EDF priority tie-breaks..

Instead of tie-breaking by PID (which is a static
priority tie-break), we can tie-break by other
job-level-unique parameters. This is desirable
because tasks are equaly affected by tardiness
since static priority tie-breaks cause tasks
with greater PID values to experience the most
tardiness.

There are four tie-break methods:

1) Lateness.  If two jobs, J_{1,i} and J_{2,j} of
tasks T_1 and T_2, respectively, have equal
deadlines, we favor the job of the task that
had the worst lateness for jobs J_{1,i-1} and
J_{2,j-1}.

Note: Unlike tardiness, lateness may be less than
zero. This occurs when a job finishes before its
deadline.

2) Normalized Lateness.  The same as #1, except
lateness is first normalized by each task's
relative deadline.  This prevents tasks with short
relative deadlines and small execution requirements
from always losing tie-breaks.

3) Hash. The job tuple (PID, Job#) is used to
generate a hash. Hash values are then compared.
A job has ~50% chance of winning a tie-break
with respect to another job.

Note: Emperical testing shows that some jobs
can have +/- ~1.5% advantage in tie-breaks.
Linux's built-in hash function is not totally
a uniform hash.

4) PIDs. PID-based tie-break used in prior
versions of Litmus.

6 files changed, 295 insertions, 10 deletions

diff --git a/include/litmus/fpmath.h b/include/litmus/fpmath.h
new file mode 100644
index 000000000000..04d4bcaeae96
--- /dev/null
+++ b/include/litmus/fpmath.h
@@ -0,0 +1,145 @@
+#ifndef __FP_MATH_H__
+#define __FP_MATH_H__
+
+#ifndef __KERNEL__
+#include <stdint.h>
+#define abs(x) (((x) < 0) ? -(x) : x)
+#endif
+
+// Use 64-bit because we want to track things at the nanosecond scale.
+// This can lead to very large numbers.
+typedef int64_t fpbuf_t;
+typedef struct
+{
+        fpbuf_t val;
+} fp_t;
+
+#define FP_SHIFT 10
+#define ROUND_BIT (FP_SHIFT - 1)
+
+#define _fp(x) ((fp_t) {x})
+
+#ifdef __KERNEL__
+static const fp_t LITMUS_FP_ZERO = {.val = 0};
+static const fp_t LITMUS_FP_ONE = {.val = (1 << FP_SHIFT)};
+#endif
+
+static inline fp_t FP(fpbuf_t x)
+{
+        return _fp(((fpbuf_t) x) << FP_SHIFT);
+}
+
+/* divide two integers to obtain a fixed point value  */
+static inline fp_t _frac(fpbuf_t a, fpbuf_t b)
+{
+        return _fp(FP(a).val / (b));
+}
+
+static inline fpbuf_t _point(fp_t x)
+{
+        return (x.val % (1 << FP_SHIFT));
+
+}
+
+#define fp2str(x) x.val
+/*(x.val >> FP_SHIFT), (x.val % (1 << FP_SHIFT)) */
+#define _FP_  "%ld/1024"
+
+static inline fpbuf_t _floor(fp_t x)
+{
+        return x.val >> FP_SHIFT;
+}
+
+/* FIXME: negative rounding */
+static inline fpbuf_t _round(fp_t x)
+{
+        return _floor(x) + ((x.val >> ROUND_BIT) & 1);
+}
+
+/* multiply two fixed point values */
+static inline fp_t _mul(fp_t a, fp_t b)
+{
+        return _fp((a.val * b.val) >> FP_SHIFT);
+}
+
+static inline fp_t _div(fp_t a, fp_t b)
+{
+#if !defined(__KERNEL__) && !defined(unlikely)
+#define unlikely(x) (x)
+#define DO_UNDEF_UNLIKELY
+#endif
+        /* try not to overflow */
+        if (unlikely(  a.val > (2l << ((sizeof(fpbuf_t)*8) - FP_SHIFT)) ))
+                return _fp((a.val / b.val) << FP_SHIFT);
+        else
+                return _fp((a.val << FP_SHIFT) / b.val);
+#ifdef DO_UNDEF_UNLIKELY
+#undef unlikely
+#undef DO_UNDEF_UNLIKELY
+#endif
+}
+
+static inline fp_t _add(fp_t a, fp_t b)
+{
+        return _fp(a.val + b.val);
+}
+
+static inline fp_t _sub(fp_t a, fp_t b)
+{
+        return _fp(a.val - b.val);
+}
+
+static inline fp_t _neg(fp_t x)
+{
+        return _fp(-x.val);
+}
+
+static inline fp_t _abs(fp_t x)
+{
+        return _fp(abs(x.val));
+}
+
+/* works the same as casting float/double to integer */
+static inline fpbuf_t _fp_to_integer(fp_t x)
+{
+        return _floor(_abs(x)) * ((x.val > 0) ? 1 : -1);
+}
+
+static inline fp_t _integer_to_fp(fpbuf_t x)
+{
+        return _frac(x,1);
+}
+
+static inline int _leq(fp_t a, fp_t b)
+{
+        return a.val <= b.val;
+}
+
+static inline int _geq(fp_t a, fp_t b)
+{
+        return a.val >= b.val;
+}
+
+static inline int _lt(fp_t a, fp_t b)
+{
+        return a.val < b.val;
+}
+
+static inline int _gt(fp_t a, fp_t b)
+{
+        return a.val > b.val;
+}
+
+static inline int _eq(fp_t a, fp_t b)
+{
+        return a.val == b.val;
+}
+
+static inline fp_t _max(fp_t a, fp_t b)
+{
+        if (a.val < b.val)
+                return b;
+        else
+                return a;
+}
+#endif
diff --git a/include/litmus/litmus.h b/include/litmus/litmus.h
index 338245abd6ed..807b7888695a 100644
--- a/include/litmus/litmus.h
+++ b/include/litmus/litmus.h
@@ -63,7 +63,7 @@ void litmus_exit_task(struct task_struct *tsk);
 #define get_exec_time(t)    (tsk_rt(t)->job_params.exec_time)
 #define get_deadline(t)         (tsk_rt(t)->job_params.deadline)
 #define get_release(t)          (tsk_rt(t)->job_params.release)
-
+#define get_lateness(t)         (tsk_rt(t)->job_params.lateness)
 
