static void
compare_mpc_pow (mpfr_prec_t pmax, int iter, unsigned long nbits)
/* copied from tpow_ui.c and replaced unsigned by signed */
{
mpfr_prec_t p;
mpc_t x, y, z, t;
long n;
int i, inex_pow, inex_pow_si;
mpc_rnd_t rnd;
mpc_init3 (y, sizeof (unsigned long) * CHAR_BIT, MPFR_PREC_MIN);
for (p = MPFR_PREC_MIN; p <= pmax; p++)
for (i = 0; i < iter; i++)
{
mpc_init2 (x, p);
mpc_init2 (z, p);
mpc_init2 (t, p);
mpc_urandom (x, rands);
n = (signed long) gmp_urandomb_ui (rands, nbits);
mpc_set_si (y, n, MPC_RNDNN);
for (rnd = 0; rnd < 16; rnd ++)
{
inex_pow = mpc_pow (z, x, y, rnd);
inex_pow_si = mpc_pow_si (t, x, n, rnd);
if (mpc_cmp (z, t) != 0)
{
printf ("mpc_pow and mpc_pow_si differ for x=");
mpc_out_str (stdout, 10, 0, x, MPC_RNDNN);
printf (" n=%li\n", n);
printf ("mpc_pow gives ");
mpc_out_str (stdout, 10, 0, z, MPC_RNDNN);
printf ("\nmpc_pow_si gives ");
mpc_out_str (stdout, 10, 0, t, MPC_RNDNN);
printf ("\n");
exit (1);
}
if (inex_pow != inex_pow_si)
{
printf ("mpc_pow and mpc_pow_si give different flags for x=");
mpc_out_str (stdout, 10, 0, x, MPC_RNDNN);
printf (" n=%li\n", n);
printf ("mpc_pow gives %d\n", inex_pow);
printf ("mpc_pow_si gives %d\n", inex_pow_si);
exit (1);
}
}
mpc_clear (x);
mpc_clear (z);
mpc_clear (t);
}
mpc_clear (y);
}
/* tests intermediate underflow; WONTFIX */
static int
test_underflow (void)
{
mpc_t z;
mpfr_exp_t emin = mpfr_get_emin ();
mpfr_set_emin (-10);
mpc_init2 (z, 21);
mpfr_set_si (mpc_realref(z), -1, GMP_RNDZ);
mpfr_set_ui_2exp (mpc_imagref(z), 1, 20, GMP_RNDZ);
mpfr_add_ui (mpc_imagref(z), mpc_imagref(z), 1, GMP_RNDZ);
mpfr_div_2exp (mpc_imagref(z), mpc_imagref(z), 20, GMP_RNDZ);
mpc_atan (z, z, MPC_RNDNN);
if (mpfr_cmp_si_2exp (mpc_realref(z), -1066635, 20) != 0 ||
mpfr_cmp_si_2exp (mpc_imagref(z), 1687619, 22))
{
printf ("Error in test_coverage\n");
printf ("expected (-1066635/2^20 1687619/2^22)\n");
printf ("got ");
mpc_out_str (stdout, 10, 20, z, MPC_RNDNN);
printf ("\n");
exit (1);
}
mpc_clear (z);
mpfr_set_emin (emin);
}
static void
test_reuse (void)
{
mpc_t z;
mpfr_t y;
int inex;
mpfr_init2 (y, 2);
mpc_init2 (z, 2);
mpc_set_si_si (z, 0, -1, MPC_RNDNN);
mpfr_neg (mpc_realref (z), mpc_realref (z), MPFR_RNDN);
mpc_div_2ui (z, z, 4, MPC_RNDNN);
mpfr_set_ui (y, 512, MPFR_RNDN);
inex = mpc_pow_fr (z, z, y, MPC_RNDNN);
if (MPC_INEX_RE(inex) != 0 || MPC_INEX_IM(inex) != 0 ||
mpfr_cmp_ui_2exp (mpc_realref(z), 1, -2048) != 0 ||
mpfr_cmp_ui (mpc_imagref(z), 0) != 0 || mpfr_signbit (mpc_imagref(z)) == 0)
{
printf ("Error in test_reuse, wrong ternary value or output\n");
printf ("inex=(%d %d)\n", MPC_INEX_RE(inex), MPC_INEX_IM(inex));
printf ("z="); mpc_out_str (stdout, 2, 0, z, MPC_RNDNN); printf ("\n");
exit (1);
}
mpfr_clear (y);
mpc_clear (z);
}
void print(Sequence seq, size_t N)
{
size_t n = 0;
while (n++ < N)
{
mpc_out_str(stdout, 10, 16, seq, RND); //cout << *seq++ << endl;
seq++;
putchar('\n');
}
}
int main() {
mpc_t z;
int inex;
mpc_init2(z, 128);
mpc_set_ui_ui(z, 0, 1, MPC_RNDNN);
inex = mpc_sqrt(z, z, MPC_RNDNN);
mpc_out_str(stdout, 10, 3, z, MPC_RNDNN);
printf("\n%i %i\n", MPC_INEX_RE(inex), MPC_INEX_IM(inex));
mpc_clear(z);
}
/* test out_str with stream=NULL */
