A library of internal sorting routines

Ariel Faigon

Keywords:- insertion sort, shellsort, radixsort, heapsort, quicksort, quickersort, sedgesort (Robert Sedgewick quicksort optimization)
This is a collection of sorting algorithms, in C. All the examples are thoroughly tested using random input generation and assertions, there are

no known bugs. I've been using these, especially the fastest``sedgesort'', in production code.

Licensing:This code is released under the GNU GPL (General Public License) version 2 which you can find at gnu.org.The source of these algorithms are classic algorithms and C texts/books which I highly recommend. In some cases I had to convert the original pseudocode to the 'C' programming language to make it actually work (Note: Sedgewick, "Algorithms in C" wasn't yet published when I wrote this code - way back in the 1980's. I used the First edition which used pseudocode for all examples). In addition I have introduced some minor modifications to the code over time to improve style, readability, and efficiency and added a unit-test suite to ensure correctness:

- Robert Sedgewick: Algorithms in C:

Fundamentals, Data Structures, Sorting, Searching- Jon Louis Bentley: Programming Pearls
- Kernighan & Ritchie: The C Programming Language
All the sorting routines are "internal" sorts, i.e. they assume your sorted data is in memory. When sorting big arrays that do not fit in memory on virtual memory systems, performance may suffer significantly.

Certain current implementations of sorting in C++ standard libraries like STL (the HP/SGI Standard Template Library which is now a part of the GNU free software collection) are comparable in speed to

```sedgesort''`

. Note however that the general C/Unix```qsort''`

routine is much slower due to its generality (e.g. element compare is done via an indirect function call passed as a function pointer.)

Array-size cut-off (CUTOFF) value for switching from recursive to non-recursive:/* * Interesting historical/technological tidbit: * * 15 has been found empirically as the optimal cutoff value in 1996 * * 10 years later, in 2006, with computers being very different and * much faster, I revisited this constant and found the optimal * value to be a close tie between 15 and 16 * * ~7 years later (end of 2013): * - On an Intel i7-4771 with hyper-threading * - Larger caches * - Newer compiler (clang replacing gcc) * - Building with -O3 -fomit-frame-pointer * Technology has finally made a difference and could make the switch * to a higher CUTOFF value. * * Here are the run times sorting a 100k element array: * -DCUTOFF=10: sedgesort: 5148 microsec. * -DCUTOFF=15: sedgesort: 5032 microsec. * -DCUTOFF=16: sedgesort: 4998 microsec. * -DCUTOFF=20: sedgesort: 4926 microsec. * -DCUTOFF=25: sedgesort: 4880 microsec. * -DCUTOFF=30: sedgesort: 4830 microsec. * -DCUTOFF=40: sedgesort: 4770 microsec. * -DCUTOFF=50: sedgesort: 4746 microsec. (minima) * -DCUTOFF=60: sedgesort: 4770 microsec. */ #ifndef CUTOFF # define CUTOFF 50 #endif

2014 update:Jann Röder has ported this library to Windows and kindly contributed his changes, saying:

Hi Ariel,

I found your sort library very useful. My tests show that your sedgesort is about 30% faster than the built-in sort function in .NET 4.51 on random inputs which happens to be my use case. I did not test other inputs. I have adapted the code a bit so it compiles on Windows. I also included a .cs class with which you can use the C code built as DLL in a .NET program.

Additionally I adapted the Dual Pivot Quicksort (http://iaroslavski.narod.ru/quicksort/DualPivotQuicksort.pdf) to C and included it. If I use your insort for the small sub array sort it is about as fast as sedgesort on random inputs. I imagine it performs better if the inputs aren't random.

Feel free to put the attached archive on your website. Maybe someone will find it useful.

Jann

You maydownload the whole sort libraryor browse the individual files below.Here are some brief descriptions of the sort library source files:

- Makefile
- Simple makefile to build the library
`sort.a`

and the test program`sorttest`

.

- sort.h
- Header file. defines the
`key_t`

type, the type of the items we are sorting, macros for key-comparisons: GT (greater than), LT (less than), GE (greater or equal), LE (less or equal). SWAP macro to swap elements in the array. Macros are used instead of a compare function for speed. You may define all the above to your liking and recompile the library.

- insort.c
- Insertion sort. Most efficient for small arrays (about 15 elements or less). For greater arrays, use one of the O(n*log(n)) methods. If you have small arrays, use this. Other methods are an overkill, and are
notfaster.

- shellsort.c
- Shell Sort. Named after its inventor, D.L. Shell (1959) More efficient than insertion sort for arrays larger than about 15 elements, but less efficient than the O(n*log(n)) methods. The beauty of this method is how small the code is. Its average time is O(n^1.2) and the worst case bound is O(n*(log(n)^2)).

- gamasort.c
- A radix sort based on bits in the binary representation of the sorted numbers. Contributed by José Gama. Gamasort will work only on unsigned integers in 2-complement representation. Thus it is less general than the other methods, it also has a relatively high complexity factor. On the positive side this is an O(n*log(n)) algorithm in which the 'n' is proportional to the largest number in the sorted array so it scales well to the cases where the array is very big but the numbers in it are relatively small like a million element array containing unsigned bytes.

- quicksort.c
- quicksort. Invented by C.A.R. Hoare. Very good average time n*log(n), where the constant K is very small. but worst case is bad: O(n^2). See, sedgesort for a significant practical improvement.

- quickersort.c
- An optimization of quicksort. Use a sentinel containing MAXINT, to make the constant K even smaller. This is similar to the
`qsort`

libc function, but without the`(*compar)()`

call penalty.

- sedgesort.c
- Robert Sedgewick optimization. Use partial quickersort with a sentinel to reach a partial order, leave the unsorted segments of length == CUTOFF unsorted. Then apply a simpler one-pass low-overhead insertion sort on the whole array to reach complete order. This method was found empirically to be one of the fastest sorting methods in practice. If you don't believe it, try to beat it. Note, worst cases are rare in big arrays, so to keep the overhead to minimum, this sort does
nottry to avoid worst cases (e.g. using median of three to select a random pivot).

- heapsort.c
- Heap sort. This is
on average, slower than quicksort. But is has the advantage that it worst case is still O(n*log(n)) rather than O(n^2). Like quicksort, and other methods which pick elements at random positions in order to possibly exchange their positions, it is not'stable'; elements of the same magnitude, might switch their relative order.This is a relatively optimized version of heap-sort which minimizes neighboring elements exchanges in the innermost loop, using an insertion strategy. To do this, it first finds the final locations, and only then does the exchanges. Another advantage of heapsort over

quicksort/sedgesortis that it enables you to do complete sorts on a top-subset of the elements. I.e. if you want only the top C (constant) elements out of N elements, heap-sort is the way to go; just create a heap, then call the'sift'function, C times only. This feature is sometimes referred to as a heap implementation of apriority-queue.

Auxilliary test routines:

- sorttest.c: Program containing
`main()`

to test the sort library`sort.a`

.- bstest.c: Program containing
`main()`

to test the binary search routine that is included here as well.- sorted.c: Test routine to verify that an array is sorted.

Feedback to:

If you used this, and found it useful, please let me know.

I'd be more inclined to enrich this collection if I know people find it useful.

Please note that this software is released under the GNU General Public License v2.