# Help to find package for DSA (Discrete Stochastic Arithmetic) implementation
**URL:** https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391
**Category:** Numerics
**Tags:** question, package
**Created:** [February 19, 2024, 5:08am UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391 "2024-02-19T05:08:46Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@hungpham3112](https://discourse.julialang.org/u/hungpham3112)
#### Post date: [February 19, 2024, 5:08am UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/1 "2024-02-19T05:08:46Z")
Hi, I’m working in a project where we use DSA method (based-on CESTAC) to validate results of numerical software. Currently, I’m using [Cadna](https://doi.org/10.1016/j.cpc.2008.02.003) (written in C) to solve this problem. The advantage of Cadna is it has example for CUDA implementation instead of just CPU like other tools.
I’m looking for a package in Julia that match my requirements:
- Good CUDA support for half and bfloat16
- Implement DSA or relevant mathematical approach. (I’m still new to DSA so I guess, there is other techniques to solve numerical validation problem).
The package [StochasticArithmetic.jl](https://github.com/ffevotte/StochasticArithmetic.jl) seems not maintain anymore and only support SFloat64. Is there any expert out there have experience in this field? I really need an suggestion, thank you.
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### Author:  [@ffevotte](https://discourse.julialang.org/u/ffevotte)
#### Post date: [February 20, 2024, 9:15am UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/2 "2024-02-20T09:15:47Z")
Hi, I’d be happy to revive `StochasticArithmetic.jl` if you have some interest in it. However, I don’t know much about GPUs, and haven’t the slightest clue how to implement DSA (or any form of Stochastic Arithmetic) in a GPU-compatible way.
I’d advise you to also look at @milankl’s work, especially [`StochasticRounding.jl`](https://github.com/milankl/StochasticRounding.jl). It’s not exactly DSA/CESTAC, but I tend to favour this kind of stochastic arithmetic these days, and this ecosystem is much more alive than my own `StochasticArithmetic.jl`. I don’t know whether `StochasticRounding.jl` supports GPUs, though.
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### Author:  [@milankl](https://discourse.julialang.org/u/milankl)
#### Post date: [February 20, 2024, 9:32pm UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/3 "2024-02-20T21:32:40Z")
> I don’t know whether `StochasticRounding.jl` supports GPUs, though.
I haven’t tested whether or which issues arise on a GPU, if someone can test it, and open issues in StochasticRounding.jl then I’d be happy to address them!
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### Author:  [@milankl](https://discourse.julialang.org/u/milankl)
#### Post date: [February 20, 2024, 9:41pm UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/4 "2024-02-20T21:41:49Z")
But yes, to clarify, StochasticRounding.jl only uses the a distance-proportional rounding mode where `x` between `a` and `b > a` is stochastically rounded to `b` at chance `p = (x-a) / (b-a)` and to `b` at chance `1-p`. So like if `x` is 1/4 of the way between a and b then there’s a 1/4 chance that it’s rounded to b. This rounding mode is exact in expectation, meaning that the average rounding error decreases for an increasing number of arithmetic operations.
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### Author:  [@hungpham3112](https://discourse.julialang.org/u/hungpham3112)
#### Post date: [February 21, 2024, 4:05pm UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/5 "2024-02-21T16:05:47Z")
What is the theory or paper that you implement in your package?
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### Author:  [@ffevotte](https://discourse.julialang.org/u/ffevotte)
#### Post date: [February 21, 2024, 4:30pm UTC](https://discourse.julialang.org/t/help-to-find-package-for-dsa-discrete-stochastic-arithmetic-implementation/110391/6 "2024-02-21T16:30:44Z")
`StochasticArithmetic.jl` implements Vignes’ CESTAC arithmetic\[1\].
[https://ffevotte.github.io/StochasticArithmetic.jl/dev/](https://ffevotte.github.io/StochasticArithmetic.jl/dev/)
In comparison to DSA:
- CESTAC is asynchronous (whereas DSA is synchronous)
- you can do as many evaluations as you like (whereas DSA fixes 3 evaluations)
In contrast, I think `StochasticRounding.jl` implements an arithmetic more similar to Stott Parker’s Monte Carlo Arithmetic\[2\] (MCA): instead of rounding upwards or downwards with probability 1/2 (like in CESTAC), the probability is adjusted so that the expectation of the stochastic result matches the real, mathematical result.
See _e.g._ this paper for a comprehensive comparison of CESTAC/DSA vs MCA (Disclaimer: I’m one of the authors)
> Devan Sohier, Pablo De Oliveira Castro, François Févotte, Bruno Lathuilière, Eric Petit, and Olivier Jamond. Confidence intervals for stochastic arithmetic. _ACM Transactions on Mathematical Software_, 47(2), 2021.
> **[Confidence Intervals for Stochastic Arithmetic](https://hal.science/hal-01827319)**
>
> Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic Arithmetic is one...
* * *
1. Jean Vignes and Michel La Porte. Error Analysis in Computing, 1974
2. Douglas Stott Parker. Monte carlo arithmetic: exploiting random-
ness in floating-point arithmetic. Technical Report CSD-970002,
UCLA Computer Science Dept., 1997.