void mpfr_taylor_nat_log(mpfr_t R, mpfr_t x, mpz_t n)
{
assert(mpz_cmp_ui(n, 0) > 0);
assert(mpfr_cmp_ui(x, 0) > 0);
mpfr_t a, t, tt;
mpfr_exp_t b;
mpz_t k;
unsigned int f = 1000, F = 1000;
mpfr_init(a);
mpfr_frexp(&b, a, x, MPFR_RNDN);
mpfr_ui_sub(a, 1, a, MPFR_RNDN);
mpfr_init_set(t, a, MPFR_RNDN);
mpfr_init(tt);
mpfr_set(R, a, MPFR_RNDN);
for(mpz_init_set_ui(k, 2); mpz_cmp(k, n) < 0; mpz_add_ui(k, k, 1))
{
mpfr_mul(t, t, a, MPFR_RNDN);
mpfr_div_z(tt, t, k, MPFR_RNDN);
mpfr_add(R, R, tt, MPFR_RNDN);
}
mpfr_mul_si(a, MPFR_NAT_LOG_2, b, MPFR_RNDN);
mpfr_sub(R, a, R, MPFR_RNDN);
}
static PyObject *
GMPy_Real_Frexp(PyObject *x, CTXT_Object *context)
{
PyObject *result;
MPFR_Object *value, *tempx;
mpfr_exp_t exp = 0;
CHECK_CONTEXT(context);
value = GMPy_MPFR_New(0, context);
tempx = GMPy_MPFR_From_Real(x, 1, context);
result = PyTuple_New(2);
if (!value || !result || !tempx) {
Py_XDECREF((PyObject*)tempx);
Py_XDECREF((PyObject*)value);
Py_XDECREF(result);
return NULL;
}
mpfr_clear_flags();
value->rc = mpfr_frexp(&exp, value->f, tempx->f, GET_MPFR_ROUND(context));
Py_DECREF((PyObject*)tempx);
_GMPy_MPFR_Cleanup(&value, context);
PyTuple_SET_ITEM(result, 0, PyIntOrLong_FromSsize_t((Py_ssize_t)exp));
PyTuple_SET_ITEM(result, 1, (PyObject*)value);
return result;
}
void mpfr_bisect_sqrt(mpfr_t R, mpfr_t N, mpfr_t T)
{
if(mpfr_cmp_ui(N, 0) < 0)
{
fprintf(stderr, "The value to square root must be non-negative\n");
exit(-1);
}
if(mpfr_cmp_ui(T, 0) < 0)
{
fprintf(stderr, "The tolerance must be non-negative\n");
exit(-1);
}
mpfr_exp_t e;
mpfr_t a, b, x, f, d, fab, n;
mpfr_init(n);
mpfr_frexp(&e, n, N, MPFR_RNDN);
if(e%2)
{
mpfr_div_ui(n, n, 2, MPFR_RNDN);
e += 1;
}
//Set a == 0
mpfr_init_set_ui(a, 0, MPFR_RNDN);
//Set b == 1
mpfr_init_set_ui(b, 1, MPFR_RNDN);
//Set x = (a + b)/2
mpfr_init(x);
mpfr_add(x, a, b, MPFR_RNDN);
mpfr_mul(x, x, MPFR_HALF, MPFR_RNDN);
//Set f = x^2 - N and fab = |f|
mpfr_init(f);
mpfr_init(fab);
mpfr_mul(f, x, x, MPFR_RNDN);
mpfr_sub(f, f, N, MPFR_RNDN);
mpfr_abs(fab, f, MPFR_RNDN);
//Set d = b - a
mpfr_init(d);
mpfr_sub(d, b, a, MPFR_RNDN);
while(mpfr_cmp(fab, T) > 0 && mpfr_cmp(d, T) > 0)
{
//Update the bounds, a and b
if(mpfr_cmp_ui(f, 0) < 0)
mpfr_set(a, x, MPFR_RNDN);
else
mpfr_set(b, x, MPFR_RNDN);
//Update x
mpfr_add(x, a, b, MPFR_RNDN);
mpfr_mul(x, x, MPFR_HALF, MPFR_RNDN);
//Update f and fab
mpfr_mul(f, x, x, MPFR_RNDN);
mpfr_sub(f, f, n, MPFR_RNDN);
mpfr_abs(fab, f, MPFR_RNDN);
}
printf("beep");
mpfr_mul_2si(R, x, e/2, MPFR_RNDN);
}
