Binary logarithm c++
The goal here is to find how many bits you need to store a range of values. That means that the solution is itself likely a template, or some kind of compile-time expression. What we need is a general case, for xand an explicit specialization for the base case, binary logarithm c++, say, x is 1. Well, whatever, this solution works perfectly, and computes the desired values: The above templates can be replaced by a much friendlier function:.
This binary logarithm c++ was posted on Tuesday, March 22nd, at You can follow any responses to this entry through the RSS 2. You can leave a responseor trackback from binary logarithm c++ own site. I may have adjusted it so that 1 and 0 take 1 bit log2 0 would be, according to the strict definition of log, -infinity, which is infintely inconvenient. You are commenting using your WordPress. You are commenting using your Twitter account.
You are binary logarithm c++ using your Facebook account. Notify me of new comments via email. Harder, Better, Faster, Stronger Explorations in better, faster, stronger code. The above templates can be replaced by a much friendlier function: Reddit Twitter More Facebook Email. August 31, at 7: August 31, at 8: Leave a Reply Cancel reply Enter your comment here Fill in your details below or click an icon to log in: Email required Address never made binary logarithm c++.
My pixel font pack is here! Enjoying my copy of brilliant new book by JoyceTyldesley in my own edgy kind of way. Post was not sent - check your email addresses! Sorry, your blog cannot share posts by email.
That is, for any real number x. The binary logarithm is the logarithm to the base 2. The binary logarithm function is the inverse function of the power of two function.
Historically, the first application of binary logarithms was in music theoryby Leonhard Euler: Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral systemor the number of bits needed to encode a message in information theory.
In computer sciencethey count the number of steps needed for binary search and related algorithms. Other areas in which the binary logarithm is frequently used include binary logarithm c++bioinformatics binary logarithm c++, the design of sports tournamentsand photography. Binary logarithms are included in the binary logarithm c++ C mathematical functions and other mathematical software packages. The integer part of a binary logarithm can be found using the find first set operation binary logarithm c++ an integer value, or by looking up the exponent of a floating point value.
The fractional part of the logarithm can be calculated efficiently. The powers of two have been known since antiquity; for instance they appear in Euclid's ElementsProps. And the binary logarithm of a power of two is just its position in the ordered sequence of powers of two. On this binary logarithm c++, Michael Stifel has been credited binary logarithm c++ publishing the first known table of binary logarithms in His book Arithmetica Integra contains several tables that show the integers with binary logarithm c++ corresponding powers of two.
Reversing the rows of these tables allow them to be interpreted as tables of binary logarithms. Earlier than Stifel, the 8th century Jain mathematician Virasena is credited with a precursor to the binary logarithm. Virasena's concept of ardhacheda has been defined as the number of times a given number can be divided evenly by two.
This definition gives rise to a function that coincides with the binary logarithm on the powers of two,  but it is different for other integers, giving the 2-adic order rather than the logarithm.
The modern form of a binary logarithm, applying to any number not just powers of two was considered explicitly by Leonhard Euler in Euler established the application of binary logarithms to music theory, long before their more significant applications in information theory and computer science became known.
As part of his work in this area, Euler published a table of binary logarithms of the integers from 1 to 8, to seven decimal digits of accuracy. The binary logarithm function may be defined as the inverse function to the power of two function, which is a strictly increasing function over binary logarithm c++ positive real numbers and therefore has a unique inverse.
Using the complex logarithm in this definition allows the binary logarithm to be extended to the complex numbers. As with other logarithms, the binary logarithm obeys the following equations, which can be used to simplify formulas that combine binary logarithms with multiplication or exponentiation: For more, see list of logarithmic identities. Some authors write the binary logarithm as lg n  the notation listed in The Chicago Manual of Style.
According to these standards, lg n should not be used for the binary logarithm, as it is instead reserved for the common logarithm log 10 n. In information theory, the binary logarithm c++ of the amount binary logarithm c++ self-information and information entropy is often expressed with the binary logarithm, corresponding to making the bit the fundamental unit of information.
However, the natural logarithm and the nat are also used in alternative notations for these definitions. Although the natural logarithm is more important than the binary logarithm in many areas of pure mathematics such as number theory and mathematical analysis binary logarithm c++ binary logarithm has several applications in combinatorics:.
