What sorting algorithm does Swift implement for its standard library?

Update 2: As we can see in Sort.swift, sort() now uses a “modified timsort” in Swift 5. Timsort is a

… hybrid stable sorting algorithm, derived from merge sort and insertion sort …

In the worst case, Timsort takes O(n log n) comparisons to sort an array of n elements. In the best case, which occurs when the input is already sorted, it runs in linear time, meaning that it is an adaptive sorting algorithm.

This means that sort() happens to be a stable sort in Swift 5, but that is still an implementation detail. The MutableCollection.sort documentation states that

The sorting algorithm is not guaranteed to be stable. A stable sort preserves the relative order of elements that compare equal.

See also Is sort() stable in Swift 5? in the Swift forum:

The algorithm was only recently made stable in preparation for a proposal to make it guaranteed as such.

---

Update: Swift is open source now, and in

• https://github.com/apple/swift/blob/master/stdlib/public/core/Sort.swift

one can see that sorting a collection is done using introsort
with a maximum recursion depth of 2*floor(log_2(N)). It switches to insertion sort for partitions with less than 20 elements, or to heapsort
if the recursion depth is reached.

---

Old answer: Defining a custom Comparable structure and setting in breakpoint in <:

struct MyStruct : Comparable {
    let val : Int
}

func ==(x: MyStruct, y: MyStruct) -> Bool {
    println("\(x.val) ==  \(y.val)")
    return x.val == y.val
}
func <(x: MyStruct, y: MyStruct) -> Bool {
    println("\(x.val) < \(y.val)")
    return x.val < y.val // <--- SET BREAKPOINT HERE
}

var array = [MyStruct]()
for _ in 1 ... 30 {
    array.append(MyStruct(val: Int(arc4random_uniform(1000))))
}
sort(&array)

shows the following stack backtrace:

(lldb) bt
* thread #1: tid = 0x5a00, 0x00000001001cb806 sort`sort. Swift.Bool + 454 at main.swift:22, queue="com.apple.main-thread", stop reason = breakpoint 1.1
  * frame #0: 0x00000001001cb806 sort`sort. Swift.Bool + 454 at main.swift:22
    frame #1: 0x00000001001cb62b sort`protocol witness for Swift._Comparable.(Swift._Comparable.Self.Type)(Swift._Comparable.Self, Swift._Comparable.Self) -> Swift.Bool in conformance sort.MyStruct : Swift._Comparable + 27 at main.swift:20
    frame #2: 0x00000001000f5a98 sort`Swift._partition (inout A, Swift.Range) -> A.Index + 3224
    frame #3: 0x00000001000f756a sort`Swift._introSortImpl (inout A, Swift.Range, Swift.Int) -> () + 2138
    frame #4: 0x00000001000f6c01 sort`Swift._introSort (inout A, Swift.Range) -> () + 1233
    frame #5: 0x00000001000fc47f sort`Swift.sort (inout A) -> () + 607
    frame #6: 0x000000010013ea77 sort`partial apply forwarder for Swift.(sort (inout Swift.Array) -> ()).(closure #1) + 183
    frame #7: 0x000000010013eaf8 sort`partial apply forwarder for reabstraction thunk helper  from @callee_owned (@inout Swift.UnsafeMutableBufferPointer) -> (@unowned ()) to @callee_owned (@inout Swift.UnsafeMutableBufferPointer) -> (@out ()) + 56
    frame #8: 0x0000000100046c4b sort`Swift.Array.withUnsafeMutableBufferPointer (inout Swift.Array)((inout Swift.UnsafeMutableBufferPointer) -> B) -> B + 475
    frame #9: 0x00000001000fc5ad sort`Swift.sort (inout Swift.Array) -> () + 157
    frame #10: 0x00000001001cb465 sort`top_level_code + 1237 at main.swift:29
    frame #11: 0x00000001001cbdca sort`main + 42 at main.swift:0
    frame #12: 0x00007fff8aa9a5fd libdyld.dylib`start + 1

and later

(lldb) bt
* thread #1: tid = 0x5a00, 0x00000001001cb806 sort`sort. Swift.Bool + 454 at main.swift:22, queue="com.apple.main-thread", stop reason = breakpoint 1.1
  * frame #0: 0x00000001001cb806 sort`sort. Swift.Bool + 454 at main.swift:22
    frame #1: 0x00000001001cb62b sort`protocol witness for Swift._Comparable.(Swift._Comparable.Self.Type)(Swift._Comparable.Self, Swift._Comparable.Self) -> Swift.Bool in conformance sort.MyStruct : Swift._Comparable + 27 at main.swift:20
    frame #2: 0x00000001000f449e sort`Swift._insertionSort (inout A, Swift.Range) -> () + 2958
    frame #3: 0x00000001000f730e sort`Swift._introSortImpl (inout A, Swift.Range, Swift.Int) -> () + 1534
    frame #4: 0x00000001000f797d sort`Swift._introSortImpl (inout A, Swift.Range, Swift.Int) -> () + 3181
    frame #5: 0x00000001000f6c01 sort`Swift._introSort (inout A, Swift.Range) -> () + 1233
    frame #6: 0x00000001000fc47f sort`Swift.sort (inout A) -> () + 607
    frame #7: 0x000000010013ea77 sort`partial apply forwarder for Swift.(sort (inout Swift.Array) -> ()).(closure #1) + 183
    frame #8: 0x000000010013eaf8 sort`partial apply forwarder for reabstraction thunk helper  from @callee_owned (@inout Swift.UnsafeMutableBufferPointer) -> (@unowned ()) to @callee_owned (@inout Swift.UnsafeMutableBufferPointer) -> (@out ()) + 56
    frame #9: 0x0000000100046c4b sort`Swift.Array.withUnsafeMutableBufferPointer (inout Swift.Array)((inout Swift.UnsafeMutableBufferPointer) -> B) -> B + 475
    frame #10: 0x00000001000fc5ad sort`Swift.sort (inout Swift.Array) -> () + 157
    frame #11: 0x00000001001cb465 sort`top_level_code + 1237 at main.swift:29
    frame #12: 0x00000001001cbdca sort`main + 42 at main.swift:0
    frame #13: 0x00007fff8aa9a5fd libdyld.dylib`start + 1

This confirms the conjecture of Airspeed’s answer that introsort is used
in combination with insertion sort for the smaller ranges.

If the array has less than 20 elements then only insertion sort seems to be used.
This could indicate that the threshold for switching from introsort to
insertion sort is 20.

Of course the implementation might change in the future.