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| author | Ruben Undheim <ruben.undheim@gmail.com> | 2018-07-29 19:05:33 +0000 |
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| committer | Ruben Undheim <ruben.undheim@gmail.com> | 2018-07-29 19:05:33 +0000 |
| commit | aa7abb5c97c20b34f159886dfc523dd8198fef98 (patch) | |
| tree | f70f75d05eb976e099dd5177e25f16b417c9b43d /fparser/docs | |
| parent | ef962f6008f25ab7cbd4ca21bcc72b97a1e2d76f (diff) | |
New upstream version 0.0.34+ds.1
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| -rw-r--r-- | fparser/docs/gpl.txt | 674 | ||||
| -rw-r--r-- | fparser/docs/lgpl.txt | 165 | ||||
| -rw-r--r-- | fparser/docs/style.css | 80 |
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diff --git a/fparser/docs/fparser.html b/fparser/docs/fparser.html deleted file mode 100644 index ffc73f4..0000000 --- a/fparser/docs/fparser.html +++ /dev/null @@ -1,1863 +0,0 @@ -<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> -<html> -<head> - <meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"> - <link href="style.css" rel="stylesheet" type="text/css" title="normal" media=screen> - <title>Function Parser for C++ v4.5.1 : Documentation</title> -</head> - -<body> -<h1>Function Parser for C++ v4.5.1 </h1> - -<p>Authors: Juha Nieminen -(<a href="http://iki.fi/warp/">http://iki.fi/warp/</a>), -Joel Yliluoma -(<a href="http://iki.fi/bisqwit/">http://iki.fi/bisqwit/</a>). - -<p>The usage license of this library is located at the end of this file. - -<h2>Table of contents:</h2> - -<ul> - <li><a href="#whatsnew">What's new</a> - <li><a href="#preface">Preface</a> - <li><a href="#usage">Usage</a> - <ul> - <li><a href="#parsertypes">Parser types</a> - <li><a href="#configuring">Configuring the compilation</a> - <li><a href="#copyassignment">Copying and assignment</a> - <li><a href="#shortdesc">Short descriptions of FunctionParser methods</a> - <li><a href="#longdesc">Long descriptions of FunctionParser methods</a> - <ul> - <li><a href="#longdesc_Parse"><code>Parse()</code></a> - <li><a href="#longdesc_setDelimiterChar"><code>setDelimiterChar()</code></a> - <li><a href="#longdesc_ErrorMsg"><code>ErrorMsg()</code></a> - <li><a href="#longdesc_GetParseErrorType"><code>GetParseErrorType()</code></a> - <li><a href="#longdesc_Eval"><code>Eval()</code></a> - <li><a href="#longdesc_EvalError"><code>EvalError()</code></a> - <li><a href="#longdesc_Optimize"><code>Optimize()</code></a> - <li><a href="#longdesc_AddConstant"><code>AddConstant()</code></a> - <li><a href="#longdesc_AddUnit"><code>AddUnit()</code></a> - <li><a href="#longdesc_AddFunction1"><code>AddFunction()</code></a> (C++ function) - <li><a href="#longdesc_AddFunction2"><code>AddFunction()</code></a> (FunctionParser) - <li><a href="#longdesc_AddFunction3"><code>AddFunctionWrapper()</code></a> - <li><a href="#longdesc_RemoveIdentifier"><code>RemoveIdentifier()</code></a> - <li><a href="#longdesc_ParseAndDeduceVariables"><code>ParseAndDeduceVariables()</code></a> - </ul> - <li><a href="#functionobjects">Specialized function objects</a> - <li><a href="#base">FunctionParserBase</a> - </ul> - <li>Syntax - <ul> - <li><a href="#literals">Numeric literals</a> - <li><a href="#identifiers">Identifier names</a> - <li><a href="#functionsyntax">The function string syntax</a> - <li><a href="#inlinevars">Inline variables</a> - <li><a href="#whitespace">Whitespace</a> - </ul> - <li>Miscellaneous - <ul> - <li><a href="#fpaccuracy">About floating point accuracy</a> - <li><a href="#evaluationchecks">About evaluation-time checks</a> - <li><a href="#threadsafety">About thread safety</a> - <li><a href="#tipsandtricks">Tips and tricks</a> - <li><a href="#contact">Contacting the author</a> - </ul> -<!