Re: GPUs. Was..Re: Should facts() show duplicate facts?

(GPUs again...)
https://arxiv.org/abs/2608.00085
Construction and Performance Evaluation of an Arbitrary-Precision
Floating-Point Arithmetic Environment on CUDA
talks about efforts that seem to implement mostly-standard mpfr
arbitrary-float capabilities on GPUs.
As expected, the need for (say) dynamic memory is not a good fit.

It could be that a case could be made for evaluation of a polynomial at a
'taylor series' point where a bigfloat is
a_0 + a_1*2^64 + a_2*2^128+a_3* 2^192  ... where a_i are each 63 bit
integers.  And the taylor series could
be some GPU compatible structure (vector, matrix,..). Just a thought/

Oh, while it is possible to sometimes make definite sign determinations
with float calculations (if error bounds are
also correctly computed), if nroots() is called, that needs
arbitrary-precision integer (and rational) arithmetic.

RJF

On Fri, Aug 28, 2026 at 1:16 PM David Scherfgen <[email protected]>
wrote:

> Oh, that sounds interesting.
> I've been working on something like that, too.
> Can you show some example expressions of which your solution can determine
> the sign?
>
> Am Fr., 28. Aug. 2026 um 22:12 Uhr schrieb Stavros Macrakis <
> [email protected]>:
>
>> Yes, Maxima currently doesn't use numerical techniques to solve symbolic
>> problems. But there are some easy cases where it could.
>>
>> For example, *sign(x^6+2*x+2)* could use *nroots/realroots *to determine
>> (reliably!) that it has no real roots and is therefore always positive.
>> Similarly that *assume(x>-1/2), sign(x^6+3*x+2) => pos*.
>>
>> I'm actually working on some enhancements to *sign/is* that incorporate
>> this and other techniques.
>>
>>          -s
>>
>> On Fri, Aug 28, 2026 at 3:32 PM Richard Fateman <[email protected]>
>> wrote:
>>
>>> Exact arithmetic in finite fields would feed into modular arithmetic
>>> routines like gcd, factoring .. are there GPU routines for arbitrary
>>> precision integer arithmetic?
>>>
>>> Floating point evaluation is not heavily used in serial, so not clear
>>> how parallel would help.
>>> ....
>>>
>> _______________________________________________
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>

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