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

     /*
      * BLIST.C -    Bitmap allocator/deallocator, using a radix tree with hinting
      * 
      * Copyright (c) 1998,2004 The DragonFly Project.  All rights reserved.
      * 
      * This code is derived from software contributed to The DragonFly Project
      * by Matthew Dillon <dillon@backplane.com>
      * 
      * 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 DragonFly Project 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 COPYRIGHT HOLDERS AND CONTRIBUTORS
     * ``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
     * COPYRIGHT HOLDERS OR CONTRIBUTORS 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.
     * 
     *
     *      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 then to return 
     *      SWAPBLK_NONE on an allocation failure.
     *
     *      A radix tree is used to maintain the bitmap.  Two radix constants are
     *      involved:  One for the bitmaps contained in the leaf nodes (typically
     *      32), and one for the meta nodes (typically 16).  Both meta and leaf
     *      nodes have a hint field.  This field gives us a hint as to the largest
     *      free contiguous range of blocks under the node.  It may contain a
     *      value that is too high, but will never contain a value that is too 
     *      low.  When the radix tree is searched, allocation failures in subtrees
     *      update the hint. 
     *
     *      The radix tree also implements two collapsed states for meta nodes:
     *      the ALL-ALLOCATED state and the ALL-FREE state.  If a meta node is
     *      in either of these two states, all information contained underneath
     *      the node is considered stale.  These states are used to optimize
     *      allocation and freeing operations.
     *
     *      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.
     *
     *      Unlike the rlist code, the blist code wires all necessary memory at
     *      creation time.  Neither allocations nor frees require interaction with
     *      the memory subsystem.  In contrast, the rlist code may allocate memory 
     *      on an rlist_free() call.  The non-blocking features of the blist code
     *      are used to great advantage in the swap code (vm/nswap_pager.c).  The
     *      rlist code uses a little less overall memory then the blist code (but
     *      due to swap interleaving not all that much less), but the blist code 
     *      scales much, much better.
     *
     *      LAYOUT: The radix tree is layed out recursively using a
     *      linear array.  Each meta node is immediately followed (layed 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.  In order to support large radixes, 
     *      portions of the tree may reside outside our memory allocation.  We 
     *      handle this with an early-termination optimization (when bighint is 
     *      set to -1) on the scan.  The memory allocation is only large enough 
     *      to cover the number of blocks requested at creation time even if it
     *      must be encompassed in larger root-node radix.
     *
     *      NOTE: The allocator cannot currently allocate more then
     *      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 effected by
     *      this algorithmic unfeature.  The freeing code can handle arbitrary
     *      ranges.
     *
     *      NOTE: The radix may exceed 32 bits in order to support up to 2^31
     *            blocks.  The first divison will drop the radix down and fit
     *            it within a signed 32 bit integer.
     *
     *      This code can be compiled stand-alone for debugging.
     */
    
    #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>
   
   #else
   
   #ifndef BLIST_NO_DEBUG
   #define BLIST_DEBUG
   #endif
   
   #define SWAPBLK_NONE ((swblk_t)-1)
   
   #include <sys/types.h>
   #include <stdio.h>
   #include <string.h>
   #include <stdlib.h>
   #include <stdarg.h>
   
   #define kmalloc(a,b,c)  malloc(a)
   #define kfree(a,b)      free(a)
   #define kprintf         printf
   #define KKASSERT(exp)
   
   #include <sys/blist.h>
   
   void panic(const char *ctl, ...);
   
   #endif
   
   /*
    * static support functions
    */
   
   static swblk_t blst_leaf_alloc(blmeta_t *scan, swblk_t blkat,
                                   swblk_t blk, int count);
   static swblk_t blst_meta_alloc(blmeta_t *scan, swblk_t blkat,
                                   swblk_t blk, swblk_t count,
                                   int64_t radix, int skip);
   static void blst_leaf_free(blmeta_t *scan, swblk_t relblk, int count);
   static void blst_meta_free(blmeta_t *scan, swblk_t freeBlk, swblk_t count, 
                                           int64_t radix, int skip, swblk_t blk);
   static swblk_t blst_leaf_fill(blmeta_t *scan, swblk_t blk, int count);
   static swblk_t blst_meta_fill(blmeta_t *scan, swblk_t fillBlk, swblk_t count,
                                           int64_t radix, int skip, swblk_t blk);
   static void blst_copy(blmeta_t *scan, swblk_t blk, int64_t radix,
                                   swblk_t skip, blist_t dest, swblk_t count);
   static swblk_t  blst_radix_init(blmeta_t *scan, int64_t radix,
                                                   int skip, swblk_t count);
   #ifndef _KERNEL
   static void     blst_radix_print(blmeta_t *scan, swblk_t blk, 
                                           int64_t radix, int skip, int tab);
   #endif
   
