subr_blist.c
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subr_blist.c
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	/*-
	* 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.
	* 4. 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 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.
	*
	* This code can be compiled stand-alone for debugging.
	*/

	#include <sys/cdefs.h>
	__FBSDID("$FreeBSD: stable/7/sys/kern/subr_blist.c 181085 2008-07-31 23:18:09Z kmacy $");

	#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/proc.h>
	#include <sys/mutex.h>

	#else

	#ifndef BLIST_NO_DEBUG
	#define BLIST_DEBUG
	#endif

	#define SWAPBLK_NONE ((daddr_t)-1)

	#include <sys/types.h>
	#include <stdio.h>
	#include <string.h>
	#include <stdlib.h>
	#include <stdarg.h>

	#define malloc(a,b,c) calloc(a, 1)
	#define free(a,b) free(a)

	typedef unsigned int u_daddr_t;

	#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 blk,
	daddr_t count, daddr_t radix, int skip);
	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,
	daddr_t radix, int skip, daddr_t blk);
	static void blst_copy(blmeta_t *scan, daddr_t blk, daddr_t radix,
	daddr_t skip, blist_t dest, daddr_t count);
	static int blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count);
	static int blst_meta_fill(blmeta_t *scan, daddr_t allocBlk, daddr_t count,
	daddr_t radix, int skip, daddr_t blk);
	static daddr_t blst_radix_init(blmeta_t *scan, daddr_t radix,
	int skip, daddr_t count);
	#ifndef _KERNEL
	static void blst_radix_print(blmeta_t *scan, daddr_t blk,
	daddr_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
	* 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;
	int radix;
	int skip = 0;

	/*
	* Calculate radix and skip field used for scanning.
	*/
	radix = BLIST_BMAP_RADIX;

	while (radix < blocks) {
	radix *= BLIST_META_RADIX;
	skip = (skip + 1) * BLIST_META_RADIX;
	}

	bl = malloc(sizeof(struct blist), M_SWAP, flags \| 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 = malloc(sizeof(blmeta_t) * bl->bl_rootblks, M_SWAP, flags);

	#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)(bl->bl_rootblks * sizeof(blmeta_t) + 1023) / 1024
	);
	printf("BLIST raw radix tree contains %lld records\n",
	(long long)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)
	{
	free(bl->bl_root, M_SWAP);
	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 = SWAPBLK_NONE;

	if (bl) {
	if (bl->bl_radix == BLIST_BMAP_RADIX)
	blk = blst_leaf_alloc(bl->bl_root, 0, count);
	else
	blk = blst_meta_alloc(bl->bl_root, 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, daddr_t blkno, daddr_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.
	*/

	int
	blist_fill(blist_t bl, daddr_t blkno, daddr_t count)
	{
	int 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, 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, 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)
	{
	printf("BLIST {\n");
	blst_radix_print(bl->bl_root, 0, bl->bl_radix, bl->bl_skip, 4);
	printf("}\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 daddr_t
	blst_leaf_alloc(
	blmeta_t *scan,
	daddr_t blk,
	int count
	) {
	u_daddr_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_daddr_t mask;
	int j = BLIST_BMAP_RADIX/2;
	int r = 0;

	mask = (u_daddr_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_daddr_t mask;

	mask = (u_daddr_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 daddr_t
	blst_meta_alloc(
	blmeta_t *scan,
	daddr_t blk,
	daddr_t count,
	daddr_t radix,
	int skip
	) {
	int i;
	int next_skip = ((u_int)skip / BLIST_META_RADIX);

	if (scan->u.bmu_avail == 0) {
	/*
	* ALL-ALLOCATED special case
	*/
	scan->bm_bighint = count;
	return(SWAPBLK_NONE);
	}

	if (scan->u.bmu_avail == radix) {
	radix /= BLIST_META_RADIX;

