Roundoff noise analysis on the basis of an improved floating point error model

Until now floating point roundoff analysis utilized the assumption of statistical decorrelation between roundoff error and internal signals subject to a signal flow graph. A quantization within a signal flow graph has been treated like a single quantization of an unquantized number. The properties of the single quantizer have been investigated. A powerful matrix based algorithm for noise power computation has been given. However simulations lead to significant differences between theory and practice. One reason for this deviation is the different behaviour of the error of a quantization of a sum of quantized operands. Careful insight into the quantization of a floating point addition of quantized operands shows that the roundoff error is not decorrelated with the result. In contrast a positive nonzero cross-correlation coefficient between error and sum has to be determined. The precise value of this cross-correlation coefficient depends on the joint density of the operands. In this paper the analysis of roundoff noise for arbitrary signal flow graphs is treated. On the basis of this improved error model examples are investigated