-- <li><a href="#algorithm">The algorithm used in the library</a> --> - <li><a href="#license">Usage license</a> -</ul> - -<a name="whatsnew"></a> -<h2>What's new</h2> - -<p>What's new in v4.5.1 - <ul> - <li>Reverted the automatic C++11 detection to a precompiler macro setting - (<code>FP_SUPPORT_CPLUSPLUS11_MATH_FUNCS</code>) because not all - compilers yet fully support the C++11 math functions. - <li>Fixed a potential duplicate symbol problem that happens with explicit - template instantiations. - </ul> - -<p>What's new in v4.5 - <ul> - <li>Removed support for the <code>"eval()"</code> function from the - supported syntax. (This function was too dangerous, too difficult to - maintain internally, not very useful, and more or less a gimmick in - the first place.) - <li>Removed several of the conditional compiling macro definitions, namely - <code>FP_SUPPORT_TR1_MATH</code>, <code>FP_ENABLE_EVAL</code>, - <code>FP_EVAL_MAX_REC_LEVEL</code>, <code>FP_NO_EVALUATION_CHECKS</code> - and <code>FP_EPSILON</code>. - <li>The epsilon value used in comparisons is now set with a member function - of FunctionParser (which allows setting different values for different - versions of the parser). - <li>The math functions previously turned on with - <code>FP_SUPPORT_TR1_MATH</code> are now automatically used if - <code>__cplusplus</code> indicates that C++11 is in use. - <li>Fixed some compilation problems with clang++. - </ul> - - - -<!-- -------------------------------------------------------------------- --> -<a name="preface"></a> -<h2>Preface</h2> - -<p>This C++ library offers a class which can be used to parse and evaluate a -mathematical function from a string (which might be eg. requested from the -user). The syntax of the function string is similar to mathematical expressions -written in C/C++ (the exact syntax is specified later in this document). -The function can then be evaluated with different values of variables. - -<p>For example, a function like "<code>sin(sqrt(x*x+y*y))</code>" can be -parsed from a string (either <code>std::string</code> or a C-style string) -and then evaluated with different values of <code>x</code> and <code>y</code>. -This library can be useful for evaluating user-inputted functions, or in -some cases interpreting mathematical expressions in a scripting language. - -<p>This library aims for maximum speed in both parsing and evaluation, while -keeping maximum portability. The library should compile and work with any -standard-conforming C++ compiler. - -<p>Different numerical types are supported: <code>double</code>, - <code>float</code>, <code>long double</code>, <code>long int</code>, - <code>std::complex</code> (of types <code>double</code>, - <code>float</code> and <code>long double</code>), - multiple-precision floating point numbers using the MPFR library, and - arbitrary precision integers using the GMP library. (Note that it's - not necessary for these two libraries to exist in the system in order - to use the Function Parser library with the other numerical types. Support - for these libraries is optionally compiled in using preprocessor settings.) - - -<!-- -------------------------------------------------------------------- --> -<a name="usage"></a> -<h2>Usage</h2> - -<p>To use the <code>FunctionParser</code> class, you have to include -<code>"fparser.hh"</code> in your source code files which use the -<code>FunctionParser</code> class. - -<p>If you are going to use the MPFR version of the library, you need to -include <code>"fparser_mpfr.hh"</code>. If you are going to use the GMP -version of the library, you need to include <code>"fparser_gmpint.hh"</code>. -(Note that support for these special parser versions needs to be specified -with preprocessor macros. See the <a href="#parsertypes">documentation -below</a> for details.) - -<p>When compiling, you have to compile <code>fparser.cc</code> and -<code>fpoptimizer.cc</code> and link them to the main program. In many -developement environments it's enough to add those two files to your -current project (usually header files don't have to be added to the -project for the compilation to work). - -<p>If you are going to use the MPFR or the GMP versions of the library, -you also need to add <code>mpfr/MpfrFloat.cc</code> or -<code>mpfr/GmpInt.cc</code> files to your project, respectively. Otherwise -they should not be added to the project. - -<p>Note that part of the library source code is inside several -<code>.inc</code> files inside the <code>extrasrc</code> subdirectory -(these files contain auto-generated C++ code), provided in the library -package. These files are used by <code>fparser.cc</code> and don't need -to be added explicitly to the project in most IDEs (such as Visual Studio). -Basically, you don't need to do anything with these files, other than keep -them in the <code>extrasrc</code> subdirectory. - -<p>Simple usage example of the library: - -<pre> - FunctionParser fp; - fp.Parse("sqrt(x*x + y*y)", "x,y"); - double variables[2] = { 1.5, 2.9 }; - double result = fp.Eval(variables); -</pre> - -<!