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Date: Mon, 1 Sep 2014 13:17:48 +0200
From: Szabolcs Nagy <nsz@...t70.net>
To: musl@...ts.openwall.com
Subject: Re: [RFC] new qsort implementation

* Bobby Bingham <koorogi@...rogi.info> [2014-09-01 02:12:43 -0500]:
> You can find my test program with this algorithm and others at [4].
> Some of the implementations included are quicksort variants, so the
> "qsort-killer" testcase will trigger quadratic behavior in them.  If you
> want to run this you should consider reducing the maximum input size in
> testcases.h, disabling the qsort-killer input at the bottom of
> testcases.c, or disabling the affected sort algorithms ("freebsd",
> "glibc quicksort", and depending on your libc, "system") in sorters.c.

(i had a few build errors: musl_heapsort and musl_smoothsort were not
declared in sorters.h and glibc needs -lrt for clock_gettime)

smooth sort is best for almost sorted lists when only a few elements
are out of order (swap some random elements in a sorted array), this
is common in practice so you should test this case too

the noise case should use much less noise imho (so you test when
only local rearrangements are needed: buffer[i] += random()%small)

another common case is sorting two concatenated sorted arrays
(merge sort should do better in this case)

it would be nice to have a benchmark that is based on common
qsort usage cases

the qsort-killer test is not very interesting for algorithms other
than quicksort (where it is the worst-case), but it would be nice
to analyze the worst cases for smoothsort and grailsort
(they are both O(n logn) so nothing spectacular is expected but it
would be interesting to see how they compare against the theoretical
optimum: ceil(lgamma(n)/log(2)) compares)

> Here are the numbers comparing musl's current smoothsort with the
> attached grailsort code for various input patterns and sizes.  The test
> was run on x86_64, compiled with gcc 4.8.3 at -Os:
> 
>                           sorted             reverse            constant
>                  compares     ms     compares     ms     compares     ms
> musl smoothsort     19976      0       268152      8        19976      0
>                    199971      2      3327332     59       199971      2
>                   1999963     29     40048748    663      1999963     27
>                  19999960    289    465600753   7505     19999960    293
> 
> grailsort           71024      0        41110      0        28004      0
>                    753996      2       412840      5       270727      3
>                   7686249     27      4177007     74      2729965     41
>                  75927601    277     42751315    901     28243939    436
> 

interesting that the sorted case is faster with much more compares
here on i386 smoothsort is faster

                            sorted             reverse            constant
                   compares     ms     compares     ms     compares     ms
musl smoothsort       19976      0       268152      7        19976      1
                     199971      8      3327332    103       199971     15
                    1999963    105     40048748   1151      1999963    103
                   19999960   1087    465600753  13339     19999960   1103

grailsort             71024      1        41110      3        28004      3
                     753996     20       412840     23       270727     23
                    7686249    151      4177007    370      2729965    224
                   75927601   1438     42751315   4507     28243939   2353

> #include <stdlib.h>
> #include <limits.h>
> 
> size_t __bsearch(const void *key, const void *base, size_t nel, size_t width, int (*cmp)(const void *, const void *))
> {
> 	size_t baseidx = 0, tryidx;
> 	void *try;
> 	int sign;
> 
> 	while (nel > 0) {
> 		tryidx = baseidx + nel/2;
> 		try = (char*)base + tryidx*width;
> 		sign = cmp(key, try);
> 		if (!sign) return tryidx;
> 		else if (sign < 0)
> 			nel /= 2;
> 		else {
> 			baseidx = tryidx + 1;
> 			nel -= nel/2 + 1;
> 		}
> 	}
> 
> 	return ~baseidx;
> }
> 
> void *bsearch(const void *key, const void *base, size_t nel, size_t width, int (*cmp)(const void *, const void *))
> {
> 	size_t idx = __bsearch(key, base, nel, width, cmp);
> 	return idx > SSIZE_MAX ? NULL : (char*)base + idx*width;
> }

musl does not malloc >=SSIZE_MAX memory, but mmap can so baseidx
may be >0x7fffffff on a 32bit system

i'm not sure if current qsort handles this case

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