static void
check_stdout (mpc_ptr read_number, mpc_ptr expected)
{
char tmp_file[] = "mpc_test";
int fd;
size_t sz;
fflush(stdout);
fd = dup(fileno(stdout));
if (freopen(tmp_file, "w", stdout) == NULL)
{
printf ("mpc_inp_str cannot redirect stdout\n");
exit (1);
}
mpc_out_str (NULL, 2, 0, expected, MPC_RNDNN);
fflush(stdout);
dup2(fd, fileno(stdout));
close(fd);
clearerr(stdout);
fflush(stdin);
fd = dup(fileno(stdin));
if (freopen(tmp_file, "r", stdin) == NULL)
{
printf ("mpc_inp_str cannot redirect stdout\n");
exit (1);
}
if (mpc_inp_str (read_number, NULL, &sz, 2, MPC_RNDNN) == -1)
{
printf ("mpc_inp_str cannot correctly re-read number "
"in file %s\n", tmp_file);
exit (1);
}
mpfr_clear_flags (); /* mpc_cmp set erange flag when an operand is
a NaN */
if (mpc_cmp (read_number, expected) != 0 || mpfr_erangeflag_p())
{
printf ("mpc_inp_str did not read the number which was written by "
"mpc_out_str\n");
OUT (read_number);
OUT (expected);
exit (1);
}
fflush(stdin);
dup2(fd, fileno(stdin));
close(fd);
clearerr(stdin);
}
static void
check_io_str (mpc_ptr read_number, mpc_ptr expected)
{
char tmp_file[] = "mpc_test";
FILE *fp;
size_t sz;
if (!(fp = fopen (tmp_file, "w")))
{
printf ("Error: Could not open file %s\n", tmp_file);
exit (1);
}
mpc_out_str (fp, 10, 0, expected, MPC_RNDNN);
fclose (fp);
if (!(fp = fopen (tmp_file, "r")))
{
printf ("Error: Could not open file %s\n", tmp_file);
exit (1);
};
if (mpc_inp_str (read_number, fp, &sz, 10, MPC_RNDNN) == -1)
{
printf ("Error: mpc_inp_str cannot correctly re-read number "
"in file %s\n", tmp_file);
exit (1);
}
fclose (fp);
/* mpc_cmp set erange flag when an operand is a NaN */
mpfr_clear_flags ();
if (mpc_cmp (read_number, expected) != 0 || mpfr_erangeflag_p())
{
printf ("Error: inp_str o out_str <> Id\n");
OUT (read_number);
OUT (expected);
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);
}
static void
cmpsqr (mpc_srcptr x, mpc_rnd_t rnd)
/* computes the square of x with the specific function or by simple */
/* multiplication using the rounding mode rnd and compares the results */
/* and return values. */
/* In our current test suite, the real and imaginary parts of x have */
/* the same precision, and we use this precision also for the result. */
/* Furthermore, we check whether computing the square in the same */
/* place yields the same result. */
/* We also compute the result with four times the precision and check */
/* whether the rounding is correct. Error reports in this part of the */
/* algorithm might still be wrong, though, since there are two */
/* consecutive roundings. */
{
mpc_t z, t, u;
int inexact_z, inexact_t;
mpc_init2 (z, MPC_MAX_PREC (x));
mpc_init2 (t, MPC_MAX_PREC (x));
mpc_init2 (u, 4 * MPC_MAX_PREC (x));
inexact_z = mpc_sqr (z, x, rnd);
inexact_t = mpc_mul (t, x, x, rnd);
if (mpc_cmp (z, t))
{
fprintf (stderr, "sqr and mul differ for rnd=(%s,%s) \nx=",
mpfr_print_rnd_mode(MPC_RND_RE(rnd)),
mpfr_print_rnd_mode(MPC_RND_IM(rnd)));
mpc_out_str (stderr, 2, 0, x, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr gives ");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nmpc_mul gives ");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
