crush: straw2 bucket type with an efficient 64-bit crush_ln()

This is an improved straw bucket that correctly avoids any data movement
between items A and B when neither A nor B's weights are changed.  Said
differently, if we adjust the weight of item C (including adding it anew
or removing it completely), we will only see inputs move to or from C,
never between other items in the bucket.

Notably, there is not intermediate scaling factor that needs to be
calculated.  The mapping function is a simple function of the item weights.

The below commits were squashed together into this one (mostly to avoid
adding and then yanking a ~6000 lines worth of crush_ln_table):

- crush: add a straw2 bucket type
- crush: add crush_ln to calculate nature log efficently
- crush: improve straw2 adjustment slightly
- crush: change crush_ln to provide 32 more digits
- crush: fix crush_get_bucket_item_weight and bucket destroy for straw2
- crush/mapper: fix divide-by-0 in straw2
  (with div64_s64() for draw = ln / w and INT64_MIN -> S64_MIN - need
   to create a proper compat.h in ceph.git)

Reflects ceph.git commits 242293c908e923d474910f2b8203fa3b41eb5a53,
                          32a1ead92efcd351822d22a5fc37d159c65c1338,
                          6289912418c4a3597a11778bcf29ed5415117ad9,
                          35fcb04e2945717cf5cfe150b9fa89cb3d2303a1,
                          6445d9ee7290938de1e4ee9563912a6ab6d8ee5f,
                          b5921d55d16796e12d66ad2c4add7305f9ce2353.
Signed-off-by: Ilya Dryomov <idryomov@gmail.com>

include/linux/crush/crush.h

@@ -96,13 +96,15 @@ struct crush_rule {
  *  uniform         O(1)       poor         poor
  *  list            O(n)       optimal      poor
  *  tree            O(log n)   good         good
- *  straw           O(n)       optimal      optimal
+ *  straw           O(n)       better       better
+ *  straw2          O(n)       optimal      optimal
  */
 enum {
 	CRUSH_BUCKET_UNIFORM = 1,
 	CRUSH_BUCKET_LIST = 2,
 	CRUSH_BUCKET_TREE = 3,
-	CRUSH_BUCKET_STRAW = 4
+	CRUSH_BUCKET_STRAW = 4,
+	CRUSH_BUCKET_STRAW2 = 5,
 };
 extern const char *crush_bucket_alg_name(int alg);
 
@@ -149,6 +151,11 @@ struct crush_bucket_straw {
 	__u32 *straws;         /* 16-bit fixed point */
 };
 
+struct crush_bucket_straw2 {
+	struct crush_bucket h;
+	__u32 *item_weights;   /* 16-bit fixed point */
+};
+
 
 
 /*
@@ -189,6 +196,7 @@ extern void crush_destroy_bucket_uniform(struct crush_bucket_uniform *b);
 extern void crush_destroy_bucket_list(struct crush_bucket_list *b);
 extern void crush_destroy_bucket_tree(struct crush_bucket_tree *b);
 extern void crush_destroy_bucket_straw(struct crush_bucket_straw *b);
+extern void crush_destroy_bucket_straw2(struct crush_bucket_straw2 *b);
 extern void crush_destroy_bucket(struct crush_bucket *b);
 extern void crush_destroy_rule(struct crush_rule *r);
 extern void crush_destroy(struct crush_map *map);

net/ceph/crush/crush.c

@@ -17,6 +17,7 @@ const char *crush_bucket_alg_name(int alg)
 	case CRUSH_BUCKET_LIST: return "list";
 	case CRUSH_BUCKET_TREE: return "tree";
 	case CRUSH_BUCKET_STRAW: return "straw";
+	case CRUSH_BUCKET_STRAW2: return "straw2";
 	default: return "unknown";
 	}
 }
@@ -40,6 +41,8 @@ int crush_get_bucket_item_weight(const struct crush_bucket *b, int p)
 		return ((struct crush_bucket_tree *)b)->node_weights[crush_calc_tree_node(p)];
 	case CRUSH_BUCKET_STRAW:
 		return ((struct crush_bucket_straw *)b)->item_weights[p];
+	case CRUSH_BUCKET_STRAW2:
+		return ((struct crush_bucket_straw2 *)b)->item_weights[p];
 	}
 	return 0;
 }
@@ -77,6 +80,14 @@ void crush_destroy_bucket_straw(struct crush_bucket_straw *b)
 	kfree(b);
 }
 
+void crush_destroy_bucket_straw2(struct crush_bucket_straw2 *b)
+{
+	kfree(b->item_weights);
+	kfree(b->h.perm);
+	kfree(b->h.items);
+	kfree(b);
+}
+
 void crush_destroy_bucket(struct crush_bucket *b)
 {
 	switch (b->alg) {
@@ -92,6 +103,9 @@ void crush_destroy_bucket(struct crush_bucket *b)
 	case CRUSH_BUCKET_STRAW:
 		crush_destroy_bucket_straw((struct crush_bucket_straw *)b);
 		break;
+	case CRUSH_BUCKET_STRAW2:
+		crush_destroy_bucket_straw2((struct crush_bucket_straw2 *)b);
+		break;
 	}
 }
 

net/ceph/crush/mapper.c

@@ -20,6 +20,7 @@
 
 #include <linux/crush/crush.h>
 #include <linux/crush/hash.h>
+#include "crush_ln_table.h"
 
 /*
  * Implement the core CRUSH mapping algorithm.
@@ -237,6 +238,102 @@ static int bucket_straw_choose(struct crush_bucket_straw *bucket,
 	return bucket->h.items[high];
 }
 
