- 21 May, 2016 40 commits
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Zhaoxiu Zeng authored
The binary GCD algorithm is based on the following facts: 1. If a and b are all evens, then gcd(a,b) = 2 * gcd(a/2, b/2) 2. If a is even and b is odd, then gcd(a,b) = gcd(a/2, b) 3. If a and b are all odds, then gcd(a,b) = gcd((a-b)/2, b) = gcd((a+b)/2, b) Even on x86 machines with reasonable division hardware, the binary algorithm runs about 25% faster (80% the execution time) than the division-based Euclidian algorithm. On platforms like Alpha and ARMv6 where division is a function call to emulation code, it's even more significant. There are two variants of the code here, depending on whether a fast __ffs (find least significant set bit) instruction is available. This allows the unpredictable branches in the bit-at-a-time shifting loop to be eliminated. If fast __ffs is not available, the "even/odd" GCD variant is used. I use the following code to benchmark: #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <string.h> #include <time.h> #include <unistd.h> #define swap(a, b) \ do { \ a ^= b; \ b ^= a; \ a ^= b; \ } while (0) unsigned long gcd0(unsigned long a, unsigned long b) { unsigned long r; if (a < b) { swap(a, b); } if (b == 0) return a; while ((r = a % b) != 0) { a = b; b = r; } return b; } unsigned long gcd1(unsigned long a, unsigned long b) { unsigned long r = a | b; if (!a || !b) return r; b >>= __builtin_ctzl(b); for (;;) { a >>= __builtin_ctzl(a); if (a == b) return a << __builtin_ctzl(r); if (a < b) swap(a, b); a -= b; } } unsigned long gcd2(unsigned long a, unsigned long b) { unsigned long r = a | b; if (!a || !b) return r; r &= -r; while (!(b & r)) b >>= 1; for (;;) { while (!(a & r)) a >>= 1; if (a == b) return a; if (a < b) swap(a, b); a -= b; a >>= 1; if (a & r) a += b; a >>= 1; } } unsigned long gcd3(unsigned long a, unsigned long b) { unsigned long r = a | b; if (!a || !b) return r; b >>= __builtin_ctzl(b); if (b == 1) return r & -r; for (;;) { a >>= __builtin_ctzl(a); if (a == 1) return r & -r; if (a == b) return a << __builtin_ctzl(r); if (a < b) swap(a, b); a -= b; } } unsigned long gcd4(unsigned long a, unsigned long b) { unsigned long r = a | b; if (!a || !b) return r; r &= -r; while (!(b & r)) b >>= 1; if (b == r) return r; for (;;) { while (!(a & r)) a >>= 1; if (a == r) return r; if (a == b) return a; if (a < b) swap(a, b); a -= b; a >>= 1; if (a & r) a += b; a >>= 1; } } static unsigned long (*gcd_func[])(unsigned long a, unsigned long b) = { gcd0, gcd1, gcd2, gcd3, gcd4, }; #define TEST_ENTRIES (sizeof(gcd_func) / sizeof(gcd_func[0])) #if defined(__x86_64__) #define rdtscll(val) do { \ unsigned long __a,__d; \ __asm__ __volatile__("rdtsc" : "=a" (__a), "=d" (__d)); \ (val) = ((unsigned long long)__a) | (((unsigned long long)__d)<<32); \ } while(0) static unsigned long long benchmark_gcd_func(unsigned long (*gcd)(unsigned long, unsigned long), unsigned long a, unsigned long b, unsigned long *res) { unsigned long long start, end; unsigned long long ret; unsigned long gcd_res; rdtscll(start); gcd_res = gcd(a, b); rdtscll(end); if (end >= start) ret = end - start; else ret = ~0ULL - start + 1 + end; *res = gcd_res; return ret; } #else static inline struct timespec read_time(void) { struct timespec time; clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &time); return time; } static inline unsigned long long diff_time(struct timespec start, struct timespec end) { struct timespec temp; if ((end.tv_nsec - start.tv_nsec) < 0) { temp.tv_sec = end.tv_sec - start.tv_sec - 1; temp.tv_nsec = 1000000000ULL + end.tv_nsec - start.tv_nsec; } else { temp.tv_sec = end.tv_sec - start.tv_sec; temp.tv_nsec = end.tv_nsec - start.tv_nsec; } return temp.tv_sec * 1000000000ULL + temp.tv_nsec; } static unsigned long long benchmark_gcd_func(unsigned long (*gcd)(unsigned long, unsigned long), unsigned long a, unsigned long b, unsigned long *res) { struct timespec start, end; unsigned long gcd_res; start = read_time(); gcd_res = gcd(a, b); end = read_time(); *res = gcd_res; return diff_time(start, end); } #endif static inline unsigned long get_rand() { if (sizeof(long) == 8) return (unsigned long)rand() << 32 | rand(); else return rand(); } int main(int argc, char **argv) { unsigned int seed = time(0); int loops = 100; int repeats = 1000; unsigned long (*res)[TEST_ENTRIES]; unsigned long long elapsed[TEST_ENTRIES]; int i, j, k; for (;;) { int opt = getopt(argc, argv, "n:r:s:"); /* End condition always first */ if (opt == -1) break; switch (opt) { case 'n': loops = atoi(optarg); break; case 'r': repeats = atoi(optarg); break; case 's': seed = strtoul(optarg, NULL, 10); break; default: /* You won't actually get here. */ break; } } res = malloc(sizeof(unsigned long) * TEST_ENTRIES * loops); memset(elapsed, 0, sizeof(elapsed)); srand(seed); for (j = 0; j < loops; j++) { unsigned long a = get_rand(); /* Do we have args? */ unsigned long b = argc > optind ? strtoul(argv[optind], NULL, 10) : get_rand(); unsigned long long min_elapsed[TEST_ENTRIES]; for (k = 0; k < repeats; k++) { for (i = 0; i < TEST_ENTRIES; i++) { unsigned long long tmp = benchmark_gcd_func(gcd_func[i], a, b, &res[j][i]); if (k == 0 || min_elapsed[i] > tmp) min_elapsed[i] = tmp; } } for (i = 0; i < TEST_ENTRIES; i++) elapsed[i] += min_elapsed[i]; } for (i = 0; i < TEST_ENTRIES; i++) printf("gcd%d: elapsed %llu\n", i, elapsed[i]); k = 0; srand(seed); for (j = 0; j < loops; j++) { unsigned long a = get_rand(); unsigned long b = argc > optind ? strtoul(argv[optind], NULL, 10) : get_rand(); for (i = 1; i < TEST_ENTRIES; i++) { if (res[j][i] != res[j][0]) break; } if (i < TEST_ENTRIES) { if (k == 0) { k = 1; fprintf(stderr, "Error:\n"); } fprintf(stderr, "gcd(%lu, %lu): ", a, b); for (i = 0; i < TEST_ENTRIES; i++) fprintf(stderr, "%ld%s", res[j][i], i < TEST_ENTRIES - 1 ? ", " : "\n"); } } if (k == 0) fprintf(stderr, "PASS\n"); free(res); return 0; } Compiled with "-O2", on "VirtualBox 4.4.0-22-generic #38-Ubuntu x86_64" got: zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10 gcd0: elapsed 10174 gcd1: elapsed 2120 gcd2: elapsed 2902 gcd3: elapsed 2039 gcd4: elapsed 2812 PASS zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10 gcd0: elapsed 9309 gcd1: elapsed 2280 gcd2: elapsed 2822 gcd3: elapsed 2217 gcd4: elapsed 2710 PASS zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10 gcd0: elapsed 9589 gcd1: elapsed 2098 gcd2: elapsed 2815 gcd3: elapsed 2030 gcd4: elapsed 2718 PASS zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10 gcd0: elapsed 9914 gcd1: elapsed 2309 gcd2: elapsed 2779 gcd3: elapsed 2228 gcd4: elapsed 2709 PASS [akpm@linux-foundation.org: avoid #defining a CONFIG_ variable] Signed-off-by:Zhaoxiu Zeng <zhaoxiu.zeng@gmail.com> Signed-off-by:
George Spelvin <linux@horizon.com> Signed-off-by:
Andrew Morton <akpm@linux-foundation.org> Signed-off-by:
Linus Torvalds <torvalds@linux-foundation.org>
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Matthew Wilcox authored
We are guaranteed that pointers to radix_tree_nodes always have the bottom two bits clear (because they come from a slab cache, and slab caches have a minimum alignment of sizeof(void *)), so we can redefine 'radix_tree_is_internal_node' to only return true if the bottom two bits have value '01'. This frees up one quarter of the potential values for use by the user. Idea from Neil Brown. Signed-off-by:
Matthew Wilcox <willy@linux.intel.com> Suggested-by:
Neil Brown <neilb@suse.de> Cc: Konstantin Khlebnikov <koct9i@gmail.com> Cc: Kirill Shutemov <kirill.shutemov@linux.intel.com> Cc: Jan Kara <jack@suse.com> Cc: Ross Zwisler <ross.zwisler@linux.intel.com> Signed-off-by:
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NeilBrown authored
These don't belong in radix-tree.h any more than PAGECACHE_TAG_* do. Let's try to maintain the idea that radix-tree simply implements an abstract data type. Signed-off-by:
NeilBrown <neilb@suse.com> Reviewed-by:
Ross Zwisler <ross.zwisler@linux.intel.com> Reviewed-by:
Jan Kara <jack@suse.cz> Signed-off-by:
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Matthew Wilcox authored
Now that the shift amount is stored in the node, radix_tree_descend() can calculate offset itself from index, which removes several lines of code from each of the tree walkers. Signed-off-by:
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Matthew Wilcox authored
In addition to replacing the entry, we also clear all associated tags. This is really a one-off special for page_cache_tree_delete() which had far too much detailed knowledge about how the radix tree works. For efficiency, factor node_tag_clear() out of radix_tree_tag_clear() It can be used by radix_tree_delete_item() as well as radix_tree_replace_clear_tags(). Signed-off-by:
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Matthew Wilcox authored
