Replace cube root algorithim with a faster version using Newton-Raphson.
Surprisingly, doing the scaled div64_64 is faster than a true 64 bit
division on 64 bit CPU's.
Signed-off-by: Stephen Hemminger <[EMAIL PROTECTED]>
--- net-2.6.16.orig/net/ipv4/tcp_cubic.c
+++ net-2.6.16/net/ipv4/tcp_cubic.c
@@ -52,6 +52,7 @@ MODULE_PARM_DESC(bic_scale, "scale (scal
module_param(tcp_friendliness, int, 0644);
MODULE_PARM_DESC(tcp_friendliness, "turn on/off tcp friendliness");
+#include <asm/div64.h>
/* BIC TCP Parameters */
struct bictcp {
@@ -93,67 +94,51 @@ static void bictcp_init(struct sock *sk)
tcp_sk(sk)->snd_ssthresh = initial_ssthresh;
}
-/* 65536 times the cubic root */
-static const u64 cubic_table[8]
- = {0, 65536, 82570, 94519, 104030, 112063, 119087, 125367};
-
-/*
- * calculate the cubic root of x
- * the basic idea is that x can be expressed as i*8^j
- * so cubic_root(x) = cubic_root(i)*2^j
- * in the following code, x is i, and y is 2^j
- * because of integer calculation, there are errors in calculation
- * so finally use binary search to find out the exact solution
- */
-static u32 cubic_root(u64 x)
+/* 64bit divisor, dividend and result. dynamic precision */
+static inline u_int64_t div64_64(u_int64_t dividend, u_int64_t divisor)
{
- u64 y, app, target, start, end, mid, start_diff, end_diff;
+ u_int32_t d = divisor;
- if (x == 0)
- return 0;
+ if (divisor > 0xffffffffULL) {
+ unsigned int shift = fls(divisor >> 32);
- target = x;
+ d = divisor >> shift;
+ dividend >>= shift;
+ }
- /* first estimate lower and upper bound */
- y = 1;
- while (x >= 8){
- x = (x >> 3);
- y = (y << 1);
- }
- start = (y*cubic_table[x])>>16;
- if (x==7)
- end = (y<<1);
- else
- end = (y*cubic_table[x+1]+65535)>>16;
+ /* avoid 64 bit division if possible */
+ if (dividend >> 32)
+ do_div(dividend, d);
+ else
+ dividend = (uint32_t) dividend / d;
- /* binary search for more accurate one */
- while (start < end-1) {
- mid = (start+end) >> 1;
- app = mid*mid*mid;
- if (app < target)
- start = mid;
- else if (app > target)
- end = mid;
- else
- return mid;
- }
+ return dividend;
+}
- /* find the most accurate one from start and end */
- app = start*start*start;
- if (app < target)
- start_diff = target - app;
- else
- start_diff = app - target;
- app = end*end*end;
- if (app < target)
- end_diff = target - app;
- else
- end_diff = app - target;
+/*
+ * calculate the cubic root of x using Newton-Raphson
+ */
+static u32 cubic_root(u64 a)
+{
+ u32 x, x1;
- if (start_diff < end_diff)
- return (u32)start;
- else
- return (u32)end;
+ /* Initial estimate is based on:
+ * cbrt(x) = exp(log(x) / 3)
+ */
+ x = 1u << (fls64(a)/3);
+
+ /*
+ * Iteration based on:
+ * 2
+ * x = ( 2 * x + a / x ) / 3
+ * k+1 k k
+ */
+ do {
+ x1 = x;
+ x = (2 * x + (uint32_t) div64_64(a, x*x)) / 3;
+ } while (abs(x1 - x) > 1);
+
+ return x;
}
/*
--
Stephen Hemminger <[EMAIL PROTECTED]>
OSDL http://developer.osdl.org/~shemminger
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