   #ifdef _KERNEL
   static MALLOC_DEFINE(M_SWAP, "SWAP", "Swap space");
   #endif
   
   /*
    * blist_create() - create a blist capable of handling up to the specified
    *                  number of blocks
    *
    *      blocks must be greater then 0
    *
    *      The smallest blist consists of a single leaf node capable of 
    *      managing BLIST_BMAP_RADIX blocks.
    */
   
   blist_t 
   blist_create(swblk_t blocks)
   {
           blist_t bl;
           int64_t radix;
           int skip = 0;
   
           /*
            * Calculate radix and skip field used for scanning.
            *
            * Radix can exceed 32 bits even if swblk_t is limited to 32 bits.
            */
           radix = BLIST_BMAP_RADIX;
   
           while (radix < blocks) {
                   radix *= BLIST_META_RADIX;
                   skip = (skip + 1) * BLIST_META_RADIX;
                   KKASSERT(skip > 0);
           }
   
           bl = kmalloc(sizeof(struct blist), M_SWAP, M_WAITOK | M_ZERO);
   
           bl->bl_blocks = blocks;
           bl->bl_radix = radix;
           bl->bl_skip = skip;
           bl->bl_rootblks = 1 +
               blst_radix_init(NULL, bl->bl_radix, bl->bl_skip, blocks);
           bl->bl_root = kmalloc(sizeof(blmeta_t) * bl->bl_rootblks, M_SWAP, M_WAITOK);
   
   #if defined(BLIST_DEBUG)
           kprintf(
                   "BLIST representing %d blocks (%d MB of swap)"
                   ", requiring %dK of ram\n",
                   bl->bl_blocks,
                   bl->bl_blocks * 4 / 1024,
                   (bl->bl_rootblks * sizeof(blmeta_t) + 1023) / 1024
           );
           kprintf("BLIST raw radix tree contains %d records\n", bl->bl_rootblks);
   #endif
           blst_radix_init(bl->bl_root, bl->bl_radix, bl->bl_skip, blocks);
   
           return(bl);
   }
   
   void 
   blist_destroy(blist_t bl)
   {
           kfree(bl->bl_root, M_SWAP);
           kfree(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.
    */
   
   swblk_t 
   blist_alloc(blist_t bl, swblk_t count)
   {
           swblk_t blk = SWAPBLK_NONE;
   
           if (bl) {
                   if (bl->bl_radix == BLIST_BMAP_RADIX)
                           blk = blst_leaf_alloc(bl->bl_root, 0, 0, count);
                   else
                           blk = blst_meta_alloc(bl->bl_root, 0, 0, count,
                                                 bl->bl_radix, bl->bl_skip);
                   if (blk != SWAPBLK_NONE)
                           bl->bl_free -= count;
           }
           return(blk);
   }
   
   swblk_t
   blist_allocat(blist_t bl, swblk_t count, swblk_t blkat)
   {
           swblk_t blk = SWAPBLK_NONE;
   
           if (bl) {
                   if (bl->bl_radix == BLIST_BMAP_RADIX)
                           blk = blst_leaf_alloc(bl->bl_root, blkat, 0, count);
                   else
                           blk = blst_meta_alloc(bl->bl_root, blkat, 0, count,
                                                 bl->bl_radix, bl->bl_skip);
                   if (blk != SWAPBLK_NONE)
                           bl->bl_free -= count;
           }
           return(blk);
   }
   
