Net2/usr/src/lib/libc/stdlib/radixsort.c
/*-
* Copyright (c) 1990 The Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)radixsort.c 5.7 (Berkeley) 2/23/91";
#endif /* LIBC_SCCS and not lint */
#include <sys/types.h>
#include <limits.h>
#include <stdlib.h>
#include <stddef.h>
#include <string.h>
/*
* __rspartition is the cutoff point for a further partitioning instead
* of a shellsort. If it changes check __rsshell_increments. Both of
* these are exported, as the best values are data dependent.
*/
#define NPARTITION 40
int __rspartition = NPARTITION;
int __rsshell_increments[] = { 4, 1, 0, 0, 0, 0, 0, 0 };
/*
* Stackp points to context structures, where each structure schedules a
* partitioning. Radixsort exits when the stack is empty.
*
* If the buckets are placed on the stack randomly, the worst case is when
* all the buckets but one contain (npartitions + 1) elements and the bucket
* pushed on the stack last contains the rest of the elements. In this case,
* stack growth is bounded by:
*
* limit = (nelements / (npartitions + 1)) - 1;
*
* This is a very large number, 52,377,648 for the maximum 32-bit signed int.
*
* By forcing the largest bucket to be pushed on the stack first, the worst
* case is when all but two buckets each contain (npartitions + 1) elements,
* with the remaining elements split equally between the first and last
* buckets pushed on the stack. In this case, stack growth is bounded when:
*
* for (partition_cnt = 0; nelements > npartitions; ++partition_cnt)
* nelements =
* (nelements - (npartitions + 1) * (nbuckets - 2)) / 2;
* The bound is:
*
* limit = partition_cnt * (nbuckets - 1);
*
* This is a much smaller number, 4590 for the maximum 32-bit signed int.
*/
#define NBUCKETS (UCHAR_MAX + 1)
typedef struct _stack {
const u_char **bot;
int indx, nmemb;
} CONTEXT;
#define STACKPUSH { \
stackp->bot = p; \
stackp->nmemb = nmemb; \
stackp->indx = indx; \
++stackp; \
}
#define STACKPOP { \
if (stackp == stack) \
break; \
--stackp; \
bot = stackp->bot; \
nmemb = stackp->nmemb; \
indx = stackp->indx; \
}
/*
* A variant of MSD radix sorting; see Knuth Vol. 3, page 177, and 5.2.5,
* Ex. 10 and 12. Also, "Three Partition Refinement Algorithms, Paige
* and Tarjan, SIAM J. Comput. Vol. 16, No. 6, December 1987.
*
* This uses a simple sort as soon as a bucket crosses a cutoff point,
* rather than sorting the entire list after partitioning is finished.
* This should be an advantage.
*
* This is pure MSD instead of LSD of some number of MSD, switching to
* the simple sort as soon as possible. Takes linear time relative to
* the number of bytes in the strings.
*/
int
#if __STDC__
radixsort(const u_char **l1, int nmemb, const u_char *tab, u_char endbyte)
#else
radixsort(l1, nmemb, tab, endbyte)
const u_char **l1;
register int nmemb;
const u_char *tab;
u_char endbyte;
#endif
{
register int i, indx, t1, t2;
register const u_char **l2;
register const u_char **p;
register const u_char **bot;
register const u_char *tr;
CONTEXT *stack, *stackp;
int c[NBUCKETS + 1], max;
u_char ltab[NBUCKETS];
static void shellsort();
if (nmemb <= 1)
return(0);
/*
* T1 is the constant part of the equation, the number of elements
* represented on the stack between the top and bottom entries.
* It doesn't get rounded as the divide by 2 rounds down (correct
* for a value being subtracted). T2, the nelem value, has to be
* rounded up before each divide because we want an upper bound;
* this could overflow if nmemb is the maximum int.
