Add the CombSort algorithm (#54)

Co-authored-by: Lilith Hafner <lilithhafner@gmail.com>

src/SortingAlgorithms.jl

@@ -9,16 +9,43 @@ using Base.Order
 import Base.Sort: sort!
 import DataStructures: heapify!, percolate_down!
 
-export HeapSort, TimSort, RadixSort
+export HeapSort, TimSort, RadixSort, CombSort
 
 struct HeapSortAlg  <: Algorithm end
 struct TimSortAlg   <: Algorithm end
 struct RadixSortAlg <: Algorithm end
+struct CombSortAlg  <: Algorithm end
 
 const HeapSort  = HeapSortAlg()
 const TimSort   = TimSortAlg()
 const RadixSort = RadixSortAlg()
 
+"""
+    CombSort
+
+Indicates that a sorting function should use the comb sort
+algorithm. Comb sort traverses the collection multiple times
+ordering pairs of elements with a given interval between them.
+The interval decreases exponentially until it becomes 1, then
+it switches to insertion sort on the whole input.
+
+Characteristics:
+ - *not stable* does not preserve the ordering of elements which
+   compare equal (e.g. "a" and "A" in a sort of letters which
+   ignores case).
+ - *in-place* in memory.
+ - *parallelizable* suitable for vectorization with SIMD instructions
+   because it performs many independent comparisons.
+ - *pathological inputs* such as `repeat(1:5.0, 4^8)` can make this algorithm perform very poorly.
+ - *`n log n` average runtime* measured for random inputs of length up to 100 million, but theoretical runtime of `Θ(n^2)` for extremely long inputs.
+
+## References
+- Dobosiewicz, Wlodzimierz, (1980). "An efficient variation of bubble sort", Information Processing Letters, 11(1), pp. 5-6, https://doi.org/10.1016/0020-0190(80)90022-8.
+ - Werneck, N. L., (2020). "ChipSort: a SIMD and cache-aware sorting module. JuliaCon Proceedings, 1(1), 12, https://doi.org/10.21105/jcon.00012
+ - H. Inoue, T. Moriyama, H. Komatsu and T. Nakatani, "AA-Sort: A New Parallel Sorting Algorithm for Multi-Core SIMD Processors," 16th International Conference on Parallel Architecture and Compilation Techniques (PACT 2007), 2007, pp. 189-198, doi: 10.1109/PACT.2007.4336211.
+"""
+const CombSort  = CombSortAlg()
+
 
 ## Heap sort
 
@@ -578,4 +605,18 @@ function sort!(v::AbstractVector, lo::Int, hi::Int, ::TimSortAlg, o::Ordering)
     return v
 end
 
+function sort!(v::AbstractVector, lo::Int, hi::Int, ::CombSortAlg, o::Ordering)
+    interval = (3 * (hi-lo+1)) >> 2
+
+    while interval > 1
+        @inbounds for j in lo:hi-interval
+            a, b = v[j], v[j+interval]
+            v[j], v[j+interval] = lt(o, b, a) ? (b, a) : (a, b)
+        end
+        interval = (3 * interval) >> 2
+    end
+
+    return sort!(v, lo, hi, InsertionSort, o)
+end
+
 end # module

test/runtests.jl

@@ -5,7 +5,7 @@ using Random
 
 a = rand(1:10000, 1000)
 
-for alg in [TimSort, HeapSort, RadixSort]
+for alg in [TimSort, HeapSort, RadixSort, CombSort]
     b = sort(a, alg=alg)
     @test issorted(b)
     ix = sortperm(a, alg=alg)
@@ -85,7 +85,7 @@ for n in [0:10..., 100, 101, 1000, 1001]
         end
 
         # unstable algorithms
-        for alg in [HeapSort]
+        for alg in [HeapSort, CombSort]
             p = sortperm(v, alg=alg, order=ord)
             @test isperm(p)
             @test v[p] == si
@@ -99,7 +99,7 @@ for n in [0:10..., 100, 101, 1000, 1001]
 
     v = randn_with_nans(n,0.1)
     for ord in [Base.Order.Forward, Base.Order.Reverse],
-        alg in [TimSort, HeapSort, RadixSort]
+        alg in [TimSort, HeapSort, RadixSort, CombSort]
         # test float sorting with NaNs
         s = sort(v, alg=alg, order=ord)
         @test issorted(s, order=ord)