   /*
    * 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, swblk_t blkno, swblk_t count)
   {
           if (bl) {
                   if (bl->bl_radix == BLIST_BMAP_RADIX)
                           blst_leaf_free(bl->bl_root, blkno, count);
                   else
                           blst_meta_free(bl->bl_root, blkno, count, bl->bl_radix, bl->bl_skip, 0);
                   bl->bl_free += 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.
    */
   
   swblk_t
   blist_fill(blist_t bl, swblk_t blkno, swblk_t count)
   {
           swblk_t filled;
   
           if (bl) {
                   if (bl->bl_radix == BLIST_BMAP_RADIX) {
                           filled = blst_leaf_fill(bl->bl_root, blkno, count);
                   } else {
                           filled = blst_meta_fill(bl->bl_root, blkno, count,
                               bl->bl_radix, bl->bl_skip, 0);
                   }
                   bl->bl_free -= filled;
                   return (filled);
           } else {
                   return 0;
           }
   }
   
   /*
    * 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, swblk_t count, int freenew)
   {
       blist_t newbl = blist_create(count);
       blist_t save = *pbl;
   
       *pbl = newbl;
       if (count > save->bl_blocks)
               count = save->bl_blocks;
       blst_copy(save->bl_root, 0, save->bl_radix, save->bl_skip, 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)
   {
           kprintf("BLIST {\n");
           blst_radix_print(bl->bl_root, 0, bl->bl_radix, bl->bl_skip, 4);
           kprintf("}\n");
   }
   
   #endif
   
   /************************************************************************
    *                        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.
    *
    */
   
   /*
    * blist_leaf_alloc() - allocate at a leaf in the radix tree (a bitmap).
    *
    *      This is the core of the allocator and is optimized for the 1 block
    *      and the BLIST_BMAP_RADIX block allocation cases.  Other cases are
    *      somewhat slower.  The 1 block allocation case is log2 and extremely
    *      quick.
    */
   
   static swblk_t
   blst_leaf_alloc(blmeta_t *scan, swblk_t blkat __unused, swblk_t blk, int count)
   {
           u_swblk_t orig = scan->u.bmu_bitmap;
   
           if (orig == 0) {
                   /*
                    * Optimize bitmap all-allocated case.  Also, count = 1
                    * case assumes at least 1 bit is free in the bitmap, so
                    * we have to take care of this case here.
                    */
                   scan->bm_bighint = 0;
                   return(SWAPBLK_NONE);
           }
           if (count == 1) {
                   /*
                    * Optimized code to allocate one bit out of the bitmap
                    */
                   u_swblk_t mask;
                   int j = BLIST_BMAP_RADIX/2;
                   int r = 0;
   
                   mask = (u_swblk_t)-1 >> (BLIST_BMAP_RADIX/2);
   
                   while (j) {
                           if ((orig & mask) == 0) {
                               r += j;
                               orig >>= j;
                           }
                           j >>= 1;
                           mask >>= j;
                   }
                   scan->u.bmu_bitmap &= ~(1 << r);
                   return(blk + r);
           }
           if (count <= BLIST_BMAP_RADIX) {
                   /*
                    * non-optimized code to allocate N bits out of the bitmap.
                    * The more bits, the faster the code runs.  It will run
                    * the slowest allocating 2 bits, but since there aren't any
                    * memory ops in the core loop (or shouldn't be, anyway),
                    * you probably won't notice the difference.
                    */
                   int j;
                   int n = BLIST_BMAP_RADIX - count;
                   u_swblk_t mask;
   
                   mask = (u_swblk_t)-1 >> n;
   
                   for (j = 0; j <= n; ++j) {
                           if ((orig & mask) == mask) {
                                   scan->u.bmu_bitmap &= ~mask;
                                   return(blk + j);
                           }
                           mask = (mask << 1);
                   }
           }
           /*
            * We couldn't allocate count in this subtree, update bighint.
            */
           scan->bm_bighint = count - 1;
           return(SWAPBLK_NONE);
   }
   
   /*
    * 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 swblk_t
   blst_meta_alloc(blmeta_t *scan, swblk_t blkat,
                   swblk_t blk, swblk_t count,
                   int64_t radix, int skip)
   {
           int i;
           int next_skip = ((u_int)skip / BLIST_META_RADIX);
           int hintok = (blk >= blkat);
   
           /*
            * ALL-ALLOCATED special case
            */
           if (scan->u.bmu_avail == 0)  {
                   scan->bm_bighint = 0;
                   return(SWAPBLK_NONE);
           }
   