The binary logarithm also frequently appears in the analysis of algorithms not only because of the frequent use of binary number arithmetic in algorithms, but also because binary logarithms occur in the analysis of algorithms based on two-way branching. This idea is binary logarithm c++ in the analysis of several algorithms and data structures. The running time of an algorithm is usually expressed in big O notationwhich is used to simplify expressions by omitting their constant factors and lower-order terms.
The base of the logarithm in expressions such as O log n or O n log n is therefore not important and can be omitted. In bioinformaticsmicroarrays are used to measure how strongly different genes are expressed in a sample of biological material.
Different rates of expression of a gene are often compared by using the binary logarithm of the ratio of expression rates: Binary logarithms allow for a convenient comparison of expression rates: Data points obtained in this way are often visualized as a scatterplot in which one or both of the coordinate axes are binary logarithms of intensity ratios, or in visualizations such as the MA plot and RA plot that rotate and scale these log ratio scatterplots.
In music theorythe interval or perceptual difference between two tones is determined by the ratio of their frequencies. Intervals coming from rational number ratios with small numerators and denominators are perceived as particularly euphonious. The simplest and most important of these intervals is the octavea frequency ratio of 2: The number of octaves by which two tones differ is the binary logarithm of their frequency ratio.
To study tuning systems and other aspects of music theory that require finer distinctions between tones, it is helpful to have a measure of the size of an interval that is finer than an octave and is additive as binary logarithm c++ are rather than multiplicative as frequency ratios are.
That is, if tones xyand z form a rising sequence of binary logarithm c++, then the measure of the interval from x to y binary logarithm c++ the measure of the interval from y to z should equal the measure of the interval from x to z. Such a measure is given by the centwhich divides the octave into equal intervals 12 semitones of cents each. Mathematically, given tones with frequencies f 1 and f 2the number of cents in the interval from f 1 to f 2 is .
The millioctave is defined in the same way, but with a multiplier of instead of In competitive games and sports involving two players or teams in each game or match, the binary logarithm indicates the binary logarithm c++ of rounds necessary in a single-elimination tournament required to determine a winner.
The same number of rounds is also necessary to determine a clear winner in a Swiss-system tournament. In photographyexposure values are measured in terms of the binary logarithm of the amount of light reaching the film or sensor, in accordance with the Weber—Fechner law describing a logarithmic response of the human visual system to light.
A single stop of exposure is one unit on a base- 2 logarithmic scale. Binary logarithms expressed as stops are also used in densitometrybinary logarithm c++ express the dynamic range of light-sensitive materials or digital sensors. The specific change of logarithm base formulae for this are: The binary logarithm can be made into a function from integers and to integers by rounding it up or down. These two forms of integer binary logarithm are related by this formula:.
Extended in this way, this function is related to the number of leading zeros of the bit unsigned binary representation of xnlz x. The integer binary logarithm can be interpreted as the zero-based index of the most significant 1 bit in the input. In this sense it is the complement of the find first set binary logarithm c++, which finds the index of the least significant 1 bit.
Many hardware platforms include support for finding the number of leading zeros, or equivalent operations, which can be used to quickly find the binary logarithm. The fls and flsl functions in the Linux kernel  and in some versions of the libc software library also compute the binary logarithm rounded up to an integer, plus one. For a general positive real binary logarithm c++the binary logarithm may be computed in two parts.
This reduces the problem to one where the argument of the logarithm is in a restricted range, the interval [1,2simplifying the second step of computing the fractional part the mantissa of the logarithm.
For normalized floating point numbers, the integer part is given by the floating point exponent,  and for integers it can be determined by performing a count leading zeros operation. In the special case binary logarithm c++ the fractional part in step 1 is found to be zero, this is a finite sequence binary logarithm c++ at some point.
Binary logarithm c++ practical use, this infinite series must be truncated binary logarithm c++ reach an approximate binary logarithm c++. The log2 function is included in the standard C mathematical functions.
The binary logarithm c++ version of binary logarithm c++ function takes double precision arguments but variants of it allow the argument to be single-precision or to be a long double. From Wikipedia, the free encyclopedia. Holt, Rinehart and Winston, p. A copy of the same table with two more entries appears on p. Non-European Roots of Mathematics 3rd ed.
De Variorum Intervallorum Receptis Appelationibus", Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae in LatinSaint Petersburg Academy, pp. The same notation was in the 2nd edition of the same book p.
Sources are available from SourceForges download page. We do binary logarithm c++ supply binaries, because of the numerous incompatible ABIs e.
