/** Pochhammer Symbol -- *rising* factorial x * (x+1) * ... (x+n-1)
* all initialization and cleanup is called in the caller
*/
int my_mpfr_poch (mpfr_t R, long n, mpfr_t X, mpfr_rnd_t RND)
{
int ans;
long i;
mpfr_t r, x;
mpfr_prec_t p_X = mpfr_get_prec(X);
mpfr_init2(x, p_X); mpfr_set(x, X, RND);
mpfr_init2(r, p_X);
if(n > 0) {
mpfr_set(r, X, RND);
for(i=1; i < n; i++) {
mpfr_add_si(x, x, 1L, RND); // x = X + i
mpfr_mul(r, r, x, RND); // r := r * x = X(X+1)..(X+i)
#ifdef DEBUG_Rmpfr
Rprintf("my_mpfr_poch(): X (= X_0 + %d)= ", i); R_PRT(x);
Rprintf("\n --> r ="); R_PRT(r); Rprintf("\n");
#endif
}
}
else // n = 0
mpfr_set_si(r, (long) 1, RND);
ans = mpfr_set(R, r, RND);
mpfr_clear (x);
mpfr_clear (r);
return ans;
}
static int synge_sum(synge_t to, synge_t number, mpfr_rnd_t round) {
/* round input */
mpfr_floor(number, number);
/* (x * (x + 1)) / 2 */
mpfr_set(to, number, round);
mpfr_add_si(number, number, 1, round);
mpfr_mul(to, to, number, round);
mpfr_div_si(to, to, 2, round);
return 0;
} /* synge_sum() */
static int synge_phi(synge_t num, mpfr_rnd_t round) {
/* get sqrt(5) */
synge_t root_five;
mpfr_init2(root_five, SYNGE_PRECISION);
mpfr_sqrt_ui(root_five, 5, round);
/* (1 + sqrt(5)) / 2 */
mpfr_add_si(num, root_five, 1, round);
mpfr_div_si(num, num, 2, round);
mpfr_clears(root_five, NULL);
return 0;
} /* synge_phi() */
int
main (int argc, char *argv[])
{
mpfr_t x, z;
int y;
int i;
tests_start_mpfr ();
mpfr_inits2 (53, x, z, (mpfr_ptr) 0);
for(i = 0 ; i < numberof (tab) ; i++)
{
mpfr_set_str (x, tab[i].op1, 16, MPFR_RNDN);
y = tab[i].op2;
mpfr_add_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_add, 16, MPFR_RNDN))
ERROR1("add_si", i, z, tab[i].res_add);
mpfr_sub_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_sub, 16, MPFR_RNDN))
ERROR1("sub_si", i, z, tab[i].res_sub);
mpfr_si_sub (z, y, x, MPFR_RNDZ);
mpfr_neg (z, z, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_sub, 16, MPFR_RNDN))
ERROR1("si_sub", i, z, tab[i].res_sub);
mpfr_mul_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_mul, 16, MPFR_RNDN))
ERROR1("mul_si", i, z, tab[i].res_mul);
mpfr_div_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_div, 16, MPFR_RNDN))
ERROR1("div_si", i, z, tab[i].res_div);
}
mpfr_set_str1 (x, "1");
mpfr_si_div (z, 1024, x, MPFR_RNDN);
if (mpfr_cmp_str1 (z, "1024"))
ERROR1("si_div", i, z, "1024");
mpfr_si_div (z, -1024, x, MPFR_RNDN);
if (mpfr_cmp_str1 (z, "-1024"))
ERROR1("si_div", i, z, "-1024");
mpfr_clears (x, z, (mpfr_ptr) 0);
check_invert ();
test_generic_add_si (2, 200, 17);
test_generic_sub_si (2, 200, 17);
test_generic_mul_si (2, 200, 17);
test_generic_div_si (2, 200, 17);
tests_end_mpfr ();
