caTools (version 1.7)

sum.exact, cumsum.exact & runsum.exact: Basic Sum Operations without Round-off Errors

Description

Functions for performing basic sum operations without round-off errors

Usage

sum.exact(..., na.rm = FALSE)
  cumsum.exact(x)
  runsum.exact(x,k)

Arguments

x

numeric vector

...

numeric vector(s), numbers or other objects to be summed

na.rm

logical. Should missing values be removed?

k

width of moving window; must be an odd integer between one and n

Value

• Function sum.exact returns single number. Function cumsum.exact returns vector of the same length as x. Function runsum.exact returns vector of length length(x)-k and attribute "count" containing number of finite (as in is.finite) elements in each window.

concept

• sum with no round-off errors
• cumulative sum with no round-off errors
• moving sum with no round-off errors
• rolling sum with no round-off errors
• running sum with no round-off errors

Details

All three functions use full precision summation using multiple doubles for intermediate values. The sum of numbers x & y is a=x+y with error term b=error(a+b). That way a+b is equal exactly x+y, so sum of 2 numbers is stored as 2 or fewer values, which when added would under-flow. By extension sum of n numbers is calculated with intermediate results stored as array of numbers that can not be added without introducing an error. Only final result is converted to a single number

References

Round-off error correction is based on: Shewchuk, Jonathan, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps and its implementation found at: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090 McCullough, D.B., (1998) Assessing the Reliability of Statistical Software, Part I, The American Statistician, Vol. 52 No 4, http://www.amstat.org/publications/tas/mccull-1.pdf McCullough, D.B., (1999) Assessing the Reliability of Statistical Software, Part II, The American Statistician, Vol. 53 No 2 http://www.amstat.org/publications/tas/mccull.pdf NIST Statistical Reference Datasets (StRD) website http://www.nist.gov/itl/div898/strd

See Also

• sumis faster but not error-save version ofsum.exact
• cumsumis equivalent tocumsum.exact
• runmean(x,k,endrule="trim")is similar torunsum.exact.

Examples

x = c(1, 1e20, 1e40, -1e40, -1e20, -1)
  a = sum(x);          print(a)
  b = sum.exact(x);    print(b)
  stopifnot(b==0)
  a = cumsum(x);       print(a)
  b = cumsum.exact(x); print(b)
  stopifnot(b[6]==0)