Normally I only read messages of this list. Now I feel I have to reply. I have seen various floating point systems. Some of them would immediately force an abort when forming an overflow or underflow. Others would abort only after referring to underflowed or overflowed floating point (with trouble to find out where the underflow or overflow was produced) The systems that would not immediately abort when producing an underflow or overflow, provided functions allowing to check for under- or overflow without aborting. I am talking about fortran here. I think DrRacket does a good job. You can check results to be inexact zero or nan or inf. When implementing a calculation that might produce underflow or overflow, it is, according to my meaning, the responsability of the programmer to take care of these cases. Scheme, and in particular DrScheme, does provide all tools for this kind of precaution. For example you can capture a division by exact zero. You can also detect division by inexact zero, just by checking that the result is not infinity (or nan when dividing zero by zero). When dealing with algorithms that may have these problems, it is the task of the programmer to deal with them. I don't think there is any computational system that could service all programmers as they are inclined to expect. A programmer who is intensionaly using ploating points (id est inexact reals, internally in fact represented by quasi exact rational numbers) should be aware of the limitations of the numerical system. In some cases it may be desirable to have exact representations for all square roots (as in parts of group theory) This is possible, but as a programmer you cannot demand that your language provides these tools without your own effort (although they may be available in a planet contribution) If you need it you may have to implement it by yourself.
Although for me the distinction betweeen exact and inexact seems rather clear, may be the documentation should provide some more information on this subjext. A good thing is that inexactness is contaguous. For example, when giving data to a program and these data may be inexact (e.g. as obtained by a measurement), make sure that each numerical datum has a period. Greetings, Jos -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Neil Toronto Sent: martes, 29 de noviembre de 2011 20:39 To: [email protected] Subject: Re: [racket-dev] Subnormal numbers? I can't answer the question about underflow. But if you don't mind installing a nightly build of Racket, you get the (currently undocumented) module `unstable/flonum', which exports these: flonum->bit-field bit-field->flonum flonum->ordinal ; number of flonums away from 0 (+ or -) ordinal->flonum flstep ; the flonum n steps away (by ordering fl<) flnext ; next largest flonum (by ordering fl<) flprev ; next smallest flonum (by ordering fl<) -max.0 ; negative flonum with greatest non-infinite magnitude -min.0 ; negative flonum with smallest nonzero magnitude +min.0 ; positive flonum with smallest nonzero magnitude +max.0 ; positive flonum with greatest non-infinite magnitude Also, the `plot' module in the nightly build deals just fine with intervals that are too small to represent using flonums. For example, to illustrate floating-point discretization and the density of flonums at different ranges: #lang racket (require plot unstable/flonum) (plot (function (λ (x) (inexact->exact (sin x))) (flstep 0.0 -10) (flstep 0.0 10))) (- (flonum->ordinal 1.0) (flonum->ordinal 0.0)) (- (flonum->ordinal 2.0) (flonum->ordinal 1.0)) (- (flonum->ordinal 3.0) (flonum->ordinal 2.0)) (- (flonum->ordinal +max.0) (flonum->ordinal 1.0)) (parameterize ([plot-x-ticks (log-ticks #:base 2)]) (plot (function (compose flonum->ordinal exact->inexact) 1.0 8.0))) Neil T On 11/29/2011 09:32 AM, J. Ian Johnson wrote: > I'm currently proctoring the freshmen's lab on inexact numbers and was curious how to denote subnormal numbers in Racket. > Turns out that's not possible, since there is no underflow. Why does Racket follow the old standard of representing underflow with inexact zero? > I imagine changing it now would break a lot of code, but I'm just curious. > -Ian > _________________________________________________ > For list-related administrative tasks: > http://lists.racket-lang.org/listinfo/dev _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