*/
t1 = ((__rspartition + 1) * (NBUCKETS - 2)) >> 1;
for (i = 0, t2 = nmemb; t2 > __rspartition; i += NBUCKETS - 1)
t2 = ((t2 + 1) >> 1) - t1;
if (i) {
if (!(stack = stackp = (CONTEXT *)malloc(i * sizeof(CONTEXT))))
return(-1);
} else
stack = stackp = NULL;
/*
* There are two arrays, one provided by the user (l1), and the
* temporary one (l2). The data is sorted to the temporary stack,
* and then copied back. The speedup of using index to determine
* which stack the data is on and simply swapping stacks back and
* forth, thus avoiding the copy every iteration, turns out to not
* be any faster than the current implementation.
*/
if (!(l2 = (const u_char **)malloc(sizeof(u_char *) * nmemb)))
return(-1);
/*
* Tr references a table of sort weights; multiple entries may
* map to the same weight; EOS char must have the lowest weight.
*/
if (tab)
tr = tab;
else {
for (t1 = 0, t2 = endbyte; t1 < t2; ++t1)
ltab[t1] = t1 + 1;
ltab[t2] = 0;
for (t1 = endbyte + 1; t1 < NBUCKETS; ++t1)
ltab[t1] = t1;
tr = ltab;
}
/* First sort is entire stack */
bot = l1;
indx = 0;
for (;;) {
/* Clear bucket count array */
bzero((char *)c, sizeof(c));
/*
* Compute number of items that sort to the same bucket
* for this index.
*/
for (p = bot, i = nmemb; --i >= 0;)
++c[tr[(*p++)[indx]]];
/*
* Sum the number of characters into c, dividing the temp
* stack into the right number of buckets for this bucket,
* this index. C contains the cumulative total of keys
* before and included in this bucket, and will later be
* used as an index to the bucket. c[NBUCKETS] contains
* the total number of elements, for determining how many
* elements the last bucket contains. At the same time
* find the largest bucket so it gets pushed first.
*/
for (i = max = t1 = 0, t2 = __rspartition; i <= NBUCKETS; ++i) {
if (c[i] > t2) {
t2 = c[i];
max = i;
}
t1 = c[i] += t1;
}
/*
* Partition the elements into buckets; c decrements through
* the bucket, and ends up pointing to the first element of
* the bucket.
*/
for (i = nmemb; --i >= 0;) {
--p;
l2[--c[tr[(*p)[indx]]]] = *p;
}
/* Copy the partitioned elements back to user stack */
bcopy(l2, bot, nmemb * sizeof(u_char *));
++indx;
/*
* Sort buckets as necessary; don't sort c[0], it's the
* EOS character bucket, and nothing can follow EOS.
*/
for (i = max; i; --i) {
if ((nmemb = c[i + 1] - (t1 = c[i])) < 2)
continue;
p = bot + t1;
if (nmemb > __rspartition)
STACKPUSH
else
shellsort(p, indx, nmemb, tr);
}
for (i = max + 1; i < NBUCKETS; ++i) {
if ((nmemb = c[i + 1] - (t1 = c[i])) < 2)
continue;
p = bot + t1;
if (nmemb > __rspartition)
STACKPUSH
else
shellsort(p, indx, nmemb, tr);
}
/* Break out when stack is empty */
STACKPOP
}
free((char *)l2);
free((char *)stack);
return(0);
}
/*
* Shellsort (diminishing increment sort) from Data Structures and
* Algorithms, Aho, Hopcraft and Ullman, 1983 Edition, page 290;
* see also Knuth Vol. 3, page 84. The increments are selected from
* formula (8), page 95. Roughly O(N^3/2).
*/
static void
shellsort(p, indx, nmemb, tr)
register u_char **p, *tr;
register int indx, nmemb;
{
register u_char ch, *s1, *s2;
register int incr, *incrp, t1, t2;
for (incrp = __rsshell_increments; incr = *incrp++;)
for (t1 = incr; t1 < nmemb; ++t1)
for (t2 = t1 - incr; t2 >= 0;) {
s1 = p[t2] + indx;
s2 = p[t2 + incr] + indx;
while ((ch = tr[*s1++]) == tr[*s2] && ch)
++s2;
if (ch > tr[*s2]) {
s1 = p[t2];
p[t2] = p[t2 + incr];
p[t2 + incr] = s1;
t2 -= incr;
} else
break;
}
}