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+/* Stable-sorting of an array using mergesort.
+ Copyright (C) 2009-2018 Free Software Foundation, Inc.
+ Written by Bruno Haible <bruno@clisp.org>, 2009.
+
+ This program is free software: you can redistribute it and/or modify it
+ under the terms of the GNU General Public License as published
+ by the Free Software Foundation; either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <https://www.gnu.org/licenses/>. */
+
+/* This file implements stable sorting of an array, using the mergesort
+ algorithm.
+ Worst-case running time for an array of length N is O(N log N).
+ Unlike the mpsort module, the algorithm here attempts to minimize not
+ only the number of comparisons, but also the number of copying operations.
+
+ Before including this file, you need to define
+ ELEMENT The type of every array element.
+ COMPARE A two-argument macro that takes two 'const ELEMENT *'
+ pointers and returns a negative, zero, or positive 'int'
+ value if the element pointed to by the first argument is,
+ respectively, less, equal, or greater than the element
+ pointed to by the second argument.
+ STATIC The storage class of the functions being defined.
+ Before including this file, you also need to include:
+ #include <stddef.h>
+ */
+
+/* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into
+ dst[0..n1+n2-1]. In case of ambiguity, put the elements of src1
+ before the elements of src2.
+ n1 and n2 must be > 0.
+ The arrays src1 and src2 must not overlap the dst array, except that
+ src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1]. */
+static void
+merge (const ELEMENT *src1, size_t n1,
+ const ELEMENT *src2, size_t n2,
+ ELEMENT *dst)
+{
+ for (;;) /* while (n1 > 0 && n2 > 0) */
+ {
+ if (COMPARE (src1, src2) <= 0)
+ {
+ *dst++ = *src1++;
+ n1--;
+ if (n1 == 0)
+ break;
+ }
+ else
+ {
+ *dst++ = *src2++;
+ n2--;
+ if (n2 == 0)
+ break;
+ }
+ }
+ /* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0. */
+ if (n1 > 0)
+ {
+ if (dst != src1)
+ do
+ {
+ *dst++ = *src1++;
+ n1--;
+ }
+ while (n1 > 0);
+ }
+ else /* n2 > 0 */
+ {
+ if (dst != src2)
+ do
+ {
+ *dst++ = *src2++;
+ n2--;
+ }
+ while (n2 > 0);
+ }
+}
+
+/* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary
+ (scratch) storage.
+ The arrays src, dst, tmp must not overlap. */
+STATIC void
+merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp)
+{
+ switch (n)
+ {
+ case 0:
+ return;
+ case 1:
+ /* Nothing to do. */
+ dst[0] = src[0];
+ return;
+ case 2:
+ /* Trivial case. */
+ if (COMPARE (&src[0], &src[1]) <= 0)
+ {
+ /* src[0] <= src[1] */
+ dst[0] = src[0];
+ dst[1] = src[1];
+ }
+ else
+ {
+ dst[0] = src[1];
+ dst[1] = src[0];
+ }
+ break;
+ case 3:
+ /* Simple case. */
+ if (COMPARE (&src[0], &src[1]) <= 0)
+ {
+ if (COMPARE (&src[1], &src[2]) <= 0)
+ {
+ /* src[0] <= src[1] <= src[2] */
+ dst[0] = src[0];
+ dst[1] = src[1];
+ dst[2] = src[2];
+ }
+ else if (COMPARE (&src[0], &src[2]) <= 0)
+ {
+ /* src[0] <= src[2] < src[1] */
+ dst[0] = src[0];
+ dst[1] = src[2];
+ dst[2] = src[1];
+ }
+ else
+ {
+ /* src[2] < src[0] <= src[1] */
+ dst[0] = src[2];
+ dst[1] = src[0];
+ dst[2] = src[1];
+ }
+ }
+ else
+ {
+ if (COMPARE (&src[0], &src[2]) <= 0)
+ {
+ /* src[1] < src[0] <= src[2] */
+ dst[0] = src[1];
+ dst[1] = src[0];
+ dst[2] = src[2];
+ }
+ else if (COMPARE (&src[1], &src[2]) <= 0)
+ {
+ /* src[1] <= src[2] < src[0] */
+ dst[0] = src[1];
+ dst[1] = src[2];
+ dst[2] = src[0];
+ }
+ else
+ {
+ /* src[2] < src[1] < src[0] */
+ dst[0] = src[2];
+ dst[1] = src[1];
+ dst[2] = src[0];
+ }
+ }
+ break;
+ default:
+ {
+ size_t n1 = n / 2;
+ size_t n2 = (n + 1) / 2;
+ /* Note: n1 + n2 = n, n1 <= n2. */
+ /* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1]. */
+ merge_sort_fromto (src + n1, dst + n1, n2, tmp);
+ /* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1]. */
+ merge_sort_fromto (src, tmp, n1, dst);
+ /* Merge the two half results. */
+ merge (tmp, n1, dst + n1, n2, dst);
+ }
+ break;
+ }
+}
+
+/* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage.
+ The arrays src, tmp must not overlap. */
+STATIC void
+merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp)
+{
+ switch (n)
+ {
+ case 0:
+ case 1:
+ /* Nothing to do. */
+ return;
+ case 2:
+ /* Trivial case. */
+ if (COMPARE (&src[0], &src[1]) <= 0)
+ {
+ /* src[0] <= src[1] */
+ }
+ else
+ {
+ ELEMENT t = src[0];
+ src[0] = src[1];
+ src[1] = t;
+ }
+ break;
+ case 3:
+ /* Simple case. */
+ if (COMPARE (&src[0], &src[1]) <= 0)
+ {
+ if (COMPARE (&src[1], &src[2]) <= 0)
+ {
+ /* src[0] <= src[1] <= src[2] */
+ }
+ else if (COMPARE (&src[0], &src[2]) <= 0)
+ {
+ /* src[0] <= src[2] < src[1] */
+ ELEMENT t = src[1];
+ src[1] = src[2];
+ src[2] = t;
+ }
+ else
+ {
+ /* src[2] < src[0] <= src[1] */
+ ELEMENT t = src[0];
+ src[0] = src[2];
+ src[2] = src[1];
+ src[1] = t;
+ }
+ }
+ else
+ {
+ if (COMPARE (&src[0], &src[2]) <= 0)
+ {
+ /* src[1] < src[0] <= src[2] */
+ ELEMENT t = src[0];
+ src[0] = src[1];
+ src[1] = t;
+ }
+ else if (COMPARE (&src[1], &src[2]) <= 0)
+ {
+ /* src[1] <= src[2] < src[0] */
+ ELEMENT t = src[0];
+ src[0] = src[1];
+ src[1] = src[2];
+ src[2] = t;
+ }
+ else
+ {
+ /* src[2] < src[1] < src[0] */
+ ELEMENT t = src[0];
+ src[0] = src[2];
+ src[2] = t;
+ }
+ }
+ break;
+ default:
+ {
+ size_t n1 = n / 2;
+ size_t n2 = (n + 1) / 2;
+ /* Note: n1 + n2 = n, n1 <= n2. */
+ /* Sort src[n1..n-1], scratching tmp[0..n2-1]. */
+ merge_sort_inplace (src + n1, n2, tmp);
+ /* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1]. */
+ merge_sort_fromto (src, tmp, n1, tmp + n1);
+ /* Merge the two half results. */
+ merge (tmp, n1, src + n1, n2, src);
+ }
+ break;
+ }
+}
+
+#undef ELEMENT
+#undef COMPARE
+#undef STATIC
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