return 0;
}
static void
check_set_sj (void)
{
mpfr_t x;
int inex;
mpfr_init2 (x, sizeof(intmax_t)*CHAR_BIT-1);
inex = mpfr_set_sj (x, -MPFR_INTMAX_MAX, MPFR_RNDN);
inex |= mpfr_add_si (x, x, -1, MPFR_RNDN);
if (inex || mpfr_sgn (x) >=0 || !mpfr_powerof2_raw (x)
|| MPFR_EXP (x) != (sizeof(intmax_t)*CHAR_BIT) )
ERROR("set_sj (-INTMAX_MAX)");
inex = mpfr_set_sj (x, 1742, MPFR_RNDN);
if (inex || mpfr_cmp_ui (x, 1742))
ERROR ("set_sj (1742)");
mpfr_clear (x);
}
static PyObject *
GMPy_Real_Add(PyObject *x, PyObject *y, CTXT_Object *context)
{
MPFR_Object *result;
CHECK_CONTEXT(context);
if (!(result = GMPy_MPFR_New(0, context)))
return NULL;
if (MPFR_Check(x) && MPFR_Check(y)) {
mpfr_clear_flags();
result->rc = mpfr_add(result->f, MPFR(x), MPFR(y), GET_MPFR_ROUND(context));
goto done;
}
if (MPFR_Check(x)) {
if (PyIntOrLong_Check(y)) {
mpz_t tempz;
long temp;
int error;
temp = GMPy_Integer_AsLongAndError(y, &error);
if (error) {
mpz_inoc(tempz);
mpz_set_PyIntOrLong(tempz, y);
mpfr_clear_flags();
result->rc = mpfr_add_z(result->f, MPFR(x), tempz, GET_MPFR_ROUND(context));
mpz_cloc(tempz);
goto done;
}
else {
mpfr_clear_flags();
result->rc = mpfr_add_si(result->f, MPFR(x), temp, GET_MPFR_ROUND(context));
goto done;
}
}
if (CHECK_MPZANY(y)) {
mpfr_clear_flags();
result->rc = mpfr_add_z(result->f, MPFR(x), MPZ(y), GET_MPFR_ROUND(context));
goto done;
}
if (IS_RATIONAL(y)) {
MPQ_Object *tempy;
if (!(tempy = GMPy_MPQ_From_Number(y, context))) {
Py_DECREF((PyObject*)result);
return NULL;
}
mpfr_clear_flags();
result->rc = mpfr_add_q(result->f, MPFR(x), tempy->q, GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempy);
goto done;
}
if (PyFloat_Check(y)) {
mpfr_clear_flags();
result->rc = mpfr_add_d(result->f, MPFR(x), PyFloat_AS_DOUBLE(y), GET_MPFR_ROUND(context));
goto done;
}
}
if (MPFR_Check(y)) {
if (PyIntOrLong_Check(x)) {
mpz_t tempz;
long temp;
int error;
temp = GMPy_Integer_AsLongAndError(x, &error);
if (error) {
mpz_inoc(tempz);
mpz_set_PyIntOrLong(tempz, x);
mpfr_clear_flags();
result->rc = mpfr_add_z(result->f, MPFR(y), tempz, GET_MPFR_ROUND(context));
mpz_cloc(tempz);
goto done;
}
else {
mpfr_clear_flags();
result->rc = mpfr_add_si(result->f, MPFR(y), temp, GET_MPFR_ROUND(context));
goto done;
}
}
if (CHECK_MPZANY(x)) {
mpfr_clear_flags();
result->rc = mpfr_add_z(result->f, MPFR(y), MPZ(x), GET_MPFR_ROUND(context));
goto done;
}
if (IS_RATIONAL(x)) {
MPQ_Object *tempx;
if (!(tempx = GMPy_MPQ_From_Number(x, context))) {
Py_DECREF((PyObject*)result);
return NULL;
}
mpfr_clear_flags();
result->rc = mpfr_add_q(result->f, MPFR(y), tempx->q, GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempx);
goto done;
}
