static void
check_different_precisions(void)
{
/* check reuse when real and imaginary part have different precisions. */
mpc_t z, expected, got;
int res;
mpc_init2(z, 128);
mpc_init2(expected, 128);
mpc_init2(got, 128);
/* change precision of one part */
mpfr_set_prec (mpc_imagref (z), 32);
mpfr_set_prec (mpc_imagref (expected), 32);
mpfr_set_prec (mpc_imagref (got), 32);
mpfr_set_str (mpc_realref (z), "0x100000000fp-32", 16, GMP_RNDN);
mpfr_set_str (mpc_imagref (z), "-1", 2, GMP_RNDN);
mpfr_set_str (mpc_realref (expected), "+1", 2, GMP_RNDN);
mpfr_set_str (mpc_imagref (expected), "0x100000000fp-32", 16, GMP_RNDN);
mpc_set (got, z, MPC_RNDNN);
res = mpc_mul_i (got, got, +1, MPC_RNDNN);
if (MPC_INEX_RE(res) != 0 || MPC_INEX_IM(res) >=0)
{
printf("Wrong inexact flag for mpc_mul_i(z, z, n)\n"
" got (re=%2d, im=%2d)\nexpected (re= 0, im=-1)\n",
MPC_INEX_RE(res), MPC_INEX_IM(res));
exit(1);
}
if (mpc_cmp(got, expected) != 0)
{
printf ("Error for mpc_mul_i(z, z, n) for\n");
MPC_OUT (z);
printf ("n=+1\n");
MPC_OUT (expected);
MPC_OUT (got);
exit (1);
}
mpc_neg (expected, expected, MPC_RNDNN);
mpc_set (got, z, MPC_RNDNN);
mpc_mul_i (got, got, -1, MPC_RNDNN);
if (mpc_cmp(got, expected) != 0)
{
printf ("Error for mpc_mul_i(z, z, n) for\n");
MPC_OUT (z);
printf ("n=-1\n");
MPC_OUT (expected);
MPC_OUT (got);
exit (1);
}
mpc_clear (z);
mpc_clear (expected);
mpc_clear (got);
}
static PyObject *
_GMPy_MPC_Minus(PyObject *x, CTXT_Object *context)
{
MPC_Object *result;
CHECK_CONTEXT(context);
if (!(result = GMPy_MPC_New(0, 0, context))) {
return NULL;
}
result->rc = mpc_neg(result->c, MPC(x), GET_MPC_ROUND(context));
GMPY_MPC_CLEANUP(result, context, "minus()");
return (PyObject*)result;
}
static void
pure_real_argument (void)
{
/* cosh(x -i*0) = cosh(x) +i*0 if x<0 */
/* cosh(x -i*0) = cosh(x) -i*0 if x>0 */
/* cosh(x +i*0) = cosh(x) -i*0 if x<0 */
/* cosh(x -i*0) = cosh(x) +i*0 if x>0 */
mpc_t u;
mpc_t z;
mpc_t cosh_z;
mpc_init2 (z, 2);
mpc_init2 (u, 100);
mpc_init2 (cosh_z, 100);
/* cosh(1 +i*0) = cosh(1) +i*0 */
mpc_set_ui_ui (z, 1, 0, MPC_RNDNN);
mpfr_cosh (MPC_RE (u), MPC_RE (z), GMP_RNDN);
mpfr_set_ui (MPC_IM (u), 0, GMP_RNDN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(1 -i*0) = cosh(1) -i*0 */
mpc_conj (z, z, MPC_RNDNN);
mpc_conj (u, u, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || !mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(-1 +i*0) = cosh(1) -i*0 */
mpc_neg (z, z, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || !mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(-1 -i*0) = cosh(1) +i*0 */
mpc_conj (z, z, MPC_RNDNN);
mpc_conj (u, u, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
mpc_clear (cosh_z);
mpc_clear (z);
mpc_clear (u);
}
static void
pure_imaginary_argument (void)
{
/* cosh(+0 +i*y) = cos y +i*0*sin y */
/* cosh(-0 +i*y) = cos y -i*0*sin y */
mpc_t u;
mpc_t z;
mpc_t cosh_z;
mpc_init2 (z, 2);
mpc_init2 (u, 100);
mpc_init2 (cosh_z, 100);
/* cosh(+0 +i) = cos(1) + i*0 */
mpc_set_ui_ui (z, 0, 1, MPC_RNDNN);
mpfr_cos (MPC_RE (u), MPC_IM (z), GMP_RNDN);
mpfr_set_ui (MPC_IM (u), 0, GMP_RNDN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(+0 -i) = cos(1) - i*0 */
mpc_conj (z, z, MPC_RNDNN);
mpc_conj (u, u, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || !mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(-0 +i) = cos(1) - i*0 */
mpc_neg (z, z, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || !mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
/* cosh(-0 -i) = cos(1) + i*0 */
mpc_conj (z, z, MPC_RNDNN);
mpc_conj (u, u, MPC_RNDNN);
mpc_cosh (cosh_z, z, MPC_RNDNN);
if (mpc_cmp (cosh_z, u) != 0 || mpfr_signbit (MPC_IM (cosh_z)))
TEST_FAILED ("mpc_cosh", z, cosh_z, u, MPC_RNDNN);
mpc_clear (cosh_z);
mpc_clear (z);
mpc_clear (u);
}
SEXP R_mpc_neg(SEXP e1) {
/* Garbage collector will be confused if we just call
* mpc_neg(*z, *z, ...) */
mpc_t *z = (mpc_t *)malloc(sizeof(mpc_t));
if (Rf_inherits(e1, "mpc")) {
mpc_t *z1 = (mpc_t *)R_ExternalPtrAddr(e1);
mpc_init2(*z, mpc_get_prec(*z1));
mpc_neg(*z, *z1, Rmpc_get_rounding());
} else {
Rf_error("Invalid operands for mpc negation.");
}
SEXP retVal = PROTECT(R_MakeExternalPtr((void *)z,
Rf_install("mpc ptr"), R_NilValue));
Rf_setAttrib(retVal, R_ClassSymbol, Rf_mkString("mpc"));
R_RegisterCFinalizerEx(retVal, mpcFinalizer, TRUE);
UNPROTECT(1);
return retVal;
}
mpcomplex mpcomplex::neg() const{
mpc_t negativeValue;
mpc_init3( negativeValue , mpc_prec, default_rnd );
mpc_neg(negativeValue, mpc_val , default_rnd );
return mpcomplex( negativeValue );
}
// 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;
}
void Lib_Mpcr_Neg(MpcrPtr f, MpcrPtr g, long rnd)
{
mpc_neg( (mpc_ptr) f, (mpc_ptr) g, (mpc_rnd_t) rnd);
}
