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\name{sum.exact, cumsum.exact & runsum.exact}
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\title{Basic Sum Operations without Round-off Errors}
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Functions for performing basic sum operations without round-off errors
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sum.exact(..., na.rm = FALSE)
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\item{x}{numeric vector}
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\item{...}{numeric vector(s), numbers or other objects to be summed}
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\item{na.rm}{logical. Should missing values be removed?}
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\item{k}{width of moving window; must be an odd integer between one and n }
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All three functions use full precision summation using multiple doubles for
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intermediate values. The sum of numbers x & y is a=x+y with error term
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b=error(a+b). That way a+b is equal exactly x+y, so sum of 2 numbers is stored
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as 2 or fewer values, which when added would under-flow. By extension sum of n
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numbers is calculated with intermediate results stored as array of numbers
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that can not be added without introducing an error. Only final result is
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converted to a single number
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Function \code{sum.exact} returns single number. Function \code{cumsum.exact}
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returns vector of the same length as \code{x}. Function \code{runsum.exact}
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returns vector of length \code{length(x)-k} and attribute "count" containing
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number of finite (as in \code{\link{is.finite}}) elements in each window.
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Round-off error correction is based on:
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Shewchuk, Jonathan, \emph{Adaptive Precision Floating-Point Arithmetic and
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Fast Robust Geometric Predicates},
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\url{http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps}
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and its implementation found at:
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\url{http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090}
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McCullough, D.B., (1998) \emph{Assessing the Reliability of Statistical
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Software, Part I}, The American Statistician, Vol. 52 No 4,
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\url{http://www.amstat.org/publications/tas/mccull-1.pdf}
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McCullough, D.B., (1999) \emph{Assessing the Reliability of Statistical
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Software, Part II}, The American Statistician, Vol. 53 No 2
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\url{http://www.amstat.org/publications/tas/mccull.pdf}
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NIST Statistical Reference Datasets (StRD) website
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\url{http://www.nist.gov/itl/div898/strd}
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\author{Jarek Tuszynski (SAIC) \email{jaroslaw.w.tuszynski@saic.com} based on
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code by Vadim Ogranovich, which is based on algorithms described in
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references, pointed out by Gabor Grothendieck.
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\item \code{\link[base]{sum}} is faster but not error-save version of
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\item \code{\link[base]{cumsum}} is equivalent to \code{cumsum.exact}
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\item \code{\link{runmean}(x,k,endrule="trim")} is similar to
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x = c(1, 1e20, 1e40, -1e40, -1e20, -1)
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b = sum.exact(x); print(b)
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a = cumsum(x); print(a)
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b = cumsum.exact(x); print(b)
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\concept{sum with no round-off errors}
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\concept{cumulative sum with no round-off errors}
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\concept{moving sum with no round-off errors}
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\concept{rolling sum with no round-off errors}
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\concept{running sum with no round-off errors}
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man/sum.exact.Rd