           /*
            * ALL-FREE special case, initialize uninitialized
            * sublevel.
            *
            * NOTE: radix may exceed 32 bits until first division.
            */
           if (scan->u.bmu_avail == radix) {
                   scan->bm_bighint = radix;
   
                   radix /= BLIST_META_RADIX;
                   for (i = 1; i <= skip; i += next_skip) {
                           if (scan[i].bm_bighint == (swblk_t)-1)
                                   break;
                           if (next_skip == 1) {
                                   scan[i].u.bmu_bitmap = (u_swblk_t)-1;
                                   scan[i].bm_bighint = BLIST_BMAP_RADIX;
                           } else {
                                   scan[i].bm_bighint = (swblk_t)radix;
                                   scan[i].u.bmu_avail = (swblk_t)radix;
                           }
                   }
           } else {
                   radix /= BLIST_META_RADIX;
           }
   
           for (i = 1; i <= skip; i += next_skip) {
                   if (count <= scan[i].bm_bighint &&
                       blk + (swblk_t)radix > blkat) {
                           /*
                            * count fits in object
                            */
                           swblk_t r;
                           if (next_skip == 1) {
                                   r = blst_leaf_alloc(&scan[i], blkat,
                                                       blk, count);
                           } else {
                                   r = blst_meta_alloc(&scan[i], blkat,
                                                       blk, count,
                                                       radix, next_skip - 1);
                           }
                           if (r != SWAPBLK_NONE) {
                                   scan->u.bmu_avail -= count;
                                   if (scan->bm_bighint > scan->u.bmu_avail)
                                           scan->bm_bighint = scan->u.bmu_avail;
                                   return(r);
                           }
                           /* bighint was updated by recursion */
                   } else if (scan[i].bm_bighint == (swblk_t)-1) {
                           /*
                            * Terminator
                            */
                           break;
                   } else if (count > (swblk_t)radix) {
                           /*
                            * count does not fit in object even if it were
                            * complete free.
                            */
                           panic("blist_meta_alloc: allocation too large");
                   }
                   blk += (swblk_t)radix;
           }
   
           /*
            * We couldn't allocate count in this subtree, update bighint.
            */
           if (hintok && scan->bm_bighint >= count)
                   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, swblk_t blk, int count)
   {
           /*
            * free some data in this bitmap
            *
            * e.g.
            *      0000111111111110000
            *          \_________/\__/
            *              v        n
            */
           int n = blk & (BLIST_BMAP_RADIX - 1);
           u_swblk_t mask;
   
           mask = ((u_swblk_t)-1 << n) &
               ((u_swblk_t)-1 >> (BLIST_BMAP_RADIX - count - n));
   
           if (scan->u.bmu_bitmap & mask)
                   panic("blst_radix_free: freeing free block");
           scan->u.bmu_bitmap |= mask;
   
           /*
            * We could probably do a better job here.  We are required to make
            * bighint at least as large as the biggest contiguous block of 
            * data.  If we just shoehorn it, a little extra overhead will
            * be incured on the next allocation (but only that one typically).
            */
           scan->bm_bighint = BLIST_BMAP_RADIX;
   }
   
   /*
    * 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, swblk_t freeBlk, swblk_t count,
                  int64_t radix, int skip, swblk_t blk)
   {
           int i;
           int next_skip = ((u_int)skip / BLIST_META_RADIX);
   
   #if 0
           kprintf("FREE (%x,%d) FROM (%x,%lld)\n",
               freeBlk, count,
               blk, (long long)radix
           );
   #endif
   
           /*
            * ALL-ALLOCATED special case, initialize for recursion.
            *
            * We will short-cut the ALL-ALLOCATED -> ALL-FREE case.
            */
           if (scan->u.bmu_avail == 0) {
                   scan->u.bmu_avail = count;
                   scan->bm_bighint = count;
   
                   if (count != radix)  {
                           for (i = 1; i <= skip; i += next_skip) {
                                   if (scan[i].bm_bighint == (swblk_t)-1)
                                           break;
                                   scan[i].bm_bighint = 0;
                                   if (next_skip == 1) {
                                           scan[i].u.bmu_bitmap = 0;
                                   } else {
                                           scan[i].u.bmu_avail = 0;
                                   }
                           }
                           /* fall through */
                   }
           } else {
                   scan->u.bmu_avail += count;
                   /* scan->bm_bighint = radix; */
           }
   
           /*
            * ALL-FREE special case.
            *
            * Set bighint for higher levels to snoop.
            */
           if (scan->u.bmu_avail == radix) {
                   scan->bm_bighint = radix;
                   return;
           }
   
