[TCP]: TCP Compound quad root function

The original code did a 64 bit divide directly, which won't work on
32 bit platforms.  Rather than doing a 64 bit square root twice,
just implement a 4th root function in one pass using Newton's method.

Signed-off-by: Stephen Hemminger <shemminger@osdl.org>
Signed-off-by: David S. Miller <davem@davemloft.net>

diff --git a/net/ipv4/tcp_compound.c b/net/ipv4/tcp_compound.c
index 8c1ebfb7659e257be5b56b8b099a10657729bbe0..ec68cb8081c16cebc9a231130133c31355f906dd 100644 (file)
--- a/net/ipv4/tcp_compound.c
+++ b/net/ipv4/tcp_compound.c
@@ -52,8 +52,6 @@
 
 #define TCP_COMPOUND_ALPHA          3U
 #define TCP_COMPOUND_BETA           1U
-#define TCP_COMPOUND_KAPPA_POW      3
-#define TCP_COMPOUND_KAPPA_NSQRT    2
 #define TCP_COMPOUND_GAMMA         30
 #define TCP_COMPOUND_ZETA           1
 
@@ -156,6 +154,58 @@ static void tcp_compound_state(struct sock *sk, u8 ca_state)
                vegas_disable(sk);
 }
 
+
+/* 64bit divisor, dividend and result. dynamic precision */
+static inline u64 div64_64(u64 dividend, u64 divisor)
+{
+       u32 d = divisor;
+
+       if (divisor > 0xffffffffULL) {
+               unsigned int shift = fls(divisor >> 32);
+
+               d = divisor >> shift;
+               dividend >>= shift;
+       }
+
+       /* avoid 64 bit division if possible */
+       if (dividend >> 32)
+               do_div(dividend, d);
+       else
+               dividend = (u32) dividend / d;
+
+       return dividend;
+}
+
+/* calculate the quartic root of "a" using Newton-Raphson */
+static u32 qroot(u64 a)
+{
+       u32 x, x1;
+
+       /* Initial estimate is based on:
+        * qrt(x) = exp(log(x) / 4)
+        */
+       x = 1u << (fls64(a) >> 2);
+
+       /*
+        * Iteration based on:
+        *                         3
+        * x    = ( 3 * x  +  a / x  ) / 4
+        *  k+1          k         k
+        */
+       do {
+               u64 x3 = x;
+
+               x1 = x;
+               x3 *= x;
+               x3 *= x;
+
+               x = (3 * x + (u32) div64_64(a, x3)) / 4;
+       } while (abs(x1 - x) > 1);
+
+       return x;
+}
+
+
 /*
  * If the connection is idle and we are restarting,
  * then we don't want to do any Vegas calculations
@@ -304,29 +354,21 @@ static void tcp_compound_cong_avoid(struct sock *sk, u32 ack,
                        dwnd = vegas->dwnd;
 
                        if (diff < (TCP_COMPOUND_GAMMA << V_PARAM_SHIFT)) {
-                               u32 i, j, x, x2;
                                u64 v;
-
-                               v = 1;
-
-                               for (i = 0; i < TCP_COMPOUND_KAPPA_POW; i++)
-                                       v *= old_wnd;
-
-                               for (i = 0; i < TCP_COMPOUND_KAPPA_NSQRT; i++) {
-                                       x = 1;
-                                       for (j = 0; j < 200; j++) {
-                                               x2 = (x + v / x) / 2;
-
-                                               if (x2 == x || !x2)
-                                                       break;
-
-                                               x = x2;
-                                       }
-                                       v = x;
-                               }
-
-                               x = (u32) v >> TCP_COMPOUND_ALPHA;
-
+                               u32 x;
+
+                               /*
+                                * The TCP Compound paper describes the choice
+                                * of "k" determines the agressiveness,
+                                * ie. slope of the response function.
+                                *
+                                * For same value as HSTCP would be 0.8
+                                * but for computaional reasons, both the
+                                * original authors and this implementation
+                                * use 0.75.
+                                */
+                               v = old_wnd;
+                               x = qroot(v * v * v) >> TCP_COMPOUND_ALPHA;
                                if (x > 1)
                                        dwnd = x - 1;
                                else