2 * Copyright (c) 1998 Matthew Dillon. All Rights Reserved.
3 * Redistribution and use in source and binary forms, with or without
4 * modification, are permitted provided that the following conditions
6 * 1. Redistributions of source code must retain the above copyright
7 * notice, this list of conditions and the following disclaimer.
8 * 2. Redistributions in binary form must reproduce the above copyright
9 * notice, this list of conditions and the following disclaimer in the
10 * documentation and/or other materials provided with the distribution.
11 * 4. Neither the name of the University nor the names of its contributors
12 * may be used to endorse or promote products derived from this software
13 * without specific prior written permission.
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
16 * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
17 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
19 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
21 * GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
22 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
23 * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
24 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
25 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 * BLIST.C - Bitmap allocator/deallocator, using a radix tree with hinting
30 * This module implements a general bitmap allocator/deallocator. The
31 * allocator eats around 2 bits per 'block'. The module does not
32 * try to interpret the meaning of a 'block' other then to return
33 * SWAPBLK_NONE on an allocation failure.
35 * A radix tree is used to maintain the bitmap. Two radix constants are
36 * involved: One for the bitmaps contained in the leaf nodes (typically
37 * 32), and one for the meta nodes (typically 16). Both meta and leaf
38 * nodes have a hint field. This field gives us a hint as to the largest
39 * free contiguous range of blocks under the node. It may contain a
40 * value that is too high, but will never contain a value that is too
41 * low. When the radix tree is searched, allocation failures in subtrees
44 * The radix tree also implements two collapsed states for meta nodes:
45 * the ALL-ALLOCATED state and the ALL-FREE state. If a meta node is
46 * in either of these two states, all information contained underneath
47 * the node is considered stale. These states are used to optimize
48 * allocation and freeing operations.
50 * The hinting greatly increases code efficiency for allocations while
51 * the general radix structure optimizes both allocations and frees. The
52 * radix tree should be able to operate well no matter how much
53 * fragmentation there is and no matter how large a bitmap is used.
55 * Unlike the rlist code, the blist code wires all necessary memory at
56 * creation time. Neither allocations nor frees require interaction with
57 * the memory subsystem. In contrast, the rlist code may allocate memory
58 * on an rlist_free() call. The non-blocking features of the blist code
59 * are used to great advantage in the swap code (vm/nswap_pager.c). The
60 * rlist code uses a little less overall memory then the blist code (but
61 * due to swap interleaving not all that much less), but the blist code
62 * scales much, much better.
64 * LAYOUT: The radix tree is layed out recursively using a
65 * linear array. Each meta node is immediately followed (layed out
66 * sequentially in memory) by BLIST_META_RADIX lower level nodes. This
67 * is a recursive structure but one that can be easily scanned through
68 * a very simple 'skip' calculation. In order to support large radixes,
69 * portions of the tree may reside outside our memory allocation. We
70 * handle this with an early-termination optimization (when bighint is
71 * set to -1) on the scan. The memory allocation is only large enough
72 * to cover the number of blocks requested at creation time even if it
73 * must be encompassed in larger root-node radix.
75 * NOTE: the allocator cannot currently allocate more then
76 * BLIST_BMAP_RADIX blocks per call. It will panic with 'allocation too
77 * large' if you try. This is an area that could use improvement. The
78 * radix is large enough that this restriction does not effect the swap
79 * system, though. Currently only the allocation code is effected by
80 * this algorithmic unfeature. The freeing code can handle arbitrary
83 * This code can be compiled stand-alone for debugging.
