replace heap sort with smoothsort implementation by Valentin Ochs

Smoothsort is an adaptive variant of heapsort. This version was
written by Valentin Ochs (apo) specifically for inclusion in musl. I
worked with him to get it working in O(1) memory usage even with giant
array element widths, and to optimize it heavily for size and speed.
It's still roughly 4 times as large as the old heap sort
implementation, but roughly 20 times faster given an almost-sorted
array of 1M elements (20 being the base-2 log of 1M), i.e. it really
does reduce O(n log n) to O(n) in the mostly-sorted case. It's still
somewhat slower than glibc's Introsort for random input, but now
considerably faster than glibc when the input is already sorted, or
mostly sorted.

COPYRIGHT

@@ -19,6 +19,10 @@ The implementation of DES for crypt (src/misc/crypt.c) is Copyright ©
 1994 David Burren. It is licensed under a BSD license compatible with
 the GNU LGPL.
 
+The smoothsort implementation (src/stdlib/qsort.c) is Copyright © 2011
+Valentin Ochs and is licensed under an MIT-style license compatible
+with the GNU LGPL.
+
 The x86_64 port was written by Nicholas J. Kain. See individual files
 for their copyright status.
 

src/stdlib/qsort.c

@@ -1,50 +1,211 @@
+/* Copyright (C) 2011 by Valentin Ochs
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to
+ * deal in the Software without restriction, including without limitation the
+ * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+ * sell copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+
+/* Minor changes by Rich Felker for integration in musl, 2011-04-27. */
+
+#include <stdint.h>
 #include <stdlib.h>
 #include <string.h>
 
-/* A simple heap sort implementation.. only in-place O(nlogn) sort I know. */
+#include "atomic.h"
+#define ntz(x) a_ctz_l((x))
 
-#define MIN(a, b) ((a)<(b) ? (a) : (b))
+typedef int (*cmpfun)(const void *, const void *);
 
-static void swap(char *a, char *b, size_t len)
+static inline int pntz(size_t p[2]) {
+	int r = ntz(p[0] - 1);
+	if(r != 0 || (r = 8*sizeof(size_t) + ntz(p[1])) != 8*sizeof(size_t)) {
+		return r;
+	}
+	return 0;
+}
+
+static void cycle(size_t width, unsigned char* ar[], int n)
 {
-	char tmp[256];
+	unsigned char tmp[256];
 	size_t l;
-	while (len) {
+	int i;
-		l = MIN(sizeof tmp, len);
+
-		memcpy(tmp, a, l);
+	if(n < 2) {
-		memcpy(a, b, l);
+		return;
-		memcpy(b, tmp, l);
+	}
-		a += l;
+
-		b += l;
+	ar[n] = tmp;
-		len -= l;
+	while(width) {
+		l = sizeof(tmp) < width ? sizeof(tmp) : width;
+		memcpy(ar[n], ar[0], l);
+		for(i = 0; i < n; i++) {
+			memcpy(ar[i], ar[i + 1], l);
+			ar[i] += l;
+		}
+		width -= l;
 	}
 }
 
-static void sift(char *base, size_t root, size_t nel, size_t width, int (*cmp)(const void *, const void *))
+/* shl() and shr() need n > 0 */
+static inline void shl(size_t p[2], int n)
 {
-	size_t max;
+	if(n >= 8 * sizeof(size_t)) {
-
+		n -= 8 * sizeof(size_t);
-	while (2*root <= nel) {
+		p[1] = p[0];
-		max = 2*root;
+		p[0] = 0;
-		if (max < nel && cmp(base+max*width, base+(max+1)*width) < 0)
-			max++;
-		if (max && cmp(base+root*width, base+max*width) < 0) {
-			swap(base+root*width, base+max*width, width);
-			root = max;
-		} else break;
 	}
+	p[1] <<= n;
+	p[1] |= p[0] >> (sizeof(size_t) * 8 - n);
+	p[0] <<= n;
 }
 
-void qsort(void *_base, size_t nel, size_t width, int (*cmp)(const void *, const void *))
+static inline void shr(size_t p[2], int n)
 {
-	char *base = _base;
+	if(n >= 8 * sizeof(size_t)) {
-	size_t i;
+		n -= 8 * sizeof(size_t);
+		p[0] = p[1];
+		p[1] = 0;
+	}
+	p[0] >>= n;
+	p[0] |= p[1] << (sizeof(size_t) * 8 - n);
+	p[1] >>= n;
+}
 
