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Many applications of INDEPENDENT DO loops do require reductions as they are typically calculating independently quantities but storing results as parts of various averages
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e.g. in High Enegry Physics Data Analysis, each measured event can be computed via an INDEPENDENT DO but one wishes to find a particular observable (histogram, scatterplot) which is averaged over each event
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Financial modelling is similar
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x = 0
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!HPF$ INDEPENDENT, NEW(xinc), REDUCTION(x)
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do i = 1 , N
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call sub(i, xinc)
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x = x + xinc
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END DO
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xinc is a separate new variable each iteration but result is accumulated into global x
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