86 #include <sys/cdefs.h>
87 __FBSDID("$FreeBSD$");
91 #include <sys/param.h>
92 #include <sys/systm.h>
94 #include <sys/kernel.h>
95 #include <sys/blist.h>
96 #include <sys/malloc.h>
98 #include <sys/mutex.h>
102 #ifndef BLIST_NO_DEBUG
106 #define SWAPBLK_NONE ((daddr_t)-1)
108 #include <sys/types.h>
114 #define malloc(a,b,c) calloc(a, 1)
115 #define free(a,b) free(a)
117 typedef unsigned int u_daddr_t;
119 #include <sys/blist.h>
121 void panic(const char *ctl, ...);
126 * static support functions
129 static daddr_t blst_leaf_alloc(blmeta_t *scan, daddr_t blk, int count);
130 static daddr_t blst_meta_alloc(blmeta_t *scan, daddr_t blk,
131 daddr_t count, daddr_t radix, int skip);
132 static void blst_leaf_free(blmeta_t *scan, daddr_t relblk, int count);
133 static void blst_meta_free(blmeta_t *scan, daddr_t freeBlk, daddr_t count,
134 daddr_t radix, int skip, daddr_t blk);
135 static void blst_copy(blmeta_t *scan, daddr_t blk, daddr_t radix,
136 daddr_t skip, blist_t dest, daddr_t count);
137 static int blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count);
138 static int blst_meta_fill(blmeta_t *scan, daddr_t allocBlk, daddr_t count,
139 daddr_t radix, int skip, daddr_t blk);
140 static daddr_t blst_radix_init(blmeta_t *scan, daddr_t radix,
141 int skip, daddr_t count);
143 static void blst_radix_print(blmeta_t *scan, daddr_t blk,
144 daddr_t radix, int skip, int tab);
148 static MALLOC_DEFINE(M_SWAP, "SWAP", "Swap space");
152 * blist_create() - create a blist capable of handling up to the specified
155 * blocks must be greater then 0
157 * The smallest blist consists of a single leaf node capable of
158 * managing BLIST_BMAP_RADIX blocks.
162 blist_create(daddr_t blocks)
169 * Calculate radix and skip field used for scanning.
171 radix = BLIST_BMAP_RADIX;
173 while (radix < blocks) {
174 radix *= BLIST_META_RADIX;
175 skip = (skip + 1) * BLIST_META_RADIX;
178 bl = malloc(sizeof(struct blist), M_SWAP, M_WAITOK | M_ZERO);
180 bl->bl_blocks = blocks;
181 bl->bl_radix = radix;
183 bl->bl_rootblks = 1 +
184 blst_radix_init(NULL, bl->bl_radix, bl->bl_skip, blocks);
185 bl->bl_root = malloc(sizeof(blmeta_t) * bl->bl_rootblks, M_SWAP, M_WAITOK);
187 #if defined(BLIST_DEBUG)
189 "BLIST representing %lld blocks (%lld MB of swap)"
190 ", requiring %lldK of ram\n",
191 (long long)bl->bl_blocks,
192 (long long)bl->bl_blocks * 4 / 1024,
193 (long long)(bl->bl_rootblks * sizeof(blmeta_t) + 1023) / 1024
195 printf("BLIST raw radix tree contains %lld records\n",
196 (long long)bl->bl_rootblks);
198 blst_radix_init(bl->bl_root, bl->bl_radix, bl->bl_skip, blocks);
204 blist_destroy(blist_t bl)
206 free(bl->bl_root, M_SWAP);
211 * blist_alloc() - reserve space in the block bitmap. Return the base
212 * of a contiguous region or SWAPBLK_NONE if space could
217 blist_alloc(blist_t bl, daddr_t count)
219 daddr_t blk = SWAPBLK_NONE;
222 if (bl->bl_radix == BLIST_BMAP_RADIX)
223 blk = blst_leaf_alloc(bl->bl_root, 0, count);
225 blk = blst_meta_alloc(bl->bl_root, 0, count, bl->bl_radix, bl->bl_skip);
226 if (blk != SWAPBLK_NONE)
227 bl->bl_free -= count;
233 * blist_free() - free up space in the block bitmap. Return the base
234 * of a contiguous region. Panic if an inconsistancy is
239 blist_free(blist_t bl, daddr_t blkno, daddr_t count)
242 if (bl->bl_radix == BLIST_BMAP_RADIX)
243 blst_leaf_free(bl->bl_root, blkno, count);
245 blst_meta_free(bl->bl_root, blkno, count, bl->bl_radix, bl->bl_skip, 0);
246 bl->bl_free += count;
251 * blist_fill() - mark a region in the block bitmap as off-limits
252 * to the allocator (i.e. allocate it), ignoring any
253 * existing allocations. Return the number of blocks
254 * actually filled that were free before the call.
