# fsum

##### Return an accurate floating point sum of values

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.

##### References

https://docs.python.org/2/library/math.html

https://code.activestate.com/recipes/393090/

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

```
# NOT RUN {
sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0
fsum(c(1,1e100,1,-1e100)) ## Gives 2.
# }
```

*Documentation reproduced from package PreciseSums, version 0.3, License: GPL (>= 2)*