Fix multiple vulnerabilities in bzip2.

[FreeBSD/FreeBSD.git] / sys / cam / cam_iosched.c

/*-
 * CAM IO Scheduler Interface
 *
 * Copyright (c) 2015 Netflix, Inc.
 * 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,
 *    without modification, immediately at the beginning of the file.
 * 2. The name of the author may not be used to endorse or promote products
 *    derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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.
 *
 * $FreeBSD$
 */

#include "opt_cam.h"
#include "opt_ddb.h"

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

#include <sys/param.h>

#include <sys/systm.h>
#include <sys/kernel.h>
#include <sys/bio.h>
#include <sys/lock.h>
#include <sys/malloc.h>
#include <sys/mutex.h>
#include <sys/sysctl.h>

#include <cam/cam.h>
#include <cam/cam_ccb.h>
#include <cam/cam_periph.h>
#include <cam/cam_xpt_periph.h>
#include <cam/cam_iosched.h>

#include <ddb/ddb.h>

static MALLOC_DEFINE(M_CAMSCHED, "CAM I/O Scheduler",
    "CAM I/O Scheduler buffers");

/*
 * Default I/O scheduler for FreeBSD. This implementation is just a thin-vineer
 * over the bioq_* interface, with notions of separate calls for normal I/O and
 * for trims.
 *
 * When CAM_IOSCHED_DYNAMIC is defined, the scheduler is enhanced to dynamically
 * steer the rate of one type of traffic to help other types of traffic (eg
 * limit writes when read latency deteriorates on SSDs).
 */

#ifdef CAM_IOSCHED_DYNAMIC

static int do_dynamic_iosched = 1;
TUNABLE_INT("kern.cam.do_dynamic_iosched", &do_dynamic_iosched);
SYSCTL_INT(_kern_cam, OID_AUTO, do_dynamic_iosched, CTLFLAG_RD,
    &do_dynamic_iosched, 1,
    "Enable Dynamic I/O scheduler optimizations.");

static int alpha_bits = 9;
TUNABLE_INT("kern.cam.iosched_alpha_bits", &alpha_bits);
SYSCTL_INT(_kern_cam, OID_AUTO, iosched_alpha_bits, CTLFLAG_RW,
    &alpha_bits, 1,
    "Bits in EMA's alpha.");



struct iop_stats;
struct cam_iosched_softc;

int iosched_debug = 0;

typedef enum {
        none = 0,                               /* No limits */
        queue_depth,                    /* Limit how many ops we queue to SIM */
        iops,                           /* Limit # of IOPS to the drive */
        bandwidth,                      /* Limit bandwidth to the drive */
        limiter_max
} io_limiter;
        
static const char *cam_iosched_limiter_names[] =
    { "none", "queue_depth", "iops", "bandwidth" };

/*
 * Called to initialize the bits of the iop_stats structure relevant to the
 * limiter. Called just after the limiter is set.
 */
typedef int l_init_t(struct iop_stats *);

/*
 * Called every tick.
 */
typedef int l_tick_t(struct iop_stats *);

/*
 * Called to see if the limiter thinks this IOP can be allowed to
 * proceed. If so, the limiter assumes that the while IOP proceeded
 * and makes any accounting of it that's needed.
 */ 
typedef int l_iop_t(struct iop_stats *, struct bio *);

/*
 * Called when an I/O completes so the limiter can updates its
 * accounting. Pending I/Os may complete in any order (even when
 * sent to the hardware at the same time), so the limiter may not
 * make any assumptions other than this I/O has completed. If it
 * returns 1, then xpt_schedule() needs to be called again.
 */
typedef int l_iodone_t(struct iop_stats *, struct bio *);

static l_iop_t cam_iosched_qd_iop;
static l_iop_t cam_iosched_qd_caniop;
static l_iodone_t cam_iosched_qd_iodone;

static l_init_t cam_iosched_iops_init;
static l_tick_t cam_iosched_iops_tick;
static l_iop_t cam_iosched_iops_caniop;
static l_iop_t cam_iosched_iops_iop;

static l_init_t cam_iosched_bw_init;
static l_tick_t cam_iosched_bw_tick;
static l_iop_t cam_iosched_bw_caniop;
static l_iop_t cam_iosched_bw_iop;

struct limswitch 
{
        l_init_t        *l_init;
        l_tick_t        *l_tick;
        l_iop_t         *l_iop;
        l_iop_t         *l_caniop;
        l_iodone_t      *l_iodone;
} limsw[] =
{
        {       /* none */
                .l_init = NULL,
                .l_tick = NULL,
                .l_iop = NULL,
                .l_iodone= NULL,
        },
        {       /* queue_depth */
                .l_init = NULL,
                .l_tick = NULL,
                .l_caniop = cam_iosched_qd_caniop,
                .l_iop = cam_iosched_qd_iop,
                .l_iodone= cam_iosched_qd_iodone,
        },
        {       /* iops */
                .l_init = cam_iosched_iops_init,
                .l_tick = cam_iosched_iops_tick,
                .l_caniop = cam_iosched_iops_caniop,
                .l_iop = cam_iosched_iops_iop,
                .l_iodone= NULL,
        },
        {       /* bandwidth */
                .l_init = cam_iosched_bw_init,
                .l_tick = cam_iosched_bw_tick,
                .l_caniop = cam_iosched_bw_caniop,
                .l_iop = cam_iosched_bw_iop,
                .l_iodone= NULL,
        },
};

struct iop_stats 
{
        /*
         * sysctl state for this subnode.
         */
        struct sysctl_ctx_list  sysctl_ctx;
        struct sysctl_oid       *sysctl_tree;

        /*
         * Information about the current rate limiters, if any
         */
        io_limiter      limiter;        /* How are I/Os being limited */
        int             min;            /* Low range of limit */
        int             max;            /* High range of limit */
        int             current;        /* Current rate limiter */
        int             l_value1;       /* per-limiter scratch value 1. */
        int             l_value2;       /* per-limiter scratch value 2. */
        

        /*
         * Debug information about counts of I/Os that have gone through the
         * scheduler.
         */
        int             pending;        /* I/Os pending in the hardware */
        int             queued;         /* number currently in the queue */
        int             total;          /* Total for all time -- wraps */
        int             in;             /* number queued all time -- wraps */
        int             out;            /* number completed all time -- wraps */
        