258 blist_fill(blist_t bl, daddr_t blkno, daddr_t count)
263 if (bl->bl_radix == BLIST_BMAP_RADIX)
264 filled = blst_leaf_fill(bl->bl_root, blkno, count);
266 filled = blst_meta_fill(bl->bl_root, blkno, count,
267 bl->bl_radix, bl->bl_skip, 0);
268 bl->bl_free -= filled;
275 * blist_resize() - resize an existing radix tree to handle the
276 * specified number of blocks. This will reallocate
277 * the tree and transfer the previous bitmap to the new
278 * one. When extending the tree you can specify whether
279 * the new blocks are to left allocated or freed.
283 blist_resize(blist_t *pbl, daddr_t count, int freenew)
285 blist_t newbl = blist_create(count);
289 if (count > save->bl_blocks)
290 count = save->bl_blocks;
291 blst_copy(save->bl_root, 0, save->bl_radix, save->bl_skip, newbl, count);
294 * If resizing upwards, should we free the new space or not?
296 if (freenew && count < newbl->bl_blocks) {
297 blist_free(newbl, count, newbl->bl_blocks - count);
305 * blist_print() - dump radix tree
309 blist_print(blist_t bl)
312 blst_radix_print(bl->bl_root, 0, bl->bl_radix, bl->bl_skip, 4);
318 /************************************************************************
319 * ALLOCATION SUPPORT FUNCTIONS *
320 ************************************************************************
322 * These support functions do all the actual work. They may seem
323 * rather longish, but that's because I've commented them up. The
324 * actual code is straight forward.
329 * blist_leaf_alloc() - allocate at a leaf in the radix tree (a bitmap).
331 * This is the core of the allocator and is optimized for the 1 block
332 * and the BLIST_BMAP_RADIX block allocation cases. Other cases are
333 * somewhat slower. The 1 block allocation case is log2 and extremely
343 u_daddr_t orig = scan->u.bmu_bitmap;
347 * Optimize bitmap all-allocated case. Also, count = 1
348 * case assumes at least 1 bit is free in the bitmap, so
349 * we have to take care of this case here.
351 scan->bm_bighint = 0;
352 return(SWAPBLK_NONE);
356 * Optimized code to allocate one bit out of the bitmap
359 int j = BLIST_BMAP_RADIX/2;
362 mask = (u_daddr_t)-1 >> (BLIST_BMAP_RADIX/2);
365 if ((orig & mask) == 0) {
372 scan->u.bmu_bitmap &= ~(1 << r);
375 if (count <= BLIST_BMAP_RADIX) {
377 * non-optimized code to allocate N bits out of the bitmap.
378 * The more bits, the faster the code runs. It will run
379 * the slowest allocating 2 bits, but since there aren't any
380 * memory ops in the core loop (or shouldn't be, anyway),
381 * you probably won't notice the difference.
384 int n = BLIST_BMAP_RADIX - count;
387 mask = (u_daddr_t)-1 >> n;
389 for (j = 0; j <= n; ++j) {
390 if ((orig & mask) == mask) {
391 scan->u.bmu_bitmap &= ~mask;
398 * We couldn't allocate count in this subtree, update bighint.
400 scan->bm_bighint = count - 1;
401 return(SWAPBLK_NONE);
405 * blist_meta_alloc() - allocate at a meta in the radix tree.
407 * Attempt to allocate at a meta node. If we can't, we update
408 * bighint and return a failure. Updating bighint optimize future
409 * calls that hit this node. We have to check for our collapse cases
410 * and we have a few optimizations strewn in as well.
