int
mpc_tanh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
/* tanh(op) = -i*tan(i*op) = conj(-i*tan(conj(-i*op))) */
mpc_t z;
mpc_t tan_z;
int inex;
/* z := conj(-i * op) and rop = conj(-i * tan(z)), in other words, we have
to switch real and imaginary parts. Let us set them without copying
significands. */
mpc_realref (z)[0] = mpc_imagref (op)[0];
mpc_imagref (z)[0] = mpc_realref (op)[0];
mpc_realref (tan_z)[0] = mpc_imagref (rop)[0];
mpc_imagref (tan_z)[0] = mpc_realref (rop)[0];
inex = mpc_tan (tan_z, z, MPC_RND (MPC_RND_IM (rnd), MPC_RND_RE (rnd)));
/* tan_z and rop parts share the same significands, copy the rest now. */
mpc_realref (rop)[0] = mpc_imagref (tan_z)[0];
mpc_imagref (rop)[0] = mpc_realref (tan_z)[0];
/* swap inexact flags for real and imaginary parts */
return MPC_INEX (MPC_INEX_IM (inex), MPC_INEX_RE (inex));
}
void
read_mpc_rounding_mode (FILE *fp, mpc_rnd_t* rnd)
{
mpfr_rnd_t re, im;
read_mpfr_rounding_mode (fp, &re);
read_mpfr_rounding_mode (fp, &im);
*rnd = MPC_RND (re, im);
}
static void
check_regular (void)
{
mpc_t x, y;
int rnd_re, rnd_im;
mpfr_prec_t prec;
testmul (247, -65, -223, 416, 8, 24);
testmul (5, -896, 5, -32, 3, 2);
testmul (-3, -512, -1, -1, 2, 16);
testmul (266013312, 121990769, 110585572, 116491059, 27, 0);
testmul (170, 9, 450, 251, 8, 0);
testmul (768, 85, 169, 440, 8, 16);
testmul (145, 1816, 848, 169, 8, 24);
mpc_init2 (x, 1000);
mpc_init2 (y, 1000);
/* Bug 20081114: mpc_mul_karatsuba returned wrong inexact value for
imaginary part */
mpc_set_prec (x, 7);
mpc_set_prec (y, 7);
mpfr_set_str (mpc_realref (x), "0xB4p+733", 16, MPFR_RNDN);
mpfr_set_str (mpc_imagref (x), "0x90p+244", 16, MPFR_RNDN);
mpfr_set_str (mpc_realref (y), "0xECp-146", 16, MPFR_RNDN);
mpfr_set_str (mpc_imagref (y), "0xACp-471", 16, MPFR_RNDN);
cmpmul (x, y, MPC_RNDNN);
mpfr_set_str (mpc_realref (x), "0xB4p+733", 16, MPFR_RNDN);
mpfr_set_str (mpc_imagref (x), "0x90p+244", 16, MPFR_RNDN);
mpfr_set_str (mpc_realref (y), "0xACp-471", 16, MPFR_RNDN);
mpfr_set_str (mpc_imagref (y), "-0xECp-146", 16, MPFR_RNDN);
cmpmul (x, y, MPC_RNDNN);
for (prec = 2; prec < 1000; prec = (mpfr_prec_t) (prec * 1.1 + 1))
{
mpc_set_prec (x, prec);
mpc_set_prec (y, prec);
test_default_random (x, -1024, 1024, 128, 0);
test_default_random (y, -1024, 1024, 128, 0);
for (rnd_re = 0; rnd_re < 4; rnd_re ++)
for (rnd_im = 0; rnd_im < 4; rnd_im ++)
cmpmul (x, y, MPC_RND (rnd_re, rnd_im));
}
mpc_clear (x);
mpc_clear (y);
}
static mpc_rnd_t
next_mpc_rnd_mode (mpc_rnd_t rnd)
{
mpfr_rnd_t rnd_re = MPC_RND_RE (rnd);
mpfr_rnd_t rnd_im = MPC_RND_IM (rnd);
rnd_im = next_mpfr_rnd_mode (rnd_im);
if (!is_valid_mpfr_rnd_mode (rnd_im))
{
rnd_re = next_mpfr_rnd_mode (rnd_re);
rnd_im = FIRST_MPFR_RND_MODE;
}
return MPC_RND(rnd_re, rnd_im);
}
static void
first_mode (mpc_fun_param_t *params, int index)
{
switch (params->T[index])
{
case MPC_RND:
params->P[index].mpc_rnd =
