Is Go's `append` Function Truly Amortized Constant Time?

Amortized Complexity of append in Go

In the Go programming language, the append function is used to resize and extend slices. Its computational complexity has been a topic of discussion due to its ability to reallocate memory, which could potentially impact performance.

Amortized Constant Time

The Go Programming Language Specification states that append takes amortized constant time to execute. This means that the average time taken to append to a slice over a series of operations is constant. The implementation of append optimizes for this amortized constant time behavior by allocating memory dynamically based on the current slice capacity.

Reallocation Strategy

The precise algorithm used to determine when to reallocate memory in append is implementation-dependent. For the current Go compiler (gc), the growslice function in the runtime package's slice.go source file implements an amortized constant time algorithm.

The algorithm calculates the new slice capacity based on the current and previous capacities using a combination of doubling and a minimum memory allocation strategy. This ensures that the slice grows gradually, avoiding the need for constant reallocations.

Example

The following example illustrates the amortized constant time behavior of append in Go:

var a []int
for i := 0; i < n; i++ {
  a = append(a, i)
}

In this loop, the append operation is performed repeatedly, causing the slice a to grow. However, due to the amortized constant time behavior of append, the overall time taken for the operation is still O(n), where n is the number of elements appended to the slice.

Implementation Notes

While the current Go compiler uses an amortized constant time algorithm for append, it's important to note that other implementations may vary. The standard allows for different approaches, including parsimonious reallocation, where memory is allocated only when necessary.

Conclusion

In conclusion, the append function in Go is optimized for amortized constant time complexity. This means that appending to a slice over a series of operations takes an average constant amount of time, providing efficient and consistent performance.

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