void mp_Imul (mp_interval_t *rop, mp_interval_t op1, mp_interval_t op2) {
// DECLARE AUX MPFR_T VARIABLE TO STORE CROSSED PRODUCTS
mpfr_t aux; mpfr_init (aux);
mpfr_t ropA; mpfr_init (ropA);
mpfr_t ropB; mpfr_init (ropB);
// FIRST CANDIDATE TO LEFT BOUNDARY
mpfr_mul (ropA, op1.a, op2.a, MPFR_RNDD);
mpfr_mul (aux, op1.a, op2.b, MPFR_RNDD); mpfr_min (ropA, ropA, aux, MPFR_RNDD);
mpfr_mul (aux, op1.b, op2.a, MPFR_RNDD); mpfr_min (ropA, ropA, aux, MPFR_RNDD);
mpfr_mul (aux, op1.b, op2.b, MPFR_RNDD); mpfr_min (ropA, ropA, aux, MPFR_RNDD);
// FIRST CANDIDATE TO RIGHT BOUNDARY
mpfr_mul (ropB, op1.a, op2.a, MPFR_RNDU);
mpfr_mul (aux, op1.a, op2.b, MPFR_RNDU); mpfr_max (ropB, ropB, aux, MPFR_RNDU);
mpfr_mul (aux, op1.b, op2.a, MPFR_RNDU); mpfr_max (ropB, ropB, aux, MPFR_RNDU);
mpfr_mul (aux, op1.b, op2.b, MPFR_RNDU); mpfr_max (rop->b, ropB, aux, MPFR_RNDU);
mpfr_set (rop->a, ropA, MPFR_RNDD);
// CLEAN AUX VARIABLE
mpfr_clear (aux);
mpfr_clear (ropA);
mpfr_clear (ropB);
}
real max(const real & a, const real & b)
{
real x;
mpfr_max(x.r, a.r, b.r, MPFR_RNDN);
return x;
}
SeedValue seed_mpfr_max (SeedContext ctx,
SeedObject function,
SeedObject this_object,
gsize argument_count,
const SeedValue args[],
SeedException *exception)
{
mpfr_rnd_t rnd;
mpfr_ptr rop, op1, op2;
gint ret;
CHECK_ARG_COUNT("mpfr.max", 3);
rop = seed_object_get_private(this_object);
rnd = seed_value_to_mpfr_rnd_t(ctx, args[2], exception);
if ( seed_value_is_object_of_class(ctx, args[0], mpfr_class) &&
seed_value_is_object_of_class(ctx, args[1], mpfr_class))
{
op1 = seed_object_get_private(args[0]);
op2 = seed_object_get_private(args[1]);
}
else
{
TYPE_EXCEPTION("mpfr.max", "mpfr_t");
}
ret = mpfr_max(rop, op1, op2, rnd);
return seed_value_from_int(ctx, ret, exception);
}
void mpfr_bisect_nRoot(mpfr_t R, mpfr_t N, mpfr_t T, unsigned int n)
{
if(mpfr_cmp_ui(N, 0) < 0)
{
fprintf(stderr, "The value to square root must be non-negative\n");
exit(-1);
}
if(mpfr_cmp_ui(T, 0) < 0)
{
fprintf(stderr, "The tolerance must be non-negative\n");
exit(-1);
}
assert(n >= 2);
mpfr_t a, b, x, f, d, fab;
//Set a == 0
mpfr_init_set_ui(a, 0, MPFR_RNDN);
//Set b = max{1, N}
mpfr_init(b);
mpfr_max(b, MPFR_ONE, N, MPFR_RNDN);
//Set x = (a + b)/2
mpfr_init(x);
mpfr_add(x, a, b, MPFR_RNDN);
mpfr_mul(x, x, MPFR_HALF, MPFR_RNDN);
//Set f = x^2 - N
mpfr_init(f);
mpfr_init(fab);
mpfr_pow_ui(f, x, n, MPFR_RNDN);
mpfr_sub(f, f, N, MPFR_RNDN);
mpfr_abs(fab, f, MPFR_RNDN);
//Set d = b - a
mpfr_init(d);
mpfr_sub(d, b, a, MPFR_RNDN);
while(mpfr_cmp(fab, T) > 0 && mpfr_cmp(d, T) > 0)
{
//Update the bounds, a and b
if(mpfr_cmp_ui(f, 0) < 0)
mpfr_set(a, x, MPFR_RNDN);
else
mpfr_set(b, x, MPFR_RNDN);
//Update x
mpfr_add(x, a, b, MPFR_RNDN);
mpfr_mul(x, x, MPFR_HALF, MPFR_RNDN);
//Update f
mpfr_pow_ui(f, x, n, MPFR_RNDN);
mpfr_sub(f, f, N, MPFR_RNDN);
mpfr_abs(fab, f, MPFR_RNDN);
}
mpfr_set(R, x, MPFR_RNDN);
}