        /*
         * Statistics on different bits of the process.
         */
                /* Exp Moving Average, alpha = 1 / (1 << alpha_bits) */
        sbintime_t      ema;
        sbintime_t      emss;           /* Exp Moving sum of the squares */
        sbintime_t      sd;             /* Last computed sd */

        struct cam_iosched_softc *softc;
};


typedef enum {
        set_max = 0,                    /* current = max */
        read_latency,                   /* Steer read latency by throttling writes */
        cl_max                          /* Keep last */
} control_type;

static const char *cam_iosched_control_type_names[] =
    { "set_max", "read_latency" };

struct control_loop
{
        /*
         * sysctl state for this subnode.
         */
        struct sysctl_ctx_list  sysctl_ctx;
        struct sysctl_oid       *sysctl_tree;

        sbintime_t      next_steer;             /* Time of next steer */
        sbintime_t      steer_interval;         /* How often do we steer? */
        sbintime_t      lolat;
        sbintime_t      hilat;
        int             alpha;
        control_type    type;                   /* What type of control? */
        int             last_count;             /* Last I/O count */

        struct cam_iosched_softc *softc;
};

#endif

struct cam_iosched_softc
{
        struct bio_queue_head bio_queue;
        struct bio_queue_head trim_queue;
                                /* scheduler flags < 16, user flags >= 16 */
        uint32_t        flags;
        int             sort_io_queue;
#ifdef CAM_IOSCHED_DYNAMIC
        int             read_bias;              /* Read bias setting */
        int             current_read_bias;      /* Current read bias state */
        int             total_ticks;

        struct bio_queue_head write_queue;
        struct iop_stats read_stats, write_stats, trim_stats;
        struct sysctl_ctx_list  sysctl_ctx;
        struct sysctl_oid       *sysctl_tree;

        int             quanta;                 /* Number of quanta per second */
        struct callout  ticker;                 /* Callout for our quota system */
        struct cam_periph *periph;              /* cam periph associated with this device */
        uint32_t        this_frac;              /* Fraction of a second (1024ths) for this tick */
        sbintime_t      last_time;              /* Last time we ticked */
        struct control_loop cl;
#endif
};

#ifdef CAM_IOSCHED_DYNAMIC
/*
 * helper functions to call the limsw functions.
 */
static int
cam_iosched_limiter_init(struct iop_stats *ios)
{
        int lim = ios->limiter;

        /* maybe this should be a kassert */
        if (lim < none || lim >= limiter_max)
                return EINVAL;

        if (limsw[lim].l_init)
                return limsw[lim].l_init(ios);

        return 0;
}

static int
cam_iosched_limiter_tick(struct iop_stats *ios)
{
        int lim = ios->limiter;

        /* maybe this should be a kassert */
        if (lim < none || lim >= limiter_max)
                return EINVAL;

        if (limsw[lim].l_tick)
                return limsw[lim].l_tick(ios);

        return 0;
}

static int
cam_iosched_limiter_iop(struct iop_stats *ios, struct bio *bp)
{
        int lim = ios->limiter;

        /* maybe this should be a kassert */
        if (lim < none || lim >= limiter_max)
                return EINVAL;

        if (limsw[lim].l_iop)
                return limsw[lim].l_iop(ios, bp);

        return 0;
}

static int
cam_iosched_limiter_caniop(struct iop_stats *ios, struct bio *bp)
{
        int lim = ios->limiter;

        /* maybe this should be a kassert */
        if (lim < none || lim >= limiter_max)
                return EINVAL;

        if (limsw[lim].l_caniop)
                return limsw[lim].l_caniop(ios, bp);

        return 0;
}

static int
cam_iosched_limiter_iodone(struct iop_stats *ios, struct bio *bp)
{
        int lim = ios->limiter;

        /* maybe this should be a kassert */
        if (lim < none || lim >= limiter_max)
                return 0;

        if (limsw[lim].l_iodone)
                return limsw[lim].l_iodone(ios, bp);

        return 0;
}

/*
 * Functions to implement the different kinds of limiters
 */

static int
cam_iosched_qd_iop(struct iop_stats *ios, struct bio *bp)
{
                
        if (ios->current <= 0 || ios->pending < ios->current)
                return 0;

        return EAGAIN;
}

static int
cam_iosched_qd_caniop(struct iop_stats *ios, struct bio *bp)
{
                
        if (ios->current <= 0 || ios->pending < ios->current)
                return 0;

        return EAGAIN;
}

static int
cam_iosched_qd_iodone(struct iop_stats *ios, struct bio *bp)
{
                
        if (ios->current <= 0 || ios->pending != ios->current)
                return 0;

        return 1;
}

static int
cam_iosched_iops_init(struct iop_stats *ios)
{

        ios->l_value1 = ios->current / ios->softc->quanta;
        if (ios->l_value1 <= 0)
                ios->l_value1 = 1;

        return 0;
}

static int
cam_iosched_iops_tick(struct iop_stats *ios)
{

        ios->l_value1 = (int)((ios->current * (uint64_t)ios->softc->this_frac) >> 16);
        if (ios->l_value1 <= 0)
                ios->l_value1 = 1;

        return 0;
}

static int
cam_iosched_iops_caniop(struct iop_stats *ios, struct bio *bp)
{

        /*
         * So if we have any more IOPs left, allow it,
         * otherwise wait.
         */
        if (ios->l_value1 <= 0)
                return EAGAIN;
        return 0;
}

static int
cam_iosched_iops_iop(struct iop_stats *ios, struct bio *bp)
{
        int rv;

        rv = cam_iosched_limiter_caniop(ios, bp);
        if (rv == 0)
                ios->l_value1--;

        return rv;
}

static int
cam_iosched_bw_init(struct iop_stats *ios)
{

        /* ios->current is in kB/s, so scale to bytes */
        ios->l_value1 = ios->current * 1000 / ios->softc->quanta;

        return 0;
}

static int
cam_iosched_bw_tick(struct iop_stats *ios)
{
        int bw;

        /*
         * If we're in the hole for available quota from
         * the last time, then add the quantum for this.
         * If we have any left over from last quantum,
         * then too bad, that's lost. Also, ios->current
         * is in kB/s, so scale.
         *
         * We also allow up to 4 quanta of credits to
         * accumulate to deal with burstiness. 4 is extremely
         * arbitrary.
         */
        bw = (int)((ios->current * 1000ull * (uint64_t)ios->softc->this_frac) >> 16);
        if (ios->l_value1 < bw * 4)
                ios->l_value1 += bw;

        return 0;
}

static int
cam_iosched_bw_caniop(struct iop_stats *ios, struct bio *bp)
{
        /*
         * So if we have any more bw quota left, allow it,
         * otherwise wait. Not, we'll go negative and that's
         * OK. We'll just get a lettle less next quota.
         *
         * Note on going negative: that allows us to process
         * requests in order better, since we won't allow
         * shorter reads to get around the long one that we
         * don't have the quota to do just yet. It also prevents
         * starvation by being a little more permissive about
         * what we let through this quantum (to prevent the
         * starvation), at the cost of getting a little less
         * next quantum.
         */
        if (ios->l_value1 <= 0)
                return EAGAIN;