-- -------------------------------------------------------------------- --> -<a name="parsertypes"></a> -<h3>Parser types</h3> - -<p>Different versions of the function parser class are supported, using - different floating point or integral types for function evaluation. - -<p>All the classes other than the default one, <code>FunctionParser</code>, - need to be enabled at compile time by defining a preprocessor macro - (specified below) either in the <code>fpconfig.hh</code> file or your - compiler settings. (The reason for this is that every parser that is - included in the compilation process will make the compilation slower - and increase the size of the executable, so they are compiled only on - demand. Also, the GMP and MPFR versions of the parser require for those - libraries to be available, which is often not the case.) - -<p>Note that if you try to use the other class types without enabling them - with the correspondent preprocessor macro, you will get a linker error - (rather than a compiler error) because those classes will not have been - instantiated when the library was compiled. - -<p>Currently the <code>Optimize()</code> method works only for the - <code>FunctionParser</code>, <code>FunctionParser_f</code> and - <code>FunctionParser_ld</code> classes. For the other types it can be - called but it does nothing. - -<p> -<dl> - <dt><p><code>FunctionParser</code></dt> - <dd> - <p>This is the default class, which uses <code>double</code> as its - numerical type. This is the only class enabled by default. - <p>If you use some other type than this one, and you don't want this - version of the class compiled into the library, you can define the - preprocessor macro <code>FP_DISABLE_DOUBLE_TYPE</code>. - </dd> - - <dt><p><code>FunctionParser_f</code></dt> - <dd> - <p>This parser uses <code>float</code> as its numerical type. - <p>The <code>FP_SUPPORT_FLOAT_TYPE</code> preprocessor macro needs to be - defined for this class to be enabled. - </dd> - - <dt><p><code>FunctionParser_ld</code></dt> - <dd> - <p>This parser uses <code>long double</code> as its numerical type. - <p>The <code>FP_SUPPORT_LONG_DOUBLE_TYPE</code> preprocessor macro needs - to be defined for this class to be enabled. - <p>Note that the <code>FP_USE_STRTOLD</code> preprocessor macro should - also be defined when using this version of the parser if the compiler - supports the (C99) function <code>strtold()</code>. (See - <a href="#configuring">documentation</a> below.) - </dd> - - <dt><p><code>FunctionParser_li</code></dt> - <dd> - <p>This parser uses <code>long int</code> as its numerical type. - <p>The <code>FP_SUPPORT_LONG_INT_TYPE</code> preprocessor macro needs - to be defined for this class to be enabled. - <p>Note that this version of the class uses a reduced function syntax - with support only for functions which are feasible to be used with - integral types (namely <code>abs()</code>, <code>eval()</code>, - <code>if()</code>, <code>min()</code> and <code>max()</code>, besides - basic arithmetic operators, except for the power operator). - </dd> - - <dt><p><code>FunctionParser_cd</code>, <code>FunctionParser_cf</code>, - <code>FunctionParser_cld</code></dt> - <dd> - <p>These parsers use <code>std::complex<double></code>, - <code>std::complex<float></code> and - <code>std::complex<long double></code> as their numerical type, - respectively. - <p>The preprocessor macros to enable them are - <code>FP_SUPPORT_COMPLEX_DOUBLE_TYPE</code>, - <code>FP_SUPPORT_COMPLEX_FLOAT_TYPE</code> and - <code>FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE</code>. - <p>If <code>FunctionParser_cld</code> is used, the - <code>FP_USE_STRTOLD</code> macro should also be defined if the compiler - supports the <code>strtold()</code> function. - </dd> - - <dt><p><code>FunctionParser_mpfr</code></dt> - <dd> - <p>This parser uses <code>MpfrFloat</code> as its numerical