422 int next_skip = ((u_int)skip / BLIST_META_RADIX);
424 if (scan->u.bmu_avail == 0) {
426 * ALL-ALLOCATED special case
428 scan->bm_bighint = count;
429 return(SWAPBLK_NONE);
432 if (scan->u.bmu_avail == radix) {
433 radix /= BLIST_META_RADIX;
436 * ALL-FREE special case, initialize uninitialize
439 for (i = 1; i <= skip; i += next_skip) {
440 if (scan[i].bm_bighint == (daddr_t)-1)
442 if (next_skip == 1) {
443 scan[i].u.bmu_bitmap = (u_daddr_t)-1;
444 scan[i].bm_bighint = BLIST_BMAP_RADIX;
446 scan[i].bm_bighint = radix;
447 scan[i].u.bmu_avail = radix;
451 radix /= BLIST_META_RADIX;
454 for (i = 1; i <= skip; i += next_skip) {
455 if (count <= scan[i].bm_bighint) {
457 * count fits in object
460 if (next_skip == 1) {
461 r = blst_leaf_alloc(&scan[i], blk, count);
463 r = blst_meta_alloc(&scan[i], blk, count, radix, next_skip - 1);
465 if (r != SWAPBLK_NONE) {
466 scan->u.bmu_avail -= count;
467 if (scan->bm_bighint > scan->u.bmu_avail)
468 scan->bm_bighint = scan->u.bmu_avail;
471 } else if (scan[i].bm_bighint == (daddr_t)-1) {
476 } else if (count > radix) {
478 * count does not fit in object even if it were
481 panic("blist_meta_alloc: allocation too large");
487 * We couldn't allocate count in this subtree, update bighint.
489 if (scan->bm_bighint >= count)
490 scan->bm_bighint = count - 1;
491 return(SWAPBLK_NONE);
495 * BLST_LEAF_FREE() - free allocated block from leaf bitmap
506 * free some data in this bitmap
509 * 0000111111111110000
513 int n = blk & (BLIST_BMAP_RADIX - 1);
516 mask = ((u_daddr_t)-1 << n) &
517 ((u_daddr_t)-1 >> (BLIST_BMAP_RADIX - count - n));
519 if (scan->u.bmu_bitmap & mask)
520 panic("blst_radix_free: freeing free block");
521 scan->u.bmu_bitmap |= mask;
524 * We could probably do a better job here. We are required to make
525 * bighint at least as large as the biggest contiguous block of
526 * data. If we just shoehorn it, a little extra overhead will
527 * be incured on the next allocation (but only that one typically).
529 scan->bm_bighint = BLIST_BMAP_RADIX;
533 * BLST_META_FREE() - free allocated blocks from radix tree meta info
535 * This support routine frees a range of blocks from the bitmap.
536 * The range must be entirely enclosed by this radix node. If a
537 * meta node, we break the range down recursively to free blocks
538 * in subnodes (which means that this code can free an arbitrary
539 * range whereas the allocation code cannot allocate an arbitrary
553 int next_skip = ((u_int)skip / BLIST_META_RADIX);
556 printf("FREE (%llx,%lld) FROM (%llx,%lld)\n",
557 (long long)freeBlk, (long long)count,
558 (long long)blk, (long long)radix
562 if (scan->u.bmu_avail == 0) {
564 * ALL-ALLOCATED special case, with possible
565 * shortcut to ALL-FREE special case.
567 scan->u.bmu_avail = count;
568 scan->bm_bighint = count;
570 if (count != radix) {
571 for (i = 1; i <= skip; i += next_skip) {
572 if (scan[i].bm_bighint == (daddr_t)-1)
574 scan[i].bm_bighint = 0;
575 if (next_skip == 1) {
576 scan[i].u.bmu_bitmap = 0;
578 scan[i].u.bmu_avail = 0;
584 scan->u.bmu_avail += count;
585 /* scan->bm_bighint = radix; */
589 * ALL-FREE special case.
