[PDF] Top 20 A Formally-Proved Algorithm to Compute the Correct Average of Decimal Floating-Point Numbers
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A Formally-Proved Algorithm to Compute the Correct Average of Decimal Floating-Point Numbers
... include decimal floating-point units, with a conforming imple- mentation of the IEEE-754 2008 ...from the computer arithmetic literature are not correct anymore ... Voir le document complet
13
Kahan's algorithm for a correct discriminant computation at last formally proven
... proved with other reasonable formats: we need a precision greater than 4 and underflow and overflow thresholds such that 2 3prec are normal floating-point ...This of course includes ... Voir le document complet
7
Formal Verification of Programs Computing the Floating-Point Average
... Abstract. The most well-known feature of floating-point arithmetic is the limited precision, which creates round-off errors and ...is the limited range, which creates underflow ... Voir le document complet
17
Symbolic execution of floating-point computations
... 7 A labelling procedure As previously said, projection functions only reduce the domains of the vari- ...neither the path conditions are satis able nor a test datum to be ... Voir le document complet
42
Contain the floating point naming explosion
... composed of many TU, this means that there is a relatively high probability of ...easy to detect because they may only manifest on platforms that are not accessible to the ... Voir le document complet
87
Verified Compilation of Floating-Point Computations
... date of receipt and acceptance should be inserted later Abstract Floating-point arithmetic is known to be tricky: roundings, formats, exceptional ...values. The IEEE-754 standard was ... Voir le document complet
32
New algorithms to compute the strength of a graph
... store the index i in step 2 when it occurs and do not introduce it anymore in step 2 until next interval for k ...in a list of indexes i when such hits occurs, each i being associated by the ... Voir le document complet
18
An algorithm of search of nearest neighbors leading to average computing time per point independent of the total number of points
... In a first time, we détermine the smallest rectangle containing our set G = E = F (in thick lines on ...make a partition in 4 X 3 equal cells. So we can set the following list of points ... Voir le document complet
23
On various ways to split a floating-point number
... sums of several floating-point numbers. The main idea is to split these numbers so that the obtained values can be affected to containers (also called bins), ... Voir le document complet
9
A Study on Convolution Operator Using Half Precision Floating Point Numbers on GPU for Radioastronomy Deconvolution
... half-precision floating-point, GPU, parallel computing ...in the IEEE standard in 2008 [1] as binary16, half-precision floating-point arithmetic (FP16) has been a topic of ... Voir le document complet
7
The average case analysis of algorithms : Saddle Point Asymptotics
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ... Voir le document complet
61
Automating the Verification of Floating-Point Programs
... is to build upon the recent support for FP arithmetic in SMT- LIB to propose an environment for deductive verification of numerical programs with a higher level of ...in ... Voir le document complet
19
How to Compute the Area of a Triangle: a Formal Revisit
... facts. The first one is that Kahan’s algorithm for computing the area of a triangle is correct, and that its error bound is much better than what Goldberg gave in ...[2]. ... Voir le document complet
9
An algorithm to efficiently and accurately compute the effective capacitances of interconnects driven by logic gates
... 3, such that the fifty percent output transition point in the effective capacitance model occurs at the same time as the corresponding point in the H model.. RI.[r] ... Voir le document complet
21
Multi-prover verification of floating-point programs
... is to support as many theorem provers as ...able to understand first-order logic with integer and real ...those of the SMT-family (Satisfiability Modulo Theo- ries) which support first-order ... Voir le document complet
16
Verification of the Functional Behavior of a Floating-Point Program: an Industrial Case Study
... results of the illustrative example ditions are the post-condition, but also a series of automatically inserted condi- tions to guarantee the absence of overflow in ... Voir le document complet
36
Computing floating-point logarithms with fixed-point operations
... In the beginning of the computer era, a lot of different floating-point formats were used in various ...with the adoption of the IEEE-754 Standard for ... Voir le document complet
10
Toward Scalable Source Level Accuracy Analysis for Floating-point to Fixed-point Conversion
... difficult to adapt in a compiler context, where the system model is implicitly specified as program source ...solve the problem by building an SFG model out of the program [3], ... Voir le document complet
9
The Euclidean Division Implemented with a Floating-Point Division and a Floor
... on the rounding mode: Rounding to nearest: It is required by the IEEE-754 standard, where it must be the default rounding mode; moreover it is even the only rounding mode in some ... Voir le document complet
20
The lattice reduction algorithm of Gauss : an average case analysis
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ... Voir le document complet
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