	/*
	* ALL-FREE special case, initialize uninitialize
	* sublevel.
	*/
	for (i = 1; i <= skip; i += next_skip) {
	if (scan[i].bm_bighint == (daddr_t)-1)
	break;
	if (next_skip == 1) {
	scan[i].u.bmu_bitmap = (u_daddr_t)-1;
	scan[i].bm_bighint = BLIST_BMAP_RADIX;
	} else {
	scan[i].bm_bighint = radix;
	scan[i].u.bmu_avail = radix;
	}
	}
	} else {
	radix /= BLIST_META_RADIX;
	}

	for (i = 1; i <= skip; i += next_skip) {
	if (count <= scan[i].bm_bighint) {
	/*
	* count fits in object
	*/
	daddr_t r;
	if (next_skip == 1) {
	r = blst_leaf_alloc(&scan[i], blk, count);
	} else {
	r = blst_meta_alloc(&scan[i], 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);
	}
	} else if (scan[i].bm_bighint == (daddr_t)-1) {
	/*
	* Terminator
	*/
	break;
	} else if (count > radix) {
	/*
	* count does not fit in object even if it were
	* complete free.
	*/
	panic("blist_meta_alloc: allocation too large");
	}
	blk += radix;
	}

	/*
	* We couldn't allocate count in this subtree, update bighint.
	*/
	if (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,
	daddr_t blk,
	int count
	) {
	/*
	* free some data in this bitmap
	*
	* e.g.
	* 0000111111111110000
	* \_________/\__/
	* v n
	*/
	int n = blk & (BLIST_BMAP_RADIX - 1);
	u_daddr_t mask;

	mask = ((u_daddr_t)-1 << n) &
	((u_daddr_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,
	daddr_t freeBlk,
	daddr_t count,
	daddr_t radix,
	int skip,
	daddr_t blk
	) {
	int i;
	int next_skip = ((u_int)skip / BLIST_META_RADIX);

	#if 0
	printf("FREE (%llx,%lld) FROM (%llx,%lld)\n",
	(long long)freeBlk, (long long)count,
	(long long)blk, (long long)radix
	);
	#endif

	if (scan->u.bmu_avail == 0) {
	/*
	* ALL-ALLOCATED special case, with possible
	* shortcut to ALL-FREE special case.
	*/
	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 == (daddr_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.
	*/

	if (scan->u.bmu_avail == radix)
	return;
	if (scan->u.bmu_avail > radix)
	panic("blst_meta_free: freeing already free blocks (%lld) %lld/%lld",
	(long long)count, (long long)scan->u.bmu_avail,
	(long long)radix);

	/*
	* Break the free down into its components
	*/

	radix /= BLIST_META_RADIX;

	i = (freeBlk - blk) / radix;
	blk += i * radix;
	i = i * next_skip + 1;

	while (i <= skip && blk < freeBlk + count) {
	daddr_t v;

	v = blk + radix - freeBlk;
	if (v > count)
	v = count;

	if (scan->bm_bighint == (daddr_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);
	}
	if (scan->bm_bighint < scan[i].bm_bighint)
	scan->bm_bighint = scan[i].bm_bighint;
	count -= v;
	freeBlk += v;
	blk += radix;
	i += next_skip;
	}
	}

	/*
	* 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,
	daddr_t blk,
	daddr_t radix,
	daddr_t skip,
	blist_t dest,
	daddr_t count
	) {
	int next_skip;
	int i;

	/*
	* Leaf node
	*/

	if (radix == BLIST_BMAP_RADIX) {
	u_daddr_t v = scan->u.bmu_bitmap;

	if (v == (u_daddr_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, 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 == (daddr_t)-1)
	break;

	if (count >= radix) {
	blst_copy(
	&scan[i],
	blk,
	radix,
	next_skip - 1,
	dest,
	radix
	);
	count -= radix;
	} else {
	if (count) {
	blst_copy(
	&scan[i],
	blk,
	radix,
	next_skip - 1,
	dest,
	count
	);
	}
	count = 0;
	}
	blk += radix;
	}
	}

	/*
	* 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 int
	blst_leaf_fill(blmeta_t *scan, daddr_t blk, int count)
	{
	int n = blk & (BLIST_BMAP_RADIX - 1);
	int nblks;
	u_daddr_t mask, bitmap;

	mask = ((u_daddr_t)-1 << n) &
	((u_daddr_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;
	}