type. - <p>The <code>FP_SUPPORT_MPFR_FLOAT_TYPE</code> preprocessor macro needs - to be defined for this class to be enabled. - <p>Note that to use this version of the parser, - <code>"fparser_mpfr.hh"</code> needs to be included. - <p><code>MpfrFloat</code> is an auxiliary class which uses the MPFR - library for multiple-precision floating point numbers. The class - behaves largely like a floating point type, and is declared in the - <code>mpfr/MpfrFloat.hh</code> file (see that file for info about - the public interface of the class). - <p>If this class is enabled, <code>mpfr/MpfrFloat.cc</code> - needs to be compiled into the project, as well as the GMP and MPFR - libraries. (With the gcc compiler this means using the linker options - "<code>-lgmp -lmpfr</code>".) - </dd> - - <dt><p><code>FunctionParser_gmpint</code></dt> - <dd> - <p>This parser uses <code>GmpInt</code> as its numerical type. - <p>The <code>FP_SUPPORT_GMP_INT_TYPE</code> preprocessor macro needs - to be defined for this class to be enabled. - <p>Note that to use this version of the parser, - <code>"fparser_gmpint.hh"</code> needs to be included. - <p><code>GmpInt</code> is an auxiliary class which uses the GMP - library for arbitrary-precision integer numbers. The class - behaves largely like an integer type, and is declared in the - <code>mpfr/GmpInt.hh</code> file (see that file for info about - the public interface of the class). - <p>If this class is enabled, <code>mpfr/GmpInt.cc</code> - needs to be compiled into the project, as well as the GMP library. - <p>This version of the class also uses a reduced version of the syntax, - like the <code>long int</code> version. - <p><b>Note:</b> Since there's no upper limit to the size of GMP - integers, this version of the class should be used with care in - situations where malicious users might be able to exploit it to - make the program run out of memory. An example of this would be - a server-side application usable through the WWW. - </dd> -</dl> - -<p>Note that these different classes are completely independent and - instances of different classes cannot be given to each other using the - <code>AddFunction()</code> method. Only objects of the same type can - be given to that method. - -<p>The rest of the documentation assumes that <code>FunctionParser</code> - (which uses the <code>double</code> type) is used. The usage of the other - classes is identical except that <code>double</code> is replaced with the - correspondent type used by that class. (In other words, whenever the - rest of this documentation uses the type keyword '<code>double</code>', - the correspondent type should be used instead, when using another version - of the class.) - -<!-- -------------------------------------------------------------------- --> -<a name="configuring"></a> -<h3>Configuring the compilation</h3> - -<p>There is a set of precompiler options in the <code>fpconfig.hh</code> file -which can be used for setting certain features on or off. All of these options -can also be specified from the outside, using precompiler settings (eg. the -<code>-D</code> option in gcc), and thus it's not necessary to modify this -file. - -<dl> - <dt><p><code>FP_USE_STRTOLD</code> : (Default off)</dt> - <dd><p>If <code>FunctionParser_ld</code> or <code>FunctionParser_cld</code> - are used, this preprocessor macro should be defined if the compiler - supports the (C99) function <code>strtold()</code>. If not, then numeric - literals will be parsed with double precision only, which in most - systems is less accurate than long double precision, which will cause - small rounding errors. (This setting has no effect on the other parser - types.) Note that <code>strtold()</code> will also be automatically used - if <code>__cplusplus</code> indicates that C++11 is in use. - </dd> - - <dt><p><code>FP_SUPPORT_CPLUSPLUS11_MATH_FUNCS</code> : (Default off)</dt> - <dd><p>Use C++11 math functions where applicable. (These are ostensibly - faster than the equivalent formulas using C++98 math functions.) Note - that not all compilers support these functions (even if they otherwise - support C++11.) - - <dt><p><code>FP_SUPPORT_OPTIMIZER</code> : (Default on)</dt> - <dd><p>If you are not going to