        return 0;
}

static int
cam_iosched_bw_iop(struct iop_stats *ios, struct bio *bp)
{
        int rv;

        rv = cam_iosched_limiter_caniop(ios, bp);
        if (rv == 0)
                ios->l_value1 -= bp->bio_length;

        return rv;
}

static void cam_iosched_cl_maybe_steer(struct control_loop *clp);

static void
cam_iosched_ticker(void *arg)
{
        struct cam_iosched_softc *isc = arg;
        sbintime_t now, delta;

        callout_reset(&isc->ticker, hz / isc->quanta, cam_iosched_ticker, isc);

        now = sbinuptime();
        delta = now - isc->last_time;
        isc->this_frac = (uint32_t)delta >> 16;         /* Note: discards seconds -- should be 0 harmless if not */
        isc->last_time = now;

        cam_iosched_cl_maybe_steer(&isc->cl);

        cam_iosched_limiter_tick(&isc->read_stats);
        cam_iosched_limiter_tick(&isc->write_stats);
        cam_iosched_limiter_tick(&isc->trim_stats);

        cam_iosched_schedule(isc, isc->periph);

        isc->total_ticks++;
}


static void
cam_iosched_cl_init(struct control_loop *clp, struct cam_iosched_softc *isc)
{

        clp->next_steer = sbinuptime();
        clp->softc = isc;
        clp->steer_interval = SBT_1S * 5;       /* Let's start out steering every 5s */
        clp->lolat = 5 * SBT_1MS;
        clp->hilat = 15 * SBT_1MS;
        clp->alpha = 20;                        /* Alpha == gain. 20 = .2 */
        clp->type = set_max;
}

static void
cam_iosched_cl_maybe_steer(struct control_loop *clp)
{
        struct cam_iosched_softc *isc;
        sbintime_t now, lat;
        int old;

        isc = clp->softc;
        now = isc->last_time;
        if (now < clp->next_steer)
                return;

        clp->next_steer = now + clp->steer_interval;
        switch (clp->type) {
        case set_max:
                if (isc->write_stats.current != isc->write_stats.max)
                        printf("Steering write from %d kBps to %d kBps\n",
                            isc->write_stats.current, isc->write_stats.max);
                isc->read_stats.current = isc->read_stats.max;
                isc->write_stats.current = isc->write_stats.max;
                isc->trim_stats.current = isc->trim_stats.max;
                break;
        case read_latency:
                old = isc->write_stats.current;
                lat = isc->read_stats.ema;
                /*
                 * Simple PLL-like engine. Since we're steering to a range for
                 * the SP (set point) that makes things a little more
                 * complicated. In addition, we're not directly controlling our
                 * PV (process variable), the read latency, but instead are
                 * manipulating the write bandwidth limit for our MV
                 * (manipulation variable), analysis of this code gets a bit
                 * messy. Also, the MV is a very noisy control surface for read
                 * latency since it is affected by many hidden processes inside
                 * the device which change how responsive read latency will be
                 * in reaction to changes in write bandwidth. Unlike the classic
                 * boiler control PLL. this may result in over-steering while
                 * the SSD takes its time to react to the new, lower load. This
                 * is why we use a relatively low alpha of between .1 and .25 to
                 * compensate for this effect. At .1, it takes ~22 steering
                 * intervals to back off by a factor of 10. At .2 it only takes
                 * ~10. At .25 it only takes ~8. However some preliminary data
                 * from the SSD drives suggests a reasponse time in 10's of
                 * seconds before latency drops regardless of the new write
                 * rate. Careful observation will be reqiured to tune this
                 * effectively.
                 *
                 * Also, when there's no read traffic, we jack up the write
                 * limit too regardless of the last read latency.  10 is
                 * somewhat arbitrary.
                 */
                if (lat < clp->lolat || isc->read_stats.total - clp->last_count < 10)
                        isc->write_stats.current = isc->write_stats.current *
                            (100 + clp->alpha) / 100;   /* Scale up */
                else if (lat > clp->hilat)
                        isc->write_stats.current = isc->write_stats.current *
                            (100 - clp->alpha) / 100;   /* Scale down */
                clp->last_count = isc->read_stats.total;

                /*
                 * Even if we don't steer, per se, enforce the min/max limits as
                 * those may have changed.
                 */
                if (isc->write_stats.current < isc->write_stats.min)
                        isc->write_stats.current = isc->write_stats.min;
                if (isc->write_stats.current > isc->write_stats.max)
                        isc->write_stats.current = isc->write_stats.max;
                if (old != isc->write_stats.current &&  iosched_debug)
                        printf("Steering write from %d kBps to %d kBps due to latency of %jdms\n",
                            old, isc->write_stats.current,
                            (uintmax_t)((uint64_t)1000000 * (uint32_t)lat) >> 32);
                break;
        case cl_max:
                break;
        }
}
#endif

                        /* Trim or similar currently pending completion */
#define CAM_IOSCHED_FLAG_TRIM_ACTIVE    (1ul << 0)
                        /* Callout active, and needs to be torn down */
#define CAM_IOSCHED_FLAG_CALLOUT_ACTIVE (1ul << 1)

                        /* Periph drivers set these flags to indicate work */
#define CAM_IOSCHED_FLAG_WORK_FLAGS     ((0xffffu) << 16)

#ifdef CAM_IOSCHED_DYNAMIC
static void
cam_iosched_io_metric_update(struct cam_iosched_softc *isc,
    sbintime_t sim_latency, int cmd, size_t size);
#endif

static inline int
cam_iosched_has_flagged_work(struct cam_iosched_softc *isc)
{
        return !!(isc->flags & CAM_IOSCHED_FLAG_WORK_FLAGS);
}

static inline int
cam_iosched_has_io(struct cam_iosched_softc *isc)
{
#ifdef CAM_IOSCHED_DYNAMIC
        if (do_dynamic_iosched) {
                struct bio *rbp = bioq_first(&isc->bio_queue);
                struct bio *wbp = bioq_first(&isc->write_queue);
                int can_write = wbp != NULL &&
                    cam_iosched_limiter_caniop(&isc->write_stats, wbp) == 0;
                int can_read = rbp != NULL &&
                    cam_iosched_limiter_caniop(&isc->read_stats, rbp) == 0;
                if (iosched_debug > 2) {
                        printf("can write %d: pending_writes %d max_writes %d\n", can_write, isc->write_stats.pending, isc->write_stats.max);
                        printf("can read %d: read_stats.pending %d max_reads %d\n", can_read, isc->read_stats.pending, isc->read_stats.max);
                        printf("Queued reads %d writes %d\n", isc->read_stats.queued, isc->write_stats.queued);
                }
                return can_read || can_write;
        }
#endif
        return bioq_first(&isc->bio_queue) != NULL;
}

static inline int
cam_iosched_has_more_trim(struct cam_iosched_softc *isc)
{
        return !(isc->flags & CAM_IOSCHED_FLAG_TRIM_ACTIVE) &&
            bioq_first(&isc->trim_queue);
}

