enc/fast_log.h

// Copyright 2013 Google Inc. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Utilities for fast computation of logarithms.

#ifndef BROTLI_ENC_FAST_LOG_H_
#define BROTLI_ENC_FAST_LOG_H_

#include <assert.h>
#include <math.h>
#include <stdint.h>

namespace brotli {

// Return floor(log2(n)) for positive integer n.  Returns -1 iff n == 0.
inline int Log2Floor(uint32_t n) {
#if defined(__clang__) ||                       \
  (defined(__GNUC__) &&                                         \
   ((__GNUC__ == 3 && __GNUC_MINOR__ >= 4) || __GNUC__ >= 4))
  return n == 0 ? -1 : 31 ^ __builtin_clz(n);
#else
  if (n == 0)
    return -1;
  int log = 0;
  uint32_t value = n;
  for (int i = 4; i >= 0; --i) {
    int shift = (1 << i);
    uint32_t x = value >> shift;
    if (x != 0) {
      value = x;
      log += shift;
    }
  }
  assert(value == 1);
  return log;
#endif
}

static inline int Log2FloorNonZero(uint32_t n) {
#ifdef __GNUC__
  return 31 ^ __builtin_clz(n);
#else
  unsigned int result = 0;
  while (n >>= 1) result++;
  return result;
#endif
}

// Return ceiling(log2(n)) for positive integer n.  Returns -1 iff n == 0.
inline int Log2Ceiling(uint32_t n) {
  int floor = Log2Floor(n);
  if (n == (n &~ (n - 1)))              // zero or a power of two
    return floor;
  else
    return floor + 1;
}