+// compute 2^44*log2(input+1)
+uint64_t crush_ln(unsigned xin)
+{
+    unsigned x=xin, x1;
+    int iexpon, index1, index2;
+    uint64_t RH, LH, LL, xl64, result;
+
+    x++;
+
+    // normalize input
+    iexpon = 15;
+    while(!(x&0x18000)) { x<<=1; iexpon--; }
+
+    index1 = (x>>8)<<1;
+    // RH ~ 2^56/index1
+    RH = __RH_LH_tbl[index1 - 256];
+    // LH ~ 2^48 * log2(index1/256)
+    LH = __RH_LH_tbl[index1 + 1 - 256];
+
+    // RH*x ~ 2^48 * (2^15 + xf), xf<2^8
+    xl64 = (int64_t)x * RH;
+    xl64 >>= 48;
+    x1 = xl64;
+
+    result = iexpon;
+    result <<= (12 + 32);
+
+    index2 = x1 & 0xff;
+    // LL ~ 2^48*log2(1.0+index2/2^15)
+    LL = __LL_tbl[index2];
+
+    LH = LH + LL;
+
+    LH >>= (48-12 - 32);
+    result += LH;
+
+    return result;
+}
+
+
+/*
+ * straw2
+ *
+ * for reference, see:
+ *
+ * http://en.wikipedia.org/wiki/Exponential_distribution#Distribution_of_the_minimum_of_exponential_random_variables
+ *
+ */
+
+static int bucket_straw2_choose(struct crush_bucket_straw2 *bucket,
+				int x, int r)
+{
+	unsigned i, high = 0;
+	unsigned u;
+	unsigned w;
+	__s64 ln, draw, high_draw = 0;
+
+	for (i = 0; i < bucket->h.size; i++) {
+		w = bucket->item_weights[i];
+		if (w) {
+			u = crush_hash32_3(bucket->h.hash, x,
+					   bucket->h.items[i], r);
+			u &= 0xffff;
+
+			/*
+			 * for some reason slightly less than 0x10000 produces
+			 * a slightly more accurate distribution... probably a
+			 * rounding effect.
+			 *
+			 * the natural log lookup table maps [0,0xffff]
+			 * (corresponding to real numbers [1/0x10000, 1] to
+			 * [0, 0xffffffffffff] (corresponding to real numbers
+			 * [-11.090355,0]).
+			 */
+			ln = crush_ln(u) - 0x1000000000000ll;
+
+			/*
+			 * divide by 16.16 fixed-point weight.  note
+			 * that the ln value is negative, so a larger
+			 * weight means a larger (less negative) value
+			 * for draw.
+			 */
+			draw = div64_s64(ln, w);
+		} else {
+			draw = S64_MIN;
+		}
+
+		if (i == 0 || draw > high_draw) {
+			high = i;
+			high_draw = draw;
+		}
+	}
+	return bucket->h.items[high];
+}
+
+
 static int crush_bucket_choose(struct crush_bucket *in, int x, int r)
 {
 	dprintk(" crush_bucket_choose %d x=%d r=%d\n", in->id, x, r);
@@ -254,12 +351,16 @@ static int crush_bucket_choose(struct crush_bucket *in, int x, int r)
 	case CRUSH_BUCKET_STRAW:
 		return bucket_straw_choose((struct crush_bucket_straw *)in,
 					   x, r);
+	case CRUSH_BUCKET_STRAW2:
+		return bucket_straw2_choose((struct crush_bucket_straw2 *)in,
+					    x, r);
 	default:
 		dprintk("unknown bucket %d alg %d\n", in->id, in->alg);
 		return in->items[0];
 	}
 }
 
+
 /*
  * true if device is marked "out" (failed, fully offloaded)
  * of the cluster

net/ceph/osdmap.c

@@ -122,6 +122,22 @@ static int crush_decode_straw_bucket(void **p, void *end,
 	return -EINVAL;
 }
 
+static int crush_decode_straw2_bucket(void **p, void *end,
+				      struct crush_bucket_straw2 *b)
+{
+	int j;
+	dout("crush_decode_straw2_bucket %p to %p\n", *p, end);
+	b->item_weights = kcalloc(b->h.size, sizeof(u32), GFP_NOFS);
+	if (b->item_weights == NULL)
+		return -ENOMEM;
+	ceph_decode_need(p, end, b->h.size * sizeof(u32), bad);
+	for (j = 0; j < b->h.size; j++)
+		b->item_weights[j] = ceph_decode_32(p);
+	return 0;
+bad:
+	return -EINVAL;
+}
+
 static int skip_name_map(void **p, void *end)
 {
         int len;
@@ -204,6 +220,9 @@ static struct crush_map *crush_decode(void *pbyval, void *end)
 		case CRUSH_BUCKET_STRAW:
 			size = sizeof(struct crush_bucket_straw);
 			break;
+		case CRUSH_BUCKET_STRAW2:
+			size = sizeof(struct crush_bucket_straw2);
+			break;
 		default:
 			err = -EINVAL;
 			goto bad;
@@ -261,6 +280,12 @@ static struct crush_map *crush_decode(void *pbyval, void *end)
 			if (err < 0)
 				goto bad;
 			break;
+		case CRUSH_BUCKET_STRAW2:
+			err = crush_decode_straw2_bucket(p, end,
+				(struct crush_bucket_straw2 *)b);
+			if (err < 0)
+				goto bad;
+			break;
 		}
 	}