FreeBSD/Linux Kernel Cross Reference
sys/kern/subr_blist.c

     /*-
      * SPDX-License-Identifier: BSD-3-Clause
      *
      * Copyright (c) 1998 Matthew Dillon.  All Rights Reserved.
      * Redistribution and use in source and binary forms, with or without
      * modification, are permitted provided that the following conditions
      * are met:
      * 1. Redistributions of source code must retain the above copyright
      *    notice, this list of conditions and the following disclaimer.
     * 2. Redistributions in binary form must reproduce the above copyright
     *    notice, this list of conditions and the following disclaimer in the
     *    documentation and/or other materials provided with the distribution.
     * 3. Neither the name of the University nor the names of its contributors
     *    may be used to endorse or promote products derived from this software
     *    without specific prior written permission.
     *
     * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
     * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
     * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
     * GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
     * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
     * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     */
    /*
     * BLIST.C -    Bitmap allocator/deallocator, using a radix tree with hinting
     *
     *      This module implements a general bitmap allocator/deallocator.  The
     *      allocator eats around 2 bits per 'block'.  The module does not
     *      try to interpret the meaning of a 'block' other than to return
     *      SWAPBLK_NONE on an allocation failure.
     *
     *      A radix tree controls access to pieces of the bitmap, and includes
     *      auxiliary information at each interior node about the availabilty of
     *      contiguous free blocks in the subtree rooted at that node.  A radix
     *      constant defines the size of the bitmaps contained in a leaf node
     *      and the number of descendents of each of the meta (interior) nodes.
     *      Each subtree is associated with a range of blocks.  The root of any
     *      subtree stores a hint field that defines an upper bound on the size
     *      of the largest allocation that can begin in the associated block
     *      range.  A hint is an upper bound on a potential allocation, but not
     *      necessarily a tight upper bound.
     *
     *      The bitmap field in each node directs the search for available blocks.
     *      For a leaf node, a bit is set if the corresponding block is free.  For a
     *      meta node, a bit is set if the corresponding subtree contains a free
     *      block somewhere within it.  The search at a meta node considers only
     *      children of that node that represent a range that includes a free block.
     *
     *      The hinting greatly increases code efficiency for allocations while
     *      the general radix structure optimizes both allocations and frees.  The
     *      radix tree should be able to operate well no matter how much
     *      fragmentation there is and no matter how large a bitmap is used.
     *
     *      The blist code wires all necessary memory at creation time.  Neither
     *      allocations nor frees require interaction with the memory subsystem.
     *      The non-blocking nature of allocations and frees is required by swap
     *      code (vm/swap_pager.c).
     *
     *      LAYOUT: The radix tree is laid out recursively using a linear array.
     *      Each meta node is immediately followed (laid out sequentially in
     *      memory) by BLIST_RADIX lower-level nodes.  This is a recursive
     *      structure but one that can be easily scanned through a very simple
     *      'skip' calculation.  The memory allocation is only large enough to
     *      cover the number of blocks requested at creation time.  Nodes that
     *      represent blocks beyond that limit, nodes that would never be read
     *      or written, are not allocated, so that the last of the
     *      BLIST_RADIX lower-level nodes of a some nodes may not be allocated.
     *
     *      NOTE: the allocator cannot currently allocate more than
     *      BLIST_RADIX blocks per call.  It will panic with 'allocation too
     *      large' if you try.  This is an area that could use improvement.  The
     *      radix is large enough that this restriction does not effect the swap
     *      system, though.  Currently only the allocation code is affected by
     *      this algorithmic unfeature.  The freeing code can handle arbitrary
     *      ranges.
     *
     *      This code can be compiled stand-alone for debugging.
     */
    
    #include <sys/cdefs.h>
    __FBSDID("$FreeBSD$");
    
    #ifdef _KERNEL
    
    #include <sys/param.h>
    #include <sys/systm.h>
    #include <sys/lock.h>
    #include <sys/kernel.h>
    #include <sys/blist.h>
    #include <sys/malloc.h>
    #include <sys/sbuf.h>
    #include <sys/proc.h>
    #include <sys/mutex.h>
    
   #else
   
   #ifndef BLIST_NO_DEBUG
   #define BLIST_DEBUG
   #endif
   
   #include <sys/errno.h>
   #include <sys/types.h>
   #include <sys/malloc.h>
   #include <sys/sbuf.h>
   #include <assert.h>
   #include <stdio.h>
   #include <string.h>
   #include <stddef.h>
   #include <stdlib.h>
   #include <stdarg.h>
   #include <stdbool.h>
   
   #define bitcount64(x)   __bitcount64((uint64_t)(x))
   #define malloc(a,b,c)   calloc(a, 1)
   #define free(a,b)       free(a)
   #define ummin(a,b)      ((a) < (b) ? (a) : (b))
   #define imin(a,b)       ((a) < (b) ? (a) : (b))
   #define KASSERT(a,b)    assert(a)
   
