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1 // Copyright (c) 2013 The Chromium Authors. All rights reserved. | |
2 // Use of this source code is governed by a BSD-style license that can be | |
3 // found in the LICENSE file. | |
4 | |
5 #include "net/quic/congestion_control/cube_root.h" | |
6 | |
7 #include "base/logging.h" | |
8 | |
9 namespace { | |
10 | |
11 // Find last bit in a 64-bit word. | |
12 int FindMostSignificantBit(uint64 x) { | |
13 if (!x) { | |
14 return 0; | |
15 } | |
16 int r = 0; | |
17 if (x & 0xffffffff00000000ull) { | |
18 x >>= 32; | |
19 r += 32; | |
20 } | |
21 if (x & 0xffff0000u) { | |
22 x >>= 16; | |
23 r += 16; | |
24 } | |
25 if (x & 0xff00u) { | |
26 x >>= 8; | |
27 r += 8; | |
28 } | |
29 if (x & 0xf0u) { | |
30 x >>= 4; | |
31 r += 4; | |
32 } | |
33 if (x & 0xcu) { | |
34 x >>= 2; | |
35 r += 2; | |
36 } | |
37 if (x & 0x02u) { | |
38 x >>= 1; | |
39 r++; | |
40 } | |
41 if (x & 0x01u) { | |
42 r++; | |
43 } | |
44 return r; | |
45 } | |
46 | |
47 // 6 bits table [0..63] | |
48 const uint32 cube_root_table[] = { | |
49 0, 54, 54, 54, 118, 118, 118, 118, 123, 129, 134, 138, 143, 147, 151, | |
50 156, 157, 161, 164, 168, 170, 173, 176, 179, 181, 185, 187, 190, 192, 194, | |
51 197, 199, 200, 202, 204, 206, 209, 211, 213, 215, 217, 219, 221, 222, 224, | |
52 225, 227, 229, 231, 232, 234, 236, 237, 239, 240, 242, 244, 245, 246, 248, | |
53 250, 251, 252, 254 | |
54 }; | |
55 } // namespace | |
56 | |
57 namespace net { | |
58 | |
59 // Calculate the cube root using a table lookup followed by one Newton-Raphson | |
60 // iteration. | |
61 uint32 CubeRoot::Root(uint64 a) { | |
62 uint32 msb = FindMostSignificantBit(a); | |
63 DCHECK_LE(msb, 64u); | |
64 | |
65 if (msb < 7) { | |
66 // MSB in our table. | |
67 return ((cube_root_table[a]) + 31) >> 6; | |
68 } | |
69 // MSB 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ... | |
70 // cubic_shift 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, ... | |
71 uint32 cubic_shift = (msb - 4); | |
72 cubic_shift = ((cubic_shift * 342) >> 10); // Div by 3, biased high. | |
73 | |
74 // 4 to 6 bits accuracy depending on MSB. | |
75 uint64 root = | |
76 ((cube_root_table[a >> (cubic_shift * 3)] + 10) << cubic_shift) >> 6; | |
77 | |
78 // Make one Newton-Raphson iteration. | |
79 // Since x has an error (inaccuracy due to the use of fix point) we get a | |
80 // more accurate result by doing x * (x - 1) instead of x * x. | |
81 root = 2 * root + (a / (root * (root - 1))); | |
82 root = ((root * 341) >> 10); // Div by 3, biased low. | |
83 return static_cast<uint32>(root); | |
84 } | |
85 | |
86 } // namespace net | |
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