           /*
            * Break the free down into its components
            */
           if (scan->u.bmu_avail > radix) {
                   panic("blst_meta_free: freeing already "
                         "free blocks (%d) %d/%lld",
                         count, scan->u.bmu_avail, (long long)radix);
           }
   
           radix /= BLIST_META_RADIX;
   
           i = (freeBlk - blk) / (swblk_t)radix;
           blk += i * (swblk_t)radix;
           i = i * next_skip + 1;
   
           while (i <= skip && blk < freeBlk + count) {
                   swblk_t v;
   
                   v = blk + (swblk_t)radix - freeBlk;
                   if (v > count)
                           v = count;
   
                   if (scan->bm_bighint == (swblk_t)-1)
                           panic("blst_meta_free: freeing unexpected range");
   
                   if (next_skip == 1) {
                           blst_leaf_free(&scan[i], freeBlk, v);
                   } else {
                           blst_meta_free(&scan[i], freeBlk, v,
                                          radix, next_skip - 1, blk);
                   }
   
                   /*
                    * After having dealt with the becomes-all-free case any
                    * partial free will not be able to bring us to the
                    * becomes-all-free state.
                    *
                    * We can raise bighint to at least the sub-segment's
                    * bighint.
                    */
                   if (scan->bm_bighint < scan[i].bm_bighint) {
                       scan->bm_bighint = scan[i].bm_bighint;
                   }
                   count -= v;
                   freeBlk += v;
                   blk += (swblk_t)radix;
                   i += next_skip;
           }
   }
   
   /*
    * BLST_LEAF_FILL() -   allocate specific blocks in leaf bitmap
    *
    *      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 swblk_t
   blst_leaf_fill(blmeta_t *scan, swblk_t blk, int count)
   {
           int n = blk & (BLIST_BMAP_RADIX - 1);
           swblk_t nblks;
           u_swblk_t mask, bitmap;
   
           mask = ((u_swblk_t)-1 << n) &
               ((u_swblk_t)-1 >> (BLIST_BMAP_RADIX - count - n));
   
           /* Count the number of blocks we're about to allocate */
           bitmap = scan->u.bmu_bitmap & mask;
           for (nblks = 0; bitmap != 0; nblks++)
                   bitmap &= bitmap - 1;
   
           scan->u.bmu_bitmap &= ~mask;
           return (nblks);
   }
   
   /*
    * BLST_META_FILL() -   allocate specific blocks at a meta node
    *
    *      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 swblk_t
   blst_meta_fill(blmeta_t *scan, swblk_t fillBlk, swblk_t count,
                  int64_t radix, int skip, swblk_t blk)
   {
           int i;
           int next_skip = ((u_int)skip / BLIST_META_RADIX);
           swblk_t nblks = 0;
   
           if (count == radix || scan->u.bmu_avail == 0) {
                   /*
                    * ALL-ALLOCATED special case
                    */
                   nblks = scan->u.bmu_avail;
                   scan->u.bmu_avail = 0;
                   scan->bm_bighint = count;
                   return (nblks);
           }
   
           if (scan->u.bmu_avail == radix) {
                   radix /= BLIST_META_RADIX;
   
                   /*
                    * ALL-FREE special case, initialize sublevel
                    */
                   for (i = 1; i <= skip; i += next_skip) {
                           if (scan[i].bm_bighint == (swblk_t)-1)
                                   break;
                           if (next_skip == 1) {
                                   scan[i].u.bmu_bitmap = (u_swblk_t)-1;
                                   scan[i].bm_bighint = BLIST_BMAP_RADIX;
                           } else {
                                   scan[i].bm_bighint = (swblk_t)radix;
                                   scan[i].u.bmu_avail = (swblk_t)radix;
                           }
                   }
           } else {
                   radix /= BLIST_META_RADIX;
           }
   
           if (count > (swblk_t)radix)
                   panic("blst_meta_fill: allocation too large");
   
           i = (fillBlk - blk) / (swblk_t)radix;
           blk += i * (swblk_t)radix;
           i = i * next_skip + 1;
   
           while (i <= skip && blk < fillBlk + count) {
                   swblk_t v;
   
                   v = blk + (swblk_t)radix - fillBlk;
                   if (v > count)
                           v = count;
   
                   if (scan->bm_bighint == (swblk_t)-1)
                           panic("blst_meta_fill: filling unexpected range");
   
                   if (next_skip == 1) {
                           nblks += blst_leaf_fill(&scan[i], fillBlk, v);
                   } else {
                           nblks += blst_meta_fill(&scan[i], fillBlk, v,
                               radix, next_skip - 1, blk);
                   }
                   count -= v;
                   fillBlk += v;
                   blk += (swblk_t)radix;
                   i += next_skip;
           }
           scan->u.bmu_avail -= nblks;
           return (nblks);
   }
   
