Merge ^/vendor/llvm/dist up to its last change, and resolve conflicts.

[FreeBSD/FreeBSD.git] / 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 <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

_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))));
}


/*
 * 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_BMAP_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_BMAP_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;
        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, 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;
        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) {
                                digit = bitpos(diff);
                                update_gap_stats(stats, i + digit);
                                diff ^= bitrange(digit, 1);
                        }
                }
                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 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_BMAP_RADIX;
        for (blk = start; blk - start < maxcount; blk += BLIST_BMAP_RADIX) {
                /* Skip meta-nodes, as long as they promise more free blocks. */
                radix = BLIST_BMAP_RADIX;
                while (((++scan)->bm_bitmap & 1) == 1 &&
                    ((blk / radix) & BLIST_META_MASK) == 0)
                        radix *= BLIST_META_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_BMAP_RADIX == 0) {
                                /*
                                 * There was no next leaf.  Back scan up to
                                 * last leaf.
                                 */
                                --scan;
                                while (radix != BLIST_BMAP_RADIX) {
                                        radix /= BLIST_META_RADIX;
                                        --scan;
                                }
                                blk -= BLIST_BMAP_RADIX;
                        }
                }
        }
        
        /*
         * 'scan' is the last leaf that provides blocks.  Clear from 1 to
         * BLIST_BMAP_RADIX bits to represent the allocation of those last
         * blocks.
         */
        if (maxcount % BLIST_BMAP_RADIX != 0)
                scan->bm_bitmap &= ~bitrange(0, maxcount % BLIST_BMAP_RADIX);
        else
                scan->bm_bitmap = 0;

        for (;;) {
                /* Back up over meta-nodes, clearing bits if necessary. */
                blk -= BLIST_BMAP_RADIX;
                radix = BLIST_BMAP_RADIX;
                while ((digit = ((blk / radix) & BLIST_META_MASK)) == 0) {
                        if ((scan--)->bm_bitmap == 0)
                                scan->bm_bitmap ^= 1;
                        radix *= BLIST_META_RADIX;
                }
                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_BMAP_MASK) != 0) {
                if ((~mask & bitrange(0, blk & BLIST_BMAP_MASK)) != 0) {
                        /* Grow bighint in case all discarded bits are set. */
                        bighint += blk & BLIST_BMAP_MASK;
                        mask |= bitrange(0, blk & BLIST_BMAP_MASK);
                        if (~mask == 0) {
                                scan->bm_bighint = bighint;
                                return (SWAPBLK_NONE);
                        }
                }
                blk -= blk & BLIST_BMAP_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_BMAP_RADIX - lo) {
                /* All the blocks we can use are available here. */
                hi = lo + maxcount;
                *count = maxcount;
                mask = ~bitrange(lo, *count);
                if (hi == BLIST_BMAP_RADIX)
                        scan->bm_bighint = bighint;
        } else {
                /* Check next leaf for some of the blocks we want or need. */
                count1 = *count - (BLIST_BMAP_RADIX - lo);
                maxcount -= BLIST_BMAP_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_BMAP_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 == BLIST_BMAP_RADIX)
                return (blst_leaf_alloc(scan, cursor, count, maxcount));
        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 {
                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);
                        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_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);
        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 == 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 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 {
                digit = bitpos(mask);
                blst_radix_print(&scan[1 + digit * skip], blk + digit * radix,
                    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)
{
        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;
                int count = 0, maxcount = 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, "%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