Modern Math Sum

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Sum

Adds up an array with compensated summation, so small values are not lost.

Syntax

Sum( byref a as Array( of T ) ) as float64

Notes

• compensated -- Neumaier

Examples

#import "std/numeric"
#import "std/containers"
using numeric
using containers

'' COMPENSATED summation (Neumaier), so the running error is tracked and
'' folded back in rather than accumulating
dim as Array( of float64 ) a = { 1e16, 1.0, -1e16, 1.0 }

print Sum( a )            '' 2 -- both 1.0s survive
print NaiveSum( a )       '' 1 -- the naive loop lost one of them

'' The difference is not a rounding detail: half the answer is missing

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Library: Math Library
Category: Math Library
Documented under: Nothing Becomes A Keyword