Re: Multiplying fixed-point by long integer

[Adam Beneschan <adam@irvine.com>]

On Thursday, October 4, 2012 9:25:33 PM UTC-7, (unknown) wrote:
> Create a 2nd fixed point type big enough to hold your long integer, and
> multiply by that?

You know, I thought of that last night, after I had posted it.  But that raises another problem.  I assume you're thinking of something like this:

  type Long_Fixed is delta 1.0 range Long_Integer'First .. Long_Integer'Last;

  F1, F2 : Some_Other_Fixed_Type;

  F2 := F1 * Long_Fixed(N);

except that the Long_Fixed declaration isn't legal, because the range bounds have to be of a real type.  But how do you get the bounds to be real?

  type Long_Fixed is delta 1.0 range Long_Float(Long_Integer'First) ..
                                     Long_Float(Long_Integer'Last);

This isn't right, because it's possible that the largest floating-point type supported by the implementation has a mantissa size smaller than the number of bits in a Long_Integer (or, if you like, Long_Long_Integer or Interfaces.Integer_64), which means that the result won't be exactly right.

This seems like a flaw in the language, that it supports a "universal real" type  for static values that can be indefinitely precise, but there's no way to convert a static integer value to a universal real without going through a predefined floating-point type that may be less accurate than the integer.

Of course, the problem at hand could be solved with something like

  type Long_Fixed is delta 1.0 range -2.0**(Long_Integer'Size - 1) ..
                                     2.0**(Long_Integer'Size - 1) - 1.0;

Seems a bit hokey that you have to go through this, though.

                         -- Adam