exit (1);
}
if (inexact_z != inexact_t)
{
fprintf (stderr, "The return values of sqr and mul differ for rnd=(%s,%s) \nx= ",
mpfr_print_rnd_mode(MPC_RND_RE(rnd)),
mpfr_print_rnd_mode(MPC_RND_IM(rnd)));
mpc_out_str (stderr, 2, 0, x, MPC_RNDNN);
fprintf (stderr, "\nx^2=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr gives %i", inexact_z);
fprintf (stderr, "\nmpc_mul gives %i", inexact_t);
fprintf (stderr, "\n");
exit (1);
}
mpc_set (t, x, MPC_RNDNN);
inexact_t = mpc_sqr (t, t, rnd);
if (mpc_cmp (z, t))
{
fprintf (stderr, "sqr and sqr in place differ for rnd=(%s,%s) \nx=",
mpfr_print_rnd_mode(MPC_RND_RE(rnd)),
mpfr_print_rnd_mode(MPC_RND_IM(rnd)));
mpc_out_str (stderr, 2, 0, x, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr gives ");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr in place gives ");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
exit (1);
}
if (inexact_z != inexact_t)
{
fprintf (stderr, "The return values of sqr and sqr in place differ for rnd=(%s,%s) \nx= ",
mpfr_print_rnd_mode(MPC_RND_RE(rnd)),
mpfr_print_rnd_mode(MPC_RND_IM(rnd)));
mpc_out_str (stderr, 2, 0, x, MPC_RNDNN);
fprintf (stderr, "\nx^2=");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr gives %i", inexact_z);
fprintf (stderr, "\nmpc_sqr in place gives %i", inexact_t);
fprintf (stderr, "\n");
exit (1);
}
mpc_sqr (u, x, rnd);
mpc_set (t, u, rnd);
if (mpc_cmp (z, t))
{
fprintf (stderr, "rounding in sqr might be incorrect for rnd=(%s,%s) \nx=",
mpfr_print_rnd_mode(MPC_RND_RE(rnd)),
mpfr_print_rnd_mode(MPC_RND_IM(rnd)));
mpc_out_str (stderr, 2, 0, x, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr gives ");
mpc_out_str (stderr, 2, 0, z, MPC_RNDNN);
fprintf (stderr, "\nmpc_sqr quadruple precision gives ");
mpc_out_str (stderr, 2, 0, u, MPC_RNDNN);
fprintf (stderr, "\nand is rounded to ");
mpc_out_str (stderr, 2, 0, t, MPC_RNDNN);
fprintf (stderr, "\n");
exit (1);
}
mpc_clear (z);
mpc_clear (t);
mpc_clear (u);
}
// See Cohen; my D is -D in his notation.
size_t pbc_hilbert(mpz_t **arr, int D) {
int a, b;
int t;
int B = (int)floor(sqrt((double) D / 3.0));
mpc_t alpha;
mpc_t j;
mpf_t sqrtD;
mpf_t f0;
darray_t Pz;
mpc_t z0, z1, z2;
double d = 1.0;
int h = 1;
int jcount = 1;
// Compute required precision.
b = D % 2;
for (;;) {
t = (b*b + D) / 4;
a = b;
if (a <= 1) {
a = 1;
goto step535_4;
}
step535_3:
if (!(t % a)) {
jcount++;
if ((a == b) || (a*a == t) || !b) {
d += 1.0 / ((double) a);
h++;
} else {
d += 2.0 / ((double) a);
h+=2;
}
}
step535_4:
a++;
if (a * a <= t) {
goto step535_3;
} else {
b += 2;
if (b > B) break;
}
}
//printf("modulus: %f\n", exp(3.14159265358979 * sqrt(D)) * d * 0.5);
d *= sqrt(D) * 3.14159265358979 / log(2);
precision_init((int)(d + 34));
pbc_info("class number %d, %d bit precision", h, (int) d + 34);
darray_init(Pz);
mpc_init(alpha);
mpc_init(j);
mpc_init(z0);
mpc_init(z1);
mpc_init(z2);
mpf_init(sqrtD);
mpf_init(f0);
mpf_sqrt_ui(sqrtD, D);
b = D % 2;
h = 0;
for (;;) {
t = (b*b + D) / 4;
if (b > 1) {
a = b;
} else {
a = 1;
}
step3:
if (t % a) {
step4:
a++;
if (a * a <= t) goto step3;
} else {
// a, b, t/a are coeffs of an appropriate primitive reduced positive
// definite form.