   #include <sys/blist.h>
   
   #endif
   
   /*
    * static support functions
    */
   static daddr_t  blst_leaf_alloc(blmeta_t *scan, daddr_t blk,
       int *count, int maxcount);
   static daddr_t  blst_meta_alloc(blmeta_t *scan, daddr_t cursor, int *count,
       int maxcount, u_daddr_t radix);
   static void blst_leaf_free(blmeta_t *scan, daddr_t relblk, int count);
   static void blst_meta_free(blmeta_t *scan, daddr_t freeBlk, daddr_t count,
                       u_daddr_t radix);
   static void blst_copy(blmeta_t *scan, daddr_t blk, daddr_t radix,
                       blist_t dest, daddr_t count);
   static daddr_t blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count);
   static daddr_t blst_meta_fill(blmeta_t *scan, daddr_t allocBlk, daddr_t count,
                       u_daddr_t radix);
   #ifndef _KERNEL
   static void     blst_radix_print(blmeta_t *scan, daddr_t blk, daddr_t radix,
                       int tab);
   #endif
   
   #ifdef _KERNEL
   static MALLOC_DEFINE(M_SWAP, "SWAP", "Swap space");
   #endif
   
   #define BLIST_MASK      (BLIST_RADIX - 1)
   
   /*
    * For a subtree that can represent the state of up to 'radix' blocks, the
    * number of leaf nodes of the subtree is L=radix/BLIST_RADIX.  If 'm'
    * is short for BLIST_RADIX, then for a tree of height h with L=m**h
    * leaf nodes, the total number of tree nodes is 1 + m + m**2 + ... + m**h,
    * or, equivalently, (m**(h+1)-1)/(m-1).  This quantity is called 'skip'
    * in the 'meta' functions that process subtrees.  Since integer division
    * discards remainders, we can express this computation as
    * skip = (m * m**h) / (m - 1)
    * skip = (m * (radix / m)) / (m - 1)
    * skip = radix / (m - 1)
    * so that simple integer division by a constant can safely be used for the
    * calculation.
    */
   static inline daddr_t
   radix_to_skip(daddr_t radix)
   {
   
           return (radix / BLIST_MASK);
   }
   
   /*
    * Provide a mask with count bits set, starting as position n.
    */
   static inline u_daddr_t
   bitrange(int n, int count)
   {
   
           return (((u_daddr_t)-1 << n) &
               ((u_daddr_t)-1 >> (BLIST_RADIX - (n + count))));
   }
   
   /*
    * Find the first bit set in a u_daddr_t.
    */
   static inline int
   generic_bitpos(u_daddr_t mask)
   {
           int hi, lo, mid;
   
           lo = 0;
           hi = BLIST_RADIX;
           while (lo + 1 < hi) {
                   mid = (lo + hi) >> 1;
                   if (mask & bitrange(0, mid))
                           hi = mid;
                   else
                           lo = mid;
           }
           return (lo);
   }
   
   static inline int
   bitpos(u_daddr_t mask)
   {
   
           switch (sizeof(mask)) {
   #ifdef HAVE_INLINE_FFSLL
           case sizeof(long long):
                   return (ffsll(mask) - 1);
   #endif
   #ifdef HAVE_INLINE_FFS
           case sizeof(int):
                   return (ffs(mask) - 1);
   #endif
           default:
                   return (generic_bitpos(mask));
           }
   }
   
   /*
    * blist_create() - create a blist capable of handling up to the specified
    *                  number of blocks
    *
    *      blocks - must be greater than 0
    *      flags  - malloc flags
    *
    *      The smallest blist consists of a single leaf node capable of
    *      managing BLIST_RADIX blocks.
    */
   blist_t
   blist_create(daddr_t blocks, int flags)
   {
           blist_t bl;
           u_daddr_t nodes, radix;
   
           KASSERT(blocks > 0, ("invalid block count"));
   
           /*
            * Calculate the radix and node count used for scanning.
            */
           nodes = 1;
           for (radix = 1; (blocks - 1) / BLIST_RADIX / radix > 0;
               radix *= BLIST_RADIX)
                   nodes += 1 + (blocks - 1) / BLIST_RADIX / radix;
   
           /*
            * Include a sentinel node to ensure that cross-leaf scans stay within
            * the bounds of the allocation.
            */
           if (blocks % BLIST_RADIX == 0)
                   nodes++;
   
           bl = malloc(offsetof(struct blist, bl_root[nodes]), M_SWAP, flags |
               M_ZERO);
           if (bl == NULL)
                   return (NULL);
   
           bl->bl_blocks = blocks;
           bl->bl_radix = radix;
   
   #if defined(BLIST_DEBUG)
           printf(
                   "BLIST representing %lld blocks (%lld MB of swap)"
                   ", requiring %lldK of ram\n",
                   (long long)bl->bl_blocks,
                   (long long)bl->bl_blocks * 4 / 1024,
                   (long long)(nodes * sizeof(blmeta_t) + 1023) / 1024
           );
           printf("BLIST raw radix tree contains %lld records\n",
               (long long)nodes);
   #endif
   
           return (bl);
   }
   
   void
   blist_destroy(blist_t bl)
   {
   
           free(bl, M_SWAP);
   }
   
   /*
    * blist_alloc() -   reserve space in the block bitmap.  Return the base
    *                   of a contiguous region or SWAPBLK_NONE if space could
    *                   not be allocated.
    */
   daddr_t
   blist_alloc(blist_t bl, int *count, int maxcount)
   {
           daddr_t blk, cursor;
   
