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Diffstat (limited to 'doc/rounding-errors.doc')
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diff --git a/doc/rounding-errors.doc b/doc/rounding-errors.doc new file mode 100644 index 00000000..433d6ed9 --- /dev/null +++ b/doc/rounding-errors.doc @@ -0,0 +1,24 @@ +/** \page rounding-errors How to Avoid Rounding Errors + +(Probably, this is a standard algorithm, so if someone knows the name, +drop me a note.) + +If something like + +\f[y_i = {x_i a \over b}\f] + +is to be calculated, and all numbers are integers, a naive +implementation would result in something, for which + +\f[\sum y_i \ne {(\sum x_i) a \over b}\f] + +because of rounding errors, due to the integer division. This can be +avoided by transforming the formula into + +\f[y_i = {(\sum_{j=0}^{j=i} x_j) a \over b} - \sum_{j=0}^{j=i} y_j\f] + +Of corse, when all \f$y_i\f$ are calculated in a sequence, +\f$\sum_{j=0}^{j=i} x_j\f$ and \f$\sum_{j=0}^{j=i} y_j\f$ can be +accumulated in the same loop. + +*/
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