#define cam_iosched_sort_queue(isc)     ((isc)->sort_io_queue >= 0 ?    \
    (isc)->sort_io_queue : cam_sort_io_queues)


static inline int
cam_iosched_has_work(struct cam_iosched_softc *isc)
{
#ifdef CAM_IOSCHED_DYNAMIC
        if (iosched_debug > 2)
                printf("has work: %d %d %d\n", cam_iosched_has_io(isc),
                    cam_iosched_has_more_trim(isc),
                    cam_iosched_has_flagged_work(isc));
#endif

        return cam_iosched_has_io(isc) ||
                cam_iosched_has_more_trim(isc) ||
                cam_iosched_has_flagged_work(isc);
}

#ifdef CAM_IOSCHED_DYNAMIC
static void
cam_iosched_iop_stats_init(struct cam_iosched_softc *isc, struct iop_stats *ios)
{

        ios->limiter = none;
        cam_iosched_limiter_init(ios);
        ios->in = 0;
        ios->max = 300000;
        ios->min = 1;
        ios->out = 0;
        ios->pending = 0;
        ios->queued = 0;
        ios->total = 0;
        ios->ema = 0;
        ios->emss = 0;
        ios->sd = 0;
        ios->softc = isc;
}

static int
cam_iosched_limiter_sysctl(SYSCTL_HANDLER_ARGS)
{
        char buf[16];
        struct iop_stats *ios;
        struct cam_iosched_softc *isc;
        int value, i, error, cantick;
        const char *p;
        
        ios = arg1;
        isc = ios->softc;
        value = ios->limiter;
        if (value < none || value >= limiter_max)
                p = "UNKNOWN";
        else
                p = cam_iosched_limiter_names[value];
        
        strlcpy(buf, p, sizeof(buf));
        error = sysctl_handle_string(oidp, buf, sizeof(buf), req);
        if (error != 0 || req->newptr == NULL)
                return error;

        cam_periph_lock(isc->periph);

        for (i = none; i < limiter_max; i++) {
                if (strcmp(buf, cam_iosched_limiter_names[i]) != 0)
                        continue;
                ios->limiter = i;
                error = cam_iosched_limiter_init(ios);
                if (error != 0) {
                        ios->limiter = value;
                        cam_periph_unlock(isc->periph);
                        return error;
                }
                cantick = !!limsw[isc->read_stats.limiter].l_tick +
                    !!limsw[isc->write_stats.limiter].l_tick +
                    !!limsw[isc->trim_stats.limiter].l_tick +
                    1;  /* Control loop requires it */
                if (isc->flags & CAM_IOSCHED_FLAG_CALLOUT_ACTIVE) {
                        if (cantick == 0) {
                                callout_stop(&isc->ticker);
                                isc->flags &= ~CAM_IOSCHED_FLAG_CALLOUT_ACTIVE;
                        }
                } else {
                        if (cantick != 0) {
                                callout_reset(&isc->ticker, hz / isc->quanta, cam_iosched_ticker, isc);
                                isc->flags |= CAM_IOSCHED_FLAG_CALLOUT_ACTIVE;
                        }
                }

                cam_periph_unlock(isc->periph);
                return 0;
        }

        cam_periph_unlock(isc->periph);
        return EINVAL;
}

static int
cam_iosched_control_type_sysctl(SYSCTL_HANDLER_ARGS)
{
        char buf[16];
        struct control_loop *clp;
        struct cam_iosched_softc *isc;
        int value, i, error;
        const char *p;
        
        clp = arg1;
        isc = clp->softc;
        value = clp->type;
        if (value < none || value >= cl_max)
                p = "UNKNOWN";
        else
                p = cam_iosched_control_type_names[value];
        
        strlcpy(buf, p, sizeof(buf));
        error = sysctl_handle_string(oidp, buf, sizeof(buf), req);
        if (error != 0 || req->newptr == NULL)
                return error;

        for (i = set_max; i < cl_max; i++) {
                if (strcmp(buf, cam_iosched_control_type_names[i]) != 0)
                        continue;
                cam_periph_lock(isc->periph);
                clp->type = i;
                cam_periph_unlock(isc->periph);
                return 0;
        }

        return EINVAL;
}

static int
cam_iosched_sbintime_sysctl(SYSCTL_HANDLER_ARGS)
{
        char buf[16];
        sbintime_t value;
        int error;
        uint64_t us;
        
        value = *(sbintime_t *)arg1;
        us = (uint64_t)value / SBT_1US;
        snprintf(buf, sizeof(buf), "%ju", (intmax_t)us);
        error = sysctl_handle_string(oidp, buf, sizeof(buf), req);
        if (error != 0 || req->newptr == NULL)
                return error;
        us = strtoul(buf, NULL, 10);
        if (us == 0)
                return EINVAL;
        *(sbintime_t *)arg1 = us * SBT_1US;
        return 0;
}

static int
cam_iosched_quanta_sysctl(SYSCTL_HANDLER_ARGS)
{
        int *quanta;
        int error, value;

        quanta = (unsigned *)arg1;
        value = *quanta;

        error = sysctl_handle_int(oidp, (int *)&value, 0, req);
        if ((error != 0) || (req->newptr == NULL))
                return (error);

        if (value < 1 || value > hz)
                return (EINVAL);

        *quanta = value;

        return (0);
}

static void
cam_iosched_iop_stats_sysctl_init(struct cam_iosched_softc *isc, struct iop_stats *ios, char *name)
{
        struct sysctl_oid_list *n;
        struct sysctl_ctx_list *ctx;

        ios->sysctl_tree = SYSCTL_ADD_NODE(&isc->sysctl_ctx,
            SYSCTL_CHILDREN(isc->sysctl_tree), OID_AUTO, name,
            CTLFLAG_RD, 0, name);
        n = SYSCTL_CHILDREN(ios->sysctl_tree);
        ctx = &ios->sysctl_ctx;

        SYSCTL_ADD_UQUAD(ctx, n,
            OID_AUTO, "ema", CTLFLAG_RD,
            &ios->ema,
            "Fast Exponentially Weighted Moving Average");
        SYSCTL_ADD_UQUAD(ctx, n,
            OID_AUTO, "emss", CTLFLAG_RD,
            &ios->emss,
            "Fast Exponentially Weighted Moving Sum of Squares (maybe wrong)");
        SYSCTL_ADD_UQUAD(ctx, n,
            OID_AUTO, "sd", CTLFLAG_RD,
            &ios->sd,
            "Estimated SD for fast ema (may be wrong)");