use the <code>Optimize()</code> method, you - can comment this line out to speed-up the compilation a bit, as - well as making the binary a bit smaller. (<code>Optimize()</code> can - still be called, but it will not do anything.) - - <p>You can also disable the optimizer by specifying the - <code>FP_NO_SUPPORT_OPTIMIZER</code> precompiler constant in your - compiler settings. - </dd> - - <dt><p><code>FP_USE_THREAD_SAFE_EVAL</code> : (Default off)</dt> - <dd><p>Define this precompiler constant to make <code>Eval()</code> - thread-safe. Refer to the <a href="#threadsafety">thread safety - section</a> later in this document for more information. - Note that defining this may make <code>Eval()</code> slightly slower. - <p>Also note that the MPFR and GMP versions of the library cannot be - made thread-safe, and thus this setting has no effect on them. - </dd> - - <dt><p><code>FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA</code> : (Default off)</dt> - <dd><p>This is like the previous, but makes <code>Eval()</code> use the - <code>alloca()</code> function (instead of <code>std::vector</code>). - This will make it faster, but the <code>alloca()</code> - function is not standard and thus not supported by all compilers. - </dd> -</dl> - - -<!-- -------------------------------------------------------------------- --> -<a name="copyassignment"></a> -<h3>Copying and assignment</h3> - -<p>The class implements a safe copy constructor and assignment operator. - -<p>It uses the copy-on-write technique for efficiency. This means that - when copying or assigning a FunctionParser instance, the internal data - (which in some cases can be quite lengthy) is not immediately copied - but only when the contents of the copy (or the original) are changed. - -<p>This means that copying/assigning is a very fast operation, and if - the copies are never modified then actual data copying never happens - either. - -<p>The <code>Eval()</code> and <code>EvalError()</code> methods of the -copy can be called without the internal data being copied. - -<p>Calling <code>Parse()</code>, <code>Optimize()</code> or the user-defined -constant/function adding methods will cause a deep-copy. - - -<!-- -------------------------------------------------------------------- --> -<a name="shortdesc"></a> -<h3>Short descriptions of FunctionParser methods</h3> - -<pre> -int Parse(const std::string& Function, const std::string& Vars, - bool useDegrees = false); - -int Parse(const char* Function, const std::string& Vars, - bool useDegrees = false); -</pre> - -<p>Parses the given function and compiles it to internal format. - Return value is -1 if successful, else the index value to the location - of the error. - -<hr> -<pre> -void setDelimiterChar(char); -</pre> - -<p>Sets an ending delimiter character for the function string. (See the - long description for more details.) - -<hr> -<pre> -static double epsilon(); -static void setEpsilon(double); -</pre> - -<p>Setter and getter for the epsilon value used with comparison operators. - -<hr> -<pre> -const char* ErrorMsg(void) const; -</pre> - -<p>Returns an error message corresponding to the error in -<code>Parse()</code>, or an empty string if no such error occurred. - -<hr> -<pre> -ParseErrorType GetParseErrorType() const; -</pre> - -<p>Returns the type of parsing error which occurred. Possible return types - are described in the long description. - -<hr> -<pre> -double Eval(const double* Vars); -</pre> - -<p>Evaluates the function given to <code>Parse()</code>. - -<hr> -<pre> -int EvalError(void) const; -</pre> - -<p>Returns <code>0</code> if no error happened in the previous call to -<code>Eval()</code>, else an error code <code>>0</code>. - -<hr> -<pre> -void Optimize(); -</pre> - -<p>Tries to optimize the bytecode for faster evaluation. - -<hr> -<pre> -bool AddConstant(const std::string& name, double value); -</pre> - -<p>Add a constant to the parser. Returns <code>false</code> if the name of -the constant is invalid, else <code>true</code>. - -<hr> -<pre> -bool AddUnit(const std::string& name, double value); -</pre> - -<p>Add a new unit to the parser. Returns <code>false</code> if the name of -the unit is invalid, else <code>true</code>. - -<hr> -<pre> -bool