We present a method for formal verification of transcendental hardware and software algorithms that scales to higher precision without suffering an exponential growth in runtimes. A class of implementations using piec...
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We present a method for formal verification of transcendental hardware and software algorithms that scales to higher precision without suffering an exponential growth in runtimes. A class of implementations using piecewise polynomial approximation to compute the result is verified using MetiTarski, an automated theorem prover, which verifies a range of inputs for each call. The method was applied to commercial implementations from Cadence Design Systems with significant runtime gains over exhaustive testing methods and was successful in proving that the expected accuracy of one implementation was overly optimistic. Reproducing the verification of a sine implementation in software, previously done using an alternative theorem-proving technique, demonstrates that the MetiTarski approach is a viable competitor. Verification of a 52-bit implementation of the square root function highlights the method's high-precision capabilities.
The minimization of cost, power consumption and time-to-market of DSP applications requires the development of methodologies for the automatic implementation of floating-point algorithms in fixed-point architectures. ...
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ISBN:
(纸本)0780374029
The minimization of cost, power consumption and time-to-market of DSP applications requires the development of methodologies for the automatic implementation of floating-point algorithms in fixed-point architectures. In this paper, a new methodology for evaluating the quality of an implementation through the automatic determination of the Signal to Quantization Noise Ratio (SQNR) is presented. The modelization of the system at the quantization noise level and the expression of the output noise power is detailed for linear systems. Then, the different phases of the methodology are explained and the ability of our approach for computing the SQNR efficiently is shown through examples.
The two-step approach to nonparametric discrimination is that of estimating class-conditional densities and deriving the Bayes decision rule as if the estimates were true. Direct implementation of such a decision rule...
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The two-step approach to nonparametric discrimination is that of estimating class-conditional densities and deriving the Bayes decision rule as if the estimates were true. Direct implementation of such a decision rule ecounters two computational problems. Complexity increases with sample size, and finite precision limits the decision rule domain. Here a recursive algorithm to reduce the expected number of operations and word-length limitations below that of the direct approach is developed. A special case of the formulation reduces to the weighted k-nearest-neighbor rule.","doi":"10.1109/TPAMI.1979.4766881","publicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","startPage":"90","endPage":"94","rightsLink":"http://***/AppDispatchServlet?publisherName=ieee&publication=0162-8828&title=Recursive+Implementation+of+a+Two-Step+Nonparametric+Decision+Rule&isbn=&publicationDate=Jan.+1979&author=Sargur+N.+Srihari&ContentID=10.1109/TPAMI.1979.4766881&orderBeanReset=true&startPage=90&endPage=94&volumeNum=PAMI-1&issueNum=1","displayPublicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","pdfPath":"/iel5/34/4766865/***","keywords":[{"type":"IEEE Keywords","kwd":["Cost function","Computer science","Kernel","Smoothing methods","Decision making","Finite wordlength effects","Size measurement"]},{"type":"Author Keywords ","kwd":["weighted k-nearestneighbor rule","Decision rule implementation","floating-point algorithms","nonparamnetric discrimination","Parzen window estimation","pattern classification","two-step decision rules"]}],"allowComments":false,"pubLink":"/xpl/***?punumber=34","issueLink":"/xpl/***?isnumber=4766865","standardTitle":"Recursive Implementation of a Two-Step Nonparametric Decision Rule
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