592 if (scan->u.bmu_avail == radix)
594 if (scan->u.bmu_avail > radix)
595 panic("blst_meta_free: freeing already free blocks (%lld) %lld/%lld",
596 (long long)count, (long long)scan->u.bmu_avail,
600 * Break the free down into its components
603 radix /= BLIST_META_RADIX;
605 i = (freeBlk - blk) / radix;
607 i = i * next_skip + 1;
609 while (i <= skip && blk < freeBlk + count) {
612 v = blk + radix - freeBlk;
616 if (scan->bm_bighint == (daddr_t)-1)
617 panic("blst_meta_free: freeing unexpected range");
619 if (next_skip == 1) {
620 blst_leaf_free(&scan[i], freeBlk, v);
622 blst_meta_free(&scan[i], freeBlk, v, radix, next_skip - 1, blk);
624 if (scan->bm_bighint < scan[i].bm_bighint)
625 scan->bm_bighint = scan[i].bm_bighint;
634 * BLIST_RADIX_COPY() - copy one radix tree to another
636 * Locates free space in the source tree and frees it in the destination
637 * tree. The space may not already be free in the destination.
640 static void blst_copy(
655 if (radix == BLIST_BMAP_RADIX) {
656 u_daddr_t v = scan->u.bmu_bitmap;
658 if (v == (u_daddr_t)-1) {
659 blist_free(dest, blk, count);
663 for (i = 0; i < BLIST_BMAP_RADIX && i < count; ++i) {
665 blist_free(dest, blk + i, 1);
675 if (scan->u.bmu_avail == 0) {
677 * Source all allocated, leave dest allocated
681 if (scan->u.bmu_avail == radix) {
683 * Source all free, free entire dest
686 blist_free(dest, blk, count);
688 blist_free(dest, blk, radix);
693 radix /= BLIST_META_RADIX;
694 next_skip = ((u_int)skip / BLIST_META_RADIX);
696 for (i = 1; count && i <= skip; i += next_skip) {
697 if (scan[i].bm_bighint == (daddr_t)-1)
700 if (count >= radix) {
728 * BLST_LEAF_FILL() - allocate specific blocks in leaf bitmap
730 * This routine allocates all blocks in the specified range
731 * regardless of any existing allocations in that range. Returns
732 * the number of blocks allocated by the call.
736 blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count)
738 int n = blk & (BLIST_BMAP_RADIX - 1);
740 u_daddr_t mask, bitmap;
742 mask = ((u_daddr_t)-1 << n) &
743 ((u_daddr_t)-1 >> (BLIST_BMAP_RADIX - count - n));
745 /* Count the number of blocks we're about to allocate */
746 bitmap = scan->u.bmu_bitmap & mask;
747 for (nblks = 0; bitmap != 0; nblks++)
748 bitmap &= bitmap - 1;
750 scan->u.bmu_bitmap &= ~mask;
755 * BLIST_META_FILL() - allocate specific blocks at a meta node
757 * This routine allocates the specified range of blocks,
758 * regardless of any existing allocations in the range. The
759 * range must be within the extent of this node. Returns the
760 * number of blocks allocated by the call.
772 int next_skip = ((u_int)skip / BLIST_META_RADIX);
775 if (count == radix || scan->u.bmu_avail == 0) {
777 * ALL-ALLOCATED special case
779 nblks = scan->u.bmu_avail;
780 scan->u.bmu_avail = 0;
781 scan->bm_bighint = count;
785 if (scan->u.bmu_avail == radix) {
786 radix /= BLIST_META_RADIX;
789 * ALL-FREE special case, initialize sublevel
791 for (i = 1; i <= skip; i += next_skip) {
792 if (scan[i].bm_bighint == (daddr_t)-1)
794 if (next_skip == 1) {
795 scan[i].u.bmu_bitmap = (u_daddr_t)-1;
796 scan[i].bm_bighint = BLIST_BMAP_RADIX;
798 scan[i].bm_bighint = radix;
799 scan[i].u.bmu_avail = radix;
803 radix /= BLIST_META_RADIX;
807 panic("blist_meta_fill: allocation too large");
809 i = (allocBlk - blk) / radix;
811 i = i * next_skip + 1;
813 while (i <= skip && blk < allocBlk + count) {
816 v = blk + radix - allocBlk;
820 if (scan->bm_bighint == (daddr_t)-1)
821 panic("blst_meta_fill: filling unexpected range");
823 if (next_skip == 1) {
824 nblks += blst_leaf_fill(&scan[i], allocBlk, v);
826 nblks += blst_meta_fill(&scan[i], allocBlk, v,
827 radix, next_skip - 1, blk);
834 scan->u.bmu_avail -= nblks;
839 * BLST_RADIX_INIT() - initialize radix tree
841 * Initialize our meta structures and bitmaps and calculate the exact
842 * amount of space required to manage 'count' blocks - this space may
843 * be considerably less then the calculated radix due to the large
844 * RADIX values we use.
