/* Copyright 2013 Google Inc. All Rights Reserved.
Distributed under MIT license.
See file LICENSE for detail or copy at https://opensource.org/licenses/MIT
*/
// 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 "./types.h"
namespace brotli {
static inline uint32_t Log2FloorNonZero(size_t n) {
#ifdef __GNUC__
return 31u ^ static_cast<uint32_t>(__builtin_clz(static_cast<uint32_t>(n)));
#else
uint32_t result = 0;
while (n >>= 1) result++;
return result;
#endif
}
// 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(size_t v) {
if (v < 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_