        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "pending", CTLFLAG_RD,
            &ios->pending, 0,
            "Instantaneous # of pending transactions");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "count", CTLFLAG_RD,
            &ios->total, 0,
            "# of transactions submitted to hardware");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "queued", CTLFLAG_RD,
            &ios->queued, 0,
            "# of transactions in the queue");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "in", CTLFLAG_RD,
            &ios->in, 0,
            "# of transactions queued to driver");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "out", CTLFLAG_RD,
            &ios->out, 0,
            "# of transactions completed");

        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "limiter", CTLTYPE_STRING | CTLFLAG_RW,
            ios, 0, cam_iosched_limiter_sysctl, "A",
            "Current limiting type.");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "min", CTLFLAG_RW,
            &ios->min, 0,
            "min resource");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "max", CTLFLAG_RW,
            &ios->max, 0,
            "max resource");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "current", CTLFLAG_RW,
            &ios->current, 0,
            "current resource");

}

static void
cam_iosched_iop_stats_fini(struct iop_stats *ios)
{
        if (ios->sysctl_tree)
                if (sysctl_ctx_free(&ios->sysctl_ctx) != 0)
                        printf("can't remove iosched sysctl stats context\n");
}

static void
cam_iosched_cl_sysctl_init(struct cam_iosched_softc *isc)
{
        struct sysctl_oid_list *n;
        struct sysctl_ctx_list *ctx;
        struct control_loop *clp;
        
        clp = &isc->cl;
        clp->sysctl_tree = SYSCTL_ADD_NODE(&isc->sysctl_ctx,
            SYSCTL_CHILDREN(isc->sysctl_tree), OID_AUTO, "control",
            CTLFLAG_RD, 0, "Control loop info");
        n = SYSCTL_CHILDREN(clp->sysctl_tree);
        ctx = &clp->sysctl_ctx;

        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "type", CTLTYPE_STRING | CTLFLAG_RW,
            clp, 0, cam_iosched_control_type_sysctl, "A",
            "Control loop algorithm");
        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "steer_interval", CTLTYPE_STRING | CTLFLAG_RW,
            &clp->steer_interval, 0, cam_iosched_sbintime_sysctl, "A",
            "How often to steer (in us)");
        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "lolat", CTLTYPE_STRING | CTLFLAG_RW,
            &clp->lolat, 0, cam_iosched_sbintime_sysctl, "A",
            "Low water mark for Latency (in us)");
        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "hilat", CTLTYPE_STRING | CTLFLAG_RW,
            &clp->hilat, 0, cam_iosched_sbintime_sysctl, "A",
            "Hi water mark for Latency (in us)");
        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "alpha", CTLFLAG_RW,
            &clp->alpha, 0,
            "Alpha for PLL (x100) aka gain");
}

static void
cam_iosched_cl_sysctl_fini(struct control_loop *clp)
{
        if (clp->sysctl_tree)
                if (sysctl_ctx_free(&clp->sysctl_ctx) != 0)
                        printf("can't remove iosched sysctl control loop context\n");
}
#endif
            
/*
 * Allocate the iosched structure. This also insulates callers from knowing
 * sizeof struct cam_iosched_softc.
 */
int
cam_iosched_init(struct cam_iosched_softc **iscp, struct cam_periph *periph)
{

        *iscp = malloc(sizeof(**iscp), M_CAMSCHED, M_NOWAIT | M_ZERO);
        if (*iscp == NULL)
                return ENOMEM;
#ifdef CAM_IOSCHED_DYNAMIC
        if (iosched_debug)
                printf("CAM IOSCHEDULER Allocating entry at %p\n", *iscp);
#endif
        (*iscp)->sort_io_queue = -1;
        bioq_init(&(*iscp)->bio_queue);
        bioq_init(&(*iscp)->trim_queue);
#ifdef CAM_IOSCHED_DYNAMIC
        if (do_dynamic_iosched) {
                bioq_init(&(*iscp)->write_queue);
                (*iscp)->read_bias = 100;
                (*iscp)->current_read_bias = 100;
                (*iscp)->quanta = 200;
                cam_iosched_iop_stats_init(*iscp, &(*iscp)->read_stats);
                cam_iosched_iop_stats_init(*iscp, &(*iscp)->write_stats);
                cam_iosched_iop_stats_init(*iscp, &(*iscp)->trim_stats);
                (*iscp)->trim_stats.max = 1;    /* Trims are special: one at a time for now */
                (*iscp)->last_time = sbinuptime();
                callout_init_mtx(&(*iscp)->ticker, cam_periph_mtx(periph), 0);
                (*iscp)->periph = periph;
                cam_iosched_cl_init(&(*iscp)->cl, *iscp);
                callout_reset(&(*iscp)->ticker, hz / (*iscp)->quanta, cam_iosched_ticker, *iscp);
                (*iscp)->flags |= CAM_IOSCHED_FLAG_CALLOUT_ACTIVE;
        }
#endif

        return 0;
}

/*
 * Reclaim all used resources. This assumes that other folks have
 * drained the requests in the hardware. Maybe an unwise assumption.
 */
void
cam_iosched_fini(struct cam_iosched_softc *isc)
{
        if (isc) {
                cam_iosched_flush(isc, NULL, ENXIO);
#ifdef CAM_IOSCHED_DYNAMIC
                cam_iosched_iop_stats_fini(&isc->read_stats);
                cam_iosched_iop_stats_fini(&isc->write_stats);
                cam_iosched_iop_stats_fini(&isc->trim_stats);
                cam_iosched_cl_sysctl_fini(&isc->cl);
                if (isc->sysctl_tree)
                        if (sysctl_ctx_free(&isc->sysctl_ctx) != 0)
                                printf("can't remove iosched sysctl stats context\n");
                if (isc->flags & CAM_IOSCHED_FLAG_CALLOUT_ACTIVE) {
                        callout_drain(&isc->ticker);
                        isc->flags &= ~ CAM_IOSCHED_FLAG_CALLOUT_ACTIVE;
                }
                        
#endif
                free(isc, M_CAMSCHED);
        }
}

/*
 * After we're sure we're attaching a device, go ahead and add
 * hooks for any sysctl we may wish to honor.
 */
void cam_iosched_sysctl_init(struct cam_iosched_softc *isc,
    struct sysctl_ctx_list *ctx, struct sysctl_oid *node)
{
#ifdef CAM_IOSCHED_DYNAMIC
        struct sysctl_oid_list *n;
#endif

        SYSCTL_ADD_INT(ctx, SYSCTL_CHILDREN(node),
                OID_AUTO, "sort_io_queue", CTLFLAG_RW | CTLFLAG_MPSAFE,
                &isc->sort_io_queue, 0,
                "Sort IO queue to try and optimise disk access patterns");

