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.  Two radix
     *      constants are involved: one for the size of the bitmaps contained in the
     *      leaf nodes (BLIST_BMAP_RADIX), and one for the number of descendents of
     *      each of the meta (interior) nodes (BLIST_META_RADIX).  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_META_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_META_RADIX lower level nodes of a some nodes may not be
     *      allocated.
     *
     *      NOTE: the allocator cannot currently allocate more than
     *      BLIST_BMAP_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 <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))
   
   #include <sys/blist.h>
   
   void panic(const char *ctl, ...);
   
   #endif
   
   /*
    * static support functions
    */
   static daddr_t  blst_leaf_alloc(blmeta_t *scan, daddr_t blk, int count);
   static daddr_t  blst_meta_alloc(blmeta_t *scan, daddr_t cursor, daddr_t count,
                       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
   
   _Static_assert(BLIST_BMAP_RADIX % BLIST_META_RADIX == 0,
       "radix divisibility error");
   #define BLIST_BMAP_MASK (BLIST_BMAP_RADIX - 1)
   #define BLIST_META_MASK (BLIST_META_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_BMAP_RADIX.  If 'm'
    * is short for BLIST_META_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 / BLIST_BMAP_RADIX)) / (m - 1)
    * and since m divides BLIST_BMAP_RADIX, we can simplify further to
    * skip = (radix / (BLIST_BMAP_RADIX / m)) / (m - 1)
    * skip = radix / ((BLIST_BMAP_RADIX / m) * (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_BMAP_RADIX / BLIST_META_RADIX) * BLIST_META_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_BMAP_RADIX - (n + count))));
   }
   
   
   /*
    * Use binary search, or a faster method, to find the 1 bit in a u_daddr_t.
    * Assumes that the argument has only one bit set.
    */
   static inline int
   bitpos(u_daddr_t mask)
   {
           int hi, lo, mid;
   
           switch (sizeof(mask)) {
   #ifdef HAVE_INLINE_FFSLL
           case sizeof(long long):
                   return (ffsll(mask) - 1);
   #endif
           default:
                   lo = 0;
                   hi = BLIST_BMAP_RADIX;
                   while (lo + 1 < hi) {
                           mid = (lo + hi) >> 1;
                           if ((mask >> mid) != 0)
                                   lo = mid;
                           else
                                   hi = mid;
                   }
                   return (lo);
           }
   }
   
   /*
    * 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_BMAP_RADIX blocks.
    */
   blist_t
   blist_create(daddr_t blocks, int flags)
   {
           blist_t bl;
           u_daddr_t nodes, radix;
   
           if (blocks == 0)
                   panic("invalid block count");
   
           /*
            * Calculate the radix and node count used for scanning.
            */
           nodes = 1;
           radix = BLIST_BMAP_RADIX;
           while (radix <= blocks) {
                   nodes += 1 + (blocks - 1) / radix;
                   radix *= BLIST_META_RADIX;
           }
   
           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, daddr_t count)
   {
           daddr_t blk;
   
           if (count > BLIST_MAX_ALLOC)
                   panic("allocation too large");
   
           /*
            * 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 (;;) {
                   blk = blst_meta_alloc(bl->bl_root, bl->bl_cursor, count,
                       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);
                   } else if (bl->bl_cursor == 0)
                           return (SWAPBLK_NONE);
                   bl->bl_cursor = 0;
           }
   }
   
   /*
    * 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.  Panic if an inconsistancy is
    *                      found.
    */
   void
   blist_free(blist_t bl, daddr_t blkno, daddr_t count)
   {
   
           if (blkno < 0 || blkno + count > bl->bl_blocks)
                   panic("freeing invalid range");
           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;
   
           if (blkno < 0 || blkno + count > bl->bl_blocks)
                   panic("filling invalid range");
           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 bit, diff, mask;
   
           init_gap_stats(stats);
           nodes = 0;
           i = bl->bl_radix;
           while (i < bl->bl_radix + bl->bl_blocks) {
                   /*
                    * Find max size subtree starting at i.
                    */
                   radix = BLIST_BMAP_RADIX;
                   while (((i / radix) & BLIST_META_MASK) == 0)
                           radix *= BLIST_META_RADIX;
   
                   /*
                    * Check for skippable subtrees starting at i.
                    */
                   while (radix > BLIST_BMAP_RADIX) {
                           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_META_RADIX;
                   }
                   if (radix == BLIST_BMAP_RADIX) {
                           /*
                            * Scan leaf.
                            */
                           mask = bl->bl_root[nodes].bm_bitmap;
                           diff = mask ^ (mask << 1);
                           if (gap_stats_counting(stats))
                                   diff ^= 1;
                           while (diff != 0) {
                                   bit = diff & -diff;
                                   update_gap_stats(stats, i + bitpos(bit));
                                   diff ^= bit;
                           }
                   }
                   nodes += radix_to_skip(radix);
                   i += 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 first few blocks in the next leaf.
    *
    *      'scan' is a leaf node, associated with a block containing 'blk'.
    *      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 'blk' to determine how many meta-nodes lie between the
    *      leaves.  If the next leaf 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 blk, int count)
   {
           blmeta_t *next;
           daddr_t skip;
           u_daddr_t radix;
           int digit;
   
           next = scan + 1;
           blk += BLIST_BMAP_RADIX;
           radix = BLIST_BMAP_RADIX;
           while ((digit = ((blk / radix) & BLIST_META_MASK)) == 0 &&
               (next->bm_bitmap & 1) == 1) {
                   next++;
                   radix *= BLIST_META_RADIX;
           }
           if (((next->bm_bitmap + 1) & ~((u_daddr_t)-1 << count)) != 0) {
                   /*
                    * The next leaf doesn't have enough free blocks at the
                    * beginning to complete the spanning allocation.
                    */
                   return (ENOMEM);
           }
           /* Clear the first 'count' bits in the next leaf to allocate. */
           next->bm_bitmap &= (u_daddr_t)-1 << count;
   
           /*
            * Update bitmaps of next-ancestors, up to least common ancestor.
            */
           skip = radix_to_skip(radix);
           while (radix != BLIST_BMAP_RADIX && next->bm_bitmap == 0) {
                   (--next)->bm_bitmap ^= 1;
                   radix /= BLIST_META_RADIX;
           }
           if (next->bm_bitmap == 0)
                   scan[-digit * skip].bm_bitmap ^= (u_daddr_t)1 << digit;
           return (0);
   }
   
   /*
    * 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)
   {
           u_daddr_t cursor_mask, mask;
           int count1, hi, lo, num_shifts, range1, range_ext;
   
           range1 = 0;
           count1 = count - 1;
           num_shifts = fls(count1);
           mask = scan->bm_bitmap;
           while ((-mask & ~mask) != 0 && num_shifts > 0) {
                   /*
                    * If bit i is set in mask, then bits in [i, i+range1] are set
                    * in scan->bm_bitmap.  The value of range1 is equal to count1
                    * >> num_shifts.  Grow range1 and reduce num_shifts to 0,
                    * while preserving these invariants.  The updates to mask
                    * leave fewer bits set, but each bit that remains set
                    * represents a longer string of consecutive bits set in
                    * scan->bm_bitmap.  If more updates to mask cannot clear more
                    * bits, because mask is partitioned with all 0 bits preceding
                    * all 1 bits, the loop terminates immediately.
                    */
                   num_shifts--;
                   range_ext = range1 + ((count1 >> num_shifts) & 1);
                   /*
                    * mask is a signed quantity for the shift because when it is
                    * shifted right, the sign bit should copied; when the last
                    * block of the leaf is free, pretend, for a while, that all the
                    * blocks that follow it are also free.
                    */
                   mask &= (daddr_t)mask >> range_ext;
                   range1 += range_ext;
           }
           if (mask == 0) {
                   /*
                    * Update bighint.  There is no allocation bigger than range1
                    * starting in this leaf.
                    */
                   scan->bm_bighint = range1;
                   return (SWAPBLK_NONE);
           }
   
           /* Discard any candidates that appear before blk. */
           if ((blk & BLIST_BMAP_MASK) != 0) {
                   cursor_mask = mask & bitrange(0, blk & BLIST_BMAP_MASK);
                   if (cursor_mask != 0) {
                           mask ^= cursor_mask;
                           if (mask == 0)
                                   return (SWAPBLK_NONE);
   
                           /*
                            * Bighint change for last block allocation cannot
                            * assume that any other blocks are allocated, so the
                            * bighint cannot be reduced much.
                            */
                           range1 = BLIST_MAX_ALLOC - 1;
                   }
                   blk &= ~BLIST_BMAP_MASK;
           }
   
           /*
            * The least significant set bit in mask marks the start of the first
            * available range of sufficient size.  Clear all the bits but that one,
            * and then find its position.
            */
           mask &= -mask;
           lo = bitpos(mask);
   
           hi = lo + count;
           if (hi > BLIST_BMAP_RADIX) {
                   /*
                    * An allocation within this leaf is impossible, so a successful
                    * allocation depends on the next leaf providing some of the blocks.
                    */
                   if (blst_next_leaf_alloc(scan, blk, hi - BLIST_BMAP_RADIX) != 0)
                           /*
                            * 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);
                   hi = BLIST_BMAP_RADIX;
           }
   
           /* Set the bits of mask at position 'lo' and higher. */
           mask = -mask;
           if (hi == BLIST_BMAP_RADIX) {
                   /*
                    * Update bighint.  There is no allocation bigger than range1
                    * available in this leaf after this allocation completes.
                    */
                   scan->bm_bighint = range1;
           } else {
                   /* Clear the bits of mask at position 'hi' and higher. */
                   mask &= (u_daddr_t)-1 >> (BLIST_BMAP_RADIX - hi);
           }
           /* 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, daddr_t count, u_daddr_t radix)
   {
           daddr_t blk, i, r, skip;
           u_daddr_t bit, mask;
           bool scan_from_start;
           int digit;
   
           if (radix == BLIST_BMAP_RADIX)
                   return (blst_leaf_alloc(scan, cursor, count));
           blk = cursor & -radix;
           scan_from_start = (cursor == blk);
           radix /= BLIST_META_RADIX;
           skip = radix_to_skip(radix);
           mask = scan->bm_bitmap;
   
           /* Discard any candidates that appear before cursor. */
           digit = (cursor / radix) & BLIST_META_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 {
                   bit = mask & -mask;
                   digit = bitpos(bit);
                   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, radix);
                           if (r != SWAPBLK_NONE) {
                                   if (scan[i].bm_bitmap == 0)
                                           scan->bm_bitmap ^= bit;
                                   return (r);
                           }
                   }
                   cursor = blk;
           } while ((mask ^= bit) != 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_META_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_BMAP_MASK, count);
           if (scan->bm_bitmap & mask)
                   panic("freeing free block");
           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 == BLIST_BMAP_RADIX)
                   return (blst_leaf_free(scan, freeBlk, count));
   
           endBlk = ummin(freeBlk + count, (freeBlk + radix) & -radix);
           radix /= BLIST_META_RADIX;
           skip = radix_to_skip(radix);
           blk = freeBlk & -radix;
           digit = (blk / radix) & BLIST_META_MASK;
           endDigit = 1 + (((endBlk - 1) / radix) & BLIST_META_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);
                   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 == BLIST_BMAP_RADIX) {
                   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;
           radix /= BLIST_META_RADIX;
           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, 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_BMAP_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 == BLIST_BMAP_RADIX)
                   return (blst_leaf_fill(scan, allocBlk, count));
   
           endBlk = ummin(allocBlk + count, (allocBlk + radix) & -radix);
           radix /= BLIST_META_RADIX;
           skip = radix_to_skip(radix);
           blk = allocBlk & -radix;
           nblks = 0;
           while (blk < endBlk) {
                   digit = (blk / radix) & BLIST_META_MASK;
                   i = 1 + digit * skip;
                   blk += radix;
                   count = ummin(blk, endBlk) - allocBlk;
                   nblks += blst_meta_fill(&scan[i], allocBlk, count, 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 bit, mask;
          int digit;
  
          if (radix == BLIST_BMAP_RADIX) {
                  printf(
                      "%*.*s(%08llx,%lld): bitmap %0*llx big=%lld\n",
                      tab, tab, "",
                      (long long)blk, (long long)radix,
                      1 + (BLIST_BMAP_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,
              (long long)radix,
              1 + (BLIST_META_RADIX - 1) / 4,
              (long long)scan->bm_bitmap,
              (long long)scan->bm_bighint
          );
  
          radix /= BLIST_META_RADIX;
          skip = radix_to_skip(radix);
          tab += 4;
  
          mask = scan->bm_bitmap;
          /* Examine the nonempty subtree associated with each bit set in mask */
          do {
                  bit = mask & -mask;
                  digit = bitpos(bit);
                  blst_radix_print(&scan[1 + digit * skip], blk + digit * radix,
                      radix, tab);
          } while ((mask ^= bit) != 0);
          tab -= 4;
  
          printf(
              "%*.*s}\n",
              tab, tab, ""
          );
  }
  
  #endif
  
  #ifdef BLIST_DEBUG
  
  int
  main(int ac, char **av)
  {
          int size = BLIST_META_RADIX * BLIST_BMAP_RADIX;
          int i;
          blist_t bl;
          struct sbuf *s;
  
          for (i = 1; i < ac; ++i) {
                  const char *ptr = av[i];
                  if (*ptr != '-') {
                          size = strtol(ptr, NULL, 0);
                          continue;
                  }
                  ptr += 2;
                  fprintf(stderr, "Bad option: %s\n", ptr - 2);
                  exit(1);
          }
          bl = blist_create(size, M_WAITOK);
          blist_free(bl, 0, size);
  
          for (;;) {
                  char buf[1024];
                  long long da = 0;
                  long long count = 0;
  
                  printf("%lld/%lld/%lld> ", (long long)blist_avail(bl),
                      (long long)size, (long long)bl->bl_radix);
                  fflush(stdout);
                  if (fgets(buf, sizeof(buf), stdin) == NULL)
                          break;
                  switch(buf[0]) {
                  case 'r':
                          if (sscanf(buf + 1, "%lld", &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, "%lld", &count) == 1) {
                                  daddr_t blk = blist_alloc(bl, count);
                                  printf("    R=%08llx\n", (long long)blk);
                          } else {
                                  printf("?\n");
                          }
                          break;
                  case 'f':
                          if (sscanf(buf + 1, "%llx %lld", &da, &count) == 2) {
                                  blist_free(bl, da, count);
                          } else {
                                  printf("?\n");
                          }
                          break;
                  case 'l':
                          if (sscanf(buf + 1, "%llx %lld", &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       -allocate\n"
                              "f %x %d    -free\n"
                              "l %x %d    -fill\n"
                              "r %d       -resize\n"
                              "h/?        -help"
                          );
                          break;
                  default:
                          printf("?\n");
                          break;
                  }
          }
          return(0);
  }
  
  void
  panic(const char *ctl, ...)
  {
          va_list va;
  
          va_start(va, ctl);
          vfprintf(stderr, ctl, va);
          fprintf(stderr, "\n");
          va_end(va);
          exit(1);
  }
  
  #endif

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