           KASSERT(*count <= maxcount,
               ("invalid parameters %d > %d", *count, maxcount));
           KASSERT(*count <= BLIST_MAX_ALLOC,
               ("minimum allocation too large: %d", *count));
   
           /*
            * This loop iterates at most twice.  An allocation failure in the
            * first iteration leads to a second iteration only if the cursor was
            * non-zero.  When the cursor is zero, an allocation failure will
            * stop further iterations.
            */
           for (cursor = bl->bl_cursor;; cursor = 0) {
                   blk = blst_meta_alloc(bl->bl_root, cursor, count, maxcount,
                       bl->bl_radix);
                   if (blk != SWAPBLK_NONE) {
                           bl->bl_avail -= *count;
                           bl->bl_cursor = blk + *count;
                           if (bl->bl_cursor == bl->bl_blocks)
                                   bl->bl_cursor = 0;
                           return (blk);
                   }
                   if (cursor == 0)
                           return (SWAPBLK_NONE);
           }
   }
   
   /*
    * blist_avail() -      return the number of free blocks.
    */
   daddr_t
   blist_avail(blist_t bl)
   {
   
           return (bl->bl_avail);
   }
   
   /*
    * blist_free() -       free up space in the block bitmap.  Return the base
    *                      of a contiguous region.
    */
   void
   blist_free(blist_t bl, daddr_t blkno, daddr_t count)
   {
   
           KASSERT(blkno >= 0 && blkno + count <= bl->bl_blocks,
               ("freeing invalid range: blkno %jx, count %d, blocks %jd",
               (uintmax_t)blkno, (int)count, (uintmax_t)bl->bl_blocks));
           blst_meta_free(bl->bl_root, blkno, count, bl->bl_radix);
           bl->bl_avail += count;
   }
   
   /*
    * blist_fill() -       mark a region in the block bitmap as off-limits
    *                      to the allocator (i.e. allocate it), ignoring any
    *                      existing allocations.  Return the number of blocks
    *                      actually filled that were free before the call.
    */
   daddr_t
   blist_fill(blist_t bl, daddr_t blkno, daddr_t count)
   {
           daddr_t filled;
   
           KASSERT(blkno >= 0 && blkno + count <= bl->bl_blocks,
               ("filling invalid range: blkno %jx, count %d, blocks %jd",
               (uintmax_t)blkno, (int)count, (uintmax_t)bl->bl_blocks));
           filled = blst_meta_fill(bl->bl_root, blkno, count, bl->bl_radix);
           bl->bl_avail -= filled;
           return (filled);
   }
   
   /*
    * blist_resize() -     resize an existing radix tree to handle the
    *                      specified number of blocks.  This will reallocate
    *                      the tree and transfer the previous bitmap to the new
    *                      one.  When extending the tree you can specify whether
    *                      the new blocks are to left allocated or freed.
    */
   void
   blist_resize(blist_t *pbl, daddr_t count, int freenew, int flags)
   {
       blist_t newbl = blist_create(count, flags);
       blist_t save = *pbl;
   
       *pbl = newbl;
       if (count > save->bl_blocks)
               count = save->bl_blocks;
       blst_copy(save->bl_root, 0, save->bl_radix, newbl, count);
   
       /*
        * If resizing upwards, should we free the new space or not?
        */
       if (freenew && count < newbl->bl_blocks) {
               blist_free(newbl, count, newbl->bl_blocks - count);
       }
       blist_destroy(save);
   }
   
   #ifdef BLIST_DEBUG
   
   /*
    * blist_print()    - dump radix tree
    */
   void
   blist_print(blist_t bl)
   {
           printf("BLIST avail = %jd, cursor = %08jx {\n",
               (uintmax_t)bl->bl_avail, (uintmax_t)bl->bl_cursor);
   
           if (bl->bl_root->bm_bitmap != 0)
                   blst_radix_print(bl->bl_root, 0, bl->bl_radix, 4);
           printf("}\n");
   }
   
   #endif
   
   static const u_daddr_t fib[] = {
           1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,
           4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811,
           514229, 832040, 1346269, 2178309, 3524578,
   };
   
   /*
    * Use 'gap' to describe a maximal range of unallocated blocks/bits.
    */
   struct gap_stats {
           daddr_t start;          /* current gap start, or SWAPBLK_NONE */
           daddr_t num;            /* number of gaps observed */
           daddr_t max;            /* largest gap size */
           daddr_t avg;            /* average gap size */
           daddr_t err;            /* sum - num * avg */
           daddr_t histo[nitems(fib)]; /* # gaps in each size range */
           int     max_bucket;     /* last histo elt with nonzero val */
   };
   