1. Rename the existing variable 'slot' to 'child'. 2. Introduce a new variable called 'slot' which is the address of the slot we're dealing with. This lets us simplify the tree insertion, and removes the recalculation of 'slot' at the end of the function. 3. Using 'slot' in the sibling pointer insertion part makes the code more readable. Signed-off-by:
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Matthew Wilcox authored
Convert radix_tree_range_tag_if_tagged to name the nodes parent, node and child instead of node & slot. Use parent->offset instead of playing games with 'upindex'. Signed-off-by:
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Matthew Wilcox authored
Convert radix_tree_next_chunk to use 'child' instead of 'slot' as the name of the child node. Also use node_maxindex() where it makes sense. The 'rnode' variable was unnecessary; it doesn't overlap in usage with 'node', so we can just use 'node' the whole way through the function. Improve the testcase to start the walk from every index in the carefully constructed tree, and to accept any index within the range covered by the entry. Signed-off-by:
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Matthew Wilcox authored
Use the more standard 'node' and 'child' instead of 'to_free' and 'slot'. Signed-off-by:
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Matthew Wilcox authored
As with indirect_to_ptr(), ptr_to_indirect() and RADIX_TREE_INDIRECT_PTR, change radix_tree_is_indirect_ptr() to radix_tree_is_internal_node(). Signed-off-by:
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Matthew Wilcox authored
Mirrors the earlier commit introducing node_to_entry(). Also change the type returned to be a struct radix_tree_node pointer. That lets us simplify a couple of places in the radix tree shrink & extend paths where we could convert an entry into a pointer, modify the node, then convert the pointer back into an entry. Signed-off-by:
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Matthew Wilcox authored
ptr_to_indirect() was a bad name. What it really means is "Convert this pointer to a node into an entry suitable for storing in the radix tree". So node_to_entry() seemed like a better name. Signed-off-by:
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Matthew Wilcox authored
The name RADIX_TREE_INDIRECT_PTR doesn't really match the meaning. RADIX_TREE_INTERNAL_NODE is a better name. Signed-off-by:
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Matthew Wilcox authored
The only remaining references to root->height were in extend and shrink, where it was updated. Now we can remove it entirely. Signed-off-by:
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Matthew Wilcox authored
verify_node() can use node->shift instead of the height. tree_verify_min_height() can be converted over to using node_maxindex() and shift_maxindex() instead of radix_tree_maxindex(). Signed-off-by:
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Matthew Wilcox authored
If radix_tree_shrink returns whether it managed to shrink, then __radix_tree_delete_node doesn't ned to query the tree to find out whether it did any work or not. Signed-off-by:
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Matthew Wilcox authored
node->shift represents the shift necessary for looking in the slots array at this level. It is equal to the old (node->height - 1) * RADIX_TREE_MAP_SHIFT. Signed-off-by:
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Matthew Wilcox authored
Neither piece of information we're storing in node->path can be larger than 64, so store each in its own unsigned char instead of shifting and masking to store them both in an unsigned int. Signed-off-by:
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Matthew Wilcox authored
Typos, whitespace, grammar, line length, using the correct types, etc. Signed-off-by:
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Matthew Wilcox authored
radix_tree_is_indirect_ptr() is an internal API. The correct call to use is radix_tree_deref_retry() which has the appropriate unlikely() annotation. Fixes: c6400ba7 ("drivers/hwspinlock: fix race between radix tree insertion and lookup") Signed-off-by:
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Matthew Wilcox authored
The multiorder support is a sufficiently large feature to be worth adding copyrigt lines for. Signed-off-by:
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Ross Zwisler authored
- Print which indices are covered by every leaf entry - Print sibling entries - Print the node pointer instead of the slot entry - Build by default in userspace, and make it accessible to the test-suite Signed-off-by:
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Matthew Wilcox authored
I had previously decided that tagging a single multiorder entry would count as tagging 2^order entries for the purposes of 'nr_to_tag'. I now believe that decision to be a mistake, and it should count as a single entry. That's more likely to be what callers expect. When walking back up the tree from a newly-tagged entry, the current code assumed we were starting from the lowest level of the tree; if we have a multiorder entry with an order at least RADIX_TREE_MAP_SHIFT in size then we need to shift the index by 'shift' before we start walking back up the tree, or we will end up not setting tags on higher entries, and then mistakenly thinking that entries below a certain point in the tree are not tagged. If the first index we examine is a sibling entry of a tagged multiorder entry, we were not tagging it. We need to examine the canonical entry, and the easiest way to do that is to use radix_tree_descend(). We then have to skip over sibling slots when looking for the next entry in the tree or we will end up walking back to the canonical entry. Add several tests for radix_tree_range_tag_if_tagged(). Signed-off-by:
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Ross Zwisler authored
Add a unit test that provides coverage for the bug fixed in the commit entitled "radix-tree: rewrite radix_tree_locate_item fix" from Hugh Dickins. I've verified that this test fails before his patch due to miscalculated 'index' values in __locate() in lib/radix-tree.c, and passes with his fix. Link: http://lkml.kernel.org/r/1462307263-20623-1-git-send-email-ross.zwisler@linux.intel.comSigned-off-by:
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Matthew Wilcox authored
Use the new multi-order support functions to rewrite radix_tree_locate_item(). Modify the locate tests to test multiorder entries too. [hughd@google.com: radix_tree_locate_item() is often returning the wrong index] Link: http://lkml.kernel.org/r/alpine.LSU.2.11.1605012108490.1166@eggly.anvilsSigned-off-by:
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Matthew Wilcox authored
If the radix tree user attempted to insert a colliding entry with an existing multiorder entry, then radix_tree_create() could encounter a sibling entry when walking down the tree to look for a slot. Use radix_tree_descend() to fix the problem, and add a test-case to make sure the problem doesn't come back in future. Signed-off-by:
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Ross Zwisler authored
Add a generic test for multi-order tag verification, and call it using several different configurations. This test creates a multi-order radix tree using the given index and order, and then sets, checks and clears tags using the indices covered by the single multi-order radix tree entry. With the various calls done by this test we verify root multi-order entries without siblings, multi-order entries without siblings in a radix tree node, as well as multi-order entries with siblings of various sizes. Signed-off-by:
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Ross Zwisler authored
Use the new multi-order support functions to rewrite radix_tree_tag_get() Signed-off-by:
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Ross Zwisler authored
Use the new multi-order support functions to rewrite radix_tree_tag_clear() Signed-off-by:
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Ross Zwisler authored
Use the new multi-order support functions to rewrite radix_tree_tag_set() Signed-off-by:
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Ross Zwisler authored
Add a unit test to verify that we can iterate over multi-order entries properly via a radix_tree_for_each_slot() loop. This was done with a single, somewhat complicated configuration that was meant to test many of the various corner cases having to do with multi-order entries: - An iteration could begin at a sibling entry, and we need to return the canonical entry. - We could have entries of various orders in the same slots[] array. - We could have multi-order entries at a nonzero height, followed by indirect pointers to more radix tree nodes later in that same slots[] array. Signed-off-by:
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Ross Zwisler authored