if (PyFloat_Check(x)) {
mpfr_clear_flags();
result->rc = mpfr_add_d(result->f, MPFR(y), PyFloat_AS_DOUBLE(x), GET_MPFR_ROUND(context));
goto done;
}
}
if (IS_REAL(x) && IS_REAL(y)) {
MPFR_Object *tempx, *tempy;
tempx = GMPy_MPFR_From_Real(x, 1, context);
tempy = GMPy_MPFR_From_Real(y, 1, context);
if (!tempx || !tempy) {
Py_XDECREF((PyObject*)tempx);
Py_XDECREF((PyObject*)tempy);
Py_DECREF((PyObject*)result);
return NULL;
}
mpfr_clear_flags();
result->rc = mpfr_add(result->f, MPFR(tempx), MPFR(tempy), GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempx);
Py_DECREF((PyObject*)tempy);
goto done;
}
Py_DECREF((PyObject*)result);
Py_RETURN_NOTIMPLEMENTED;
done:
GMPY_MPFR_CLEANUP(result, context, "addition");
return (PyObject*)result;
}
int fmpq_poly_oz_sqrt_approx_pade(fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, const int p, const mpfr_prec_t prec, const mpfr_prec_t bound, oz_flag_t flags, const fmpq_poly_t init) {
fmpq_poly_t y; fmpq_poly_init(y);
fmpq_poly_t y_next; fmpq_poly_init(y_next);
fmpq_poly_t z; fmpq_poly_init(z);
fmpq_poly_t z_next; fmpq_poly_init(z_next);
mpfr_t norm; mpfr_init2(norm, prec);
mpfr_t prev_norm; mpfr_init2(prev_norm, prec);
mpfr_t log_f; mpfr_init2(log_f, prec);
if (init) {
// z = y/x
fmpq_poly_set(y, init);
_fmpq_poly_oz_invert_approx(z, f, n, prec);
fmpq_poly_oz_mul(z, z, y, n);
} else {
fmpq_poly_set(y, f);
fmpq_poly_set_coeff_si(z, 0, 1);
}
fmpq_t *xi = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_t *a2 = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_t *c = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_poly_t *t_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t));
fmpq_poly_t *s_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t));
mpfr_t pi; mpfr_init2(pi, 4*prec);
mpfr_const_pi(pi, MPFR_RNDN);
#pragma omp parallel for
for(int i=0; i<p; i++) {
mpfr_t xi_r; mpfr_init2(xi_r, 4*prec);
mpfr_t a2_r; mpfr_init2(a2_r, 4*prec);
/* ζ_i = 1/2 * (1 + cos( (2·i -1)·π/(2·p) )) */
mpfr_set_si(xi_r, 2*i+1, MPFR_RNDN);
mpfr_mul(xi_r, xi_r, pi, MPFR_RNDN);
mpfr_div_si(xi_r, xi_r, 2*p, MPFR_RNDN);
mpfr_cos(xi_r, xi_r, MPFR_RNDN);
mpfr_add_si(xi_r, xi_r, 1, MPFR_RNDN);
mpfr_div_si(xi_r, xi_r, 2, MPFR_RNDN);
/* α_i^2 = 1/ζ_i -1 */
mpfr_set_si(a2_r, 1, MPFR_RNDN);
mpfr_div(a2_r, a2_r, xi_r, MPFR_RNDN);
mpfr_sub_si(a2_r, a2_r, 1, MPFR_RNDN);
fmpq_init(xi[i]);
fmpq_init(a2[i]);
fmpq_set_mpfr(xi[i], xi_r, MPFR_RNDN);
fmpq_set_mpfr(a2[i], a2_r, MPFR_RNDN);
fmpq_init(c[i]);
fmpq_poly_init(t_[i]);
fmpq_poly_init(s_[i]);
mpfr_clear(xi_r);
mpfr_clear(a2_r);
}
mpfr_clear(pi);
uint64_t t = oz_walltime(0);
int r = 0;
int cont = 1;
for(long k=0; cont; k++) {
if (k == 0 || mpfr_cmp_ui(prev_norm, 1) > 0)
