/* checks that x+y gives the same results in double
and with mpfr with 53 bits of precision */
void
_check (double x, double y, double z1, mp_rnd_t rnd_mode, unsigned int px,
unsigned int py, unsigned int pz)
{
double z2; mpfr_t xx,yy,zz; int cert=0;
mpfr_init2(xx, px);
mpfr_init2(yy, py);
mpfr_init2(zz, pz);
mpfr_set_d(xx, x, rnd_mode);
mpfr_set_d(yy, y, rnd_mode);
mpfr_add(zz, xx, yy, rnd_mode);
#ifdef MPFR_HAVE_FESETROUND
mpfr_set_machine_rnd_mode(rnd_mode);
if (px==53 && py==53 && pz==53) cert=1;
#endif
if (z1==0.0) z1=x+y; else cert=1;
z2 = mpfr_get_d1 (zz);
mpfr_set_d (yy, z2, GMP_RNDN);
if (!mpfr_cmp (zz, yy) && cert && z1!=z2 && !(isnan(z1) && isnan(z2))) {
printf("expected sum is %1.20e, got %1.20e\n",z1,z2);
printf("mpfr_add failed for x=%1.20e y=%1.20e with rnd_mode=%s\n",
x, y, mpfr_print_rnd_mode(rnd_mode));
exit(1);
}
mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}
/* idem than check for mpfr_add(x, x, x) */
void
check5 (double x, mp_rnd_t rnd_mode)
{
double z1,z2; mpfr_t xx, yy; int neg;
mpfr_init2(xx, 53);
mpfr_init2(yy, 53);
neg = LONG_RAND() % 2;
mpfr_set_d(xx, x, rnd_mode);
if (neg) mpfr_sub(xx, xx, xx, rnd_mode);
else mpfr_add(xx, xx, xx, rnd_mode);
mpfr_set_machine_rnd_mode(rnd_mode);
z1 = (neg) ? x-x : x+x;
z2 = mpfr_get_d1 (xx);
mpfr_set_d (yy, z2, GMP_RNDN);
/* check NaNs first since mpfr_cmp does not like them */
if (!(isnan(z1) && isnan(z2)) && !mpfr_cmp (xx, yy) && z1!=z2)
{
printf ("expected result is %1.20e, got %1.20e\n",z1,z2);
printf ("mpfr_%s(x,x,x) failed for x=%1.20e with rnd_mode=%s\n",
(neg) ? "sub" : "add", x, mpfr_print_rnd_mode (rnd_mode));
exit (1);
}
mpfr_clear(xx);
mpfr_clear(yy);
}
/* idem than check for mpfr_add(x, y, x) */
void
check4 (double x, double y, mp_rnd_t rnd_mode)
{
double z1, z2;
mpfr_t xx, yy;
int neg;
neg = LONG_RAND() % 2;
mpfr_init2(xx, 53);
mpfr_init2(yy, 53);
mpfr_set_d(xx, x, rnd_mode);
mpfr_set_d(yy, y, rnd_mode);
if (neg) mpfr_sub(xx, yy, xx, rnd_mode);
else mpfr_add(xx, yy, xx, rnd_mode);
mpfr_set_machine_rnd_mode(rnd_mode);
z1 = (neg) ? y-x : x+y;
z2 = mpfr_get_d1 (xx);
mpfr_set_d (yy, z2, GMP_RNDN);
/* check that xx is representable as a double and no overflow occurred */
if ((mpfr_cmp (xx, yy) == 0) && (z1 != z2)) {
printf("expected result is %1.20e, got %1.20e\n", z1, z2);
printf("mpfr_%s(x,y,x) failed for x=%1.20e y=%1.20e with rnd_mode=%s\n",
(neg) ? "sub" : "add", x, y, mpfr_print_rnd_mode(rnd_mode));
exit(1);
}
mpfr_clear(xx); mpfr_clear(yy);
}
int
check_denorms ()
{
mp_rnd_t rnd_mode;
mpfr_t x;
double d, d2, dd, f;
int fail = 0, k, n;