MPC_RND(FIRST_MPFR_RND_MODE, FIRST_MPFR_RND_MODE);
break;
case MPFR_RND:
params->P[index].mpfr_rnd = FIRST_MPFR_RND_MODE;
break;
default:
printf ("The rounding mode is expected to be"
" the last input parameter.\n");
exit (-1);
}
}
static void
foo (int f(mpc_ptr, mpc_srcptr, mpc_rnd_t), char *s)
{
mpc_t z, t;
int rnd_re, rnd_im, rnd;
#define N 5
mpfr_exp_t exy[N][2] = {{200, 800}, {800, 200}, {-50, 50}, {-10, 1000},
{0, 1000}};
int n, inex, inex_re, inex_im, sgn;
mpc_init2 (z, MPFR_PREC_MIN);
mpc_init2 (t, MPFR_PREC_MIN);
for (n = 0; n < N; n++)
for (sgn = 0; sgn < 4; sgn++)
{
if (exy[n][0])
mpfr_set_ui_2exp (mpc_realref (z), 1, exy[n][0], MPFR_RNDN);
else
mpfr_set_ui (mpc_realref (z), 0, MPFR_RNDN);
if (sgn & 1)
mpfr_neg (mpc_realref (z), mpc_realref (z), MPFR_RNDN);
if (exy[n][1])
mpfr_set_ui_2exp (mpc_imagref (z), 1, exy[n][1], MPFR_RNDN);
else
mpfr_set_ui (mpc_imagref (z), 0, MPFR_RNDN);
if (sgn & 2)
mpfr_neg (mpc_imagref (z), mpc_imagref (z), MPFR_RNDN);
inex = f (t, z, MPC_RNDZZ);
inex_re = MPC_INEX_RE(inex);
inex_im = MPC_INEX_IM(inex);
if (inex_re != 0 && mpfr_inf_p (mpc_realref (t)))
{
fprintf (stderr, "Error, wrong real part with rounding towards zero\n");
fprintf (stderr, "f = %s\n", s);
fprintf (stderr, "z=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nt=");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
exit (1);
}
if (inex_im != 0 && mpfr_inf_p (mpc_imagref (t)))
{
fprintf (stderr, "Error, wrong imag part with rounding towards zero\n");
fprintf (stderr, "f = %s\n", s);
fprintf (stderr, "z=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nt=");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
exit (1);
}
rnd_re = mpfr_signbit (mpc_realref (t)) == 0 ? MPFR_RNDU : MPFR_RNDD;
rnd_im = mpfr_signbit (mpc_imagref (t)) == 0 ? MPFR_RNDU : MPFR_RNDD;
rnd = MPC_RND(rnd_re,rnd_im); /* round away */
inex = f (t, z, rnd);
inex_re = MPC_INEX_RE(inex);
inex_im = MPC_INEX_IM(inex);
if (inex_re != 0 && mpfr_zero_p (mpc_realref (t)))
{
fprintf (stderr, "Error, wrong real part with rounding away from zero\n");
fprintf (stderr, "f = %s\n", s);
fprintf (stderr, "z=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nt=");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
fprintf (stderr, "rnd=%s\n", mpfr_print_rnd_mode (rnd_re));
exit (1);
}
if (inex_im != 0 && mpfr_zero_p (mpc_imagref (t)))
{
fprintf (stderr, "Error, wrong imag part with rounding away from zero\n");
fprintf (stderr, "f = %s\n", s);
fprintf (stderr, "z=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nt=");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
fprintf (stderr, "rnd=%s\n", mpfr_print_rnd_mode (rnd_im));
exit (1);
}
}
mpc_clear (z);
mpc_clear (t);
}
/* tgeneric(prec_min, prec_max, step, exp_max) checks rounding with random
numbers:
- with precision ranging from prec_min to prec_max with an increment of
step,
- with exponent between -exp_max and exp_max.