_fmpq_poly_oz_sqrt_approx_scale(y, z, n, prec);
/* T = sum([1/xi[i] * ~(Z*Y + a2[i]) for i in range(p)]) */
#pragma omp parallel for
for(int i=0; i<p; i++) {
fmpq_poly_oz_mul(t_[i], z, y, n);
fmpq_poly_get_coeff_fmpq(c[i], t_[i], 0);
fmpq_add(c[i], c[i], a2[i]);
fmpq_poly_set_coeff_fmpq(t_[i], 0, c[i]);
fmpq_poly_scalar_mul_fmpq(t_[i], t_[i], xi[i]);
_fmpq_poly_oz_invert_approx(s_[i], t_[i], n, prec);
}
for(int i=1; i<p; i++)
fmpq_poly_add(s_[0], s_[0], s_[i]);
#pragma omp parallel sections
{
#pragma omp section
{
fmpq_poly_oz_mul(y_next, y, s_[0], n);
fmpq_poly_scalar_div_si(y_next, y_next, p);
fmpq_poly_set(y, y_next);
}
#pragma omp section
{
fmpq_poly_oz_mul(z_next, z, s_[0], n);
fmpq_poly_scalar_div_si(z_next, z_next, p);
fmpq_poly_set(z, z_next);
}
}
cont = !_fmpq_poly_oz_sqrt_approx_break(norm, y, f, n, bound, prec);
if(flags & OZ_VERBOSE) {
mpfr_log2(log_f, norm, MPFR_RNDN);
mpfr_fprintf(stderr, "Computing sqrt(Σ):: k: %4d, Δ=|sqrt(Σ)^2-Σ|: %7.2Rf", k, log_f);
fprintf(stderr, " <? %4ld, ", -bound);
fprintf(stderr, "t: %8.2fs\n", oz_seconds(oz_walltime(t)));
fflush(0);
}
if (cont) {
if (k>0 && mpfr_cmp_ui_2exp(norm, 1, bound) >= 0) {
/* something went really wrong */
r = -1;
break;
}
if (k>0 && mpfr_cmp(norm, prev_norm) >= 0) {
/* we don't converge any more */
r = 1;
break;
}
mpfr_set(prev_norm, norm, MPFR_RNDN);
}
}
for(int i=0; i<p; i++) {
fmpq_clear(xi[i]);
fmpq_clear(a2[i]);
fmpq_clear(c[i]);
fmpq_poly_clear(t_[i]);
fmpq_poly_clear(s_[i]);
}
free(xi);
free(a2);
free(c);
free(t_);
free(s_);
mpfr_clear(log_f);
fmpq_poly_set(f_sqrt, y);
mpfr_clear(norm);
mpfr_clear(prev_norm);
fmpq_poly_clear(y_next);
fmpq_poly_clear(y);
fmpq_poly_clear(z_next);
fmpq_poly_clear(z);
return r;
}
static PyObject *
GMPy_Real_Add(PyObject *x, PyObject *y, CTXT_Object *context)
{
MPFR_Object *result = NULL;
CHECK_CONTEXT(context);
if (!(result = GMPy_MPFR_New(0, context))) {
/* LCOV_EXCL_START */
return NULL;
/* LCOV_EXCL_STOP */
}
if (MPFR_Check(x) && MPFR_Check(y)) {
mpfr_clear_flags();
SET_MPFR_MPFR_WAS_NAN(context, x, y);
result->rc = mpfr_add(result->f, MPFR(x), MPFR(y), GET_MPFR_ROUND(context));
goto done;
}
if (MPFR_Check(x)) {
if (PyIntOrLong_Check(y)) {
int error;
long temp = GMPy_Integer_AsLongAndError(y, &error);
if (!error) {
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, x);
result->rc = mpfr_add_si(result->f, MPFR(x), temp, GET_MPFR_ROUND(context));
goto done;
}
else {
mpz_set_PyIntOrLong(global.tempz, y);
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, x);
result->rc = mpfr_add_z(result->f, MPFR(x), global.tempz, GET_MPFR_ROUND(context));
goto done;
}
}
if (CHECK_MPZANY(y)) {