mpfr_init2 (x, BITS_PER_MP_LIMB);
for (rnd_mode = 0; rnd_mode <= 3; rnd_mode++)
{
#ifdef MPFR_HAVE_FESETROUND
mpfr_set_machine_rnd_mode (rnd_mode);
#else
if (rnd_mode)
break; /* second iteration */
rnd_mode = GMP_RNDN;
#endif
for (k = -17; k <= 17; k += 2)
{
d = k * DBL_MIN; /* k * 2^(-1022) */
f = 1.0;
mpfr_set_si (x, k, GMP_RNDN);
mpfr_div_2exp (x, x, 1022, GMP_RNDN); /* k * 2^(-1022) */
for (n = 0; n <= 58; n++)
{
d2 = d * f;
dd = mpfr_get_d (x, rnd_mode);
if (d2 != dd) /* should be k * 2^(-1022-n) for n < 53 */
{
fprintf (stderr,
"Wrong result for %d * 2^(%d), rnd_mode %d\n",
k, -1022-n, rnd_mode);
fprintf (stderr, "got %.20e instead of %.20e\n", dd, d2);
fail = 1;
}
f *= 0.5;
mpfr_div_2exp (x, x, 1, GMP_RNDN);
}
}
}
mpfr_clear (x);
return fail;
}
void
checknan (double x, double y, mp_rnd_t rnd_mode, unsigned int px,
unsigned int py, unsigned int pz)
{
double z2; mpfr_t xx, yy, zz;
mpfr_init2(xx, px);
mpfr_init2(yy, py);
mpfr_init2(zz, pz);
mpfr_set_d(xx, x, rnd_mode);
mpfr_set_d(yy, y, rnd_mode);
mpfr_add(zz, xx, yy, rnd_mode);
#ifdef MPFR_HAVE_FESETROUND
mpfr_set_machine_rnd_mode(rnd_mode);
#endif
if (MPFR_IS_NAN(zz) == 0) { printf("Error, not an MPFR_NAN for xx = %1.20e, y = %1.20e\n", x, y); exit(1); }
z2 = mpfr_get_d1 (zz);
if (!isnan(z2)) { printf("Error, not a NaN after conversion, xx = %1.20e yy = %1.20e, got %1.20e\n", x, y, z2); exit(1); }
mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}
void
check2 (double x, int px, double y, int py, int pz, mp_rnd_t rnd_mode)
{
mpfr_t xx, yy, zz; double z,z2; int u;
mpfr_init2(xx,px); mpfr_init2(yy,py); mpfr_init2(zz,pz);
mpfr_set_d(xx, x, rnd_mode);
mpfr_set_d(yy, y, rnd_mode);
mpfr_add(zz, xx, yy, rnd_mode);
mpfr_set_machine_rnd_mode(rnd_mode);
z = x+y; z2=mpfr_get_d1 (zz); u=ulp(z,z2);
/* one ulp difference is possible due to composed rounding */
if (px>=53 && py>=53 && pz>=53 && ABS(u)>1) {
printf("x=%1.20e,%d y=%1.20e,%d pz=%d,rnd=%s\n",
x,px,y,py,pz,mpfr_print_rnd_mode(rnd_mode));
printf("got %1.20e\n",z2);
printf("result should be %1.20e (diff=%d ulp)\n",z,u);
mpfr_set_d(zz, z, rnd_mode);
printf("i.e."); mpfr_print_binary(zz); putchar('\n');
exit(1); }
mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz);
}
static void
test_against_libc (void)
{
mpfr_rnd_t r = MPFR_RNDN;
#if HAVE_ROUND
TEST_FCT (round);
#endif
#if HAVE_TRUNC
TEST_FCT (trunc);
#endif
#if HAVE_FLOOR
TEST_FCT (floor);
#endif
#if HAVE_CEIL
TEST_FCT (ceil);
#endif
#if HAVE_NEARBYINT
for (r = 0; r < MPFR_RND_MAX ; r++)
if (mpfr_set_machine_rnd_mode (r) == 0)
test_fct (&nearbyint, &mpfr_rint, "rint", r);