It also checks parameter reuse (it is assumed here that either two mpc_t
variables are equal or they are different, in the sense that the real part
of one of them cannot be the imaginary part of the other). */
void
tgeneric (mpc_function function, mpfr_prec_t prec_min,
mpfr_prec_t prec_max, mpfr_prec_t step, mpfr_exp_t exp_max)
{
unsigned long ul1 = 0, ul2 = 0;
long lo = 0;
int i = 0;
mpfr_t x1, x2, xxxx;
mpc_t z1, z2, z3, z4, z5, zzzz, zzzz2;
mpfr_rnd_t rnd_re, rnd_im, rnd2_re, rnd2_im;
mpfr_prec_t prec;
mpfr_exp_t exp_min;
int special, special_cases;
mpc_init2 (z1, prec_max);
switch (function.type)
{
case C_CC:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (z4, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 8;
break;
case CCCC:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (z4, prec_max);
mpc_init2 (z5, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 8;
break;
case FC:
mpfr_init2 (x1, prec_max);
mpfr_init2 (x2, prec_max);
mpfr_init2 (xxxx, 4*prec_max);
mpc_init2 (z2, prec_max);
special_cases = 4;
break;
case CCF: case CFC:
mpfr_init2 (x1, prec_max);
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 6;
break;
case CCI: case CCS:
case CCU: case CUC:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 5;
break;
case CUUC:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 6;
break;
case CC_C:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (z4, prec_max);
mpc_init2 (z5, prec_max);
mpc_init2 (zzzz, 4*prec_max);
mpc_init2 (zzzz2, 4*prec_max);
special_cases = 4;
break;
case CC:
default:
mpc_init2 (z2, prec_max);
mpc_init2 (z3, prec_max);
mpc_init2 (zzzz, 4*prec_max);
special_cases = 4;
}
exp_min = mpfr_get_emin ();
if (exp_max <= 0 || exp_max > mpfr_get_emax ())
exp_max = mpfr_get_emax();
if (-exp_max > exp_min)
exp_min = - exp_max;
if (step < 1)
step = 1;
for (prec = prec_min, special = 0;
prec <= prec_max || special <= special_cases;
prec+=step, special += (prec > prec_max ? 1 : 0)) {
/* In the end, test functions in special cases of purely real, purely
imaginary or infinite arguments. */
/* probability of one zero part in 256th (25 is almost 10%) */
const unsigned int zero_probability = special != 0 ? 0 : 25;
mpc_set_prec (z1, prec);
test_default_random (z1, exp_min, exp_max, 128, zero_probability);
switch (function.type)
{
case C_CC:
mpc_set_prec (z2, prec);
test_default_random (z2, exp_min, exp_max, 128, zero_probability);
mpc_set_prec (z3, prec);
mpc_set_prec (z4, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
mpfr_set_ui (mpc_realref (z2), 0, MPFR_RNDN);
break;
case 6:
mpfr_set_inf (mpc_realref (z2), -1);
break;
case 7:
mpfr_set_ui (mpc_imagref (z2), 0, MPFR_RNDN);
break;
case 8:
mpfr_set_inf (mpc_imagref (z2), +1);
break;
}
break;
case CCCC:
mpc_set_prec (z2, prec);
test_default_random (z2, exp_min, exp_max, 128, zero_probability);
mpc_set_prec (z3, prec);
mpc_set_prec (z4, prec);
mpc_set_prec (z5, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
mpfr_set_ui (mpc_realref (z2), 0, MPFR_RNDN);
break;
case 6:
mpfr_set_inf (mpc_realref (z2), -1);
break;
case 7:
mpfr_set_ui (mpc_imagref (z2), 0, MPFR_RNDN);
break;
case 8:
mpfr_set_inf (mpc_imagref (z2), +1);
break;
}
break;
case FC:
mpc_set_prec (z2, prec);
mpfr_set_prec (x1, prec);
mpfr_set_prec (x2, prec);
mpfr_set_prec (xxxx, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
}
break;
case CCU: case CUC:
mpc_set_prec (z2, 128);
do {
test_default_random (z2, 0, 64, 128, zero_probability);
} while (!mpfr_fits_ulong_p (mpc_realref (z2), MPFR_RNDN));
ul1 = mpfr_get_ui (mpc_realref(z2), MPFR_RNDN);
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
ul1 = 0;
break;
}
break;
case CUUC:
mpc_set_prec (z2, 128);
do {
test_default_random (z2, 0, 64, 128, zero_probability);
} while (!mpfr_fits_ulong_p (mpc_realref (z2), MPFR_RNDN)
||!mpfr_fits_ulong_p (mpc_imagref (z2), MPFR_RNDN));
ul1 = mpfr_get_ui (mpc_realref(z2), MPFR_RNDN);
ul2 = mpfr_get_ui (mpc_imagref(z2), MPFR_RNDN);
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
ul1 = 0;
break;
case 6:
ul2 = 0;
break;
}
break;
case CCS:
mpc_set_prec (z2, 128);
do {
test_default_random (z2, 0, 64, 128, zero_probability);
} while (!mpfr_fits_slong_p (mpc_realref (z2), MPFR_RNDN));
lo = mpfr_get_si (mpc_realref(z2), MPFR_RNDN);
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
lo = 0;
break;
}
break;
case CCI:
mpc_set_prec (z2, 128);
do {
test_default_random (z2, 0, 64, 128, zero_probability);
} while (!mpfr_fits_slong_p (mpc_realref (z2), MPFR_RNDN));
i = (int)mpfr_get_si (mpc_realref(z2), MPFR_RNDN);
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
i = 0;
break;
}
break;
case CCF: case CFC:
mpfr_set_prec (x1, prec);
mpfr_set (x1, mpc_realref (z1), MPFR_RNDN);
test_default_random (z1, exp_min, exp_max, 128, zero_probability);
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
case 5:
mpfr_set_ui (x1, 0, MPFR_RNDN);
break;
case 6:
mpfr_set_inf (x1, +1);
break;
}
break;
case CC_C:
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (z4, prec);
mpc_set_prec (z5, prec);
mpc_set_prec (zzzz, 4*prec);
mpc_set_prec (zzzz2, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
}
break;
case CC:
default:
mpc_set_prec (z2, prec);
mpc_set_prec (z3, prec);
mpc_set_prec (zzzz, 4*prec);
switch (special)
{
case 1:
mpfr_set_ui (mpc_realref (z1), 0, MPFR_RNDN);
break;
case 2:
mpfr_set_inf (mpc_realref (z1), +1);
break;
case 3:
mpfr_set_ui (mpc_imagref (z1), 0, MPFR_RNDN);
break;
case 4:
mpfr_set_inf (mpc_imagref (z1), -1);
break;
}
}
for (rnd_re = first_rnd_mode (); is_valid_rnd_mode (rnd_re); rnd_re = next_rnd_mode (rnd_re))
switch (function.type)
{
case C_CC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_c_cc (&function, z1, z2, z3, zzzz, z4,
MPC_RND (rnd_re, rnd_im));
reuse_c_cc (&function, z1, z2, z3, z4);
break;
case CCCC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cccc (&function, z1, z2, z3, z4, zzzz, z5,
MPC_RND (rnd_re, rnd_im));
reuse_cccc (&function, z1, z2, z3, z4, z5);
break;
case FC:
tgeneric_fc (&function, z1, x1, xxxx, x2, rnd_re);
reuse_fc (&function, z1, z2, x1);
break;
case CC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cc (&function, z1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_cc (&function, z1, z2, z3);
break;
case CC_C:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
for (rnd2_re = first_rnd_mode (); is_valid_rnd_mode (rnd2_re); rnd2_re = next_rnd_mode (rnd2_re))
for (rnd2_im = first_rnd_mode (); is_valid_rnd_mode (rnd2_im); rnd2_im = next_rnd_mode (rnd2_im))
tgeneric_cc_c (&function, z1, z2, z3, zzzz, zzzz2, z4, z5,
MPC_RND (rnd_re, rnd_im), MPC_RND (rnd2_re, rnd2_im));
