> | Waldek Hebisch writes: > | > | > Martin, first I _really_ prefer to get exceptions in normal code. > | > Ignoring exceptions is a great way to do not see bugs. Also, things > | > like infinities and (particularly nasty) "not a number" break normal > | > mathematical reasoning. > |
> Martin Rubey writes: > > | Don't worry, I see your point. One thing though: > | > | > (basically IEEE defined a new formal system quite unlike mathematical > | > real numbers). > | > | Is it really different? I thought that computation with +infinity and > | -infinity was OK - except for imagpart... > | > | I don't care about nan. On Wed, Oct 29, 2008 at 9:43 AM, Gabriel Dos Reis wrote: > > If you have +infinity and -infinity, then you get +0, -0 and NaN to > have an algebraically closed system. Most rants about NaNs and > signed zeros tend to reflect misunderstanding of the floating point > systems. I think the correct *algebraic* representation of the floating point variants (Float, DoubleFloat, and MachineFloat) is an important subject for panAxiom. Perhaps DFLOAT follows (more or less) the IEEE 754-2008 standard but I think it is clear that the domain Float in panAxiom implements something quite different. I am not well informed about the standards issues, but mathematically I think IEEE values like +infinity, -infinity, +0 and -0 make sense as limits when floating point values are taken as (possibly open) intervals of the real line. However as I understand it, values in the domain FLOAT are to be taken as exact rationals that approximate real numbers in a well defined manner. Is this an accurate view? Are there specific changes that should be made to these floating point domains that would make their associated algebra more obvious? Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
