECK53(y, "584169e229", GMP_RNDU, x,
"0.11101011001010111000001011001110111000111100110101011E780",
36);
CHECK53(y, "5783893e-128", GMP_RNDD, x,
"0.10011000111100000110011110000101100111110011101110100E-402",
37);
CHECK53(y, "5783893e-128", GMP_RNDU, x,
"0.10011000111100000110011110000101100111110011101110101E-402",
38);
CHECK53(y, "87575437e-310", GMP_RNDD, x,
"0.11000000001011100000110011110011010000000010001010110E-1003",
39);
CHECK53(y, "87575437e-310", GMP_RNDU, x,
"0.11000000001011100000110011110011010000000010001010111E-1003",
40);
CHECK53(y, "245540327e121", GMP_RNDD, x,
"0.11100010101101001111010010110100011100000100101000100E430",
41);
CHECK53(y, "245540327e121", GMP_RNDU, x,
"0.11100010101101001111010010110100011100000100101000101E430",
42);
CHECK53(y, "9078555839e-109", GMP_RNDD, x,
"0.11111110001010111010110000110011100110001010011101101E-329",
43);
CHECK53(y, "9078555839e-109", GMP_RNDU, x,
"0.11111110001010111010110000110011100110001010011101110E-329",
44);
CHECK53(y, "42333842451e201", GMP_RNDD, x,
"0.10000000110001001101000100110110111110101011101011111E704",
45);
CHECK53(y, "42333842451e201", GMP_RNDU, x,
"0.10000000110001001101000100110110111110101011101100000E704",
46);
CHECK53(y, "778380362293e218", GMP_RNDD, x,
"0.11001101010111000001001100001100110010000001010010010E764",
47);
CHECK53(y, "778380362293e218", GMP_RNDU, x,
"0.11001101010111000001001100001100110010000001010010011E764",
48);
CHECK53(y, "7812878489261e-179", GMP_RNDD, x,
"0.10010011011011010111001111011101111101101101001110100E-551",
49);
CHECK53(y, "7812878489261e-179", GMP_RNDU, x,
"0.10010011011011010111001111011101111101101101001110101E-551",
50);
CHECK53(y, "77003665618895e-73", GMP_RNDD, x,
"0.11000101111110111111001111111101001101111000000101001E-196",
51);
CHECK53(y, "77003665618895e-73", GMP_RNDU, x,
"0.11000101111110111111001111111101001101111000000101010E-196",
52);
CHECK53(y, "834735494917063e-300", GMP_RNDD, x,
"0.11111110001101100001001101111100010011001110111010001E-947",
53);
CHECK53(y, "834735494917063e-300", GMP_RNDU, x,
"0.11111110001101100001001101111100010011001110111010010E-947",
54);
CHECK53(y, "6182410494241627e-119", GMP_RNDD, x,
"0.10001101110010110010001011000010001000101110100000111E-342",
55);
CHECK53(y, "6182410494241627e-119", GMP_RNDU, x,
"0.10001101110010110010001011000010001000101110100001000E-342",
56);
CHECK53(y, "26153245263757307e49", GMP_RNDD, x,
"0.10011110111100000000001011011110101100010000011011110E218",
57);
CHECK53(y, "26153245263757307e49", GMP_RNDU, x,
"0.10011110111100000000001011011110101100010000011011111E218",
58);
/* to check this problem : I convert limb (10--0 or 101--1) into base b
with more than mp_bits_per_limb digits,
so when convert into base 2 I should have
the limb that I have choose */
/* this use mpfr_get_str */
{
size_t nb_digit = mp_bits_per_limb;
mp_limb_t check_limb[2] = {MPFR_LIMB_HIGHBIT, ~(MPFR_LIMB_HIGHBIT >> 1)};
int base[3] = {10, 16, 19};
mp_rnd_t rnd[3] = {GMP_RNDU, GMP_RNDN, GMP_RNDD};
int cbase, climb, crnd;
char *str;
mpfr_set_prec (x, mp_bits_per_limb); /* x and y have only one limb */
mpfr_set_prec (y, mp_bits_per_limb);
str = (char*) (*__gmp_allocate_func) (N + 20);
mpfr_set_ui (x, 1, GMP_RNDN); /* ensures that x is not NaN or Inf */
for (; nb_digit < N; nb_digit *= 10)
for (cbase = 0; cbase < 3; cbase++)
for (climb = 0; climb < 2; climb++)
for (crnd = 0; crnd < 3; crnd++)
{
char *str1;
mp_exp_t exp;
*(MPFR_MANT(x)) = check_limb[climb];
MPFR_EXP(x) = 0;
mpfr_get_str (str + 2, &exp, base[cbase],
nb_digit, x, rnd[crnd]);