reuse_cc_c (&function, z1, z2, z3, z4, z5);
break;
case CFC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cfc (&function, x1, z1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_cfc (&function, z1, x1, z2, z3);
break;
case CCF:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_ccf (&function, z1, x1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_ccf (&function, z1, x1, z2, z3);
break;
case CCU:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_ccu (&function, z1, ul1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_ccu (&function, z1, ul1, z2, z3);
break;
case CUC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cuc (&function, ul1, z1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_cuc (&function, ul1, z1, z2, z3);
break;
case CCS:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_ccs (&function, z1, lo, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_ccs (&function, z1, lo, z2, z3);
break;
case CCI:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cci (&function, z1, i, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_cci (&function, z1, i, z2, z3);
break;
case CUUC:
for (rnd_im = first_rnd_mode (); is_valid_rnd_mode (rnd_im); rnd_im = next_rnd_mode (rnd_im))
tgeneric_cuuc (&function, ul1, ul2, z1, z2, zzzz, z3,
MPC_RND (rnd_re, rnd_im));
reuse_cuuc (&function, ul1, ul2, z1, z2, z3);
break;
default:
printf ("tgeneric not yet implemented for this kind of"
"function\n");
exit (1);
}
}
mpc_clear (z1);
switch (function.type)
{
case C_CC:
mpc_clear (z2);
mpc_clear (z3);
mpc_clear (z4);
mpc_clear (zzzz);
break;
case CCCC:
mpc_clear (z2);
mpc_clear (z3);
mpc_clear (z4);
mpc_clear (z5);
mpc_clear (zzzz);
break;
case FC:
mpc_clear (z2);
mpfr_clear (x1);
mpfr_clear (x2);
mpfr_clear (xxxx);
break;
case CCF: case CFC:
mpfr_clear (x1);
mpc_clear (z2);
mpc_clear (z3);
mpc_clear (zzzz);
break;
case CC_C:
mpc_clear (z2);
mpc_clear (z3);
mpc_clear (z4);
mpc_clear (z5);
mpc_clear (zzzz);
mpc_clear (zzzz2);
break;
case CUUC:
case CCI: case CCS:
case CCU: case CUC:
case CC:
default:
mpc_clear (z2);
mpc_clear (z3);
mpc_clear (zzzz);
}
}
int
mpc_acos (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
int inex_re, inex_im, inex;
mpfr_prec_t p_re, p_im, p;
mpc_t z1;
mpfr_t pi_over_2;
mpfr_exp_t e1, e2;
mpfr_rnd_t rnd_im;
mpc_rnd_t rnd1;
inex_re = 0;
inex_im = 0;
/* 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_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? +1 : -1);
mpfr_set_nan (mpc_realref (rop));
}
else if (mpfr_zero_p (mpc_realref (op)))
{
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
mpfr_set_nan (mpc_imagref (rop));
}
else
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
return MPC_INEX (inex_re, 0);
}
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
if (mpfr_inf_p (mpc_realref (op)))
{
if (mpfr_inf_p (mpc_imagref (op)))
{
if (mpfr_sgn (mpc_realref (op)) > 0)
{
inex_re =
set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
}
else
{
/* the real part of the result is 3*pi/4
a = o(pi) error(a) < 1 ulp(a)
b = o(3*a) error(b) < 2 ulp(b)
c = b/4 exact
thus 1 bit is lost */
mpfr_t x;
mpfr_prec_t prec;
int ok;
mpfr_init (x);
prec = mpfr_get_prec (mpc_realref (rop));
p = prec;
do
{
p += mpc_ceil_log2 (p);
mpfr_set_prec (x, p);
mpfr_const_pi (x, GMP_RNDD);
mpfr_mul_ui (x, x, 3, GMP_RNDD);
