Re: guile & r5rs

[Jim Blandy <jimb@red-bean.com>]

>  > Guile could do better.  To compute B / C, where B and C are
>  > bignums, as a floating-point value with a mantissa at most p bits
>  > long, Guile should find the closest integer to (B * 2^p) / C ==
>  > (B/C) * 2^p, using only exact bignum arithmetic, and then use the
>  > IEEE 754 scalb function to simultaneously divide by 2^p and convert
>  > to double, without losing bits.
> 
> The integer you refer to is (quotient (* B (expt 2 mantissa_bits)) C)
> or this number + 1 (depending on whether the remainder is > or <
> C/2).

Right.

> But this fails when this number is > the largest double, which is when the
> result is within 2^p of max_double.

You mean, it fails when the result doesn't fit into a double?  That's
fine; this is only to be used when the remainder is non-zero, in which
case R5RS leaves us no choice (given that we don't have rationals, or
inexact bignums) but to use a double.  Maybe I'm missing something.


> This also fails when C is large relative to B.  In particular, if C >
> B*2^p, then the closest integer is zero, even though the quotient is
> easily representable in a double.

You're right.  I guess we need to multiply B by 2 until it is between
C*2^(p-1) and C*2^p, and then divide by the appropriate amount.

> Also, I can't find scalb on my system (linux) either in the header
> files or in the libs.  How does it differ from ldexp?

The only difference is that scalb's exponnent is a double too.  ldexp
should work fine.