   /*
    * gap_stats_counting()    - is the state 'counting 1 bits'?
    *                           or 'skipping 0 bits'?
    */
   static inline bool
   gap_stats_counting(const struct gap_stats *stats)
   {
   
           return (stats->start != SWAPBLK_NONE);
   }
   
   /*
    * init_gap_stats()    - initialize stats on gap sizes
    */
   static inline void
   init_gap_stats(struct gap_stats *stats)
   {
   
           bzero(stats, sizeof(*stats));
           stats->start = SWAPBLK_NONE;
   }
   
   /*
    * update_gap_stats()    - update stats on gap sizes
    */
   static void
   update_gap_stats(struct gap_stats *stats, daddr_t posn)
   {
           daddr_t size;
           int hi, lo, mid;
   
           if (!gap_stats_counting(stats)) {
                   stats->start = posn;
                   return;
           }
           size = posn - stats->start;
           stats->start = SWAPBLK_NONE;
           if (size > stats->max)
                   stats->max = size;
   
           /*
            * Find the fibonacci range that contains size,
            * expecting to find it in an early range.
            */
           lo = 0;
           hi = 1;
           while (hi < nitems(fib) && fib[hi] <= size) {
                   lo = hi;
                   hi *= 2;
           }
           if (hi >= nitems(fib))
                   hi = nitems(fib);
           while (lo + 1 != hi) {
                   mid = (lo + hi) >> 1;
                   if (fib[mid] <= size)
                           lo = mid;
                   else
                           hi = mid;
           }
           stats->histo[lo]++;
           if (lo > stats->max_bucket)
                   stats->max_bucket = lo;
           stats->err += size - stats->avg;
           stats->num++;
           stats->avg += stats->err / stats->num;
           stats->err %= stats->num;
   }
   
   /*
    * dump_gap_stats()    - print stats on gap sizes
    */
   static inline void
   dump_gap_stats(const struct gap_stats *stats, struct sbuf *s)
   {
           int i;
   
           sbuf_printf(s, "number of maximal free ranges: %jd\n",
               (intmax_t)stats->num);
           sbuf_printf(s, "largest free range: %jd\n", (intmax_t)stats->max);
           sbuf_printf(s, "average maximal free range size: %jd\n",
               (intmax_t)stats->avg);
           sbuf_printf(s, "number of maximal free ranges of different sizes:\n");
           sbuf_printf(s, "               count  |  size range\n");
           sbuf_printf(s, "               -----  |  ----------\n");
           for (i = 0; i < stats->max_bucket; i++) {
                   if (stats->histo[i] != 0) {
                           sbuf_printf(s, "%20jd  |  ",
                               (intmax_t)stats->histo[i]);
                           if (fib[i] != fib[i + 1] - 1)
                                   sbuf_printf(s, "%jd to %jd\n", (intmax_t)fib[i],
                                       (intmax_t)fib[i + 1] - 1);
                           else
                                   sbuf_printf(s, "%jd\n", (intmax_t)fib[i]);
                   }
           }
           sbuf_printf(s, "%20jd  |  ", (intmax_t)stats->histo[i]);
           if (stats->histo[i] > 1)
                   sbuf_printf(s, "%jd to %jd\n", (intmax_t)fib[i],
                       (intmax_t)stats->max);
           else
                   sbuf_printf(s, "%jd\n", (intmax_t)stats->max);
   }
   
   /*
    * blist_stats()    - dump radix tree stats
    */
   void
   blist_stats(blist_t bl, struct sbuf *s)
   {
           struct gap_stats gstats;
           struct gap_stats *stats = &gstats;
           daddr_t i, nodes, radix;
           u_daddr_t diff, mask;
           int digit;
   
           init_gap_stats(stats);
           nodes = 0;
           radix = bl->bl_radix;
           for (i = 0; i < bl->bl_blocks; ) {
                   /*
                    * Check for skippable subtrees starting at i.
                    */
                   while (radix != 1) {
                           if (bl->bl_root[nodes].bm_bitmap == 0) {
                                   if (gap_stats_counting(stats))
                                           update_gap_stats(stats, i);
                                   break;
                           }
   
                           /*
                            * Skip subtree root.
                            */
                           nodes++;
                           radix /= BLIST_RADIX;
                   }
                   if (radix == 1) {
                           /*
                            * Scan leaf.
                            */
                           mask = bl->bl_root[nodes].bm_bitmap;
                           diff = mask ^ (mask << 1);
                           if (gap_stats_counting(stats))
                                   diff ^= 1;
                           while (diff != 0) {
                                   digit = bitpos(diff);
                                   update_gap_stats(stats, i + digit);
                                   diff ^= bitrange(digit, 1);
                           }
                   }
                   nodes += radix_to_skip(radix * BLIST_RADIX);
                   i += radix * BLIST_RADIX;
   
                   /*
                    * Find max size subtree starting at i.
                    */
                   for (radix = 1; 
                       ((i / BLIST_RADIX / radix) & BLIST_MASK) == 0;
                       radix *= BLIST_RADIX)
                           ;
           }
           update_gap_stats(stats, i);
           dump_gap_stats(stats, s);
   }
   
   /************************************************************************
    *                        ALLOCATION SUPPORT FUNCTIONS                  *
    ************************************************************************
    *
    *      These support functions do all the actual work.  They may seem
    *      rather longish, but that's because I've commented them up.  The
    *      actual code is straight forward.
    *
    */
   
