net/quic/congestion_control/cube_root.cc

   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[static_cast<uint32>(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   uint32 down_shifted_to_6bit = (a >> (cubic_shift * 3));
  76   uint64 root = ((cube_root_table[down_shifted_to_6bit] + 10) << cubic_shift)
  77       >> 6;
  78
  79   // Make one Newton-Raphson iteration.
  80   // Since x has an error (inaccuracy due to the use of fix point) we get a
  81   // more accurate result by doing x * (x - 1) instead of x * x.
  82   root = 2 * root + (a / (root * (root - 1)));
  83   root = ((root * 341) >> 10);  // Div by 3, biased low.
  84   return static_cast<uint32>(root);
  85 }
  86
  87 }  // namespace net