Oct 10, 2017 - representation offers more accuracy and a larger dynamic range than floats with the same number of bits,
Oct 10, 2017 - If the user asks for the square root of a negative number, zero divided ...... pare properties of their c
Abstract. The goal of the Provably Correct Systems project (ProCoS) is to develop a mathematical basis for development of embedded, real- time, computer ...
creasingly applied in practical design flows to verify reg- ... the execution and, as a result, decrease the simulation ... those bits across word boundaries. ... cal design description and replaced by black boxes. The hi ... two switched terminals a
conditions required of it as follows: hf establishes a bijection between .... Intuitively, lifting of computations means that an enhancement interleaves its compu- ... Before attempting to answer this question, a problem needs to be highlighted.
Note that correctness is a function of the software's environment. â A component can ... Thereafter, just one chance to get it right â rover has to land safely. â Then, ability to ... Exhaustively examine all execution paths through a logical m
Lakhneche, Hans Langmaack, Markus Miiller-Olm *. Institut fiir Informatik und Praktische Mathematik. Christian-Albrecht s-Universit gt Kiel. PreuBerstr.
Apr 27, 2015 - of bugs. This paper presents Alive, a domain-specific language for ... Categories and Subject Descriptors
Apr 27, 2015 - This paper presents Alive, a domain-specific language for writing optimizations and for automatically eit
Sep 30, 2003 - Architecture Refinement. 5 ... erate an architecture level model of a system from its speci- ..... behavior bij must ensure execution of eij,bi and e.
results of any interval arithmetic are correct or not. .... However, is the achieved result correct? ..... 11 explains that if uncertainty of the right-hand side of in-.
With its use one can e.g. add two quantities a and b, values of which are .... Addition operation of two precise numbers a + b = x =? can be called âforward calcula ...
of concurrent and distributed programming languages (e.g. [19]). MMC also ... than that of traditional model checkers for non-mobile systems, such as SPIN and.
16] Martin begins with a speci cation for a circuit written in a high-level language modeled after Hoare's CSP ...... 2] Robert S. Boyer and J. Strother Moore.
Martin Ward and Hussein Zedan. Software ...... Martin Ward, Hussein Zedan, Matthias Ladkau & Stefan Natelberg, âConditioned Semantic. Slicing for Abstraction ...
The PoET/PSLang toolset by ... the type system can then use this property to check for policy compliance. .... the sequences of security-relevant events that an application can generate ... state contains a definition of all the variables that will b
code verification is a data flow analysis problem, or more generally, a ..... ALGEBRA as formal parameter: spec ALGEBRA is sort Dom sort Fun op arity : Fun -> Nat op apply : Fun ..... http://www.kestrel.edu/HTML/keep.html/. [3] Qian, Z. A Formal ...
schedule, assignment and a circuit implementation for the Unmanned. Aerial Vehicle ..... Hence in the SensPG, there are arcs from (CASE state of) node, (! =)1 ...
of laws may be found in HPB90]. A mathematical definition of the relation v, and the consistency of the laws with respec
where the correctness can be demonstrated with formal tech- niques. The methodology ... ally not applicable in realtime programs, this loop bounds analysis is sufficient for the ...... IEEE Real-Time Systems. Symposium, Orlando FL, USA, Nov.
The advantages of starting the development of a software ..... structure of the specification, the validation cycle is e
g; f; g have multiset status and fs1;:::;smg rpos ft1;:::;tng; or. (d) f g; s >rpos tj for all j = 1;:::;n ..... ming Language, Proc. of ESPRIT'90, Brussels (ed. Commission of ...
Fail-stop processors: an approach to designing fault-tolerant computing ... The free lunch is over: A fundamental turn t
Mar 28, 2018 - 28/3/18. 4. Intersection point rounded to front or back of the triangle? Page 5. Posit Implementations. ⢠Posit rounding is omitted in many implementations. 28/3/18. 5. Issues were fixed ... Rounded up: 0 1 1 1 1 0 0 1 1 0 0 0 0 0 ...
PROVABLY CORRECT POSIT ARITHMETIC Conference for Next Generation Arithmetic 28 March 2018
Chung ShinYee SpeedGo Computing
28/3/18
About Myself • Love algorithms. • Like parallel programming. • Enjoy mathematics. • Not necessary good at any above.
2
28/3/18
3
Inspiration • Unum type I
è variable bit size è difficult to index. • Posit è fixed bit size è easy to index. è higher accuracy than floats. • Reduce memory footprint? • Resolve accuracy issues in rendering?
4
28/3/18
Research Plan • Ray tracing: self intersecting problem Intersection point rounded to front or back of the triangle?
5
28/3/18
Posit Implementations Issues were fixed after paper submission.
Issues still persist.
• Posit rounding is omitted in many implementations.
PROVABLY CORRECT POSIT ARITHMETIC Conference for Next Generation Arithmetic 28 March 2018
Rounding Residual • Value of residual: • Round down: • Round to even: • Round up:
Need not knowing exact r and y values.
28/3/18
Reduced Residual
32
28/3/18
Software Tests and Verifications • Special posit arithmetic tests. • Normal posit arithmetic tests. • Posit encoding and decoding tests. • Checksum comparisons.
33
34
28/3/18
Special Posit Arithmetic Tests Special posits: • Zero • NaR (Not-a-Real) or
35
28/3/18
Normal Posit Arithmetic Tests • Use rational numbers as reference. P+ = Smallest number greater than P NaR Computed posit P (bogus implementation) -1
1
0
P− = Greatest number smaller than P Exact rational V
36
28/3/18
Normal Posit Arithmetic Tests • Use rational numbers as reference. P+ = Smallest number greater than P Exact rational V
NaR
Computed posit P (Truncated) -1
1
0
P− = Greatest number smaller than P
37
28/3/18
Normal Posit Arithmetic Tests • Use rational numbers as reference. P+ = Smallest number greater than P NaR
Exact rational V (equally near to P and P+) Computed posit P
-1
1
0
P− = Greatest number smaller than P
28/3/18
38
Posit Encoding and Decoding Tests • Symmetry tests. • Posit bits + 1 has strictly increasing value,
except ±maxpos and NaR. • Intervals of s, k, e, f, and h are well defined.
28/3/18
39
Checksum Comparisons • Generate arithmetic inputs deterministically. • Use the computed results to compute
checksum. • Subsequent implementation updates just match the expected checksum.
28/3/18
40
Conclusion • Posit arithmetic based on fixed-point. • Division result consists of a residual. • Conditions for posit rounding. • Reduced residual with 2-bit information. • Systematic software tests.