   /*
    * BLST_NEXT_LEAF_ALLOC() - allocate the blocks starting with the next leaf.
    *
    *      'scan' is a leaf node, and its first block is at address 'start'.  The
    *      next leaf node could be adjacent, or several nodes away if the least
    *      common ancestor of 'scan' and its neighbor is several levels up.  Use
    *      addresses to determine how many meta-nodes lie between the leaves.  If
    *      sequence of leaves starting with the next one has enough initial bits
    *      set, clear them and clear the bits in the meta nodes on the path up to
    *      the least common ancestor to mark any subtrees made completely empty.
    */
   static int
   blst_next_leaf_alloc(blmeta_t *scan, daddr_t start, int count, int maxcount)
   {
           u_daddr_t radix;
           daddr_t blk;
           int avail, digit;
   
           start += BLIST_RADIX;
           for (blk = start; blk - start < maxcount; blk += BLIST_RADIX) {
                   /* Skip meta-nodes, as long as they promise more free blocks. */
                   radix = BLIST_RADIX;
                   while (((++scan)->bm_bitmap & 1) == 1 &&
                       ((blk / radix) & BLIST_MASK) == 0)
                           radix *= BLIST_RADIX;
                   if (~scan->bm_bitmap != 0) {
                           /*
                            * Either there is no next leaf with any free blocks,
                            * or we've reached the next leaf and found that some
                            * of its blocks are not free.  In the first case,
                            * bitpos() returns zero here.
                            */
                           avail = blk - start + bitpos(~scan->bm_bitmap);
                           if (avail < count || avail == 0) {
                                   /*
                                    * There isn't a next leaf with enough free
                                    * blocks at its beginning to bother
                                    * allocating.
                                    */
                                   return (avail);
                           }
                           maxcount = imin(avail, maxcount);
                           if (maxcount % BLIST_RADIX == 0) {
                                   /*
                                    * There was no next leaf.  Back scan up to
                                    * last leaf.
                                    */
                                   do {
                                           radix /= BLIST_RADIX;
                                           --scan;
                                   } while (radix != 1);
                                   blk -= BLIST_RADIX;
                           }
                   }
           }
   
           /*
            * 'scan' is the last leaf that provides blocks.  Clear from 1 to
            * BLIST_RADIX bits to represent the allocation of those last blocks.
            */
           if (maxcount % BLIST_RADIX != 0)
                   scan->bm_bitmap &= ~bitrange(0, maxcount % BLIST_RADIX);
           else
                   scan->bm_bitmap = 0;
   
           for (;;) {
                   /* Back up over meta-nodes, clearing bits if necessary. */
                   blk -= BLIST_RADIX;
                   for (radix = BLIST_RADIX;
                       (digit = ((blk / radix) & BLIST_MASK)) == 0;
                       radix *= BLIST_RADIX) {
                           if ((scan--)->bm_bitmap == 0)
                                   scan->bm_bitmap ^= 1;
                   }
                   if ((scan--)->bm_bitmap == 0)
                           scan[-digit * radix_to_skip(radix)].bm_bitmap ^=
                               (u_daddr_t)1 << digit;
   
                   if (blk == start)
                           break;
                   /* Clear all the bits of this leaf. */
                   scan->bm_bitmap = 0;
           }
           return (maxcount);
   }
   
   /*
    * BLST_LEAF_ALLOC() -  allocate at a leaf in the radix tree (a bitmap).
    *
    *      This function is the core of the allocator.  Its execution time is
    *      proportional to log(count), plus height of the tree if the allocation
    *      crosses a leaf boundary.
    */
   static daddr_t
   blst_leaf_alloc(blmeta_t *scan, daddr_t blk, int *count, int maxcount)
   {
           u_daddr_t mask;
           int bighint, count1, hi, lo, num_shifts;
   
           count1 = *count - 1;
           num_shifts = fls(count1);
           mask = ~scan->bm_bitmap;
           while ((mask & (mask + 1)) != 0 && num_shifts > 0) {
                   /*
                    * If bit i is 0 in mask, then bits in [i, i + (count1 >>
                    * num_shifts)] are 1 in scan->bm_bitmap.  Reduce num_shifts to
                    * 0, while preserving this invariant.  The updates to mask
                    * leave fewer bits 0, but each bit that remains 0 represents a
                    * longer string of consecutive 1-bits in scan->bm_bitmap.  If
                    * more updates to mask cannot set more bits, because mask is
                    * partitioned with all 1 bits following all 0 bits, the loop
                    * terminates immediately.
                    */
                   num_shifts--;
                   mask |= mask >> ((count1 >> num_shifts) + 1) / 2;
           }
           bighint = count1 >> num_shifts;
           if (~mask == 0) {
                   /*
                    * Update bighint.  There is no allocation bigger than
                    * count1 >> num_shifts starting in this leaf.
                    */
                   scan->bm_bighint = bighint;
                   return (SWAPBLK_NONE);
           }
   
