ida: Use exceptional entries for small IDAs

We can use the root entry as a bitmap and save allocating a 128 byte
bitmap for an IDA that contains only a few entries (30 on a 32-bit
machine, 62 on a 64-bit machine).  This costs about 300 bytes of kernel
text on x86-64, so as long as 3 IDAs fall into this category, this
is a net win for memory consumption.

Thanks to Rasmus Villemoes for his work documenting the problem and
collecting statistics on IDAs.

Signed-off-by: Matthew Wilcox <mawilcox@microsoft.com>

lib/idr.c

@@ -194,6 +194,39 @@ EXPORT_SYMBOL(idr_replace);
  * limitation, it should be quite straightforward to raise the maximum.
  */
 
+/*
+ * Developer's notes:
+ *
+ * The IDA uses the functionality provided by the IDR & radix tree to store
+ * bitmaps in each entry.  The IDR_FREE tag means there is at least one bit
+ * free, unlike the IDR where it means at least one entry is free.
+ *
+ * I considered telling the radix tree that each slot is an order-10 node
+ * and storing the bit numbers in the radix tree, but the radix tree can't
+ * allow a single multiorder entry at index 0, which would significantly
+ * increase memory consumption for the IDA.  So instead we divide the index
+ * by the number of bits in the leaf bitmap before doing a radix tree lookup.
+ *
+ * As an optimisation, if there are only a few low bits set in any given
+ * leaf, instead of allocating a 128-byte bitmap, we use the 'exceptional
+ * entry' functionality of the radix tree to store BITS_PER_LONG - 2 bits
+ * directly in the entry.  By being really tricksy, we could store
+ * BITS_PER_LONG - 1 bits, but there're diminishing returns after optimising
+ * for 0-3 allocated IDs.
+ *
+ * We allow the radix tree 'exceptional' count to get out of date.  Nothing
+ * in the IDA nor the radix tree code checks it.  If it becomes important
+ * to maintain an accurate exceptional count, switch the rcu_assign_pointer()
+ * calls to radix_tree_iter_replace() which will correct the exceptional
+ * count.
+ *
+ * The IDA always requires a lock to alloc/free.  If we add a 'test_bit'
+ * equivalent, it will still need locking.  Going to RCU lookup would require
+ * using RCU to free bitmaps, and that's not trivial without embedding an
+ * RCU head in the bitmap, which adds a 2-pointer overhead to each 128-byte
+ * bitmap, which is excessive.
+ */
+
 #define IDA_MAX (0x80000000U / IDA_BITMAP_BITS)
 
 /**
@@ -221,11 +254,12 @@ int ida_get_new_above(struct ida *ida, int start, int *id)
 	struct radix_tree_iter iter;
 	struct ida_bitmap *bitmap;
 	unsigned long index;
-	unsigned bit;
+	unsigned bit, ebit;
 	int new;
 
 	index = start / IDA_BITMAP_BITS;
 	bit = start % IDA_BITMAP_BITS;
+	ebit = bit + RADIX_TREE_EXCEPTIONAL_SHIFT;
 
 	slot = radix_tree_iter_init(&iter, index);
 	for (;;) {
@@ -240,10 +274,29 @@ int ida_get_new_above(struct ida *ida, int start, int *id)
 				return PTR_ERR(slot);
 			}
 		}
-		if (iter.index > index)
+		if (iter.index > index) {
 			bit = 0;
+			ebit = RADIX_TREE_EXCEPTIONAL_SHIFT;
+		}
 		new = iter.index * IDA_BITMAP_BITS;
 		bitmap = rcu_dereference_raw(*slot);
+		if (radix_tree_exception(bitmap)) {
+			unsigned long tmp = (unsigned long)bitmap;
+			ebit = find_next_zero_bit(&tmp, BITS_PER_LONG, ebit);
+			if (ebit < BITS_PER_LONG) {
+				tmp |= 1UL << ebit;
+				rcu_assign_pointer(*slot, (void *)tmp);
+				*id = new + ebit - RADIX_TREE_EXCEPTIONAL_SHIFT;
+				return 0;
+			}
+			bitmap = this_cpu_xchg(ida_bitmap, NULL);
+			if (!bitmap)
+				return -EAGAIN;
+			memset(bitmap, 0, sizeof(*bitmap));
+			bitmap->bitmap[0] = tmp >> RADIX_TREE_EXCEPTIONAL_SHIFT;
+			rcu_assign_pointer(*slot, bitmap);
+		}
+
 		if (bitmap) {
 			bit = find_next_zero_bit(bitmap->bitmap,
 							IDA_BITMAP_BITS, bit);
@@ -261,6 +314,14 @@ int ida_get_new_above(struct ida *ida, int start, int *id)
 			new += bit;
 			if (new < 0)
 				return -ENOSPC;
+			if (ebit < BITS_PER_LONG) {
+				bitmap = (void *)((1UL << ebit) |
+						RADIX_TREE_EXCEPTIONAL_ENTRY);
+				radix_tree_iter_replace(root, &iter, slot,
+						bitmap);
+				*id = new;
+				return 0;
+			}
 			bitmap = this_cpu_xchg(ida_bitmap, NULL);
 			if (!bitmap)
 				return -EAGAIN;
@@ -287,6 +348,7 @@ void ida_remove(struct ida *ida, int id)
 	unsigned long index = id / IDA_BITMAP_BITS;
 	unsigned offset = id % IDA_BITMAP_BITS;
 	struct ida_bitmap *bitmap;
+	unsigned long *btmp;
 	struct radix_tree_iter iter;
 	void **slot;
 