-	if (!nel) return;
+static void sift(unsigned char *head, size_t width, cmpfun cmp, int pshift, size_t lp[])
-	for (i=(nel+1)/2; i; i--)
+{
-		sift(base, i-1, nel-1, width, cmp);
+	unsigned char *rt, *lf;
-	for (i=nel-1; i; i--) {
+	unsigned char *ar[14 * sizeof(size_t) + 1];
-		swap(base, base+i*width, width);
+	int i = 1;
-		sift(base, 0, i-1, width, cmp);
+
+	ar[0] = head;
+	while(pshift > 1) {
+		rt = head - width;
+		lf = head - width - lp[pshift - 2];
+
+		if((*cmp)(ar[0], lf) >= 0 && (*cmp)(ar[0], rt) >= 0) {
+			break;
+		}
+		if((*cmp)(lf, rt) >= 0) {
+			ar[i++] = lf;
+			head = lf;
+			pshift -= 1;
+		} else {
+			ar[i++] = rt;
+			head = rt;
+			pshift -= 2;
+		}
+	}
+	cycle(width, ar, i);
+}
+
+static void trinkle(unsigned char *head, size_t width, cmpfun cmp, size_t pp[2], int pshift, int trusty, size_t lp[])
+{
+	unsigned char *stepson,
+	              *rt, *lf;
+	size_t p[2];
+	unsigned char *ar[14 * sizeof(size_t) + 1];
+	int i = 1;
+	int trail;
+
+	p[0] = pp[0];
+	p[1] = pp[1];
+
+	ar[0] = head;
+	while(p[0] != 1 || p[1] != 0) {
+		stepson = head - lp[pshift];
+		if((*cmp)(stepson, ar[0]) <= 0) {
+			break;
+		}
+		if(!trusty && pshift > 1) {
+			rt = head - width;
+			lf = head - width - lp[pshift - 2];
+			if((*cmp)(rt, stepson) >= 0 || (*cmp)(lf, stepson) >= 0) {
+				break;
+			}
+		}
+
+		ar[i++] = stepson;
+		head = stepson;
+		trail = pntz(p);
+		shr(p, trail);
+		pshift += trail;
+		trusty = 0;
+	}
+	if(!trusty) {
+		cycle(width, ar, i);
+		sift(head, width, cmp, pshift, lp);
+	}
+}
+
+void qsort(void *base, size_t nel, size_t width, cmpfun cmp)
+{
+	size_t lp[12*sizeof(size_t)];
+	size_t i, size = width * nel;
+	unsigned char *head = base,
+	              *high = head + size - width;
+	size_t p[2] = {1, 0};
+	int pshift = 1;
+	int trail;
+
+	/* Precompute Leonardo numbers, scaled by element width */
+	for(lp[0]=lp[1]=width, i=2; (lp[i]=lp[i-2]+lp[i-1]+width) < size; i++);
+
+	while(head < high) {
+		if((p[0] & 3) == 3) {
+			sift(head, width, cmp, pshift, lp);
+			shr(p, 2);
+			pshift += 2;
+		} else {
+			if(lp[pshift - 1] >= high - head) {
+				trinkle(head, width, cmp, p, pshift, 0, lp);
+			} else {
+				sift(head, width, cmp, pshift, lp);
+			}
+			
+			if(pshift == 1) {
+				shl(p, 1);
+				pshift = 0;
+			} else {
+				shl(p, pshift - 1);
+				pshift = 1;
+			}
+		}
+		
+		p[0] |= 1;
+		head += width;
+	}
+
+	trinkle(head, width, cmp, p, pshift, 0, lp);
+
+	while(pshift != 1 || p[0] != 1 || p[1] != 0) {
+		if(pshift <= 1) {
+			trail = pntz(p);
+			shr(p, trail);
+			pshift += trail;
+		} else {
+			shl(p, 2);
+			pshift -= 2;
+			p[0] ^= 7;
+			shr(p, 1);
+			trinkle(head - lp[pshift] - width, width, cmp, p, pshift + 1, 1, lp);
+			shl(p, 1);
+			p[0] |= 1;
+			trinkle(head - width, width, cmp, p, pshift, 1, lp);
+		}
+		head -= width;
 	}
 }