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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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