@@ -295,12 +357,24 @@ void ida_remove(struct ida *ida, int id)
 		goto err;
 
 	bitmap = rcu_dereference_raw(*slot);
-	if (!test_bit(offset, bitmap->bitmap))
+	if (radix_tree_exception(bitmap)) {
+		btmp = (unsigned long *)slot;
+		offset += RADIX_TREE_EXCEPTIONAL_SHIFT;
+		if (offset >= BITS_PER_LONG)
+			goto err;
+	} else {
+		btmp = bitmap->bitmap;
+	}
+	if (!test_bit(offset, btmp))
 		goto err;
 
-	__clear_bit(offset, bitmap->bitmap);
+	__clear_bit(offset, btmp);
 	radix_tree_iter_tag_set(&ida->ida_rt, &iter, IDR_FREE);
-	if (bitmap_empty(bitmap->bitmap, IDA_BITMAP_BITS)) {
+	if (radix_tree_exception(bitmap)) {
+		if (rcu_dereference_raw(*slot) ==
+					(void *)RADIX_TREE_EXCEPTIONAL_ENTRY)
+			radix_tree_iter_delete(&ida->ida_rt, &iter, slot);
+	} else if (bitmap_empty(btmp, IDA_BITMAP_BITS)) {
 		kfree(bitmap);
 		radix_tree_iter_delete(&ida->ida_rt, &iter, slot);
 	}
@@ -326,7 +400,8 @@ void ida_destroy(struct ida *ida)
 
 	radix_tree_for_each_slot(slot, &ida->ida_rt, &iter, 0) {
 		struct ida_bitmap *bitmap = rcu_dereference_raw(*slot);
-		kfree(bitmap);
+		if (!radix_tree_exception(bitmap))
+			kfree(bitmap);
 		radix_tree_iter_delete(&ida->ida_rt, &iter, slot);
 	}
 }

lib/radix-tree.c

@@ -338,6 +338,14 @@ static void dump_ida_node(void *entry, unsigned long index)
 		for (i = 0; i < RADIX_TREE_MAP_SIZE; i++)
 			dump_ida_node(node->slots[i],
 					index | (i << node->shift));
+	} else if (radix_tree_exceptional_entry(entry)) {
+		pr_debug("ida excp: %p offset %d indices %lu-%lu data %lx\n",
+				entry, (int)(index & RADIX_TREE_MAP_MASK),
+				index * IDA_BITMAP_BITS,
+				index * IDA_BITMAP_BITS + BITS_PER_LONG -
+					RADIX_TREE_EXCEPTIONAL_SHIFT,
+				(unsigned long)entry >>
+					RADIX_TREE_EXCEPTIONAL_SHIFT);
 	} else {
 		struct ida_bitmap *bitmap = entry;
 

tools/testing/radix-tree/idr-test.c

@@ -11,6 +11,7 @@
  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
  * more details.
  */
+#include <linux/bitmap.h>
 #include <linux/idr.h>
 #include <linux/slab.h>
 #include <linux/kernel.h>
@@ -214,7 +215,7 @@ void ida_check_nomem(void)
 	DEFINE_IDA(ida);
 	int id, err;
 
