bisect: use a PRNG with a bias when skipping away from untestable commits

Using a PRNG (pseudo random number generator) with a bias should be better
than alternating between 3 fixed ratios.

In repositories with many untestable commits it should prevent alternating
between areas where many commits are untestable. The bias should favor
commits that can give more information, so that the bisection process
should not loose much efficiency.

HPA suggested to use a PRNG and found that the best bias is to raise a
ratio between 0 and 1 given by the PRNG to the power 1.5.

An integer square root function is implemented to avoid including
<math.h> and linking with -lm.

A PRNG function is implemented to get the same number sequence on
different machines as suggested by "man 3 rand".

Signed-off-by: Christian Couder <chriscool@tuxfamily.org>
Signed-off-by: Junio C Hamano <gitster@pobox.com>

bisect.c

@@ -585,16 +585,49 @@ struct commit_list *filter_skipped(struct commit_list *list,
 	return filtered;
 }
 
-static struct commit_list *apply_skip_ratio(struct commit_list *list,
-					    int count,
-					    int skip_num, int skip_denom)
+#define PRN_MODULO 32768
+
+/*
+ * This is a pseudo random number generator based on "man 3 rand".
+ * It is not used properly because the seed is the argument and it
+ * is increased by one between each call, but that should not matter
+ * for this application.
+ */
+int get_prn(int count) {
+	count = count * 1103515245 + 12345;
+	return ((unsigned)(count/65536) % PRN_MODULO);
+}
+
+/*
+ * Custom integer square root from
+ * http://en.wikipedia.org/wiki/Integer_square_root
+ */
+static int sqrti(int val)
+{
+	float d, x = val;
+
+	if (val == 0)
+		return 0;
+
+	do {
+		float y = (x + (float)val / x) / 2;
+		d = (y > x) ? y - x : x - y;
+		x = y;
+	} while (d >= 0.5);
+
+	return (int)x;
+}
+
+static struct commit_list *skip_away(struct commit_list *list, int count)
 {
-	int index, i;
 	struct commit_list *cur, *previous;
+	int prn, index, i;
+
+	prn = get_prn(count);
+	index = (count * prn / PRN_MODULO) * sqrti(prn) / sqrti(PRN_MODULO);
 
 	cur = list;
 	previous = NULL;
-	index = count * skip_num / skip_denom;
 
 	for (i = 0; cur; cur = cur->next, i++) {
 		if (i == index) {
@@ -614,7 +647,6 @@ static struct commit_list *managed_skipped(struct commit_list *list,
 					   struct commit_list **tried)
 {
 	int count, skipped_first;
-	int skip_num, skip_denom;
 
 	*tried = NULL;
 
@@ -626,11 +658,7 @@ static struct commit_list *managed_skipped(struct commit_list *list,
 	if (!skipped_first)
 		return list;
 
-	/* Use alternatively 1/5, 2/5 and 3/5 as skip ratio. */
-	skip_num = count % 3 + 1;
-	skip_denom = 5;
-
-	return apply_skip_ratio(list, count, skip_num, skip_denom);
+	return skip_away(list, count);
 }
 
 static void bisect_rev_setup(struct rev_info *revs, const char *prefix,

t/t6030-bisect-porcelain.sh

@@ -563,8 +563,8 @@ test_expect_success 'skipping away from skipped commit' '
 	hash7=$(git rev-parse --verify HEAD) &&
 	test "$hash7" = "$HASH7" &&
         git bisect skip &&
-	hash3=$(git rev-parse --verify HEAD) &&
-	test "$hash3" = "$HASH3"
+	para3=$(git rev-parse --verify HEAD) &&
+	test "$para3" = "$PARA_HASH3"
 '
 
 #