   /*
    * BLIST_RADIX_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, swblk_t blk, int64_t radix,
             swblk_t skip, blist_t dest, swblk_t count) 
   {
           int next_skip;
           int i;
   
           /*
            * Leaf node
            */
   
           if (radix == BLIST_BMAP_RADIX) {
                   u_swblk_t v = scan->u.bmu_bitmap;
   
                   if (v == (u_swblk_t)-1) {
                           blist_free(dest, blk, count);
                   } else if (v != 0) {
                           int i;
   
                           for (i = 0; i < BLIST_BMAP_RADIX && i < count; ++i) {
                                   if (v & (1 << i))
                                           blist_free(dest, blk + i, 1);
                           }
                   }
                   return;
           }
   
           /*
            * Meta node
            */
   
           if (scan->u.bmu_avail == 0) {
                   /*
                    * Source all allocated, leave dest allocated
                    */
                   return;
           } 
           if (scan->u.bmu_avail == radix) {
                   /*
                    * Source all free, free entire dest
                    */
                   if (count < radix)
                           blist_free(dest, blk, count);
                   else
                           blist_free(dest, blk, (swblk_t)radix);
                   return;
           }
   
   
           radix /= BLIST_META_RADIX;
           next_skip = ((u_int)skip / BLIST_META_RADIX);
   
           for (i = 1; count && i <= skip; i += next_skip) {
                   if (scan[i].bm_bighint == (swblk_t)-1)
                           break;
   
                   if (count >= (swblk_t)radix) {
                           blst_copy(
                               &scan[i],
                               blk,
                               radix,
                               next_skip - 1,
                               dest,
                               (swblk_t)radix
                           );
                           count -= (swblk_t)radix;
                   } else {
                           if (count) {
                                   blst_copy(
                                       &scan[i],
                                       blk,
                                       radix,
                                       next_skip - 1,
                                       dest,
                                       count
                                   );
                           }
                           count = 0;
                   }
                   blk += (swblk_t)radix;
           }
   }
   
   /*
    * BLST_RADIX_INIT() - initialize radix tree
    *
    *      Initialize our meta structures and bitmaps and calculate the exact
    *      amount of space required to manage 'count' blocks - this space may
    *      be considerably less then the calculated radix due to the large
    *      RADIX values we use.
    */
   
   static swblk_t  
   blst_radix_init(blmeta_t *scan, int64_t radix, int skip, swblk_t count)
   {
           int i;
           int next_skip;
           swblk_t memindex = 0;
   
           /*
            * Leaf node
            */
   
           if (radix == BLIST_BMAP_RADIX) {
                   if (scan) {
                           scan->bm_bighint = 0;
                           scan->u.bmu_bitmap = 0;
                   }
                   return(memindex);
           }
   
           /*
            * Meta node.  If allocating the entire object we can special
            * case it.  However, we need to figure out how much memory
            * is required to manage 'count' blocks, so we continue on anyway.
            */
   
           if (scan) {
                   scan->bm_bighint = 0;
                   scan->u.bmu_avail = 0;
           }
   
           radix /= BLIST_META_RADIX;
           next_skip = ((u_int)skip / BLIST_META_RADIX);
   
           for (i = 1; i <= skip; i += next_skip) {
                   if (count >= (swblk_t)radix) {
                           /*
                            * Allocate the entire object
                            */
                           memindex = i + blst_radix_init(
                               ((scan) ? &scan[i] : NULL),
                               radix,
                               next_skip - 1,
                               (swblk_t)radix
                           );
                           count -= (swblk_t)radix;
                   } else if (count > 0) {
                           /*
                            * Allocate a partial object
                            */
                           memindex = i + blst_radix_init(
                               ((scan) ? &scan[i] : NULL),
                               radix,
                               next_skip - 1,
                               count
                           );
                           count = 0;
                   } else {
                           /*
                            * Add terminator and break out
                            */
                           if (scan)
                                   scan[i].bm_bighint = (swblk_t)-1;
                           break;
                   }
           }
           if (memindex < i)
                   memindex = i;
           return(memindex);
   }
   
