I've just discovered, to my embarrassment, that feeding negative exponents to `mpz_pow_ui`

doesn't work very well. ("The manual does say unsigned long, you know.") For the other `mpz_pow`

functions, the manual uses concepts I don't understand. For example "*base*^*exp* mod *mod*" in the following:

```
void mpz_powm (mpz_t rop, mpz_t base, mpz_t exp, mpz_t mod)
void mpz_powm_ui (mpz_t rop, mpz_t base, unsigned long int exp, mpz_t mod)
Set _rop_ to _base_^_exp_ mod _mod_.
Negative exp is supported if an inverse base-1 mod mod exists (see mpz_invert in Section 5.9 [Number Theoretic Functions], page 35). If an inverse doesnâ€™t exist then a divide by zero is raised.
```

In the following code, what do I have to change to make it able to handle negative exponents?

```
#define Z(x) mpz_t x; mpz_init( x );
BSTR __stdcall IBIGPOWER(BSTR p1, long p2 ) {
USES_CONVERSION;
Z(n1);
Z(res);
LPSTR sNum1 = W2A( p1 );
mpz_set_str( n1, sNum1, 10 );
mpz_pow_ui( res, n1, p2 );
char * buff = (char *) _alloca( mpz_sizeinbase( res, 10 ) + 2 );
mpz_get_str(buff, 10, res);
BSTR bResult = _com_util::ConvertStringToBSTR( buff );
return bResult;
}
```

## Best Solution

The

`mpz_t`

data type can only store integers, and 2^{-18}is not an integer. To calculate that, you'll have to use the floating-point type`mpf_t`

or the rational number type`mpq_t`

.