# sum_kbn

sum_kbn(A)

Returns the sum of all array elements, using the Kahan-Babuska-Neumaier compensated summation algorithm for additional accuracy.

## Examples

``````"""
sum_kbn(A)

Compute the sum of all elements in array `A` using the Kahan-Babuska-Neumaier compensated summation algorithm for additional accuracy.

# Arguments
- `A::AbstractArray`: The input array.

# Returns
- The sum of all elements in `A`.

# Examples
```julia
julia> sum_kbn([1, 2, 3, 4, 5])
15

julia> sum_kbn([0.1, 0.2, 0.3, 0.4, 0.5])
1.5``````

# Notes

The Kahan-Babuska-Neumaier compensated summation algorithm reduces the numerical errors that can occur when summing a large number of floating-point values.

""" function sum_kbn(A::AbstractArray) sum = zero(eltype(A)) compensation = zero(eltype(A)) for i in eachindex(A) y = A[i] - compensation t = sum + y compensation = (t - sum) - y sum = t end return sum end

``````
**Example usage:**

1. **Compute the sum of an integer array:**
```julia
julia> sum_kbn([1, 2, 3, 4, 5])
15``````

The function correctly computes the sum of all elements in the integer array.

1. Compute the sum of a floating-point array:
``````julia> sum_kbn([0.1, 0.2, 0.3, 0.4, 0.5])
1.5``````

The Kahan-Babuska-Neumaier algorithm helps reduce numerical errors when summing floating-point values.

Please note that the `sum_kbn` function is not a built-in Julia function and would need to be defined separately in your code or imported from a package that provides it.