           /* Discard any candidates that appear before blk. */
           if ((blk & BLIST_MASK) != 0) {
                   if ((~mask & bitrange(0, blk & BLIST_MASK)) != 0) {
                           /* Grow bighint in case all discarded bits are set. */
                           bighint += blk & BLIST_MASK;
                           mask |= bitrange(0, blk & BLIST_MASK);
                           if (~mask == 0) {
                                   scan->bm_bighint = bighint;
                                   return (SWAPBLK_NONE);
                           }
                   }
                   blk -= blk & BLIST_MASK;
           }
   
           /*
            * The least significant set bit in mask marks the start of the first
            * available range of sufficient size.  Find its position.
            */
           lo = bitpos(~mask);
   
           /*
            * Find how much space is available starting at that position.
            */
           if ((mask & (mask + 1)) != 0) {
                   /* Count the 1 bits starting at position lo. */
                   hi = bitpos(mask & (mask + 1)) + count1;
                   if (maxcount < hi - lo)
                           hi = lo + maxcount;
                   *count = hi - lo;
                   mask = ~bitrange(lo, *count);
           } else if (maxcount <= BLIST_RADIX - lo) {
                   /* All the blocks we can use are available here. */
                   hi = lo + maxcount;
                   *count = maxcount;
                   mask = ~bitrange(lo, *count);
                   if (hi == BLIST_RADIX)
                           scan->bm_bighint = bighint;
           } else {
                   /* Check next leaf for some of the blocks we want or need. */
                   count1 = *count - (BLIST_RADIX - lo);
                   maxcount -= BLIST_RADIX - lo;
                   hi = blst_next_leaf_alloc(scan, blk, count1, maxcount);
                   if (hi < count1)
                           /*
                            * The next leaf cannot supply enough blocks to reach
                            * the minimum required allocation.  The hint cannot be
                            * updated, because the same allocation request could
                            * be satisfied later, by this leaf, if the state of
                            * the next leaf changes, and without any changes to
                            * this leaf.
                            */
                           return (SWAPBLK_NONE);
                   *count = BLIST_RADIX - lo + hi;
                   scan->bm_bighint = bighint;
           }
   
           /* Clear the allocated bits from this leaf. */
           scan->bm_bitmap &= mask;
           return (blk + lo);
   }
   
   /*
    * blist_meta_alloc() - allocate at a meta in the radix tree.
    *
    *      Attempt to allocate at a meta node.  If we can't, we update
    *      bighint and return a failure.  Updating bighint optimize future
    *      calls that hit this node.  We have to check for our collapse cases
    *      and we have a few optimizations strewn in as well.
    */
   static daddr_t
   blst_meta_alloc(blmeta_t *scan, daddr_t cursor, int *count,
       int maxcount, u_daddr_t radix)
   {
           daddr_t blk, i, r, skip;
           u_daddr_t mask;
           bool scan_from_start;
           int digit;
   
           if (radix == 1)
                   return (blst_leaf_alloc(scan, cursor, count, maxcount));
           blk = cursor & -(radix * BLIST_RADIX);
           scan_from_start = (cursor == blk);
           skip = radix_to_skip(radix);
           mask = scan->bm_bitmap;
   
           /* Discard any candidates that appear before cursor. */
           digit = (cursor / radix) & BLIST_MASK;
           mask &= (u_daddr_t)-1 << digit;
           if (mask == 0)
                   return (SWAPBLK_NONE);
   
           /*
            * If the first try is for a block that includes the cursor, pre-undo
            * the digit * radix offset in the first call; otherwise, ignore the
            * cursor entirely.
            */
           if (((mask >> digit) & 1) == 1)
                   cursor -= digit * radix;
           else
                   cursor = blk;
   
           /*
            * Examine the nonempty subtree associated with each bit set in mask.
            */
           do {
                   digit = bitpos(mask);
                   i = 1 + digit * skip;
                   if (*count <= scan[i].bm_bighint) {
                           /*
                            * The allocation might fit beginning in the i'th subtree.
                            */
                           r = blst_meta_alloc(&scan[i], cursor + digit * radix,
                               count, maxcount, radix / BLIST_RADIX);
                           if (r != SWAPBLK_NONE) {
                                   if (scan[i].bm_bitmap == 0)
                                           scan->bm_bitmap ^= bitrange(digit, 1);
                                   return (r);
                           }
                   }
                   cursor = blk;
           } while ((mask ^= bitrange(digit, 1)) != 0);
   
           /*
            * We couldn't allocate count in this subtree.  If the whole tree was
            * scanned, and the last tree node is allocated, update bighint.
            */
           if (scan_from_start && !(digit == BLIST_RADIX - 1 &&
               scan[i].bm_bighint == BLIST_MAX_ALLOC))
                   scan->bm_bighint = *count - 1;
   
           return (SWAPBLK_NONE);
   }
   
   /*
    * BLST_LEAF_FREE() -   free allocated block from leaf bitmap
    *
    */
   static void
   blst_leaf_free(blmeta_t *scan, daddr_t blk, int count)
   {
           u_daddr_t mask;
   
           /*
            * free some data in this bitmap
            * mask=0000111111111110000
            *          \_________/\__/
            *              count   n
            */
           mask = bitrange(blk & BLIST_MASK, count);
           KASSERT((scan->bm_bitmap & mask) == 0,
               ("freeing free block: %jx, size %d, mask %jx",
               (uintmax_t)blk, count, (uintmax_t)scan->bm_bitmap & mask));
           scan->bm_bitmap |= mask;
   }
   
