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Re: fix for expt bug
From: |
Andy Wingo |
Subject: |
Re: fix for expt bug |
Date: |
Sat, 20 Nov 2010 22:49:46 +0100 |
User-agent: |
Gnus/5.13 (Gnus v5.13) Emacs/23.2 (gnu/linux) |
Hi,
On Mon 08 Nov 2010 22:08, address@hidden (Ludovic Courtès) writes:
> Mark H Weaver <address@hidden> writes:
>
>> No, (integer? 3.0) returns #t, as it should, according to R5RS.
>> R5RS's description of "integer?" gives this precise example, and
>> guile's implementation agrees.
>
> Damn, I had never realized that, shame on me.
Bill Schottstaedt has a nice rant on
https://ccrma.stanford.edu/software/snd/snd/s7.html. I think all of his
examples are taken from Guile...
I can't find the right tone for this section; this is the 400-th
revision; I wish I were a better writer! I think the exact/inexact
distinction in Scheme is confused and useless, and leads to verbose
and buggy code. In some Schemes, "rational" means "could possibly be
expressed equally well as a ratio (floats are approximations)". In
s7 it's: "is actually expressed as a ratio (or an integer of
course)"; otherwise "rational?" is the same as "real?":
(not-s7-scheme)> (rational? (sqrt 2))
#t
As I understand it, "inexact" originally meant "floating point", and
"exact" meant integer or ratio of integers. But words have a life of
their own. 0.0 somehow became an "inexact" integer (although it can
be represented exactly in floating point). +inf.0 must be an integer
— its fractional part is explicitly zero! But +nan.0... And then
there's:
(not-s7-scheme)> (integer? 9007199254740993.1)
#t
When does this matter? I often need to index into a vector, but the
index is a float (a "real" in Scheme-speak: its fractional part can
be non-zero). In one scheme:
(not-s7-scheme)> (vector-ref #(0) (floor 0.1))
ERROR: Wrong type (expecting exact integer): 0.0 ; [why? "it's probably
a programmer mistake"!]
Not to worry, I'll use inexact->exact:
(not-s7-scheme)> (inexact->exact 0.1) ; [why? "floats are
ratios"!]
3602879701896397/36028797018963968
So I end up using the verbose (floor (inexact->exact ...))
everywhere, and even then I have no guarantee that I'll get a legal
vector index. When I started work on s7, I thought perhaps "exact"
could mean "is represented exactly in the computer". We'd have
integers and ratios exact; reals and complex exact if they are
exactly represented in the current floating point
implementation. 0.0 and 0.5 might be exact if the printout isn't
misleading, and 0.1 is inexact. "integer?" and friends would refer
instead to the programmer's point of view. That is, if the
programmer uses 1 or if the thing prints as 1, it is the integer 1,
whereas 1.0 means floating point (not integer!). And to keep
exactness in view, we'd have to monitor which operations introduce
inexactness — a kind of interval arithmetic. But then what would
inexact->exact do? If we discard the exact/inexact distinction, we
can maintain backwards compatibility via:
(define exact? rational?)
(define (inexact? x) (not (rational? x)))
(define inexact->exact rationalize) ; or floor
(define (exact->inexact x) (* x 1.0))
There is also Mike Sperber's paper a few years ago about Scheme's
numeric tower being borked.
Anyway, just to say that you're in good company :)
Andy
--
http://wingolog.org/
- Re: fix for expt bug, (continued)
- Re: fix for expt bug, Mark H Weaver, 2010/11/02
- Re: fix for expt bug, Ramakrishnan Muthukrishnan, 2010/11/03
- Re: fix for expt bug, Mark H Weaver, 2010/11/03
- Re: fix for expt bug, Ramakrishnan Muthukrishnan, 2010/11/03
- Re: fix for expt bug, Mark H Weaver, 2010/11/03
- Re: fix for expt bug, Ramakrishnan Muthukrishnan, 2010/11/03
- Re: fix for expt bug, Ramakrishnan Muthukrishnan, 2010/11/03
- Re: fix for expt bug, Ludovic Courtès, 2010/11/03
- Re: fix for expt bug, Mark H Weaver, 2010/11/04
- Re: fix for expt bug, Ludovic Courtès, 2010/11/08
- Re: fix for expt bug,
Andy Wingo <=
- Re: fix for expt bug, Ludovic Courtès, 2010/11/21
- [PATCH] Fix bugs in expt and integer-expt, Mark H Weaver, 2010/11/04
- Re: [PATCH] Fix bugs in expt and integer-expt, Ludovic Courtès, 2010/11/10