// A lookup table for small values of log2(int) to be used in entropy
// computation.
//
// ", ".join(["%.16ff" % x for x in [0.0]+[log2(x) for x in range(1, 256)]])
static const float kLog2Table[] = {
  0.0000000000000000f, 0.0000000000000000f, 1.0000000000000000f,
  1.5849625007211563f, 2.0000000000000000f, 2.3219280948873622f,
  2.5849625007211561f, 2.8073549220576042f, 3.0000000000000000f,
  3.1699250014423126f, 3.3219280948873626f, 3.4594316186372978f,
  3.5849625007211565f, 3.7004397181410922f, 3.8073549220576037f,
  3.9068905956085187f, 4.0000000000000000f, 4.0874628412503400f,
  4.1699250014423122f, 4.2479275134435852f, 4.3219280948873626f,
  4.3923174227787607f, 4.4594316186372973f, 4.5235619560570131f,
  4.5849625007211570f, 4.6438561897747244f, 4.7004397181410926f,
  4.7548875021634691f, 4.8073549220576037f, 4.8579809951275728f,
  4.9068905956085187f, 4.9541963103868758f, 5.0000000000000000f,
  5.0443941193584534f, 5.0874628412503400f, 5.1292830169449664f,
  5.1699250014423122f, 5.2094533656289501f, 5.2479275134435852f,
  5.2854022188622487f, 5.3219280948873626f, 5.3575520046180838f,
  5.3923174227787607f, 5.4262647547020979f, 5.4594316186372973f,
  5.4918530963296748f, 5.5235619560570131f, 5.5545888516776376f,
  5.5849625007211570f, 5.6147098441152083f, 5.6438561897747244f,
  5.6724253419714961f, 5.7004397181410926f, 5.7279204545631996f,
  5.7548875021634691f, 5.7813597135246599f, 5.8073549220576046f,
  5.8328900141647422f, 5.8579809951275719f, 5.8826430493618416f,
  5.9068905956085187f, 5.9307373375628867f, 5.9541963103868758f,
  5.9772799234999168f, 6.0000000000000000f, 6.0223678130284544f,
  6.0443941193584534f, 6.0660891904577721f, 6.0874628412503400f,
  6.1085244567781700f, 6.1292830169449672f, 6.1497471195046822f,
  6.1699250014423122f, 6.1898245588800176f, 6.2094533656289510f,
  6.2288186904958804f, 6.2479275134435861f, 6.2667865406949019f,
  6.2854022188622487f, 6.3037807481771031f, 6.3219280948873617f,
  6.3398500028846252f, 6.3575520046180847f, 6.3750394313469254f,
  6.3923174227787598f, 6.4093909361377026f, 6.4262647547020979f,
  6.4429434958487288f, 6.4594316186372982f, 6.4757334309663976f,
  6.4918530963296748f, 6.5077946401986964f, 6.5235619560570131f,
  6.5391588111080319f, 6.5545888516776376f, 6.5698556083309478f,
  6.5849625007211561f, 6.5999128421871278f, 6.6147098441152092f,
  6.6293566200796095f, 6.6438561897747253f, 6.6582114827517955f,
  6.6724253419714952f, 6.6865005271832185f, 6.7004397181410917f,
  6.7142455176661224f, 6.7279204545631988f, 6.7414669864011465f,
  6.7548875021634691f, 6.7681843247769260f, 6.7813597135246599f,
  6.7944158663501062f, 6.8073549220576037f, 6.8201789624151887f,
  6.8328900141647422f, 6.8454900509443757f, 6.8579809951275719f,
  6.8703647195834048f, 6.8826430493618416f, 6.8948177633079437f,
  6.9068905956085187f, 6.9188632372745955f, 6.9307373375628867f,
  6.9425145053392399f, 6.9541963103868758f, 6.9657842846620879f,
  6.9772799234999168f, 6.9886846867721664f, 7.0000000000000000f,
  7.0112272554232540f, 7.0223678130284544f, 7.0334230015374501f,
  7.0443941193584534f, 7.0552824355011898f, 7.0660891904577721f,
  7.0768155970508317f, 7.0874628412503400f, 7.0980320829605272f,
  7.1085244567781700f, 7.1189410727235076f, 7.1292830169449664f,
  7.1395513523987937f, 7.1497471195046822f, 7.1598713367783891f,
  7.1699250014423130f, 7.1799090900149345f, 7.1898245588800176f,
  7.1996723448363644f, 7.2094533656289492f, 7.2191685204621621f,
  7.2288186904958804f, 7.2384047393250794f, 7.2479275134435861f,
  7.2573878426926521f, 7.2667865406949019f, 7.2761244052742384f,
  7.2854022188622487f, 7.2946207488916270f, 7.3037807481771031f,
  7.3128829552843557f, 7.3219280948873617f, 7.3309168781146177f,
  7.3398500028846243f, 7.3487281542310781f, 7.3575520046180847f,
  7.3663222142458151f, 7.3750394313469254f, 7.3837042924740528f,
  7.3923174227787607f, 7.4008794362821844f, 7.4093909361377026f,
  7.4178525148858991f, 7.4262647547020979f, 7.4346282276367255f,
  7.4429434958487288f, 7.4512111118323299f, 7.4594316186372973f,
  7.4676055500829976f, 7.4757334309663976f, 7.4838157772642564f,
  7.4918530963296748f, 7.4998458870832057f, 7.5077946401986964f,
  7.5156998382840436f, 7.5235619560570131f, 7.5313814605163119f,
  7.5391588111080319f, 7.5468944598876373f, 7.5545888516776376f,
  7.5622424242210728f, 7.5698556083309478f, 7.5774288280357487f,
  7.5849625007211561f, 7.5924570372680806f, 7.5999128421871278f,
  7.6073303137496113f, 7.6147098441152075f, 7.6220518194563764f,
  7.6293566200796095f, 7.6366246205436488f, 7.6438561897747244f,
  7.6510516911789290f, 7.6582114827517955f, 7.6653359171851765f,
  7.6724253419714952f, 7.6794800995054464f, 7.6865005271832185f,
  7.6934869574993252f, 7.7004397181410926f, 7.7073591320808825f,
  7.7142455176661224f, 7.7210991887071856f, 7.7279204545631996f,
  7.7347096202258392f, 7.7414669864011465f, 7.7481928495894596f,
  7.7548875021634691f, 7.7615512324444795f, 7.7681843247769260f,
  7.7747870596011737f, 7.7813597135246608f, 7.7879025593914317f,
  7.7944158663501062f, 7.8008998999203047f, 7.8073549220576037f,
  7.8137811912170374f, 7.8201789624151887f, 7.8265484872909159f,
  7.8328900141647422f, 7.8392037880969445f, 7.8454900509443757f,
  7.8517490414160571f, 7.8579809951275719f, 7.8641861446542798f,
  7.8703647195834048f, 7.8765169465650002f, 7.8826430493618425f,
  7.8887432488982601f, 7.8948177633079446f, 7.9008668079807496f,
  7.9068905956085187f, 7.9128893362299619f, 7.9188632372745955f,
  7.9248125036057813f, 7.9307373375628867f, 7.9366379390025719f,
  7.9425145053392399f, 7.9483672315846778f, 7.9541963103868758f,
  7.9600019320680806f, 7.9657842846620870f, 7.9715435539507720f,
  7.9772799234999168f, 7.9829935746943104f, 7.9886846867721664f,
  7.9943534368588578f
};

// Faster logarithm for small integers, with the property of log2(0) == 0.
static inline double FastLog2(int v) {
  if (v < (int)(sizeof(kLog2Table) / sizeof(kLog2Table[0]))) {
    return kLog2Table[v];
  }
#if defined(_MSC_VER) && _MSC_VER <= 1600
  // Visual Studio 2010 does not have the log2() function defined, so we use
  // log() and a multiplication instead.
  static const double kLog2Inv = 1.4426950408889634f;
  return log(static_cast<double>(v)) * kLog2Inv;
#else
  return log2(static_cast<double>(v));
#endif
}

}  // namespace brotli

#endif  // BROTLI_ENC_FAST_LOG_H_