   /*
    * BLST_META_FREE() - free allocated blocks from radix tree meta info
    *
    *      This support routine frees a range of blocks from the bitmap.
    *      The range must be entirely enclosed by this radix node.  If a
    *      meta node, we break the range down recursively to free blocks
    *      in subnodes (which means that this code can free an arbitrary
    *      range whereas the allocation code cannot allocate an arbitrary
    *      range).
    */
   static void
   blst_meta_free(blmeta_t *scan, daddr_t freeBlk, daddr_t count, u_daddr_t radix)
   {
           daddr_t blk, endBlk, i, skip;
           int digit, endDigit;
   
           /*
            * We could probably do a better job here.  We are required to make
            * bighint at least as large as the biggest allocable block of data.
            * If we just shoehorn it, a little extra overhead will be incurred
            * on the next allocation (but only that one typically).
            */
           scan->bm_bighint = BLIST_MAX_ALLOC;
   
           if (radix == 1)
                   return (blst_leaf_free(scan, freeBlk, count));
   
           endBlk = freeBlk + count;
           blk = (freeBlk + radix * BLIST_RADIX) & -(radix * BLIST_RADIX);
           /*
            * blk is first block past the end of the range of this meta node,
            * or 0 in case of overflow.
            */
           if (blk != 0)
                   endBlk = ummin(endBlk, blk);
           skip = radix_to_skip(radix);
           blk = freeBlk & -radix;
           digit = (blk / radix) & BLIST_MASK;
           endDigit = 1 + (((endBlk - 1) / radix) & BLIST_MASK);
           scan->bm_bitmap |= bitrange(digit, endDigit - digit);
           for (i = 1 + digit * skip; blk < endBlk; i += skip) {
                   blk += radix;
                   count = ummin(blk, endBlk) - freeBlk;
                   blst_meta_free(&scan[i], freeBlk, count, radix / BLIST_RADIX);
                   freeBlk = blk;
           }
   }
   
   /*
    * BLST_COPY() - copy one radix tree to another
    *
    *      Locates free space in the source tree and frees it in the destination
    *      tree.  The space may not already be free in the destination.
    */
   static void
   blst_copy(blmeta_t *scan, daddr_t blk, daddr_t radix, blist_t dest,
       daddr_t count)
   {
           daddr_t endBlk, i, skip;
   
           /*
            * Leaf node
            */
   
           if (radix == 1) {
                   u_daddr_t v = scan->bm_bitmap;
   
                   if (v == (u_daddr_t)-1) {
                           blist_free(dest, blk, count);
                   } else if (v != 0) {
                           int i;
   
                           for (i = 0; i < count; ++i) {
                                   if (v & ((u_daddr_t)1 << i))
                                           blist_free(dest, blk + i, 1);
                           }
                   }
                   return;
           }
   
           /*
            * Meta node
            */
   
           if (scan->bm_bitmap == 0) {
                   /*
                    * Source all allocated, leave dest allocated
                    */
                   return;
           }
   
           endBlk = blk + count;
           skip = radix_to_skip(radix);
           for (i = 1; blk < endBlk; i += skip) {
                   blk += radix;
                   count = radix;
                   if (blk >= endBlk)
                           count -= blk - endBlk;
                   blst_copy(&scan[i], blk - radix,
                       radix / BLIST_RADIX, dest, count);
           }
   }
   
   /*
    * BLST_LEAF_FILL() -   allocate specific blocks in leaf bitmap
    *
    *      This routine allocates all blocks in the specified range
    *      regardless of any existing allocations in that range.  Returns
    *      the number of blocks allocated by the call.
    */
   static daddr_t
   blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count)
   {
          daddr_t nblks;
          u_daddr_t mask;
  
          mask = bitrange(blk & BLIST_MASK, count);
  
          /* Count the number of blocks that we are allocating. */
          nblks = bitcount64(scan->bm_bitmap & mask);
  
          scan->bm_bitmap &= ~mask;
          return (nblks);
  }
  
  /*
   * BLIST_META_FILL() -  allocate specific blocks at a meta node
   *
   *      This routine allocates the specified range of blocks,
   *      regardless of any existing allocations in the range.  The
   *      range must be within the extent of this node.  Returns the
   *      number of blocks allocated by the call.
   */
  static daddr_t
  blst_meta_fill(blmeta_t *scan, daddr_t allocBlk, daddr_t count, u_daddr_t radix)
  {
          daddr_t blk, endBlk, i, nblks, skip;
          int digit;
  
          if (radix == 1)
                  return (blst_leaf_fill(scan, allocBlk, count));
  
          endBlk = allocBlk + count;
          blk = (allocBlk + radix * BLIST_RADIX) & -(radix * BLIST_RADIX);
          /*
           * blk is first block past the end of the range of this meta node,
           * or 0 in case of overflow.
           */
          if (blk != 0)
                  endBlk = ummin(endBlk, blk);
          skip = radix_to_skip(radix);
          blk = allocBlk & -radix;
          nblks = 0;
          while (blk < endBlk) {
                  digit = (blk / radix) & BLIST_MASK;
                  i = 1 + digit * skip;
                  blk += radix;
                  count = ummin(blk, endBlk) - allocBlk;
                  nblks += blst_meta_fill(&scan[i], allocBlk, count,
                      radix / BLIST_RADIX);
                  if (scan[i].bm_bitmap == 0)
                          scan->bm_bitmap &= ~((u_daddr_t)1 << digit);
                  allocBlk = blk;
          }
          return (nblks);
  }
  
