path: root/wikisort.c

#include <math.h>
#include <stddef.h>
#include <stdint.h>
#include <string.h>

#include "sorters.h"

struct array {
	char  *base;
	size_t nmel;
};

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)
{
	if (shift == 0 || shift == nmel) return;
	reverse(base, shift, width);
	reverse(base + shift * width, nmel - shift, width);
	reverse(base, nmel, width);
}

/* buf must be large enough to hold a_count elements */
static void merge_blocks(char *buf, char *base, size_t as, size_t bs, size_t width, cmpfun cmp)
{
	char *a = buf;
	char *b = base + as * width;
	char *target = base;

	swap(a, base, as * width);

	while (as > 0 && bs > 0) {
		if (cmp(a, b) <= 0) {
			swap(target, a, width);
			a += width; as--;
		} else {
			swap(target, b, width);
			b += width; bs--;
		}
		target += width;
	}

	swap(target, a, as * width);
}

static char *find_min_block(char *base, size_t count, size_t bwidth, size_t width, cmpfun cmp)
{
	char *min = base;
	for (base += bwidth, count--; count--; base += bwidth) {
		if (cmp(min + bwidth - width, base) > 0) min = base;
	}
	return min;
}

/* 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 roll(struct array *a, struct array *b,
	size_t bwidth, size_t width, char **mina, cmpfun cmp)
{
	size_t iters = 0;
	while (b->nmel && cmp(b->base , *mina + bwidth - width) < 0) {
		swap(a->base, b->base, bwidth);
		if (*mina == a->base) *mina = b->base;
		a->base += bwidth;
		b->base += bwidth;
		b->nmel--;
		iters++;
	}
	return iters;
}

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 };

void wikisort(void *unsorted, size_t nmel, size_t width, cmpfun cmp)
{
	char *base = unsorted;

	/* use a sorting network for small inputs */
	if (nmel <= 8) {
		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);
		}
		return;
	}

	size_t bnmel  = sqrt(nmel);   /* elements in a block */
	size_t bcount = nmel / bnmel;
	size_t bwidth = bnmel * width;

	/* temporary buffer: nmel is measured in array elements */
	struct array buf = { .base = base, .nmel = bnmel + nmel % bnmel };

	/* A and B subarrays: nmel is measured in blocks of bnmel elements each */
	struct array a = { .base = buf.base +  width * buf.nmel, .nmel = (bcount - 1) / 2 };
	struct array b = { .base =   a.base + bwidth *   a.nmel, .nmel =  bcount - 1 - a.nmel };

	/* sort the buffer as if it were part of the a array */
	wikisort(buf.base, buf.nmel + a.nmel * bnmel, width, cmp);
	wikisort(b.base,              b.nmel * bnmel, width, cmp);

	/* if already sorted, nothing to do */
	if (cmp(b.base - width, b.base) <= 0) return;

	/* if blocks in b are all less than those in a, just need a rotate */
	if (cmp(base + (nmel - 1) * width, base) <= 0) {
		rotate(base, nmel, width, a.nmel * bnmel + buf.nmel);
		return;
	}

	size_t nmel_pend_a = 0, nmel_pend_b = 0;
	char *mina = a.base, *penda;
	while (a.nmel) {
		size_t rolled_blocks = b.nmel ? roll(&a, &b, bwidth, width, &mina, cmp) : 0;

		/* move mina block to immediately after rolled b blocks */
		if (mina != a.base) swap(mina, a.base, bwidth);

		/* rotate mina into correct spot in the last rolled b */
		nmel_pend_b += rolled_blocks * bnmel;
		if (nmel_pend_b) {
			size_t offset = nmel_pend_b - binary_search(a.base, a.base - nmel_pend_b * width, nmel_pend_b, width, cmp);
			rotate(a.base - offset * width, bnmel + offset, width, offset);

			nmel_pend_b -= offset;
			if (nmel_pend_a && nmel_pend_b) {
				merge_blocks(buf.base, penda, nmel_pend_a, nmel_pend_b, width, cmp);
			}

			penda = a.base - offset * width;
			nmel_pend_a = bnmel;
			nmel_pend_b = offset;
		} else {
			nmel_pend_a = 0;
			nmel_pend_b = 0;
		}

		a.base += bwidth;
		if (--a.nmel) {
			mina = find_min_block(a.base, a.nmel, bwidth, width, cmp);
		}
	}

	if (nmel_pend_a) {
		merge_blocks(buf.base, penda, nmel_pend_a, b.nmel * bnmel + nmel_pend_b, width, cmp);
	}

	wikisort(buf.base, buf.nmel, width, cmp);
	distribute_buffer(buf.base, buf.nmel, nmel - buf.nmel, width, cmp);
}