How to calculate 2 ^ -18 using GMP?

Question

I just discovered, to my embarrassment, that suppressing negative metrics before mpz_pow_ui does not work very well. (“The manual does say unsigned, you know.”) For other mpz_pow functions, the manual uses concepts that I don’t understand. For example, "base ^ exp mod mod" is as follows:

 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 doesn't exist then a divide by zero is raised. 

In the following code, what do I need to change so that it can handle negative metrics?

 #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; } 

Answer 1

The mpz_t data mpz_t can only store integers, and 2 ^{-18 is} not an integer. To calculate this, you will have to use the floating point mpf_t or the rational number type mpq_t .

Answer 2

I will not cut the code for you, but I will inform you that:

2 -n = 1 / 2 n

So, you can simply pass a positive exponent, then divide 1 by this number (and select a non-integer type of type mpf_t - type mpz_t is an integral, so it cannot represent real numbers like 2 -18 ).

Answer 3

I don't know anything about GMP, but:

 2 ^ -18 

is equivalent to:

 1 / (2 ^ 18) 

So, why not write a function that processes negative metrics this way?

Answer 4

A negative exp is supported if inverse mod-1 mod mod exists (see mpz_invert in Section 5.9 [Number Theoretical Functions], page 35). If inverse does not exist, then division by zero is increased.

If you talk about this, it is connected with number theory. A division or, more precisely, the converse to multiplication, exists only under certain conditions. I don’t remember the rules exactly, but basically it means that the division operation will not work if the mod-1 mod mode does not exist.

Answer 5

What you need to do depends on what you want to do with the bits that will be lost in the operation. Since you are dealing with integers, escalating to a negative force implies division (well, reciprocity), but GMP offers several forms of division .