fsum: Return an accurate floating point sum of values

In PreciseSums: Accurate Floating Point Sums and Products

Return an accurate floating point sum of values

Description

This method avoids loss of precision by tracking multiple intermediate partial sums. Based on python's math.fsum

Usage

fsum(numbers)

Arguments

numbers

A vector of numbers to sum.

Value

Sum of numbers without loss of precision

The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.

Author(s)

Matthew Fidler (R implementation), Raymond Hettinger, Jonathan Shewchuk, Python Team

References

https://docs.python.org/2/library/math.html https://github.com/python/cpython/blob/a0ce375e10b50f7606cb86b072fed7d8cd574fe7/Modules/mathmodule.c

Shewchuk, JR. (1996) 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

Examples

sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0
fsum(c(1,1e100,1,-1e100)) ## Gives 2.

PreciseSums documentation built on Sept. 30, 2024, 9:46 a.m.