On Jan 21, 2009, at 9:19 AM, rjf wrote:

> On Jan 21, 2:44 am, Harald Schilly <harald.schi...@gmail.com> wrote:
>> On Jan 21, 6:21 am, rjf <fate...@gmail.com> wrote:
>>
>>> In my experience, people doing scientific calculations for a living
>>> will not tolerate a language implementation X whose programs are
>>> substantially slower than equivalent ones in a language  
>>> implementation
>>> Y.
>>
>> I don't know any details, but I think there are valid cases where one
>> wants calculation to act the same on all platforms.
>
> Sure.
>> One possible
>> example are spacecrafts, where the calculations in space should act
>> the same way as they were developed on ground.
>
> Sure. I can't imagine any engineer debugging a life-critical system on
> a Mac and then running it on a PC,
> putting one of them on a spacecraft and leaving one on the ground.
>
> Surely your supposition that this is a justification for anything has
> no support in reality.

I can. Most embedding systems are much easier to write and debug for  
on some emulated/general purpose system before putting them on the  
device (and testing them there too of course).

>  So, I think the developer/user has to think about the actual
>> goals, speed vs. reproducibility, and if possible control what
>> happens.
>
> I am sure that some Sage people have thought about such things, but
> probably not
> enough. Which is why I try to poke holes in some of these comments!

Sage has thought about this--we have models for both:

RDF -- The real double "field" with provides wrappers around the  
machine's native (double) floating point arithmetic, fast but  
possibly machine-dependent
RealField(n) -- n-bit mentissa real numbers, based on mpfr. Slower,  
but every operation follows strict and reproducible rounding rules.

There is also support for real interval fields, and the (now  
deprecated for reasons very similar to the start of topic of this  
thread) quad-double model, and even "real lazy" fields whose entries  
are computed on the fly to whatever precision is needed.

- Robert


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