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Code Editor : rounding-errors.doc
/** \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-1} 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$\sum_{j=0}^{j=i-1} y_j\f$ can be accumulated in the same loop. Regard this as sample: \code int n, x[n], a, b; // Should all be initialized. int y[n], cumX = 0, cumY = 0; for (int i = 0; i < n; i++) { cumX += x[i] y[i] = (cumX * a) / b - cumY; cumY += y[i]; } \endcode */
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