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18,809
Roundoff Errors in FixedPoint FFT
"... Abstract – The general assumptions made about roundoff noise are that its samples form a white sequence. and they are uniformly distributed between ±q/2, where q is the size of the LSB. While this is often true, strange cases may appear, e.g. misleading peaks can occur in the spectrum. This paper in ..."
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investigates the roundoff error of fixedpoint FFT. It reproduces the results of Welch (1969) with modern tools, points at an error in his simulations, and investigates the consequences of the violation of the assumption for almost pure sine waves. The maximum amplitude of spurious peaks is determined
Checking Roundoff Errors using CounterexampleGuided Narrowing
"... This paper proposes a counterexampleguided narrowing approach, which mutually refines analyses and testing if (possibly spurious) counterexamples are found. A prototype tool CANAT for checking roundoff errors between floating point and fixed point numbers is reported with preliminary experiments ..."
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This paper proposes a counterexampleguided narrowing approach, which mutually refines analyses and testing if (possibly spurious) counterexamples are found. A prototype tool CANAT for checking roundoff errors between floating point and fixed point numbers is reported with preliminary exper
Semantics of roundoff error propagation in finite precision computations
 Journal of Higher Order and Symbolic Computation
, 2006
"... Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary ..."
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Cited by 20 (10 self)
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Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary
A Note on Geometric Ergodicity and FloatingPoint Roundoff Error
, 2000
"... We consider the extent to which Markov chain convergence properties are affected by the presence of computer floatingpoint roundoff error. This paper extends previous work of Roberts, Rosenthal, and Schwartz (1998) to the case of proportional errors. ..."
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Cited by 3 (1 self)
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We consider the extent to which Markov chain convergence properties are affected by the presence of computer floatingpoint roundoff error. This paper extends previous work of Roberts, Rosenthal, and Schwartz (1998) to the case of proportional errors.
Should We be Concerned about Roundoff Error?
"... ) conclude that the double precision result is accurate since it agrees to 13 digits with the extended precision result. Surprising to many, all three results are wrong evenintherstdigit! For that matter, the sign itself is incorrect! The exact result, obtained using the variable precision interval ..."
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Cited by 1 (0 self)
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arithmetic of VPI [1] with about 40 decimal digits of accuracy, is \trapped" tightly in the following interval: [ 0:827396059946821368141165095479816292005; 0:827396059946821368141165095479816291986 ] The point to be made here is twofold: 1. Roundo error can seriously compromise the reliability
LIMITED DYNAMIC RANGE OF SPECTRUM ANALYSIS WE TO ROUNDOFF ERRORS OF THE FFT
"... Ab $ t rac t Roundoff errors of the blockfloat Fast Fourier Transform (FFT) are treated. Special emphasis is given to the case when signals containing sine waves are analyzed. In the detection and analysis of sine waves, rms values and overall signaltonoise ratios do not provide adequate informat ..."
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Ab $ t rac t Roundoff errors of the blockfloat Fast Fourier Transform (FFT) are treated. Special emphasis is given to the case when signals containing sine waves are analyzed. In the detection and analysis of sine waves, rms values and overall signaltonoise ratios do not provide adequate
Propagation of roundoff errors in finite precision computations: a semantics approach
 In ESOP’02, number 2305 in LNCS
, 2002
"... Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a interpretation which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later co ..."
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Cited by 23 (7 self)
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Abstract. We introduce a concrete semantics for floatingpoint operations which describes the propagation of roundoff errors throughout a interpretation which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later
HOW ROUNDOFF ERRORS HELP TO COMPUTE THE ROTATION SET OF TORUS HOMEOMORPHISMS
"... Abstract. The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the notion of observable rotation set, which takes into ..."
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and simulations suggest that the asymptotic discretized rotation set is a much better approximation of the rotation set than the observable rotation set, in other words we need to do coarse roundoff errors to obtain numerically the rotation set. 1.
Instrumentation Of Fortran Programs For Automatic Roundoff Error Analysis And Performance Evaluation
, 1990
"... A pass to the Cedar Fortran preprocessor, cftn, has been developed which allows the user to instrument his source code in a variety of ways. By specifying different command line options and linking with different libraries, one can automatically generate a report of the program's use of the All ..."
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Cited by 1 (0 self)
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development at CSRD. A library for statistical roundoff error analysis has also been developed for ...
Roundoff error analysis of the Fast Cosine Transform and of its application to the Chebyshev pseudospectral method.
, 1994
"... The roundoff error analysis of several algorithms commonly used to compute the Fast Cosine Transform and the derivatives using the Chebyshev pseudospectral method are studied. We derive precise expressions for the algorithmic error, and using them we give new theoretical upper bounds and produce a s ..."
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Cited by 2 (1 self)
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The roundoff error analysis of several algorithms commonly used to compute the Fast Cosine Transform and the derivatives using the Chebyshev pseudospectral method are studied. We derive precise expressions for the algorithmic error, and using them we give new theoretical upper bounds and produce a
Results 1  10
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18,809