### Cumulative Summation with Kahan Summation

Source: https://github.com/juliamath/kahansummation.jl/blob/master/README.md

Demonstrates the difference between standard `cumsum` and `cumsum_kbn` for a specific vector. This highlights potential precision gains in cumulative sums. Ensure `KahanSummation` is imported.

```julia
julia> vec = [1.0, 1.0e16, 1.0, -1.0e16];

julia> cumsum_kbn(vec) .- cumsum(vec)
4-element Array{Float64,1}:
 0.0
 0.0
 2.0
 1.0
```

--------------------------------

### Summation with Kahan Summation

Source: https://github.com/juliamath/kahansummation.jl/blob/master/README.md

Compares the standard `sum` function with `sum_kbn` for a vector containing large and small numbers to show precision differences. Ensure `KahanSummation` is imported.

```julia
julia> using KahanSummation

julia> vec = [1.0, 1.0e16, -1.0e16, -0.5];

julia> sum(vec), sum_kbn(vec)
(-0.5, 0.5)
```

--------------------------------

### KahanSummation.cumsum_kbn Function

Source: https://github.com/juliamath/kahansummation.jl/blob/master/docs/src/index.md

This snippet documents the `cumsum_kbn` function, which computes the cumulative sum of an array using the Kahan-Babuska-Neumaier algorithm. It's useful for scenarios where accumulating sums with high precision is critical.

```julia
using KahanSummation

# Example usage:
array = [1.0, 2.0, 3.0, 4.0, 5.0]
result = cumsum_kbn(array)
println(result) # Output will be a more accurate cumulative sum
```

--------------------------------

### KahanSummation.sum_kbn Function

Source: https://github.com/juliamath/kahansummation.jl/blob/master/docs/src/index.md

This snippet documents the `sum_kbn` function, which computes the sum of an array using the Kahan-Babuska-Neumaier algorithm. Use this for applications requiring high precision summation.

```julia
using KahanSummation

# Example usage:
array = [1.0, 2.0, 3.0, 4.0, 5.0]
result = sum_kbn(array)
println(result) # Output will be a more accurate sum than standard sum()
```

=== COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.