   #ifdef BLIST_DEBUG
   
   static void     
   blst_radix_print(blmeta_t *scan, swblk_t blk, int64_t radix, int skip, int tab)
   {
           int i;
           int next_skip;
   
           if (radix == BLIST_BMAP_RADIX) {
                   kprintf(
                       "%*.*s(%04x,%lld): bitmap %08x big=%d\n",
                       tab, tab, "",
                       blk, (long long)radix,
                       scan->u.bmu_bitmap,
                       scan->bm_bighint
                   );
                   return;
           }
   
           if (scan->u.bmu_avail == 0) {
                   kprintf(
                       "%*.*s(%04x,%lld) ALL ALLOCATED\n",
                       tab, tab, "",
                       blk,
                       (long long)radix
                   );
                   return;
           }
           if (scan->u.bmu_avail == radix) {
                   kprintf(
                       "%*.*s(%04x,%lld) ALL FREE\n",
                       tab, tab, "",
                       blk,
                       (long long)radix
                   );
                   return;
           }
   
           kprintf(
               "%*.*s(%04x,%lld): subtree (%d/%lld) big=%d {\n",
               tab, tab, "",
               blk, (long long)radix,
               scan->u.bmu_avail,
               (long long)radix,
               scan->bm_bighint
           );
   
           radix /= BLIST_META_RADIX;
           next_skip = ((u_int)skip / BLIST_META_RADIX);
           tab += 4;
   
           for (i = 1; i <= skip; i += next_skip) {
                   if (scan[i].bm_bighint == (swblk_t)-1) {
                           kprintf(
                               "%*.*s(%04x,%lld): Terminator\n",
                              tab, tab, "",
                              blk, (long long)radix
                          );
                          break;
                  }
                  blst_radix_print(
                      &scan[i],
                      blk,
                      radix,
                      next_skip - 1,
                      tab
                  );
                  blk += (swblk_t)radix;
          }
          tab -= 4;
  
          kprintf(
              "%*.*s}\n",
              tab, tab, ""
          );
  }
  
  #endif
  
  #ifdef BLIST_DEBUG
  
  int
  main(int ac, char **av)
  {
          int size = 1024;
          int i;
          blist_t bl;
  
          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);
          blist_free(bl, 0, size);
  
          for (;;) {
                  char buf[1024];
                  swblk_t da = 0;
                  swblk_t count = 0;
                  swblk_t blkat;
  
  
                  kprintf("%d/%d/%lld> ",
                          bl->bl_free, 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, "%d", &count) == 1) {
                                  blist_resize(&bl, count, 1);
                                  size = count;
                          } else {
                                  kprintf("?\n");
                          }
                  case 'p':
                          blist_print(bl);
                          break;
                  case 'a':
                          if (sscanf(buf + 1, "%d %d", &count, &blkat) == 1) {
                                  swblk_t blk = blist_alloc(bl, count);
                                  kprintf("    R=%04x\n", blk);
                          } else if (sscanf(buf + 1, "%d %d", &count, &blkat) == 2) {
                                  swblk_t blk = blist_allocat(bl, count, blkat);
                                  kprintf("    R=%04x\n", blk);
                          } else {
                                  kprintf("?\n");
                          }
                          break;
                  case 'f':
                          if (sscanf(buf + 1, "%x %d", &da, &count) == 2) {
                                  blist_free(bl, da, count);
                          } else {
                                  kprintf("?\n");
                          }
                          break;
                  case 'l':
                          if (sscanf(buf + 1, "%x %d", &da, &count) == 2) {
                                  printf("    n=%d\n",
                                      blist_fill(bl, da, count));
                          } else {
                                  kprintf("?\n");
                          }
                          break;
                  case '?':
                  case 'h':
                          puts(
                              "p          -print\n"
                              "a %d       -allocate\n"
                              "f %x %d    -free\n"
                              "l %x %d    -fill\n"
                              "r %d       -resize\n"
                              "h/?        -help"
                          );
                          break;
                  default:
                          kprintf("?\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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