[racket] read of numbers with decimal point default to exact?

From: Jos Koot (jos.koot at telefonica.net)
Date: Fri Jul 23 05:24:14 EDT 2010

 (/ (read (open-input-string "#e5.55")) #e1.11)

5.55 and 1.11 are read as inexact reals, which are flonums. In fact in
Racket all reals are rationals.
There is good reason to distinguish exact reals from inexact ones, because
arithmetic operations on flonums usually are much faster. Operations on
exact reals may become very slow, for example:

(void (time (expt #e1.0001 1000000)))
cpu time: 10920 real time: 10910 gc time: 63

(time (expt 1.0001 1000000))
cpu time: 0 real time: 0 gc time: 0


> -----Original Message-----
> From: users-bounces at racket-lang.org 
> [mailto:users-bounces at racket-lang.org] On Behalf Of Neil Van Dyke
> Sent: 23 July 2010 08:21
> To: Racket Users List
> Subject: [racket] read of numbers with decimal point default to exact?
> This is just a small idea, not something I'd argue for strongly...
> How about making numbers formatted with decimal points, like 
> "12.34", read as exact rather than inexact?
> The rationale being: decimal point format is a commonplace 
> and very useful format for writing exact rational numbers, 
> and if one writes a number like "5.55", there is nothing 
> except an old Scheme convention to imply that one intends 
> "5.55" to be any less exact than "555/100".  (I'm ignoring 
> any question of precision here, which Scheme does not address
> either.)
> For example, with this change, the following expression would 
> evaluate to an exact 5 rather than what it currently does: an 
> inexact 4.999999999999999.
> (/ (read (open-input-string "5.55")) 1.11)
> The exact 5 result would also be what I imagine is expected 
> by, say, casual programmers using Racket for financial 
> calculations, which I think would be a small selling point for Racket.
> Python 2.5.2 (r252:60911, Jan 24 2010, 14:53:14) [GCC 4.3.2] 
> on linux2 Type "help", "copyright", "credits" or "license" 
> for more information.
>  >>> 5.55 / 1.11
> 4.9999999999999991
> The only good linguistic argument I can think of against this 
> is that, when we have Racket *write* (as in the "write" 
> procedure, not "display") inexact rationals in decimal-point 
> form, they'd need to be written with an "#i" prefix, so that 
> inexactness is preserved on a *read* of that same format by 
> Racket.  The drawbacks I see to the "#i" on write are
> small: (1) visually, it's a little bit more cluttered; (2) it 
> will break any legacy code that assumes it can do a write of 
> numbers for some interoperation or UI purpose that doesn't 
> work if the "#i" prefix is added.  "#i" could even be 
> considered helpful, as in a heads-up to the programmer that 
> they have a number that might be corrupted by IEEE 
> floating-point operations they didn't expect.
> The only implementation efficiency argument I can think of 
> against this is perhaps wanting numbers to be inexact by 
> default, so that native floating-point representation and 
> operations can be used more often.  If that is indeed a 
> consideration, I'd prefer to leave adding "#i" prefixes and 
> "exact->inexact" calls as optimizations that can be added 
> consciously by programmers, with the default being more exact 
> than efficient.
> --
> http://www.neilvandyke.org/
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