Re: [Bug-apl] Useful range of decode function is limited.

[Frederick H. Pitts]

Hello Elias,

1) "MOST-NEGATIVE-FIXNUM" and "largest negative integer" are much closer
in connotation to each other than either is to "smallest (negative)
integer".  "smallest" and "largest" are generally used when comparing
the magnitudes (or absolute values) of numbers irrespective of the signs
of those numbers.  So I think we are in agreement the label needs to
change.

2) 2*63 does not produce the right answer but 2*62 does.  So GNU-APL is
capable of doing integer arithmetic well outside the 53-bit integer
range of double precision floating point.  Unfortunately, that
capability is not fully utilized.  It's disingenuous to claim GNU-APL
supports 64-bit integer arithmetic when primitive operations like ⊥
(decode) and ! (binomial) yield results of accuracy limited by the
53-bit integer range of floating point when they do not have to be.
There are ways to force the use of the use of the APL_Integer!  It's a
simple matter of programming.  If you are
interested I can supply you with defined functions that work around
the ! (binomial) accuracy limitation. (Jim Weigang presented the
functions in comp.lang.apl years ago). I wonder how much faster the
functions would be if they were implemented in C++.

Regards,

Fred

On Tue, 2014-08-05 at 11:34 +0800, Elias Mårtenson wrote:
> Mathematically, the term "small" is ambiguous. Perhaps that's why
> Common Lisp names its corresponding value MOST-NEGATIVE-FIXNUM.
> 
> 
> That said, in GNU APL, these numbers are somewhat bogus anyway. In
> particular, the actual maximum number that can be stored without loss
> of precision depends on the underlying data type of the value.
> 
> 
> For real numbers, this data type can be either APL_Integer in which
> the largest number is 9223372036854775808 (2^63), but if you try to
> create this number in GNU APL using the expression 2⋆63, you will get
> an APL_Float back, which has a smaller maximum precise value
> of 9007199254740992 (2^53).
> 
> 
> So, in summary. You can never rely on integral numbers being precise
> to more than 53 bits of precision unless there is a way to force the
> use of APL_Integer which I don't believe there is.
> 
> 
> It would be nice to have support for bignums in GNU APL. It wouldn't
> be overly difficult to implement I think. Perhaps I'll try that one
> day unless Jürgen is completely against the idea.
> 
> 
> Regards,
> Elias
> 
> 
> On 5 August 2014 09:37, Frederick H. Pitts <address@hidden>
> wrote:
>         Juergen,
>         
>                 Please consider the following:
>         
>               ( 62 ⍴ 2 ) ⊤ ⎕ ← 2 ⊥ 53 ⍴ 1
>         9007199254740991
>         0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
>         1 1 1 1 1
>         1 1 1 1
>               1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
>               ( 62 ⍴ 2 ) ⊤ ⎕ ← 2 ⊥ 54 ⍴ 1
>         18014398509481984
>         0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>         0 0 0 0 0
>         0 0 0 0
>               0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>         
>                 Between 53 bits and 54 bits, decode starts returning
>         an incorrect
>         result (the reported value is even when it should be odd).
>          Presumably
>         floating point numbers start creeping in at that point.
>                 Is it possible to tweak the decode code so that at
>         least 62 bits of a
>         64-bit integer are usable with encode and decode?  I'd really
>         like to
>         use 9 7-bit fields (63 bit total) to track powers of
>         dimensions in
>         unit-of-measure calculations but I'm confident that is asking
>         for too
>         much. I can cut the range of one of the dimensions in half.
>         
>                 BTW, the "smallest (negative) integer" label of the
>         ⎕SYL output would
>         read better as "largest negative integer".
>          ¯9200000000000000000 is not
>         small.
>         ¯1, 0, and 1 are small.
>         
>         Regards,
>         
>         Fred
>         Retired Chemical Engineer
>         
>         
> 
>