848 blst_radix_init(blmeta_t *scan, daddr_t radix, int skip, daddr_t count)
852 daddr_t memindex = 0;
858 if (radix == BLIST_BMAP_RADIX) {
860 scan->bm_bighint = 0;
861 scan->u.bmu_bitmap = 0;
867 * Meta node. If allocating the entire object we can special
868 * case it. However, we need to figure out how much memory
869 * is required to manage 'count' blocks, so we continue on anyway.
873 scan->bm_bighint = 0;
874 scan->u.bmu_avail = 0;
877 radix /= BLIST_META_RADIX;
878 next_skip = ((u_int)skip / BLIST_META_RADIX);
880 for (i = 1; i <= skip; i += next_skip) {
881 if (count >= radix) {
883 * Allocate the entire object
885 memindex = i + blst_radix_init(
886 ((scan) ? &scan[i] : NULL),
892 } else if (count > 0) {
894 * Allocate a partial object
896 memindex = i + blst_radix_init(
897 ((scan) ? &scan[i] : NULL),
905 * Add terminator and break out
908 scan[i].bm_bighint = (daddr_t)-1;
920 blst_radix_print(blmeta_t *scan, daddr_t blk, daddr_t radix, int skip, int tab)
926 if (radix == BLIST_BMAP_RADIX) {
928 "%*.*s(%08llx,%lld): bitmap %08llx big=%lld\n",
930 (long long)blk, (long long)radix,
931 (long long)scan->u.bmu_bitmap,
932 (long long)scan->bm_bighint
937 if (scan->u.bmu_avail == 0) {
939 "%*.*s(%08llx,%lld) ALL ALLOCATED\n",
946 if (scan->u.bmu_avail == radix) {
948 "%*.*s(%08llx,%lld) ALL FREE\n",
957 "%*.*s(%08llx,%lld): subtree (%lld/%lld) big=%lld {\n",
959 (long long)blk, (long long)radix,
960 (long long)scan->u.bmu_avail,
962 (long long)scan->bm_bighint
965 radix /= BLIST_META_RADIX;
966 next_skip = ((u_int)skip / BLIST_META_RADIX);
969 for (i = 1; i <= skip; i += next_skip) {
970 if (scan[i].bm_bighint == (daddr_t)-1) {
972 "%*.*s(%08llx,%lld): Terminator\n",
974 (long long)blk, (long long)radix
1001 main(int ac, char **av)
1007 for (i = 1; i < ac; ++i) {
1008 const char *ptr = av[i];
1010 size = strtol(ptr, NULL, 0);
1014 fprintf(stderr, "Bad option: %s\n", ptr - 2);
1017 bl = blist_create(size);
1018 blist_free(bl, 0, size);
1026 printf("%lld/%lld/%lld> ", (long long)bl->bl_free,
1027 (long long)size, (long long)bl->bl_radix);
1029 if (fgets(buf, sizeof(buf), stdin) == NULL)
1033 if (sscanf(buf + 1, "%lld", &count) == 1) {
1034 blist_resize(&bl, count, 1);
1042 if (sscanf(buf + 1, "%lld", &count) == 1) {
1043 daddr_t blk = blist_alloc(bl, count);
1044 printf(" R=%08llx\n", (long long)blk);
1050 if (sscanf(buf + 1, "%llx %lld",
1051 (long long *)&da, (long long *)&count) == 2) {
1052 blist_free(bl, da, count);
1058 if (sscanf(buf + 1, "%llx %lld",
1059 (long long *)&da, (long long *)&count) == 2) {
1061 blist_fill(bl, da, count));
1086 panic(const char *ctl, ...)
1091 vfprintf(stderr, ctl, va);
1092 fprintf(stderr, "\n");