codel: use Newton method instead of sqrt() and divides

As Van pointed out, interval/sqrt(count) can be implemented using
multiplies only.

http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots

This patch implements the Newton method and reciprocal divide.

Total cost is 15 cycles instead of 120 on my Corei5 machine (64bit
kernel).

There is a small 'error' for count values < 5, but we don't really care.

I reuse a hole in struct codel_vars :
 - pack the dropping boolean into one bit
 - use 31bit to store the reciprocal value of sqrt(count).

Suggested-by: Van Jacobson <van@pollere.net>
Signed-off-by: Eric Dumazet <edumazet@google.com>
Cc: Dave Taht <dave.taht@bufferbloat.net>
Cc: Kathleen Nichols <nichols@pollere.com>
Cc: Tom Herbert <therbert@google.com>
Cc: Matt Mathis <mattmathis@google.com>
Cc: Yuchung Cheng <ycheng@google.com>
Cc: Nandita Dukkipati <nanditad@google.com>
Cc: Stephen Hemminger <shemminger@vyatta.com>
Signed-off-by: David S. Miller <davem@davemloft.net>

1 files changed, 37 insertions, 31 deletions

diff --git a/include/net/codel.h b/include/net/codel.h
index bce2cefa8c94..bd8747c3ba69 100644
--- a/include/net/codel.h
+++ b/include/net/codel.h
@@ -46,6 +46,7 @@
 #include <linux/skbuff.h>
 #include <net/pkt_sched.h>
 #include <net/inet_ecn.h>
+#include <linux/reciprocal_div.h>
 
 /* Controlling Queue Delay (CoDel) algorithm
  * =========================================
@@ -123,6 +124,7 @@ struct codel_params {
  *                      entered dropping state
  * @lastcount:          count at entry to dropping state
  * @dropping:           set to true if in dropping state
+ * @rec_inv_sqrt:       reciprocal value of sqrt(count) >> 1
  * @first_above_time:   when we went (or will go) continuously above target
  *                      for interval
  * @drop_next:          time to drop next packet, or when we dropped last
@@ -131,7 +133,8 @@ struct codel_params {
 struct codel_vars {
         u32             count;
         u32             lastcount;
-        bool            dropping;
+        bool            dropping:1;
+        u32             rec_inv_sqrt:31;
         codel_time_t    first_above_time;
         codel_time_t    drop_next;
         codel_time_t    ldelay;
@@ -158,11 +161,7 @@ static void codel_params_init(struct codel_params *params)
 
 static void codel_vars_init(struct codel_vars *vars)
 {
-        vars->drop_next = 0;
-        vars->first_above_time = 0;
-        vars->dropping = false; /* exit dropping state */
-        vars->count = 0;
-        vars->lastcount = 0;
+        memset(vars, 0, sizeof(*vars));
 }
 
 static void codel_stats_init(struct codel_stats *stats)
@@ -170,38 +169,37 @@ static void codel_stats_init(struct codel_stats *stats)
         stats->maxpacket = 256;
 }
 
-/* return interval/sqrt(x) with good precision
- * relies on int_sqrt(unsigned long x) kernel implementation
+/*
+ * http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots
+ * new_invsqrt = (invsqrt / 2) * (3 - count * invsqrt^2)
+ *
+ * Here, invsqrt is a fixed point number (< 1.0), 31bit mantissa)
  */
-static u32 codel_inv_sqrt(u32 _interval, u32 _x)
+static void codel_Newton_step(struct codel_vars *vars)
 {
-        u64 interval = _interval;
-        unsigned long x = _x;
+        u32 invsqrt = vars->rec_inv_sqrt;
+        u32 invsqrt2 = ((u64)invsqrt * invsqrt) >> 31;
+        u64 val = (3LL << 31) - ((u64)vars->count * invsqrt2);
 
-        /* Scale operands for max precision */
-
-#if BITS_PER_LONG == 64
-        x <<= 32; /* On 64bit arches, we can prescale x by 32bits */
-        interval <<= 16;
-#endif
+        val = (val * invsqrt) >> 32;
 
-        while (x < (1UL << (BITS_PER_LONG - 2))) {
-                x <<= 2;
-                interval <<= 1;
-        }
-        do_div(interval, int_sqrt(x));
-        return (u32)interval;
+        vars->rec_inv_sqrt = val;
 }
 
+/*
+ * CoDel control_law is t + interval/sqrt(count)
+ * We maintain in rec_inv_sqrt the reciprocal value of sqrt(count) to avoid
+ * both sqrt() and divide operation.
+ */
 static codel_time_t codel_control_law(codel_time_t t,
                                       codel_time_t interval,
-                                      u32 count)
+                                      u32 rec_inv_sqrt)
 {
-        return t + codel_inv_sqrt(interval, count);
+        return t + reciprocal_divide(interval, rec_inv_sqrt << 1);
 }
 
 
-static bool codel_should_drop(struct sk_buff *skb,
+static bool codel_should_drop(const struct sk_buff *skb,
                               unsigned int *backlog,
                               struct codel_vars *vars,
                               struct codel_params *params,
@@ -274,14 +272,16 @@ static struct sk_buff *codel_dequeue(struct Qdisc *sch,
                          */
                         while (vars->dropping &&
                                codel_time_after_eq(now, vars->drop_next)) {
-                                if (++vars->count == 0) /* avoid zero divides */
-                                        vars->count = ~0U;
+                                vars->count++; /* dont care of possible wrap
+                                                * since there is no more divide
+                                                */
+                                codel_Newton_step(vars);
                                 if (params->ecn && INET_ECN_set_ce(skb)) {
                                         stats->ecn_mark++;
                                         vars->drop_next =
                                                 codel_control_law(vars->drop_next,
                                                                   params->interval,
-                                                                  vars->count);
+                                                                  vars->rec_inv_sqrt);
                                         goto end;
                                 }
                                 qdisc_drop(skb, sch);
@@ -296,7 +296,7 @@ static struct sk_buff *codel_dequeue(struct Qdisc *sch,
                                         vars->drop_next =
                                                 codel_control_law(vars->drop_next,
                                                                   params->interval,
-                                                                  vars->count);
+                                                                  vars->rec_inv_sqrt);
                                 }
                         }
                 }
@@ -319,12 +319,18 @@ static struct sk_buff *codel_dequeue(struct Qdisc *sch,
                 if (codel_time_before(now - vars->drop_next,
                                       16 * params->interval)) {
                         vars->count = (vars->count - vars->lastcount) | 1;
+                        /* we dont care if rec_inv_sqrt approximation
+                         * is not very precise :
+                         * Next Newton steps will correct it quadratically.
+                         */
+                        codel_Newton_step(vars);
                 } else {
                         vars->count = 1;
+                        vars->rec_inv_sqrt = 0x7fffffff;
                 }
                 vars->lastcount = vars->count;
                 vars->drop_next = codel_control_law(now, params->interval,
-                                                    vars->count);
+                                                    vars->rec_inv_sqrt);
         }
 end:
         return skb;