#endif
}
/* idem than check for mpfr_add(x, x, y) */
void
check3 (double x, double y, mp_rnd_t rnd_mode)
{
double z1,z2; mpfr_t xx,yy; int neg;
neg = LONG_RAND() % 2;
mpfr_init2(xx, 53);
mpfr_init2(yy, 53);
mpfr_set_d(xx, x, rnd_mode);
mpfr_set_d(yy, y, rnd_mode);
if (neg) mpfr_sub(xx, xx, yy, rnd_mode);
else mpfr_add(xx, xx, yy, rnd_mode);
mpfr_set_machine_rnd_mode(rnd_mode);
z1 = (neg) ? x-y : x+y;
z2 = mpfr_get_d1 (xx);
mpfr_set_d (yy, z2, GMP_RNDN);
if (!mpfr_cmp (xx, yy) && z1!=z2 && !(isnan(z1) && isnan(z2))) {
printf("expected result is %1.20e, got %1.20e\n",z1,z2);
printf("mpfr_%s(x,x,y) failed for x=%1.20e y=%1.20e with rnd_mode=%u\n",
(neg) ? "sub" : "add",x,y,rnd_mode);
exit(1);
}
mpfr_clear(xx); mpfr_clear(yy);
}
int
main (void)
{
#ifdef MPFR_HAVE_FESETROUND
mpfr_t half, x, y;
mp_rnd_t rnd_mode;
#endif
mpfr_test_init ();
#ifdef MPFR_HAVE_FESETROUND
mpfr_init2(half, 2);
mpfr_set_ui(half, 1, GMP_RNDZ);
mpfr_div_2ui(half, half, 1, GMP_RNDZ); /* has exponent 0 */
mpfr_init2(x, 128);
mpfr_init2(y, 128);
for (rnd_mode = 0; rnd_mode <= 3; rnd_mode++)
{
int i, j, si, sj;
double di, dj;
mpfr_set_machine_rnd_mode (rnd_mode);
for (i = 1, di = 0.25; i < 127; i++, di *= 0.5)
for (si = 0; si <= 1; si++)
{
mpfr_div_2ui (x, half, i, GMP_RNDZ);
(si ? mpfr_sub : mpfr_add)(x, half, x, GMP_RNDZ);
/* x = 1/2 +/- 1/2^(1+i) */
for (j = i+1, dj = di * 0.5; j < 128 && j < i+53; j++, dj *= 0.5)
for (sj = 0; sj <= 1; sj++)
{
double c, d, dd;
int exp;
char *f;
mpfr_div_2ui (y, half, j, GMP_RNDZ);
(sj ? mpfr_sub : mpfr_add)(y, x, y, GMP_RNDZ);
/* y = 1/2 +/- 1/2^(1+i) +/- 1/2^(1+j) */
exp = (LONG_RAND() % 47) - 23;
mpfr_mul_2si (y, y, exp, GMP_RNDZ);
if (mpfr_inexflag_p())
{
fprintf(stderr, "Error in tget_d: inexact flag for "
"(i,si,j,sj,rnd,exp) = (%d,%d,%d,%d,%d,%d)\n",
i, si, j, sj, rnd_mode, exp);
exit(1);
}
dd = si != sj ? di - dj : di + dj;
d = si ? 0.5 - dd : 0.5 + dd;
if ((LONG_RAND() / 1024) & 1)
{
c = mpfr_get_d (y, rnd_mode);
f = "mpfr_get_d";
}
else
{
exp = (LONG_RAND() % 47) - 23;
c = mpfr_get_d3 (y, exp, rnd_mode);
f = "mpfr_get_d3";
if (si) /* then real d < 0.5 */
d *= sj && i == 1 ? 4 : 2; /* normalize real d */
}
if (exp > 0)
d *= 1 << exp;
if (exp < 0)
d /= 1 << -exp;
if (c != d)
{
fprintf (stderr, "Error in tget_d (%s) for "
"(i,si,j,sj,rnd,exp) = (%d,%d,%d,%d,%d,%d)\n"
"got %.25Le instead of %.25Le\n"
"Difference: %.19e\n",
f, i, si, j, sj, rnd_mode, exp,
(long double) c, (long double) d, d - c);
exit (1);
}
}
}
}
mpfr_clear(half);
mpfr_clear(x);
mpfr_clear(y);
#endif
if (check_denorms ())
exit (1);
return 0;
}