// Compute j((-b + sqrt{-D})/(2a)).
h++;
pbc_info("[%d/%d] a b c = %d %d %d", h, jcount, a, b, t/a);
mpf_set_ui(f0, 1);
mpf_div_ui(f0, f0, 2 * a);
mpf_mul(mpc_im(alpha), sqrtD, f0);
mpf_mul_ui(f0, f0, b);
mpf_neg(mpc_re(alpha), f0);
compute_j(j, alpha);
if (0) {
int i;
for (i=Pz->count - 1; i>=0; i--) {
printf("P %d = ", i);
mpc_out_str(stdout, 10, 4, Pz->item[i]);
printf("\n");
}
}
if (a == b || a * a == t || !b) {
// P *= X - j
int i, n;
mpc_ptr p0;
p0 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
mpc_init(p0);
mpc_neg(p0, j);
n = Pz->count;
if (n) {
mpc_set(z1, Pz->item[0]);
mpc_add(Pz->item[0], z1, p0);
for (i=1; i<n; i++) {
mpc_mul(z0, z1, p0);
mpc_set(z1, Pz->item[i]);
mpc_add(Pz->item[i], z1, z0);
}
mpc_mul(p0, p0, z1);
}
darray_append(Pz, p0);
} else {
// P *= X^2 - 2 Re(j) X + |j|^2
int i, n;
mpc_ptr p0, p1;
p0 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
p1 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
mpc_init(p0);
mpc_init(p1);
// p1 = - 2 Re(j)
mpf_mul_ui(f0, mpc_re(j), 2);
mpf_neg(f0, f0);
mpf_set(mpc_re(p1), f0);
// p0 = |j|^2
mpf_mul(f0, mpc_re(j), mpc_re(j));
mpf_mul(mpc_re(p0), mpc_im(j), mpc_im(j));
mpf_add(mpc_re(p0), mpc_re(p0), f0);
n = Pz->count;
if (!n) {
} else if (n == 1) {
mpc_set(z1, Pz->item[0]);
mpc_add(Pz->item[0], z1, p1);
mpc_mul(p1, z1, p1);
mpc_add(p1, p1, p0);
mpc_mul(p0, p0, z1);
} else {
mpc_set(z2, Pz->item[0]);
mpc_set(z1, Pz->item[1]);
mpc_add(Pz->item[0], z2, p1);
mpc_mul(z0, z2, p1);
mpc_add(Pz->item[1], z1, z0);
mpc_add(Pz->item[1], Pz->item[1], p0);
for (i=2; i<n; i++) {
mpc_mul(z0, z1, p1);
mpc_mul(alpha, z2, p0);
mpc_set(z2, z1);
mpc_set(z1, Pz->item[i]);
mpc_add(alpha, alpha, z0);
mpc_add(Pz->item[i], z1, alpha);
}
mpc_mul(z0, z2, p0);
mpc_mul(p1, p1, z1);
mpc_add(p1, p1, z0);
mpc_mul(p0, p0, z1);
}
darray_append(Pz, p1);
darray_append(Pz, p0);
}
goto step4;
}
b+=2;
if (b > B) break;
}
// Round polynomial and assign.
int k = 0;
{
*arr = pbc_malloc(sizeof(mpz_t) * (Pz->count + 1));
int i;
for (i=Pz->count - 1; i>=0; i--) {
if (mpf_sgn(mpc_re(Pz->item[i])) < 0) {
mpf_set_d(f0, -0.5);
} else {
mpf_set_d(f0, 0.5);
}
mpf_add(f0, f0, mpc_re(Pz->item[i]));
mpz_init((*arr)[k]);
mpz_set_f((*arr)[k], f0);
k++;
mpc_clear(Pz->item[i]);
pbc_free(Pz->item[i]);
}
mpz_init((*arr)[k]);
mpz_set_ui((*arr)[k], 1);
k++;
}
darray_clear(Pz);
mpc_clear(z0);
mpc_clear(z1);
mpc_clear(z2);
mpf_clear(f0);
mpf_clear(sqrtD);
mpc_clear(alpha);
mpc_clear(j);
precision_clear();
return k;
}