int mp_IntersectInterval (mp_interval_t *rop, mp_interval_t op1, mp_interval_t op2) {
//rop->a = MAX (op1.a, op2.a);
mpfr_max (rop->a, op1.a, op2.a, MPFR_RNDD);
//rop->b = MIN (op1.b, op2.b);
mpfr_min (rop->b, op1.b, op2.b, MPFR_RNDU);
//if (rop->a < rop->b) return 1;
if (mpfr_cmp (rop->a, rop->b) < 0) return 1;
return 0;
}
int
main (void)
{
mpfr_t x, y, z;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
/* case x=NaN && y=NAN */
mpfr_set_nan (x);
mpfr_set_nan (y);
mpfr_min (z, x, y, MPFR_RNDN);
if (!mpfr_nan_p (z))
{
printf ("Error in mpfr_min (NaN, NaN)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if (!mpfr_nan_p (z))
{
printf ("Error in mpfr_max (NaN, NaN)\n");
exit (1);
}
/* case x=NaN */
mpfr_set_nan (x);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_min (z, x, y, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_min (NaN, 0)\n");
exit (1);
}
mpfr_min (z, y, x, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_min (0, NaN)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_max (NaN, 0)\n");
exit (1);
}
mpfr_max (z, y, x, MPFR_RNDN);
if (mpfr_cmp_ui (z, 0))
{
printf ("Error in mpfr_max (0, NaN)\n");
exit (1);
}
/* Case x=0+ and x=0- */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN); MPFR_SET_NEG(y);
mpfr_max (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error in mpfr_max (0+, 0-)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error in mpfr_min (0+, 0-)\n");
exit (1);
}
/* Case x=0- and y=0+ */
mpfr_set_ui (x, 0, MPFR_RNDN); MPFR_SET_NEG(x);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_NEG(z))
{
printf ("Error in mpfr_max (0+, 0-)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if (!MPFR_IS_ZERO(z) || MPFR_IS_POS(z))
{
printf ("Error in mpfr_min (0+, 0-)\n");
exit (1);
}
/* case x=+Inf */
mpfr_set_inf (x, 1);
mpfr_set_si (y, -12, MPFR_RNDN);
mpfr_min (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_si (z, -12) )
{
printf ("Error in mpfr_min (+Inf, -12)\n");
exit (1);
}
mpfr_max (z, x, y, MPFR_RNDN);
if ( !MPFR_IS_INF(z) || MPFR_IS_NEG(z) )
{
printf ("Error in mpfr_max (+Inf, 12)\n");
exit (1);
}
/* case x=-Inf */
mpfr_set_inf (x, -1);
mpfr_set_ui (y, 12, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 12) )
{
printf ("Error in mpfr_max (-Inf, 12)\n");
exit (1);
}
mpfr_min (z, x, y, MPFR_RNDN);
if ( !MPFR_IS_INF(z) || MPFR_IS_POS(z) )
{
printf ("Error in mpfr_min (-Inf, 12)\n");
exit (1);
}
/* case x=17 and y=42 */
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_max (z, x, y, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 42) )
{
printf ("Error in mpfr_max (17, 42)\n");
exit (1);
}
mpfr_max (z, y, x, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 42) )
{
printf ("Error in mpfr_max (42, 17)\n");
exit (1);
}
mpfr_min (z, y, x, MPFR_RNDN);
if ( mpfr_cmp_ui (z, 17) )
{
printf ("Error in mpfr_min (42, 17)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
tests_end_mpfr ();
return 0;
}