flex_array: avoid divisions when accessing elements

On most architectures division is an expensive operation and accessing an
element currently requires four of them. This performance penalty
effectively precludes flex arrays from being used on any kind of fast
path. However, two of these divisions can be handled at creation time and
the others can be replaced by a reciprocal divide, completely avoiding
real divisions on access.

[[e-mail]: rebase on top of changes to support 0 len elements]
[[e-mail]: initialize part_nr when array fits entirely in base]
Signed-off-by: Jesse Gross <[e-mail]>
Signed-off-by: Eric Paris <[e-mail]>
Cc: Dave Hansen <[e-mail]>
Cc: David Rientjes <[e-mail]>
Signed-off-by: Andrew Morton <[e-mail]>
Signed-off-by: Linus Torvalds <[e-mail]>

include/linux/flex_array.h

···
 		struct {
 			int element_size;
 			int total_nr_elements;
+			int elems_per_part;
+			u32 reciprocal_elems;
 			struct flex_array_part *parts[];
 		};
 		/*

lib/flex_array.c

···
 #include <linux/slab.h>
 #include <linux/stddef.h>
 #include <linux/module.h>
+#include <linux/reciprocal_div.h>
 
 struct flex_array_part {
 	char elements[FLEX_ARRAY_PART_SIZE];
···
  * Element size | Objects | Objects |
  * PAGE_SIZE=4k |  32-bit |  64-bit |
  * ---------------------------------|
- *      1 bytes | 4186112 | 2093056 |
- *      2 bytes | 2093056 | 1046528 |
- *      3 bytes | 1395030 |  697515 |
- *      4 bytes | 1046528 |  523264 |
- *     32 bytes |  130816 |   65408 |
- *     33 bytes |  126728 |   63364 |
- *   2048 bytes |    2044 |    1022 |
- *   2049 bytes |    1022 |     511 |
- *       void * | 1046528 |  261632 |
+ *      1 bytes | 4177920 | 2088960 |
+ *      2 bytes | 2088960 | 1044480 |
+ *      3 bytes | 1392300 |  696150 |
+ *      4 bytes | 1044480 |  522240 |
+ *     32 bytes |  130560 |   65408 |
+ *     33 bytes |  126480 |   63240 |
+ *   2048 bytes |    2040 |    1020 |
+ *   2049 bytes |    1020 |     510 |
+ *       void * | 1044480 |  261120 |
  *
  * Since 64-bit pointers are twice the size, we lose half the
  * capacity in the base structure.  Also note that no effort is made
···
 					gfp_t flags)
 {
 	struct flex_array *ret;
+	int elems_per_part = 0;
+	int reciprocal_elems = 0;
 	int max_size = 0;
 
-	if (element_size)
-		max_size = FLEX_ARRAY_NR_BASE_PTRS *
-			   FLEX_ARRAY_ELEMENTS_PER_PART(element_size);
+	if (element_size) {
+		elems_per_part = FLEX_ARRAY_ELEMENTS_PER_PART(element_size);
+		reciprocal_elems = reciprocal_value(elems_per_part);
+		max_size = FLEX_ARRAY_NR_BASE_PTRS * elems_per_part;
+	}
 
 	/* max_size will end up 0 if element_size > PAGE_SIZE */
 	if (total > max_size)
···
 		return NULL;
 	ret->element_size = element_size;
 	ret->total_nr_elements = total;
+	ret->elems_per_part = elems_per_part;
+	ret->reciprocal_elems = reciprocal_elems;
 	if (elements_fit_in_base(ret) && !(flags & __GFP_ZERO))
 		memset(&ret->parts[0], FLEX_ARRAY_FREE,
 						FLEX_ARRAY_BASE_BYTES_LEFT);
···
 static int fa_element_to_part_nr(struct flex_array *fa,
 					unsigned int element_nr)
 {
-	return element_nr / FLEX_ARRAY_ELEMENTS_PER_PART(fa->element_size);
+	return reciprocal_divide(element_nr, fa->reciprocal_elems);
 }
 
 /**
···
 EXPORT_SYMBOL(flex_array_free);
 
 static unsigned int index_inside_part(struct flex_array *fa,
-					unsigned int element_nr)
+					unsigned int element_nr,
+					unsigned int part_nr)
 {
 	unsigned int part_offset;
 
-	part_offset = element_nr %
-				FLEX_ARRAY_ELEMENTS_PER_PART(fa->element_size);
+	part_offset = element_nr - part_nr * fa->elems_per_part;
 	return part_offset * fa->element_size;
 }
 
···
 int flex_array_put(struct flex_array *fa, unsigned int element_nr, void *src,
 			gfp_t flags)
 {
-	int part_nr;
+	int part_nr = 0;
 	struct flex_array_part *part;
 	void *dst;
 
···
 		if (!part)
 			return -ENOMEM;
 	}
-	dst = &part->elements[index_inside_part(fa, element_nr)];
+	dst = &part->elements[index_inside_part(fa, element_nr, part_nr)];
 	memcpy(dst, src, fa->element_size);
 	return 0;
 }
···
  */
 int flex_array_clear(struct flex_array *fa, unsigned int element_nr)
 {
-	int part_nr;
+	int part_nr = 0;
 	struct flex_array_part *part;
 	void *dst;
 
···
 		if (!part)
 			return -EINVAL;
 	}
-	dst = &part->elements[index_inside_part(fa, element_nr)];
+	dst = &part->elements[index_inside_part(fa, element_nr, part_nr)];
 	memset(dst, FLEX_ARRAY_FREE, fa->element_size);
 	return 0;
 }
···
  */
 void *flex_array_get(struct flex_array *fa, unsigned int element_nr)
 {
-	int part_nr;
+	int part_nr = 0;
 	struct flex_array_part *part;
 
 	if (!fa->element_size)
···
 		if (!part)
 			return NULL;
 	}
-	return &part->elements[index_inside_part(fa, element_nr)];
+	return &part->elements[index_inside_part(fa, element_nr, part_nr)];
 }
 EXPORT_SYMBOL(flex_array_get);