#ifdef CAM_IOSCHED_DYNAMIC
        if (!do_dynamic_iosched)
                return;

        isc->sysctl_tree = SYSCTL_ADD_NODE(&isc->sysctl_ctx,
            SYSCTL_CHILDREN(node), OID_AUTO, "iosched",
            CTLFLAG_RD, 0, "I/O scheduler statistics");
        n = SYSCTL_CHILDREN(isc->sysctl_tree);
        ctx = &isc->sysctl_ctx;

        cam_iosched_iop_stats_sysctl_init(isc, &isc->read_stats, "read");
        cam_iosched_iop_stats_sysctl_init(isc, &isc->write_stats, "write");
        cam_iosched_iop_stats_sysctl_init(isc, &isc->trim_stats, "trim");
        cam_iosched_cl_sysctl_init(isc);

        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "read_bias", CTLFLAG_RW,
            &isc->read_bias, 100,
            "How biased towards read should we be independent of limits");

        SYSCTL_ADD_PROC(ctx, n,
            OID_AUTO, "quanta", CTLTYPE_UINT | CTLFLAG_RW,
            &isc->quanta, 0, cam_iosched_quanta_sysctl, "I",
            "How many quanta per second do we slice the I/O up into");

        SYSCTL_ADD_INT(ctx, n,
            OID_AUTO, "total_ticks", CTLFLAG_RD,
            &isc->total_ticks, 0,
            "Total number of ticks we've done");
#endif
}

/*
 * Flush outstanding I/O. Consumers of this library don't know all the
 * queues we may keep, so this allows all I/O to be flushed in one
 * convenient call.
 */
void
cam_iosched_flush(struct cam_iosched_softc *isc, struct devstat *stp, int err)
{
        bioq_flush(&isc->bio_queue, stp, err);
        bioq_flush(&isc->trim_queue, stp, err);
#ifdef CAM_IOSCHED_DYNAMIC
        if (do_dynamic_iosched)
                bioq_flush(&isc->write_queue, stp, err);
#endif
}

#ifdef CAM_IOSCHED_DYNAMIC
static struct bio *
cam_iosched_get_write(struct cam_iosched_softc *isc)
{
        struct bio *bp;

        /*
         * We control the write rate by controlling how many requests we send
         * down to the drive at any one time. Fewer requests limits the
         * effects of both starvation when the requests take a while and write
         * amplification when each request is causing more than one write to
         * the NAND media. Limiting the queue depth like this will also limit
         * the write throughput and give and reads that want to compete to
         * compete unfairly.
         */
        bp = bioq_first(&isc->write_queue);
        if (bp == NULL) {
                if (iosched_debug > 3)
                        printf("No writes present in write_queue\n");
                return NULL;
        }

        /*
         * If pending read, prefer that based on current read bias
         * setting.
         */
        if (bioq_first(&isc->bio_queue) && isc->current_read_bias) {
                if (iosched_debug)
                        printf("Reads present and current_read_bias is %d queued writes %d queued reads %d\n", isc->current_read_bias, isc->write_stats.queued, isc->read_stats.queued);
                isc->current_read_bias--;
                return NULL;
        }

        /*
         * See if our current limiter allows this I/O.
         */
        if (cam_iosched_limiter_iop(&isc->write_stats, bp) != 0) {
                if (iosched_debug)
                        printf("Can't write because limiter says no.\n");
                return NULL;
        }

        /*
         * Let's do this: We've passed all the gates and we're a go
         * to schedule the I/O in the SIM.
         */
        isc->current_read_bias = isc->read_bias;
        bioq_remove(&isc->write_queue, bp);
        if (bp->bio_cmd == BIO_WRITE) {
                isc->write_stats.queued--;
                isc->write_stats.total++;
                isc->write_stats.pending++;
        }
        if (iosched_debug > 9)
                printf("HWQ : %p %#x\n", bp, bp->bio_cmd);
        return bp;
}
#endif

/*
 * Put back a trim that you weren't able to actually schedule this time.
 */
void
cam_iosched_put_back_trim(struct cam_iosched_softc *isc, struct bio *bp)
{
        bioq_insert_head(&isc->trim_queue, bp);
#ifdef CAM_IOSCHED_DYNAMIC
        isc->trim_stats.queued++;
        isc->trim_stats.total--;                /* since we put it back, don't double count */
        isc->trim_stats.pending--;
#endif
}

/*
 * gets the next trim from the trim queue.
 *
 * Assumes we're called with the periph lock held.  It removes this
 * trim from the queue and the device must explicitly reinstert it
 * should the need arise.
 */
struct bio *
cam_iosched_next_trim(struct cam_iosched_softc *isc)
{
        struct bio *bp;

        bp  = bioq_first(&isc->trim_queue);
        if (bp == NULL)
                return NULL;
        bioq_remove(&isc->trim_queue, bp);
#ifdef CAM_IOSCHED_DYNAMIC
        isc->trim_stats.queued--;
        isc->trim_stats.total++;
        isc->trim_stats.pending++;
#endif
        return bp;
}

/*
 * gets the an available trim from the trim queue, if there's no trim
 * already pending. It removes this trim from the queue and the device
 * must explicitly reinstert it should the need arise.
 *
 * Assumes we're called with the periph lock held.
 */
struct bio *
cam_iosched_get_trim(struct cam_iosched_softc *isc)
{

        if (!cam_iosched_has_more_trim(isc))
                return NULL;

        return cam_iosched_next_trim(isc);
}

/*
 * Determine what the next bit of work to do is for the periph. The
 * default implementation looks to see if we have trims to do, but no
 * trims outstanding. If so, we do that. Otherwise we see if we have
 * other work. If we do, then we do that. Otherwise why were we called?
 */
struct bio *
cam_iosched_next_bio(struct cam_iosched_softc *isc)
{
        struct bio *bp;

        /*
         * See if we have a trim that can be scheduled. We can only send one
         * at a time down, so this takes that into account.
         *
         * XXX newer TRIM commands are queueable. Revisit this when we
         * implement them.
         */
        if ((bp = cam_iosched_get_trim(isc)) != NULL)
                return bp;

#ifdef CAM_IOSCHED_DYNAMIC
        /*
         * See if we have any pending writes, and room in the queue for them,
         * and if so, those are next.
         */
        if (do_dynamic_iosched) {
                if ((bp = cam_iosched_get_write(isc)) != NULL)
                        return bp;
        }
#endif

        /*
         * next, see if there's other, normal I/O waiting. If so return that.
         */
        if ((bp = bioq_first(&isc->bio_queue)) == NULL)
                return NULL;

#ifdef CAM_IOSCHED_DYNAMIC
        /*
         * For the netflix scheduler, bio_queue is only for reads, so enforce
         * the limits here. Enforce only for reads.
         */
        if (do_dynamic_iosched) {
                if (bp->bio_cmd == BIO_READ &&
                    cam_iosched_limiter_iop(&isc->read_stats, bp) != 0)
                        return NULL;
        }
#endif
        bioq_remove(&isc->bio_queue, bp);
#ifdef CAM_IOSCHED_DYNAMIC
        if (do_dynamic_iosched) {
                if (bp->bio_cmd == BIO_READ) {
                        isc->read_stats.queued--;
                        isc->read_stats.total++;
                        isc->read_stats.pending++;
                } else
                        printf("Found bio_cmd = %#x\n", bp->bio_cmd);
        }
        if (iosched_debug > 9)
                printf("HWQ : %p %#x\n", bp, bp->bio_cmd);
#endif
        return bp;
}
        
/*
 * Driver has been given some work to do by the block layer. Tell the
 * scheduler about it and have it queue the work up. The scheduler module
 * will then return the currently most useful bit of work later, possibly
 * deferring work for various reasons.
 */
void
cam_iosched_queue_work(struct cam_iosched_softc *isc, struct bio *bp)
{

        /*
         * Put all trims on the trim queue sorted, since we know
         * that the collapsing code requires this. Otherwise put
         * the work on the bio queue.
         */
        if (bp->bio_cmd == BIO_DELETE) {
                bioq_disksort(&isc->trim_queue, bp);
#ifdef CAM_IOSCHED_DYNAMIC
                isc->trim_stats.in++;
                isc->trim_stats.queued++;
#endif
        }
#ifdef CAM_IOSCHED_DYNAMIC
        else if (do_dynamic_iosched &&
            (bp->bio_cmd == BIO_WRITE || bp->bio_cmd == BIO_FLUSH)) {
                if (cam_iosched_sort_queue(isc))
                        bioq_disksort(&isc->write_queue, bp);
                else
                        bioq_insert_tail(&isc->write_queue, bp);
                if (iosched_debug > 9)
                        printf("Qw  : %p %#x\n", bp, bp->bio_cmd);
                if (bp->bio_cmd == BIO_WRITE) {
                        isc->write_stats.in++;
                        isc->write_stats.queued++;
                }
        }
#endif
        else {
                if (cam_iosched_sort_queue(isc))
                        bioq_disksort(&isc->bio_queue, bp);
                else
                        bioq_insert_tail(&isc->bio_queue, bp);
#ifdef CAM_IOSCHED_DYNAMIC
                if (iosched_debug > 9)
                        printf("Qr  : %p %#x\n", bp, bp->bio_cmd);
                if (bp->bio_cmd == BIO_READ) {
                        isc->read_stats.in++;
                        isc->read_stats.queued++;
                } else if (bp->bio_cmd == BIO_WRITE) {
                        isc->write_stats.in++;
                        isc->write_stats.queued++;
                }
#endif
        }
}

/* 
 * If we have work, get it scheduled. Called with the periph lock held.
 */
void
cam_iosched_schedule(struct cam_iosched_softc *isc, struct cam_periph *periph)
{

        if (cam_iosched_has_work(isc))
                xpt_schedule(periph, CAM_PRIORITY_NORMAL);
}

/*
 * Complete a trim request
 */
void
cam_iosched_trim_done(struct cam_iosched_softc *isc)
{

        isc->flags &= ~CAM_IOSCHED_FLAG_TRIM_ACTIVE;
}

/*
 * Complete a bio. Called before we release the ccb with xpt_release_ccb so we
 * might use notes in the ccb for statistics.
 */
int
cam_iosched_bio_complete(struct cam_iosched_softc *isc, struct bio *bp,
    union ccb *done_ccb)
{
        int retval = 0;
#ifdef CAM_IOSCHED_DYNAMIC
        if (!do_dynamic_iosched)
                return retval;

        if (iosched_debug > 10)
                printf("done: %p %#x\n", bp, bp->bio_cmd);
        if (bp->bio_cmd == BIO_WRITE) {
                retval = cam_iosched_limiter_iodone(&isc->write_stats, bp);
                isc->write_stats.out++;
                isc->write_stats.pending--;
        } else if (bp->bio_cmd == BIO_READ) {
                retval = cam_iosched_limiter_iodone(&isc->read_stats, bp);
                isc->read_stats.out++;
                isc->read_stats.pending--;
        } else if (bp->bio_cmd == BIO_DELETE) {
                isc->trim_stats.out++;
                isc->trim_stats.pending--;
        } else if (bp->bio_cmd != BIO_FLUSH) {
                if (iosched_debug)
                        printf("Completing command with bio_cmd == %#x\n", bp->bio_cmd);
        }

        if (!(bp->bio_flags & BIO_ERROR))
                cam_iosched_io_metric_update(isc, done_ccb->ccb_h.qos.sim_data,
                    bp->bio_cmd, bp->bio_bcount);
#endif
        return retval;
}

/*
 * Tell the io scheduler that you've pushed a trim down into the sim.
 * xxx better place for this?
 */
void
cam_iosched_submit_trim(struct cam_iosched_softc *isc)
{

        isc->flags |= CAM_IOSCHED_FLAG_TRIM_ACTIVE;
}

/*
 * Change the sorting policy hint for I/O transactions for this device.
 */
void
cam_iosched_set_sort_queue(struct cam_iosched_softc *isc, int val)
{

        isc->sort_io_queue = val;
}

int
cam_iosched_has_work_flags(struct cam_iosched_softc *isc, uint32_t flags)
{
        return isc->flags & flags;
}

void
cam_iosched_set_work_flags(struct cam_iosched_softc *isc, uint32_t flags)
{
        isc->flags |= flags;
}

void
cam_iosched_clr_work_flags(struct cam_iosched_softc *isc, uint32_t flags)
{
        isc->flags &= ~flags;
}

#ifdef CAM_IOSCHED_DYNAMIC
/*
 * After the method presented in Jack Crenshaw's 1998 article "Integer
 * Suqare Roots," reprinted at
 * http://www.embedded.com/electronics-blogs/programmer-s-toolbox/4219659/Integer-Square-Roots
 * and well worth the read. Briefly, we find the power of 4 that's the
 * largest smaller than val. We then check each smaller power of 4 to
 * see if val is still bigger. The right shifts at each step divide
 * the result by 2 which after successive application winds up
 * accumulating the right answer. It could also have been accumulated
 * using a separate root counter, but this code is smaller and faster
 * than that method. This method is also integer size invariant.
 * It returns floor(sqrt((float)val)), or the larget integer less than
 * or equal to the square root.
 */
static uint64_t
isqrt64(uint64_t val)
{
        uint64_t res = 0;
        uint64_t bit = 1ULL << (sizeof(uint64_t) * NBBY - 2);

        /*
         * Find the largest power of 4 smaller than val.
         */
        while (bit > val)
                bit >>= 2;

        /*
         * Accumulate the answer, one bit at a time (we keep moving
         * them over since 2 is the square root of 4 and we test
         * powers of 4). We accumulate where we find the bit, but
         * the successive shifts land the bit in the right place
         * by the end.
         */
        while (bit != 0) {
                if (val >= res + bit) {
                        val -= res + bit;
                        res = (res >> 1) + bit;
                } else
                        res >>= 1;
                bit >>= 2;
        }
        
        return res;
}

/*
 * a and b are 32.32 fixed point stored in a 64-bit word.
 * Let al and bl be the .32 part of a and b.
 * Let ah and bh be the 32 part of a and b.
 * R is the radix and is 1 << 32
 *
 * a * b
 * (ah + al / R) * (bh + bl / R)
 * ah * bh + (al * bh + ah * bl) / R + al * bl / R^2
 *
 * After multiplicaiton, we have to renormalize by multiply by
 * R, so we wind up with
 *      ah * bh * R + al * bh + ah * bl + al * bl / R
 * which turns out to be a very nice way to compute this value
 * so long as ah and bh are < 65536 there's no loss of high bits
 * and the low order bits are below the threshold of caring for
 * this application.
 */
static uint64_t
mul(uint64_t a, uint64_t b)
{
        uint64_t al, ah, bl, bh;
        al = a & 0xffffffff;
        ah = a >> 32;
        bl = b & 0xffffffff;
        bh = b >> 32;
        return ((ah * bh) << 32) + al * bh + ah * bl + ((al * bl) >> 32);
}

static void
cam_iosched_update(struct iop_stats *iop, sbintime_t sim_latency)
{
        sbintime_t y, yy;
        uint64_t var;

        /* 
         * Classic expoentially decaying average with a tiny alpha
         * (2 ^ -alpha_bits). For more info see the NIST statistical
         * handbook.
         *
         * ema_t = y_t * alpha + ema_t-1 * (1 - alpha)
         * alpha = 1 / (1 << alpha_bits)
         *
         * Since alpha is a power of two, we can compute this w/o any mult or
         * division.
         */
        y = sim_latency;
        iop->ema = (y + (iop->ema << alpha_bits) - iop->ema) >> alpha_bits;

        yy = mul(y, y);
        iop->emss = (yy + (iop->emss << alpha_bits) - iop->emss) >> alpha_bits;

        /*
         * s_1 = sum of data
         * s_2 = sum of data * data
         * ema ~ mean (or s_1 / N)
         * emss ~ s_2 / N
         *
         * sd = sqrt((N * s_2 - s_1 ^ 2) / (N * (N - 1)))
         * sd = sqrt((N * s_2 / N * (N - 1)) - (s_1 ^ 2 / (N * (N - 1))))
         *
         * N ~ 2 / alpha - 1
         * alpha < 1 / 16 (typically much less)
         * N > 31 --> N large so N * (N - 1) is approx N * N
         *
         * substituting and rearranging:
         * sd ~ sqrt(s_2 / N - (s_1 / N) ^ 2)
         *    ~ sqrt(emss - ema ^ 2);
         * which is the formula used here to get a decent estimate of sd which
         * we use to detect outliers. Note that when first starting up, it
         * takes a while for emss sum of squares estimator to converge on a
         * good value.  during this time, it can be less than ema^2. We
         * compute a sd of 0 in that case, and ignore outliers.
         */
        var = iop->emss - mul(iop->ema, iop->ema);
        iop->sd = (int64_t)var < 0 ? 0 : isqrt64(var);
}

#ifdef CAM_IOSCHED_DYNAMIC
static void
cam_iosched_io_metric_update(struct cam_iosched_softc *isc,
    sbintime_t sim_latency, int cmd, size_t size)
{
        /* xxx Do we need to scale based on the size of the I/O ? */
        switch (cmd) {
        case BIO_READ:
                cam_iosched_update(&isc->read_stats, sim_latency);
                break;
        case BIO_WRITE:
                cam_iosched_update(&isc->write_stats, sim_latency);
                break;
        case BIO_DELETE:
                cam_iosched_update(&isc->trim_stats, sim_latency);
                break;
        default:
                break;
        }
}
#endif

#ifdef DDB
static int biolen(struct bio_queue_head *bq)
{
        int i = 0;
        struct bio *bp;

        TAILQ_FOREACH(bp, &bq->queue, bio_queue) {
                i++;
        }
        return i;
}

/*
 * Show the internal state of the I/O scheduler.
 */
DB_SHOW_COMMAND(iosched, cam_iosched_db_show)
{
        struct cam_iosched_softc *isc;

        if (!have_addr) {
                db_printf("Need addr\n");
                return;
        }
        isc = (struct cam_iosched_softc *)addr;
        db_printf("pending_reads:     %d\n", isc->read_stats.pending);
        db_printf("min_reads:         %d\n", isc->read_stats.min);
        db_printf("max_reads:         %d\n", isc->read_stats.max);
        db_printf("reads:             %d\n", isc->read_stats.total);
        db_printf("in_reads:          %d\n", isc->read_stats.in);
        db_printf("out_reads:         %d\n", isc->read_stats.out);
        db_printf("queued_reads:      %d\n", isc->read_stats.queued);
        db_printf("Current Q len      %d\n", biolen(&isc->bio_queue));
        db_printf("pending_writes:    %d\n", isc->write_stats.pending);
        db_printf("min_writes:        %d\n", isc->write_stats.min);
        db_printf("max_writes:        %d\n", isc->write_stats.max);
        db_printf("writes:            %d\n", isc->write_stats.total);
        db_printf("in_writes:         %d\n", isc->write_stats.in);
        db_printf("out_writes:        %d\n", isc->write_stats.out);
        db_printf("queued_writes:     %d\n", isc->write_stats.queued);
        db_printf("Current Q len      %d\n", biolen(&isc->write_queue));
        db_printf("pending_trims:     %d\n", isc->trim_stats.pending);
        db_printf("min_trims:         %d\n", isc->trim_stats.min);
        db_printf("max_trims:         %d\n", isc->trim_stats.max);
        db_printf("trims:             %d\n", isc->trim_stats.total);
        db_printf("in_trims:          %d\n", isc->trim_stats.in);
        db_printf("out_trims:         %d\n", isc->trim_stats.out);
        db_printf("queued_trims:      %d\n", isc->trim_stats.queued);
        db_printf("Current Q len      %d\n", biolen(&isc->trim_queue));
        db_printf("read_bias:         %d\n", isc->read_bias);
        db_printf("current_read_bias: %d\n", isc->current_read_bias);
        db_printf("Trim active?       %s\n", 
            (isc->flags & CAM_IOSCHED_FLAG_TRIM_ACTIVE) ? "yes" : "no");
}
#endif
#endif