str[0] = '-';
str[(str[2] == '-')] = '0';
str[(str[2] == '-') + 1] = '.';
for (str1 = str; *str1 != 0; str1++)
;
sprintf (str1, "@%i", (int) exp);
mpfr_set_str (y, str, base[cbase], rnd[2 - crnd]);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error in mpfr_set_str for nb_digit=%u, base=%d, "
"rnd=%s:\n", (unsigned int) nb_digit, base[cbase],
mpfr_print_rnd_mode (rnd[crnd]));
printf ("instead of: ");
mpfr_print_binary (x);
puts ("");
printf ("return : ");
mpfr_print_binary (y);
puts ("");
exit (1);
}
}
(*__gmp_free_func) (str, N + 20);
}
/* end of tests added by Alain Delplanque */
/* check that flags are correctly cleared */
mpfr_set_nan (x);
mpfr_set_str (x, "+0.0", 10, GMP_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) < 0)
{
printf ("x <- +0.0 failed after x=NaN\n");
exit (1);
}
mpfr_set_str (x, "-0.0", 10, GMP_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) > 0)
{
printf ("x <- -0.0 failed after x=NaN\n");
exit (1);
}
/* check invalid input */
ret = mpfr_set_str (x, "1E10toto", 10, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1p10toto", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "+", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "-", 16, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "this_is_an_invalid_number_in_base_36", 36, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1.2.3", 10, GMP_RNDN);
MPFR_ASSERTN (ret == -1);
mpfr_set_prec (x, 135);
ret = mpfr_set_str (x, "thisisavalidnumberinbase36", 36, GMP_RNDN);
mpfr_set_prec (y, 135);
mpfr_set_str (y, "23833565676460972739462619524519814462546", 10, GMP_RNDN);
MPFR_ASSERTN (mpfr_cmp (x, y) == 0 && ret == 0);
/* coverage test for set_str_binary */
mpfr_set_str_binary (x, "NaN");
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_str_binary (x, "Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "+Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "-Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "0.01E2");
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_str_binary (x, "-0.01E2");
MPFR_ASSERTN(mpfr_cmp_si (x, -1) == 0);
mpfr_clear (x);
mpfr_clear (y);
check_underflow ();
tests_end_mpfr ();
return 0;
}
int
main (void)
{
mpfr_t x;
mpfr_exp_t emax;
tests_start_mpfr ();
mpfr_init (x);
mpfr_set_nan (x);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_inf (x, -1);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG(x));
emax = mpfr_get_emax ();
set_emax (0);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "0.111");
mpfr_prec_round (x, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_prec (x, mp_bits_per_limb + 2);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, MPFR_RNDN);
mpfr_prec_round (x, 2, MPFR_RNDN);
if (mpfr_cmp_ui(x, 4))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 4\n");
exit (1);
}
/* check case when reallocation is needed */
mpfr_set_prec (x, 3);
mpfr_set_ui (x, 5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
mpfr_init2 (x, 3);
mpfr_set_si (x, -5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, mp_bits_per_limb + 1, MPFR_RNDN);
if (mpfr_cmp_si(x, -5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of -5\n");
exit (1);
}
/* check case when new precision needs less limbs */
mpfr_set_prec (x, mp_bits_per_limb + 1);
mpfr_set_ui (x, 5, MPFR_RNDN); /* exact */
mpfr_prec_round (x, 3, MPFR_RNDN); /* exact */
if (mpfr_cmp_ui(x, 5))
{
printf ("Error in tround: got ");
mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
printf (" instead of 5\n");
exit (1);
}
mpfr_clear(x);
tests_end_mpfr ();
return 0;
}