  #ifdef BLIST_DEBUG
  
  static void
  blst_radix_print(blmeta_t *scan, daddr_t blk, daddr_t radix, int tab)
  {
          daddr_t skip;
          u_daddr_t mask;
          int digit;
  
          if (radix == 1) {
                  printf(
                      "%*.*s(%08llx,%lld): bitmap %0*llx big=%lld\n",
                      tab, tab, "",
                      (long long)blk, (long long)BLIST_RADIX,
                      (int)(1 + (BLIST_RADIX - 1) / 4),
                      (long long)scan->bm_bitmap,
                      (long long)scan->bm_bighint
                  );
                  return;
          }
  
          printf(
              "%*.*s(%08llx): subtree (%lld/%lld) bitmap %0*llx big=%lld {\n",
              tab, tab, "",
              (long long)blk, (long long)radix * BLIST_RADIX,
              (long long)radix * BLIST_RADIX,
              (int)(1 + (BLIST_RADIX - 1) / 4),
              (long long)scan->bm_bitmap,
              (long long)scan->bm_bighint
          );
  
          skip = radix_to_skip(radix);
          tab += 4;
  
          mask = scan->bm_bitmap;
          /* Examine the nonempty subtree associated with each bit set in mask */
          do {
                  digit = bitpos(mask);
                  blst_radix_print(&scan[1 + digit * skip], blk + digit * radix,
                      radix / BLIST_RADIX, tab);
          } while ((mask ^= bitrange(digit, 1)) != 0);
          tab -= 4;
  
          printf(
              "%*.*s}\n",
              tab, tab, ""
          );
  }
  
  #endif
  
  #ifdef BLIST_DEBUG
  
  int
  main(int ac, char **av)
  {
          daddr_t size = BLIST_RADIX * BLIST_RADIX;
          int i;
          blist_t bl;
          struct sbuf *s;
  
          for (i = 1; i < ac; ++i) {
                  const char *ptr = av[i];
                  if (*ptr != '-') {
                          size = strtoll(ptr, NULL, 0);
                          continue;
                  }
                  ptr += 2;
                  fprintf(stderr, "Bad option: %s\n", ptr - 2);
                  exit(1);
          }
          bl = blist_create(size, M_WAITOK);
          if (bl == NULL) {
                  fprintf(stderr, "blist_create failed\n");
                  exit(1);
          }
          blist_free(bl, 0, size);
  
          for (;;) {
                  char buf[1024];
                  long long da = 0;
                  int count = 0, maxcount = 0;
  
                  printf("%lld/%lld/%lld> ", (long long)blist_avail(bl),
                      (long long)size, (long long)bl->bl_radix * BLIST_RADIX);
                  fflush(stdout);
                  if (fgets(buf, sizeof(buf), stdin) == NULL)
                          break;
                  switch(buf[0]) {
                  case 'r':
                          if (sscanf(buf + 1, "%d", &count) == 1) {
                                  blist_resize(&bl, count, 1, M_WAITOK);
                          } else {
                                  printf("?\n");
                          }
                  case 'p':
                          blist_print(bl);
                          break;
                  case 's':
                          s = sbuf_new_auto();
                          blist_stats(bl, s);
                          sbuf_finish(s);
                          printf("%s", sbuf_data(s));
                          sbuf_delete(s);
                          break;
                  case 'a':
                          if (sscanf(buf + 1, "%d%d", &count, &maxcount) == 2) {
                                  daddr_t blk = blist_alloc(bl, &count, maxcount);
                                  printf("    R=%08llx, c=%08d\n",
                                      (long long)blk, count);
                          } else {
                                  printf("?\n");
                          }
                          break;
                  case 'f':
                          if (sscanf(buf + 1, "%llx %d", &da, &count) == 2) {
                                  blist_free(bl, da, count);
                          } else {
                                  printf("?\n");
                          }
                          break;
                  case 'l':
                          if (sscanf(buf + 1, "%llx %d", &da, &count) == 2) {
                                  printf("    n=%jd\n",
                                      (intmax_t)blist_fill(bl, da, count));
                          } else {
                                  printf("?\n");
                          }
                          break;
                  case '?':
                  case 'h':
                          puts(
                              "p          -print\n"
                              "s          -stats\n"
                              "a %d %d    -allocate\n"
                              "f %x %d    -free\n"
                              "l %x %d    -fill\n"
                              "r %d       -resize\n"
                              "h/?        -help\n"
                              "q          -quit"
                          );
                          break;
                  case 'q':
                          break;
                  default:
                          printf("?\n");
                          break;
                  }
                  if (buf[0] == 'q')
                          break;
          }
          return (0);
  }
  
  #endif

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