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, x);
result->rc = mpfr_add_z(result->f, MPFR(x), MPZ(y), GET_MPFR_ROUND(context));
goto done;
}
if (IS_RATIONAL(y)) {
MPQ_Object *tempy = NULL;
if (!(tempy = GMPy_MPQ_From_Number(y, context))) {
/* LCOV_EXCL_START */
Py_DECREF((PyObject*)result);
return NULL;
/* LCOV_EXCL_STOP */
}
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, x);
result->rc = mpfr_add_q(result->f, MPFR(x), tempy->q, GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempy);
goto done;
}
if (PyFloat_Check(y)) {
mpfr_clear_flags();
SET_MPFR_FLOAT_WAS_NAN(context, x, y);
result->rc = mpfr_add_d(result->f, MPFR(x), PyFloat_AS_DOUBLE(y), GET_MPFR_ROUND(context));
goto done;
}
}
if (MPFR_Check(y)) {
if (PyIntOrLong_Check(x)) {
int error;
long temp = GMPy_Integer_AsLongAndError(x, &error);
if (!error) {
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, y);
result->rc = mpfr_add_si(result->f, MPFR(y), temp, GET_MPFR_ROUND(context));
goto done;
}
else {
mpz_set_PyIntOrLong(global.tempz, x);
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, y);
result->rc = mpfr_add_z(result->f, MPFR(y), global.tempz, GET_MPFR_ROUND(context));
goto done;
}
}
if (CHECK_MPZANY(x)) {
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, y);
result->rc = mpfr_add_z(result->f, MPFR(y), MPZ(x), GET_MPFR_ROUND(context));
goto done;
}
if (IS_RATIONAL(x)) {
MPQ_Object *tempx = NULL;
if (!(tempx = GMPy_MPQ_From_Number(x, context))) {
/* LCOV_EXCL_START */
Py_DECREF((PyObject*)result);
return NULL;
/* LCOV_EXCL_STOP */
}
mpfr_clear_flags();
SET_MPFR_WAS_NAN(context, y);
result->rc = mpfr_add_q(result->f, MPFR(y), tempx->q, GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempx);
goto done;
}
if (PyFloat_Check(x)) {
mpfr_clear_flags();
SET_MPFR_FLOAT_WAS_NAN(context, y, x);
result->rc = mpfr_add_d(result->f, MPFR(y), PyFloat_AS_DOUBLE(x), GET_MPFR_ROUND(context));
goto done;
}
}
if (IS_REAL(x) && IS_REAL(y)) {
MPFR_Object *tempx = NULL, *tempy = NULL;
if (!(tempx = GMPy_MPFR_From_Real(x, 1, context)) ||
!(tempy = GMPy_MPFR_From_Real(y, 1, context))) {
/* LCOV_EXCL_START */
Py_XDECREF((PyObject*)tempx);
Py_XDECREF((PyObject*)tempy);
Py_DECREF((PyObject*)result);
return NULL;
/* LCOV_EXCL_STOP */
}
mpfr_clear_flags();
SET_MPFR_MPFR_WAS_NAN(context, tempx, tempy);
result->rc = mpfr_add(result->f, MPFR(tempx), MPFR(tempy), GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempx);
Py_DECREF((PyObject*)tempy);
goto done;
}
/* LCOV_EXCL_START */
Py_DECREF((PyObject*)result);
SYSTEM_ERROR("Internal error in GMPy_Real_Add().");
return NULL;
/* LCOV_EXCL_STOP */
done:
_GMPy_MPFR_Cleanup(&result, context);
return (PyObject*)result;
}
