Re: rationals in guile?

[Valentin Kamyshenko <val@kamysh.materials.kiev.ua>]

>>>>> "Dirk" == Dirk Herrmann <dirk@ida.ing.tu-bs.de> writes:

Dirk> On 12 Nov 1998, Valentin Kamyshenko wrote:

Dirk> If I understand R5RS correctly, the tower has to be

Dirk>   integers -- rational -- real -- complex
I've just meant, that 'after rationals' can be 'complex rationals' and
'floats' (both real and complex). Of course, it was not the best
illustration :). Moreover, it was misleading, because I wanted to say,
that the main difficulty, in my opinion, is that each function
that works with numbers (like ATAN, for example), must recognize
also rational argument(s). Am I right?

Dirk> Although it is assumed that converting an exact integer to an
Dirk> inexact with
exact-> inexact will use a floating point representation, this is not
Dirk> necessarily the case: Bignums could simply have an added
Dirk> inexact-flag which is set accordingly by exact->inexact and
Dirk> inexact->exact.
Can you say few more words, in what situations it could be useful?


Dirk> Still, there are a couple of possibilities to represent the
Dirk> different numbers and the types they correspond to: (N: integer,
Dirk> Q: rational, R: real, C: complex)

Dirk> immediate (exact) --> NQRC bignum (exact) --> NQRC
Dirk> immediate1/immediate2 (exact) --> N if immediate2 == 1, QRC
Dirk> bignum/immediate2 (exact) --> N if immediate2 == 1, QRC
Dirk> immediage1/bignum2 (exact) --> N if bignum2 == 1, QRC
Dirk> bignum1/bignum2 (exact) --> N if bignum2 == 1, QRC float
Dirk> (inexact) --> N if (= x (round x)), QRC
Could not we exclude many possibilities at once, stating that we
use 'the most effective representation'?
I mean, each bignum should be transformed to immediate int. as soon  
as it becomes possible; rationals with denominator 1 -> integer
(bignum or immediate); in complex, if Re is inexact, then Im
is transformed to inexact, and vise-versa. Does not it lead to unique representation? 

By the way, do you know, how is it organized now? I suppose, that
	(let ((A (expt 2 100)))
	   (-  A (- A 10)))
returns 10 as immediate, does not it?

Dirk> Some time ago I took a look at numbers.c and numbers.h to figure
Dirk> out how to minimize the interface, maybe to make it easier to
Dirk> try out the gmp representation (GNU multiprecision library). gmp
Dirk> offers very effective implementations for bignums and rationals
Dirk> with a nice and well designed interface. The results have made
Dirk> their way onto Jim's TODO list.

Well, 1/2 of the work has been done :).

--
All the best,
	V.Kamyshenko.