A stable but older version of log4cpp is available in Debian binary logarithm c++, see http: FreeBSD users can find log4cpp in the ports collection, see http: Binary logarithm c++ of version 0. No further license changes are planned: API Documentation generated by Doxygen can be found here. Recommended reading if you trying to figure out how to use log4cpp! Of course the proper solution would be if the offending party binary logarithm c++ use one of the above methods, but we could have to wait some time for this to actually happen.
As an alternative log4cpp can workaround these defines. Once log4cpp has been updated to binary logarithm c++ log4j 1. Loggers and appenders are created and configured manually. Example makes use of both function-style logging and stream-style logging. There are three loggers including root and three appenders. Root logger redirects all its own input and input of its descendant onto binary logarithm c++.
Descendant sub1 writes into two files, filtering output by message priority for second of them. To start working with a freshly checked out log4cpp revision, run.
You'll need at least autoconf 2. Coding on Log4cpp was initiated by me Bastiaan Bakker late Since then other people have joined the project or contributed code:.
About log4cpp What is log4cpp? Download Sources are available from SourceForges download page. Building Log4cpp Autoconf As of version 0. This will give you an IdsaAppender Appender class. Create symlinks where necessary. At the moment August omniORB4 is in beta, however most parts and specifically the threading library appear to be quite stable.
This option is mutually exclusive binary logarithm c++ --with-omnithreads. Defaults to yes if doxygen can be found in the search path. The primary binary logarithm c++ platform is RedHat Linux 7. Also static libraries appear not to work.
Win32 - Cygwin Use '. Be warned that there have been very few success or failure reports for this platform, so either it works very smoothly or noone actively uses log4cpp with Cygwin: License As of version 0. It is modeled after the Log for Java library http: Is it a straight binary logarithm c++ However the implementation is not a translation of the Java code.
So in that sense it is not a 'port' of Log4j. Versions before that have been released under the GPL. Technically it may be binary logarithm c++ if every contributor agrees, which due to their growing number has become increasingly difficult.
But even if that could be overcome it will not binary logarithm c++. I've succesfully compiled log4cpp, now how do I use this stuff? Have a glance at Simple example and Properties file example. For some small examples using log4cpp, see the 'tests' subdirectory. Also see the documentation section for a pointer for API documentation and more usage information.
The same instance of the log4cpp:: Category object a logger can be used from different threads simultaneously without explicit synchronization.
Concurrent access to the appenders will be prevented by the logger object itself. It will lock internal mutex each time when it comes to writing into appenders. So, it is safe, for example, to write from the multiple threads to the same logger which appends to the same file. Binary logarithm c++, log4cpp is configured in such a way that two different loggers append to the same appender it may be a filethen there will be no way for the logging framework to arrange proper addition and things can get mixed up.
So this way of configuration is not recommended. What are possible format characters for the custom log message? PatternLayout supports following set of format characters: The date format character may be followed by binary logarithm c++ date format specifier enclosed between braces.
If no date format specifier is given then the following format is used: Please read the FAQ for a workaround. In particular this conflicts with log4cpp:: These latter two names come from log4j, so they are not something we made up ourselves. They Win32 authors should not have rudelessly claimed these generic names through the preprocessor.
There are much better alternatives: If they use it as an integer constant, declare it using a language construct. The library builds, but the testmain code fails to link properly. A proper solution for this problem has not been found yet suggestions are welcomebinary logarithm c++ James Emery reported success with the following workaround: In short, configure with: In particular, binary logarithm c++ should strictly honour the 'string size' parameter to avoid potential buffer overflow problems.
Simple example Sample main. Streamed sub1 error WARN sub1: Properties file example Sample main. Git Repository log4cpp is moved to git SourceForge Git page since version 1. CVS had two branches: Replaced PatternLayout with a new, faster and more complete implementation. Fixed log facility in RemoteSyslogAppender. Fixed relocatability of binary logarithm c++ RPM.
Handled feature requests, Binary logarithm c++ implementation uses omniORB4s threading library. Other threading libraries, such as Boosts, may be used as well, but this has not been implemented yet. Version update should have been done in 0. Status The latest stable release is 1. People Coding on Log4cpp was initiated by me Bastiaan Bakker late Since then other people have joined the project or contributed code: Project Pages Log4cpp is hosted on SourceForge at http: Here's an incomplete list: Worth checking out if binary logarithm c++ don't like Log4cpp for some reason.
Log4cpp is hosted on SourceForge at http: