Re: [Axiom-developer] Directions

[William Sit]

Dear Tim:

I don't have pointers applying FPGA techniques to symbolic 
computations. However, the trend is to use something 
similar to FPGA all the way down to the manufacture level. 
For some background, see 
http://www.rambus.com/technology/item/979-rambus-cryptography-research-division-unveils-cryptomanager-secure-feature-management-platform.
Qualcomm, for example already licenses this technology, as 
do many other companies. Their idea is to tailor each 
individual chip at the single consumer level to enhance 
security.

By the way, the link
https://github.com/Gladdy/numerical-fpga-thesis/blob/master/thesis/thesis.pdf
is not readable by Adobe or Preview on Macs.

However, according to your link (scroll down to bottom), 
the abstract mentions:
" This thesis describes the process of implementing an 
accelerator in which the computational part is specified 
using the functional hardware description language CλaSH 
and discusses the feasibility of performing numerical 
mathematics on this accelerator by computing 
approximations to ordinary differential equations. The 
accelerator is capable of using the methods of Euler and 
Runge-Kutta (second order) to perform the approximations, 
but due to the use of a fixed-point number representation 
the accuracy suffers."

So this is mainly a numerical set up. Graphics processors 
have been used for numerical scientific work for a long 
time already since GPUs have improved tremendously in 
power (my layman observation is the advance is faster than 
CPUs in terms of number of cores, speed, and low power 
consumption).

Since Axiom is software, I am not sure how the technique 
may be applied, unless you are thinking about an Axiom 
chip, or some hybrid numerical-symbolic approach is used. 
However, Axiom is a relatively small system (compared to 
modern mammoth bloated software), and I think the priority 
should be to make Axiom's learning curve less steep than 
make Axiom run faster, or even more securely.

William

On Sat, 4 Jul 2015 10:13:18 -0500
 address@hidden wrote:
> I've been spending a lot of time working on Field 
> Programmable Gate
> Arrays (FPGAs) which is basically hardware that can be 
> reprogrammed.
>
> There have been some interesting developments in this 
> area. 
>
> First, FPGAs are a lot more powerful and much cheaper.
>
> Second, Intel just bought the second largest FPGA 
> company, Altera.
> http://www.cnbc.com/id/102723697
>
> Third, FPGAs are moving toward computational 
> mathematics.
> https://github.com/Gladdy/numerical-fpga-thesis
>
> I believe, though I don't know for sure, that Intel will 
> eventually
> put an FPGA fabric on the same chip (Sytem on a Chip, 
> SoC) as their
> CPUs.
>
> Axiom is in a unique position to exploit this kind of 
> hardware merger. 
> If anyone has pointers to work on hardware-based 
> symbolic/numeric
> work, please send me a link.
>
> Tim
>
>
>
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William Sit, Professor Emeritus
Mathematics, City College of New York
Office: R6/291D Tel: 212-650-5179
Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/