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