calculating exp(-300)

[David T. Ashley]

> While the standard function, exp(), doesn't seem to exist for rational
> numbers, I see that an alternative form, mpq_div_2exp() does exist.  I
> feel like there should be some way to represent exp(-a) as y / 2^x, but
> with the constraint that x be an integer the best method of
> representation isn't immediately obvious to me.

Nathan,

Where you're trying to go has absolutely confused me.

You wrote:

<BEGIN>
like there should be some way to represent exp(-a) as y / 2^x
<END>

As best I can tell, you are wanting to use the GMP to approximate real
numbers as a 2-tuple, where one integer is the mantissa and the other is the
exponent used to exponentiate 2.

Every arbitrary-precision floating-point package does exactly that under the
hood, so why do it again.  The nature of fixed-point arithmetic is that the
radix point is between two bits somewhere, and that necessarily implies that
the number is expressible as y/2^x.

If you want to re-implement an arbitrary-precision floating-point package
using GMP ... it will only waste your time.

What did I miss?

Dave.