ok =
mpfr_can_round (x, p - 1, GMP_RNDD, MPC_RND_RE (rnd),
prec+(MPC_RND_RE (rnd) == GMP_RNDN));
} while (ok == 0);
inex_re =
mpfr_div_2ui (mpc_realref (rop), x, 2, MPC_RND_RE (rnd));
mpfr_clear (x);
}
}
else
{
if (mpfr_sgn (mpc_realref (op)) > 0)
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
else
inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
}
}
else
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
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 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),
MPC_RND_IM (rnd));
else
inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
INV_RND (MPC_RND_IM (rnd)));
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
}
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,
MPC_RND_IM (rnd));
else
inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re,
INV_RND (MPC_RND_IM (rnd)));
inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
}
else
{
inex_re = mpfr_acos (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
}
if (!s_im)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
/* pure imaginary argument */
if (mpfr_zero_p (mpc_realref (op)))
{
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
inex_im = -mpfr_asinh (mpc_imagref (rop), mpc_imagref (op),
INV_RND (MPC_RND_IM (rnd)));
mpc_conj (rop,rop, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
/* regular complex argument: acos(z) = Pi/2 - asin(z) */
p_re = mpfr_get_prec (mpc_realref(rop));
p_im = mpfr_get_prec (mpc_imagref(rop));
p = p_re;
mpc_init3 (z1, p, p_im); /* we round directly the imaginary part to p_im,
with rounding mode opposite to rnd_im */
rnd_im = MPC_RND_IM(rnd);
/* the imaginary part of asin(z) has the same sign as Im(z), thus if
Im(z) > 0 and rnd_im = RNDZ, we want to round the Im(asin(z)) to -Inf
so that -Im(asin(z)) is rounded to zero */
if (rnd_im == GMP_RNDZ)
rnd_im = mpfr_sgn (mpc_imagref(op)) > 0 ? GMP_RNDD : GMP_RNDU;
else
rnd_im = rnd_im == GMP_RNDU ? GMP_RNDD
: rnd_im == GMP_RNDD ? GMP_RNDU
: rnd_im; /* both RNDZ and RNDA map to themselves for -asin(z) */
rnd1 = MPC_RND (GMP_RNDN, rnd_im);
mpfr_init2 (pi_over_2, p);
for (;;)
{
p += mpc_ceil_log2 (p) + 3;
mpfr_set_prec (mpc_realref(z1), p);
mpfr_set_prec (pi_over_2, p);
set_pi_over_2 (pi_over_2, +1, GMP_RNDN);
e1 = 1; /* Exp(pi_over_2) */
inex = mpc_asin (z1, op, rnd1); /* asin(z) */
MPC_ASSERT (mpfr_sgn (mpc_imagref(z1)) * mpfr_sgn (mpc_imagref(op)) > 0);
inex_im = MPC_INEX_IM(inex); /* inex_im is in {-1, 0, 1} */
e2 = mpfr_get_exp (mpc_realref(z1));
mpfr_sub (mpc_realref(z1), pi_over_2, mpc_realref(z1), GMP_RNDN);
if (!mpfr_zero_p (mpc_realref(z1)))
{
/* the error on x=Re(z1) is bounded by 1/2 ulp(x) + 2^(e1-p-1) +
2^(e2-p-1) */
e1 = e1 >= e2 ? e1 + 1 : e2 + 1;
/* the error on x is bounded by 1/2 ulp(x) + 2^(e1-p-1) */
e1 -= mpfr_get_exp (mpc_realref(z1));
/* the error on x is bounded by 1/2 ulp(x) [1 + 2^e1] */
e1 = e1 <= 0 ? 0 : e1;
/* the error on x is bounded by 2^e1 * ulp(x) */
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN); /* exact */
inex_im = -inex_im;
if (mpfr_can_round (mpc_realref(z1), p - e1, GMP_RNDN, GMP_RNDZ,
p_re + (MPC_RND_RE(rnd) == GMP_RNDN)))
break;
}
}
inex = mpc_set (rop, z1, rnd);
inex_re = MPC_INEX_RE(inex);
mpc_clear (z1);
mpfr_clear (pi_over_2);
return MPC_INEX(inex_re, inex_im);
}
