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From: carlton@husc10.harvard.edu (david carlton)
Newsgroups: comp.lang.scheme
Subject: Re: Logical operations on integers.
Message-ID: <CARLTON.91Apr12234636@husc10.harvard.edu>
Date: 13 Apr 91 03:46:36 GMT
References: <CARLTON.91Apr8201836@husc10.harvard.edu>
	<9104090602.AA06996@cymbal.reasoning.com.>
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In-reply-to: gyro@cymbal.reasoning.COM's message of 9 Apr 91 06:02:43 GMT

In article <9104090602.AA06996@cymbal.reasoning.com.> gyro@cymbal.reasoning.COM (Scott Layson Burson) writes:
 [ I write, talking about logical operations on integers: ]
      Do these really make sense when operating on bignums?  And and or I
      can buy, at least when operating on non-negative bignums, but not not.
      Of course, at least one of the standards mentions fixnums - maybe it
      could encourage implementors to stick them in if the implementation
      supports fixnums.  I think that it would be a bit ugly, though.

   Of course they make sense on bignums.  One way to think about it is that
   the sign bit of an integer, whether fixnum or bignum, is repeated
   infinitely to the left.  Another way is simply to define (assuming two's
   complement)

     (lognot x) = (- -1 x)

   In one's complement, of course, LOGNOT and unary negation are the same
   operation.

All right - I misspoke.  None of them really make sense, and and or no
more than not.  All three of them are implementation-dependent -
operations which are defined on the bits of integers depend on the
representation of those bits in the computer, and since bignums have
(in my opinion, at least) no one representation that is inherently
superior to all others, I don't think that it really makes sense to
define bitwise operations on them.  Yes, you can define them in the
manner that you suggested, but why define them at all?  Bitwise
operations are (in my experience) used mainly as a manner for packing
data, and are only particularly useful if they are efficient.  But in
Scheme, it is a good deal less likely that these will be efficient for
bignums, and since there are no guarantees about the size of numbers a
given implementation will support, you can't even use them to portably
pack data.  (And, for that matter, packing data is something fairly
foreign to the Scheme mindset.)  And the only uses that I can think of
them that make much sense when you are thinking of numbers as
mathematical abstractions, rather than a sequence of bits, are special
cases of quotient and remainder.  I really don't think that the
standard should define bitwise operations for bignums (and hence for
integers, since fixnums haven't really made it into the standard yet)
any more than it should for floating-point numbers (which at least
have a representation that is encouraged, though not required, by the
standard.)

david carlton
carlton@husc9.harvard.edu

	Very little immediate tradition lies behind _Le Sacre du
	printemps_, however, and no theory.  I had only my ear to help
	me; I heard and I wrote what I heard.  I am the vessel through
	which _Le Sacre_ passed.
                                        - Igor Stravinsky