This enables the macros radix_tree_for_each_slot() and friends to be used with multi-order entries. The way that this works is that we treat all entries in a given slots[] array as a single chunk. If the index given to radix_tree_next_chunk() happens to point us to a sibling entry, we will back up iter->index so that it points to the canonical entry, and that will be the place where we start our iteration. As we're processing a chunk in radix_tree_next_slot(), we process canonical entries, skip over sibling entries, and restart the chunk lookup if we find a non-sibling indirect pointer. This drops back to the radix_tree_next_chunk() code, which will re-walk the tree and look for another chunk. This allows us to properly handle multi-order entries mixed with other entries that are at various heights in the radix tree. Signed-off-by:
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Matthew Wilcox authored
These BUG_ON tests are to ensure that all the tags are clear when inserting a new entry. If we insert a multiorder entry, we'll end up looking at the tags for a different node, and so the BUG_ON can end up triggering spuriously. Also, we now have three tags, not two, so check all three are clear, and check all the root tags with a single call to BUG_ON since the bits are stored contiguously. Include a test-case to ensure this problem does not reoccur. Signed-off-by:
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Matthew Wilcox authored
Use the new multi-order support functions to rewrite __radix_tree_lookup() Signed-off-by:
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Matthew Wilcox authored
Setting the indirect bit on the user data entry used to be unambiguous because the tree walking code knew not to expect internal nodes in the last level of the tree. Multiorder entries can appear at any level of the tree, and a leaf with the indirect bit set is indistinguishable from a pointer to a node. Introduce a special entry (RADIX_TREE_RETRY) which is neither a valid user entry, nor a valid pointer to a node. The radix_tree_deref_retry() function continues to work the same way, but tree walking code can distinguish it from a pointer to a node. Also fix the condition for setting slot->parent to NULL; it does not matter what height the tree is, it only matters whether slot is an indirect pointer. Move this code above the comment which is referring to the assignment to root->rnode. Also fix the condition for preventing the tree from shrinking to a single entry if it's a multiorder entry. Add a test-case to the test suite that checks that the tree goes back down to its original height after an item is inserted & deleted from a higher index in the tree. Signed-off-by:
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Matthew Wilcox authored
Test suite infrastructure for working with multiorder entries. The test itself is pretty basic: Add an entry, check that all expected indices return that entry and that indices around that entry don't return an entry. Then delete the entry and check no index returns that entry. Tests a few edge conditions including the multiorder entry at index 0 and at a higher index. Also tests deleting through an alias as well as through the canonical index. Signed-off-by:
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Matthew Wilcox authored
The current code will insert entries at each level, as if we're going to add a new entry at the bottom level, so we then get an -EEXIST when we try to insert the entry into the tree. The best way to fix this is to not check 'order' when inserting into an empty tree. We still need to 'extend' the tree to the height necessary for the maximum index corresponding to this entry, so pass that value to radix_tree_extend() rather than the index we're asked to create, or we won't create a tree that's deep enough. Signed-off-by:
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Matthew Wilcox authored
All the tree walking functions start with some variant of this code; centralise it in one place so we're not chasing subtly different bugs everywhere. Signed-off-by:
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Matthew Wilcox authored
Now that sibling pointers are handled explicitly, there is no purpose served by restricting the order to be >= RADIX_TREE_MAP_SHIFT. Signed-off-by:
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Matthew Wilcox authored
If we deleted an entry through an index which looked up a sibling pointer, we'd end up zeroing out the wrong slots in the node. Use get_slot_offset() to find the right slot. Signed-off-by:
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