Add an implementation of grailsort

1 files changed, 192 insertions, 0 deletions

diff --git a/grailsort.c b/grailsort.c
new file mode 100644
index 0000000..c7a4074
--- /dev/null
+++ b/grailsort.c
@@ -0,0 +1,192 @@
+#include <math.h>
+#include <stddef.h>
+#include <stdint.h>
+
+#include "sorters.h"
+
+#define TAIL(base,nmel,width) ((base) + ((nmel) - 1) * (width))
+
+static void swap(char *a, char *b, size_t width)
+{
+	while (width--) {
+		char tmp = *a;
+		*a++ = *b;
+		*b++ = tmp;
+	}
+}
+
+static void reverse(char *base, size_t nmel, size_t width)
+{
+	char *last = base + (nmel - 1) * width;
+	while (last > base) {
+		swap(base, last, width);
+		base += width;
+		last -= width;
+	}
+}
+
+/* rotates left */
+static void rotate(char *base, size_t nmel, size_t width, size_t shift)
+{
+	reverse(base, shift, width);
+	reverse(base + shift * width, nmel - shift, width);
+	reverse(base, nmel, width);
+}
+
+/* If a matching element exists, returns index of one of them.
+   If none exists, returns index where such an element should be inserted. */
+static size_t binary_search(const char *needle, char *haystack,
+	size_t nmel, size_t width, cmpfun cmp)
+{
+	size_t baseidx = 0;
+	while (nmel) {
+		size_t tryidx = baseidx + nmel / 2;
+		char *try = haystack + tryidx * width;
+		int sign = cmp(try, needle);
+		if (!sign) return tryidx;
+		else if (sign < 0) {
+			baseidx = tryidx + 1;
+			nmel -= nmel / 2 + 1;
+		}
+		else {
+			nmel /= 2;
+		}
+	}
+	return baseidx;
+}
+
+static size_t merge(char *buf, char *base, size_t anmel, size_t bnmel, size_t width, cmpfun cmp)
+{
+	char *a = buf;
+	char *b = base + anmel * width;
+	size_t sorted = binary_search(b, base, anmel, width, cmp);
+	base  += sorted * width;
+	anmel -= sorted;
+
+	swap(base, a, anmel * width);
+
+	while (anmel > 0 && bnmel > 0) {
+		if (cmp(a, b) <= 0) {
+			swap(base, a, width);
+			a += width;
+			anmel--;
+		} else {
+			swap(base, b, width);
+			b += width;
+			bnmel--;
+		}
+		base += width;
+	}
+
+	swap(base, a, anmel * width);
+	return sorted;
+}
+
+/* get index of last block whose head is less than the previous block's tail */
+static size_t last_overlap(char *base, size_t bcount, size_t bwidth, size_t width, cmpfun cmp)
+{
+	for (char *cur = TAIL(base, bcount, bwidth); --bcount; cur -= bwidth)
+		if (cmp(cur - width, cur) > 0) break;
+	return bcount;
+}
+
+static void distribute_buffer(char *base, size_t bufnmel, size_t sortnmel, size_t width, cmpfun cmp)
+{
+	char *sorted = base + bufnmel * width;
+	while (bufnmel) {
+		char *last = sorted - width;
+		size_t equals;
+		for (equals = 1; equals < bufnmel; equals++) {
+			if (cmp(last, last - equals * width)) break;
+		}
+
+		size_t insertpos = binary_search(last, sorted, sortnmel, width, cmp);
+		rotate(sorted - equals * width, insertpos + equals, width, equals);
+
+		bufnmel  -= equals;
+		sortnmel += equals;
+		sorted   -= equals * width;
+	}
+}
+
+static const uint8_t sortnet[][2] = {
+	/* 0: index =  0 */
+	/* 1: index =  0 */
+	/* 2: index =  0 */
+	{0,1},
+	/* 3: index =  1 */
+	{0,1}, {0,2}, {1,2},
+	/* 4: index =  4 */
+	{0,1}, {2,3}, {0,2}, {1,3}, {1,2},
+	/* 5: index =  9 */
+	{0,1}, {3,4}, {2,4}, {2,3}, {1,4}, {0,3}, {0,2}, {1,3}, {1,2},
+	/* 6: index = 18 */
+	{1,2}, {4,5}, {0,2}, {3,5}, {0,1}, {3,4}, {2,5}, {0,3}, {1,4}, {2,4},
+	{1,3}, {2,3},
+	/* 7: index = 30 */
+	{1,2}, {3,4}, {5,6}, {0,2}, {3,5}, {4,6}, {0,1}, {4,5}, {2,6}, {0,4},
+	{1,5}, {0,3}, {2,5}, {1,3}, {2,4}, {2,3},
+	/* 8: index = 46 */
+	{0,1}, {2,3}, {4,5}, {6,7}, {0,2}, {1,3}, {4,6}, {5,7}, {1,2}, {5,6},
+	{0,4}, {3,7}, {1,5}, {2,6}, {1,4}, {3,6}, {2,4}, {3,5}, {3,4},
+	/* 9: index = 65, if we used a sorting network this large */
+};
+
+static const uint8_t sortnet_index[] = { 0, 0, 0, 1, 4, 9, 18, 30, 46, 65 };
+
+static void sorting_network(char *base, size_t nmel, size_t width, cmpfun cmp)
+{
+	for (int i = sortnet_index[nmel]; i < sortnet_index[nmel+1]; i++) {
+		char *elem1 = base + sortnet[i][0] * width;
+		char *elem2 = base + sortnet[i][1] * width;
+		if (cmp(elem1, elem2) > 0) swap(elem1, elem2, width);
+	}
+}
+
+void grailsort(void *unsorted, size_t nmel, size_t width, cmpfun cmp)
+{
+	char *base = unsorted;
+
+	if (nmel <= 8) {
+		sorting_network(base, nmel, width, cmp);
+		return;
+	}
+
+	size_t blknmel = sqrt(nmel);               /* elements in a block */
+	size_t bufnmel = blknmel + nmel % blknmel; /* elements in the buffer */
+	size_t bwidth  = blknmel * width;          /* size of a block in bytes */
+	size_t blocks  = nmel / blknmel - 1;       /* number of blocks in a + b */
+	size_t acount  = blocks / 2;
+	size_t bcount  = blocks - acount;
+
+	char *a = base + bufnmel * width;
+	char *b = a    + acount  * bwidth;
+
+	/* sort the buffer as if it were part of the a array */
+	grailsort(base, bufnmel + acount * blknmel, width, cmp);
+	grailsort(b,              bcount * blknmel, width, cmp);
+
+	/* if already sorted, nothing to do */
+	if (cmp(TAIL(a, acount * blknmel, width), b) <= 0) return;
+
+	/* if blocks in b are all less than those in a, just need a rotate */
+	if (cmp(TAIL(base, nmel, width), base) <= 0) {
+		rotate(base, nmel, width, acount * blknmel + bufnmel);
+		return;
+	}
+
+	/* sort all the a and b blocks together by their head elements */
+	grailsort(a, blocks, bwidth, cmp);
+
+	/* merge, starting from the end and working towards the beginning */
+	size_t pending = 0;
+	while (blocks > 1) {
+		size_t overlap = last_overlap(a, blocks, bwidth, width, cmp);
+		if (overlap == 0) break;
+		pending = merge(base, TAIL(a, overlap, bwidth), blknmel, (blocks - overlap) * blknmel, width, cmp);
+		blocks  = overlap;
+	}
+
+	grailsort(base, bufnmel, width, cmp);
+	distribute_buffer(base, bufnmel, nmel - bufnmel, width, cmp);
+}