	/*
	* 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 int
	blst_meta_fill(
	blmeta_t *scan,
	daddr_t allocBlk,
	daddr_t count,
	daddr_t radix,
	int skip,
	daddr_t blk
	) {
	int i;
	int next_skip = ((u_int)skip / BLIST_META_RADIX);
	int 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 == (daddr_t)-1)
	break;
	if (next_skip == 1) {
	scan[i].u.bmu_bitmap = (u_daddr_t)-1;
	scan[i].bm_bighint = BLIST_BMAP_RADIX;
	} else {
	scan[i].bm_bighint = radix;
	scan[i].u.bmu_avail = radix;
	}
	}
	} else {
	radix /= BLIST_META_RADIX;
	}

	if (count > radix)
	panic("blist_meta_fill: allocation too large");

	i = (allocBlk - blk) / radix;
	blk += i * radix;
	i = i * next_skip + 1;

	while (i <= skip && blk < allocBlk + count) {
	daddr_t v;

	v = blk + radix - allocBlk;
	if (v > count)
	v = count;

	if (scan->bm_bighint == (daddr_t)-1)
	panic("blst_meta_fill: filling unexpected range");

	if (next_skip == 1) {
	nblks += blst_leaf_fill(&scan[i], allocBlk, v);
	} else {
	nblks += blst_meta_fill(&scan[i], allocBlk, v,
	radix, next_skip - 1, blk);
	}
	count -= v;
	allocBlk += v;
	blk += radix;
	i += next_skip;
	}
	scan->u.bmu_avail -= nblks;
	return nblks;
	}

	/*
	* 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 daddr_t
	blst_radix_init(blmeta_t *scan, daddr_t radix, int skip, daddr_t count)
	{
	int i;
	int next_skip;
	daddr_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 >= radix) {
	/*
	* Allocate the entire object
	*/
	memindex = i + blst_radix_init(
	((scan) ? &scan[i] : NULL),
	radix,
	next_skip - 1,
	radix
	);
	count -= 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 = (daddr_t)-1;
	break;
	}
	}
	if (memindex < i)
	memindex = i;
	return(memindex);
	}

	#ifdef BLIST_DEBUG

	static void
	blst_radix_print(blmeta_t *scan, daddr_t blk, daddr_t radix, int skip, int tab)
	{
	int i;
	int next_skip;
	int lastState = 0;

	if (radix == BLIST_BMAP_RADIX) {
	printf(
	"%.s(%08llx,%lld): bitmap %08llx big=%lld\n",
	tab, tab, "",
	(long long)blk, (long long)radix,
	(long long)scan->u.bmu_bitmap,
	(long long)scan->bm_bighint
	);
	return;
	}

	if (scan->u.bmu_avail == 0) {
	printf(
	"%.s(%08llx,%lld) ALL ALLOCATED\n",
	tab, tab, "",
	(long long)blk,
	(long long)radix
	);
	return;
	}
	if (scan->u.bmu_avail == radix) {
	printf(
	"%.s(%08llx,%lld) ALL FREE\n",
	tab, tab, "",
	(long long)blk,
	(long long)radix
	);
	return;
	}

	printf(
	"%.s(%08llx,%lld): subtree (%lld/%lld) big=%lld {\n",
	tab, tab, "",
	(long long)blk, (long long)radix,
	(long long)scan->u.bmu_avail,
	(long long)radix,
	(long long)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 == (daddr_t)-1) {
	printf(
	"%.s(%08llx,%lld): Terminator\n",
	tab, tab, "",
	(long long)blk, (long long)radix
	);
	lastState = 0;
	break;
	}
	blst_radix_print(
	&scan[i],
	blk,
	radix,
	next_skip - 1,
	tab
	);
	blk += radix;
	}
	tab -= 4;

	printf(
	"%.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, M_WAITOK);
	blist_free(bl, 0, size);

	for (;;) {
	char buf[1024];
	daddr_t da = 0;
	daddr_t count = 0;


	printf("%lld/%lld/%lld> ", (long long)bl->bl_free,
	(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);
	} else {
	printf("?\n");
	}
	case 'p':
	blist_print(bl);
	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",
	(long long )&da, (long long )&count) == 2) {
	blist_free(bl, da, count);
	} else {
	printf("?\n");
	}
	break;
	case 'l':
	if (sscanf(buf + 1, "%llx %lld",
	(long long )&da, (long long )&count) == 2) {
	printf(" n=%d\n",
	blist_fill(bl, da, count));
	} else {
	printf("?\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:
	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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