 #define is_hrt(t)               \
         (tsk_rt(t)->task_params.cls == RT_CLASS_HARD)
diff --git a/include/litmus/rt_param.h b/include/litmus/rt_param.h
index 89ac0dda7d3d..fac939dbd33a 100644
--- a/include/litmus/rt_param.h
+++ b/include/litmus/rt_param.h
@@ -110,6 +110,12 @@ struct rt_job {
         /* How much service has this job received so far? */
         lt_t    exec_time;
 
+        /* By how much did the prior job miss its deadline by?
+         * Value differs from tardiness in that lateness may
+         * be negative (when job finishes before its deadline).
+         */
+        long long       lateness;
+
         /* Which job is this. This is used to let user space
          * specify which job to wait for, which is important if jobs
          * overrun. If we just call sys_sleep_next_period() then we
diff --git a/litmus/Kconfig b/litmus/Kconfig
index 68459d4dca41..48ff3e3c657c 100644
--- a/litmus/Kconfig
+++ b/litmus/Kconfig
@@ -79,6 +79,52 @@ config SCHED_CPU_AFFINITY
 
           Say Yes if unsure.
 
+choice
+        prompt "EDF Tie-Break Behavior"
+        default EDF_TIE_BREAK_LATENESS_NORM
+        help
+          Allows the configuration of tie-breaking behavior when the deadlines
+          of two EDF-scheduled tasks are equal.
+        
+        config EDF_TIE_BREAK_LATENESS
+        bool "Lateness-based Tie Break"
+        help
+          Break ties between to jobs, A and B, based upon the lateness of their
+          prior jobs. The job with the greatest lateness has priority. Note that
+          lateness has a negative value if the prior job finished before its
+          deadline.
+        
+        config EDF_TIE_BREAK_LATENESS_NORM
+        bool "Normalized Lateness-based Tie Break"
+        help
+          Break ties between to jobs, A and B, based upon the lateness, normalized
+          by relative deadline, their prior jobs. The job with the greatest
+          normalized lateness has priority. Note that lateness has a negative value
+          if the prior job finished before its deadline.
+          
+          Normalized lateness tie-breaks are likely desireable over non-normalized
+          tie-breaks if the execution times and/or relative deadlines of tasks in a
+          task set vary greatly.
+        
+        config EDF_TIE_BREAK_HASH
+        bool "Hash-based Tie Breaks"
+        help
+          Break ties between two jobs, A and B, with equal deadlines by using a
+          uniform hash; i.e.: hash(A.pid, A.job_num) < hash(B.pid, B.job_num). Job
+          A has ~50% of winning a given tie-break.
+        
+        config EDF_PID_TIE_BREAK
+        bool "PID-based Tie Breaks"
+        help
+          Break ties based upon OS-assigned process IDs. Use this option if
+          required by algorithm's real-time analysis or per-task response-time
+          jitter must be minimized in overload conditions.
+        
+          NOTES:
+            * This tie-breaking method was default in Litmus 2012.2 and before.
+                
+endchoice
+
 endmenu
 
 menu "Tracing"
diff --git a/litmus/edf_common.c b/litmus/edf_common.c
index 668737f0fbf9..d71a6921dbc1 100644
--- a/litmus/edf_common.c
+++ b/litmus/edf_common.c
@@ -14,6 +14,32 @@
 
 #include <litmus/edf_common.h>
 
+#ifdef CONFIG_EDF_TIE_BREAK_LATENESS_NORM
+#include <litmus/fpmath.h>
+#endif
+
+#ifdef CONFIG_EDF_TIE_BREAK_HASH
+#include <linux/hash.h>
+static inline long edf_hash(struct task_struct *t)
+{
+        /* pid is 32 bits, so normally we would shove that into the
+         * upper 32-bits and and put the job number in the bottom
+         * and hash the 64-bit number with hash_64(). Sadly,
+         * in testing, hash_64() doesn't distribute keys were the
+         * upper bits are close together (as would be the case with
+         * pids) and job numbers are equal (as would be the case with
+         * synchronous task sets with all relative deadlines equal).
+         *
+         * A 2006 Linux patch proposed the following solution
+         * (but for some reason it wasn't accepted...).
+         *
+         * At least this workaround works for 32-bit systems as well.
+         */
+        return hash_32(hash_32((u32)tsk_rt(t)->job_params.job_no, 32) ^ t->pid, 32);
+}
+#endif
+
+
 /* edf_higher_prio -  returns true if first has a higher EDF priority
  *                    than second. Deadline ties are broken by PID.
  *
@@ -76,19 +102,73 @@ int edf_higher_prio(struct task_struct* first,
                 return 1;
         }
         else if (get_deadline(first_task) == get_deadline(second_task)) {
-                /* Need to tie break */
-
-                /* Tie break by pid */
-                if (first_task->pid < second_task->pid) {
+                /* Need to tie break. All methods must set pid_break to 0/1 if
+                 * first_task does not have priority over second_task.
+                 */
+                int pid_break;
+                
+                
+#if defined(CONFIG_EDF_TIE_BREAK_LATENESS)
+                /* Tie break by lateness. Jobs with greater lateness get
+                 * priority. This should spread tardiness across all tasks,
+                 * especially in task sets where all tasks have the same
+                 * period and relative deadlines.
+                 */
+                if (get_lateness(first_task) > get_lateness(second_task)) {
+                        return 1;
+                }
+                pid_break = (get_lateness(first_task) == get_lateness(second_task));
+                
+                
+#elif defined(CONFIG_EDF_TIE_BREAK_LATENESS_NORM)
+                /* Tie break by lateness, normalized by relative deadline. Jobs with
+                 * greater normalized lateness get priority.
+                 *
+                 * Note: Considered using the algebraically equivalent
+                 *      lateness(first)*relative_deadline(second) >
+                                        lateness(second)*relative_deadline(first)
+                 * to avoid fixed-point math, but values are prone to overflow if inputs
+                 * are on the order of several seconds, even in 64-bit.
+                 */
+                fp_t fnorm = _frac(get_lateness(first_task),
+                                                   get_rt_relative_deadline(first_task));
+                fp_t snorm = _frac(get_lateness(second_task),
+                                                   get_rt_relative_deadline(second_task));
+                if (_gt(fnorm, snorm)) {
+                        return 1;
+                }
+                pid_break = _eq(fnorm, snorm);
+                
+                
+#elif defined(CONFIG_EDF_TIE_BREAK_HASH)
+                /* Tie break by comparing hashs of (pid, job#) tuple.  There should be
+                 * a 50% chance that first_task has a higher priority than second_task.
+                 */
+                long fhash = edf_hash(first_task);
+                long shash = edf_hash(second_task);
+                if (fhash < shash) {
                         return 1;
                 }
-                else if (first_task->pid == second_task->pid) {
-                        /* If the PIDs are the same then the task with the
-                         * inherited priority wins.
-                         */
-                        if (!second_task->rt_param.inh_task) {
+                pid_break = (fhash == shash);
+#else
+                
+                
+                /* CONFIG_EDF_PID_TIE_BREAK */
+                pid_break = 1; // fall through to tie-break by pid;
+#endif
+                /* Tie break by pid */
+                if(pid_break) {
+                        if (first_task->pid < second_task->pid) {
                                 return 1;
                         }
+                        else if (first_task->pid == second_task->pid) {
+                                /* If the PIDs are the same then the task with the
+                                 * inherited priority wins.
+                                 */
+                                if (!second_task->rt_param.inh_task) {
+                                        return 1;
+                                }
+                        }
                 }
         }
         return 0; /* fall-through. prio(second_task) > prio(first_task) */
diff --git a/litmus/jobs.c b/litmus/jobs.c
index bc8246572e54..fb093c03d53d 100644
--- a/litmus/jobs.c
+++ b/litmus/jobs.c
@@ -23,6 +23,14 @@ static inline void setup_release(struct task_struct *t, lt_t release)
 void prepare_for_next_period(struct task_struct *t)
 {
         BUG_ON(!t);
+
+        /* Record lateness before we set up the next job's
+         * release and deadline. Lateness may be negative.
+         */
+        t->rt_param.job_params.lateness =
+                (long long)litmus_clock() - 
+                (long long)t->rt_param.job_params.deadline;
+
         setup_release(t, get_release(t) + get_rt_period(t));
 }