-	err = ida_get_new(&ida, &id);
+	err = ida_get_new_above(&ida, 256, &id);
 	assert(err == -EAGAIN);
 	err = ida_get_new_above(&ida, 1UL << 30, &id);
 	assert(err == -EAGAIN);
@@ -246,6 +247,66 @@ void ida_check_leaf(void)
 	assert(ida_is_empty(&ida));
 }
 
+/*
+ * Check handling of conversions between exceptional entries and full bitmaps.
+ */
+void ida_check_conv(void)
+{
+	DEFINE_IDA(ida);
+	int id;
+	unsigned long i;
+
+	for (i = 0; i < IDA_BITMAP_BITS * 2; i += IDA_BITMAP_BITS) {
+		assert(ida_pre_get(&ida, GFP_KERNEL));
+		assert(!ida_get_new_above(&ida, i + 1, &id));
+		assert(id == i + 1);
+		assert(!ida_get_new_above(&ida, i + BITS_PER_LONG, &id));
+		assert(id == i + BITS_PER_LONG);
+		ida_remove(&ida, i + 1);
+		ida_remove(&ida, i + BITS_PER_LONG);
+		assert(ida_is_empty(&ida));
+	}
+
+	assert(ida_pre_get(&ida, GFP_KERNEL));
+
+	for (i = 0; i < IDA_BITMAP_BITS * 2; i++) {
+		assert(ida_pre_get(&ida, GFP_KERNEL));
+		assert(!ida_get_new(&ida, &id));
+		assert(id == i);
+	}
+
+	for (i = IDA_BITMAP_BITS * 2; i > 0; i--) {
+		ida_remove(&ida, i - 1);
+	}
+	assert(ida_is_empty(&ida));
+
+	for (i = 0; i < IDA_BITMAP_BITS + BITS_PER_LONG - 4; i++) {
+		assert(ida_pre_get(&ida, GFP_KERNEL));
+		assert(!ida_get_new(&ida, &id));
+		assert(id == i);
+	}
+
+	for (i = IDA_BITMAP_BITS + BITS_PER_LONG - 4; i > 0; i--) {
+		ida_remove(&ida, i - 1);
+	}
+	assert(ida_is_empty(&ida));
+
+	radix_tree_cpu_dead(1);
+	for (i = 0; i < 1000000; i++) {
+		int err = ida_get_new(&ida, &id);
+		if (err == -EAGAIN) {
+			assert((i % IDA_BITMAP_BITS) == (BITS_PER_LONG - 2));
+			assert(ida_pre_get(&ida, GFP_KERNEL));
+			err = ida_get_new(&ida, &id);
+		} else {
+			assert((i % IDA_BITMAP_BITS) != (BITS_PER_LONG - 2));
+		}
+		assert(!err);
+		assert(id == i);
+	}
+	ida_destroy(&ida);
+}
+
 /*
  * Check allocations up to and slightly above the maximum allowed (2^31-1) ID.
  * Allocating up to 2^31-1 should succeed, and then allocating the next one
@@ -273,6 +334,34 @@ void ida_check_max(void)
 	}
 }
 
+void ida_check_random(void)
+{
+	DEFINE_IDA(ida);
+	DECLARE_BITMAP(bitmap, 2048);
+	int id;
+	unsigned int i;
+	time_t s = time(NULL);
+
+ repeat:
+	memset(bitmap, 0, sizeof(bitmap));
+	for (i = 0; i < 100000; i++) {
+		int i = rand();
+		int bit = i & 2047;
+		if (test_bit(bit, bitmap)) {
+			__clear_bit(bit, bitmap);
+			ida_remove(&ida, bit);
+		} else {
+			__set_bit(bit, bitmap);
+			ida_pre_get(&ida, GFP_KERNEL);
+			assert(!ida_get_new_above(&ida, bit, &id));
+			assert(id == bit);
+		}
+	}
+	ida_destroy(&ida);
+	if (time(NULL) < s + 10)
+		goto repeat;
+}
+
 void ida_checks(void)
 {
 	DEFINE_IDA(ida);
@@ -337,6 +426,8 @@ void ida_checks(void)
 
 	ida_check_leaf();
 	ida_check_max();
+	ida_check_conv();
+	ida_check_random();
 
 	radix_tree_cpu_dead(1);
 }