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[TCP]: cubic optimization 

Use willy's work in optimizing cube root by having table for small values.

Signed-off-by: Stephen Hemminger <shemminger@linux-foundation.org>
Signed-off-by: David S. Miller <davem@davemloft.net>
This commit is contained in:
Stephen Hemminger 2007-03-22 12:10:58 -07:00 committed by David S. Miller
parent 22b9a0a3a4
commit 7e58886b45
1 changed files with 39 additions and 11 deletions
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50
net/ipv4/tcp_cubic.c
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@ -91,23 +91,51 @@ static void bictcp_init(struct sock *sk)
tcp_sk(sk)->snd_ssthresh = initial_ssthresh;
}
/*
* calculate the cubic root of x using Newton-Raphson
/* calculate the cubic root of x using a table lookup followed by one
* Newton-Raphson iteration.
* Avg err ~= 0.195%
*/
static u32 cubic_root(u64 a)
{
u32 x;
/* Initial estimate is based on:
* cbrt(x) = exp(log(x) / 3)
u32 x, b, shift;
/*
* cbrt(x) MSB values for x MSB values in [0..63].
* Precomputed then refined by hand - Willy Tarreau
*
* For x in [0..63],
* v = cbrt(x << 18) - 1
* cbrt(x) = (v[x] + 10) >> 6
*/
x = 1u << (fls64(a)/3);
static const u8 v[] = {
/* 0x00 */ 0, 54, 54, 54, 118, 118, 118, 118,
/* 0x08 */ 123, 129, 134, 138, 143, 147, 151, 156,
/* 0x10 */ 157, 161, 164, 168, 170, 173, 176, 179,
/* 0x18 */ 181, 185, 187, 190, 192, 194, 197, 199,
/* 0x20 */ 200, 202, 204, 206, 209, 211, 213, 215,
/* 0x28 */ 217, 219, 221, 222, 224, 225, 227, 229,
/* 0x30 */ 231, 232, 234, 236, 237, 239, 240, 242,
/* 0x38 */ 244, 245, 246, 248, 250, 251, 252, 254,
};
/* converges to 32 bits in 3 iterations */
x = (2 * x + (u32)div64_64(a, (u64)x*(u64)x)) / 3;
x = (2 * x + (u32)div64_64(a, (u64)x*(u64)x)) / 3;
x = (2 * x + (u32)div64_64(a, (u64)x*(u64)x)) / 3;
b = fls64(a);
if (b < 7) {
/* a in [0..63] */
return ((u32)v[(u32)a] + 35) >> 6;
}
b = ((b * 84) >> 8) - 1;
shift = (a >> (b * 3));
x = ((u32)(((u32)v[shift] + 10) << b)) >> 6;
/*
* Newton-Raphson iteration
* 2
* x = ( 2 * x + a / x ) / 3
* k+1 k k
*/
x = (2 * x + (u32)div64_64(a, (u64)x * (u64)(x - 1)));
x = ((x * 341) >> 10);
return x;
}