AddFunction(const std::string& name, - double (*functionPtr)(const double*), - unsigned paramsAmount); -</pre> - -<p>Add a user-defined function to the parser (as a function pointer). -Returns <code>false</code> if the name of the function is invalid, else -<code>true</code>. - -<hr> -<pre> -bool AddFunction(const std::string& name, FunctionParser&); -</pre> - -<p>Add a user-defined function to the parser (as a <code>FunctionParser</code> -instance). Returns <code>false</code> if the name of the function is invalid, -else <code>true</code>. - -<hr> -<pre> -bool RemoveIdentifier(const std::string& name); -</pre> - -<p>Removes the constant, unit or user-defined function with the specified -name from the parser. - -<hr> -<pre> -int ParseAndDeduceVariables(const std::string& function, - int* amountOfVariablesFound = 0, - bool useDegrees = false); -int ParseAndDeduceVariables(const std::string& function, - std::string& resultVarString, - int* amountOfVariablesFound = 0, - bool useDegrees = false); -int ParseAndDeduceVariables(const std::string& function, - std::vector<std::string>& resultVars, - bool useDegrees = false); -</pre> - -<p>Like <code>Parse()</code>, but the variables in the function are deduced -automatically. The amount of found variables and the variable names themselves -are returned by the different versions of the function. - -<!-- -------------------------------------------------------------------- --> -<a name="longdesc"></a> -<h3>Long descriptions of FunctionParser methods</h3> - -<hr> -<a name="longdesc_Parse"></a> -<pre> -int Parse(const std::string& Function, const std::string& Vars, - bool useDegrees = false); - -int Parse(const char* Function, const std::string& Vars, - bool useDegrees = false); -</pre> - -<p>Parses the given function (and compiles it to internal format). -Destroys previous function. Following calls to <code>Eval()</code> will evaluate -the given function. - -<p>The strings given as parameters are not needed anymore after parsing. - -<p>Parameters: - -<table border=2> - <tr> - <td><code>Function</code></td> - <td>String containing the function to parse.</td> - </tr><tr> - <td><code>Vars</code></td> - <td>String containing the variable names, separated by commas.<br> - Eg. <code>"x,y"</code>, <code>"VarX,VarY,VarZ,n"</code> or - <code>"x1,x2,x3,x4,__VAR__"</code>. - </tr><tr> - <td><code>useDegrees</code></td> - <td>(Optional.) Whether to use degrees or radians in - trigonometric functions. (Default: radians)</td> - </tr> -</table> - -<p>If a <code>char*</code> is given as the <code>Function</code> parameter, -it must be a null-terminated string. - -<p>Variables can have any size and they are case sensitive (ie. -<code>"var"</code>, <code>"VAR"</code> and <code>"Var"</code> are -<em>different</em> variable names). Letters, digits, underscores and -UTF8-encoded characters can be used in variable names, but the name of -a variable can't begin with a digit. Each variable name can appear only -once in the '<code>Vars</code>' string. Function names are not legal -variable names. - -<p>Using longer variable names causes no overhead whatsoever to the -<code>Eval()</code> method, so it's completely safe to use variable names -of any size. - -<p>The third, optional parameter specifies whether angles should be - interpreted as radians or degrees in trigonometrical functions. - If not specified, the default value is radians. - -<p>Return values: - -<ul> - <li>On success the function returns <code>-1</code>. - <li>On error the function returns an index to where the error was found - (<code>0</code> is the first character, <code>1</code> the second, etc). - If the error was not a parsing error returns an index to the end of the - string. -</ul> - -<p>Example: <code>parser.Parse("3*x+y", "x,y");</code> - - -<hr> -<a name="longdesc_setDelimiterChar"></a> -<pre> -void setDelimiterChar(char); -</pre> - -<p>By default the parser expects the entire function string to be valid -(ie. the entire contents of the given <code>std::string</code>, or a C string -ending in the null character <code>'\0'</code>). - -<p>If a delimiter character is specified with this function, then if it's -encountered at the outermost parsing level by the <code>Parse()</code> -function, and the input function has been valid so far, <code>Parse()</code> -will return an index to this character inside the input string, but rather -than set an error code, <code>FP_NO_ERROR</code> will be set. - -<p>The idea is that this can be used to more easily parse functions which -are embedded inside larger strings, containing surrounding data, without -having to explicitly extract the function to a separate string. - -<p>For example, suppose you are writing an interpreter for a scripting - language, which can have commands like this: - -<p><code>let MyFunction(x,y) = { sin(x*x+y*y) } // A 2-dimensional function</code> - -<p>Normally when parsing such a line you would have to extract the part -inside the curly brackets into a separate string and parse it that way. -With this feature what you can do instead is to set <code>'}'</code> as -the delimiter character and then simply give a pointer to the character -which comes after the <code>'{'</code>. If all goes well, the -<code>Parse()</code> function will return an index to the <code>'}'</code> -character (from the given starting point) and <code>GetParseErrorType()</code> -will return <code>FP_NO_ERROR</code>. You can use the return -value (if it's not <code>-1</code>) to jump forward in the string to the -delimiter character. - -<p>Note that a null character (<code>'\0'</code>) or the end of the -<code>std::string</code> (if one was given) will still be a valid end of -the function string even if a delimiter character was specified. (In this -case <code>Parse()</code> will return <code>-1</code> if there was no error, -as usual.) - -<p>Also note that the delimiter character cannot be any valid operator -or alphanumeric (including the underscore) character, nor the other -characters defined in the function syntax. It must be a character not -supported by the function parser (such as <code>'}'</code>, -<code>'"'</code>, <code>']'</code>, etc). - - -<hr> -<a name="longdesc_Epsilon"></a> -<pre> -static double epsilon(); -static void setEpsilon(double); -</pre> - -<p>Comparison operators (for the non-integral versions of the parser) use an -epsilon value to account for floating point calculation rounding errors. -This epsilon value can be set and read with these functions. (Note that the -specified value will be used by all instances of FunctionParser.) If not -specified, the default values are: - -<ul> - <li>double: 1e-12 - <li>float: 1e-5 - <li>long double: 1e-14 - <li>MpfrFloat: The value of MpfrFloat::someEpsilon() -</ul> - - -<hr> -<a name="longdesc_ErrorMsg"></a> -<pre> -const char* ErrorMsg(void) const; -</pre> - -<p>Returns a pointer to an error message string corresponding to the error -caused by <code>Parse()</code> (you can use this to print the proper error -message to the user). If no such error has occurred, returns an empty string. - - -<hr> -<a name="longdesc_GetParseErrorType"></a> -<pre> -ParseErrorType GetParseErrorType() const; -</pre> - -<p>Returns the type of parse error which occurred. - -<p>This method can be used to get the error type if <code>ErrorMsg()</code> -is not enough for printing the error message. In other words, this can be -used for printing customized error messages (eg. in another language). -If the default error messages suffice, then this method doesn't need -to be called. - -<code>FunctionParser::ParseErrorType</code> is an enumerated type inside -the class (ie. its values are accessed like -"<code>FunctionParser::SYNTAX_ERROR</code>"). - -<p>The possible values for FunctionParser::ParseErrorType are listed below, -along with their equivalent error message returned by the -<code>ErrorMsg()</code> method: - -<p><table border=2> -<tr> - <td><code>FP_NO_ERROR</code></td> - <td>If no error occurred in the previous call to <code>Parse()</code>.</td> -</tr><tr> - <td><code>SYNTAX_ERROR</code></td> - <td>"Syntax error"</td> -</tr><tr> - <td><code>MISM_PARENTH</code></td> - <td>"Mismatched parenthesis"</td> -</tr><tr> - <td><code>MISSING_PARENTH</code></td> - <td>"Missing ')'"</td> -</tr><tr> - <td><code>EMPTY_PARENTH</code></td> - <td>"Empty parentheses"</td> -</tr><tr> - <td><code>EXPECT_OPERATOR</code></td> - <td>"Syntax error: Operator expected"</td> -</tr><tr> - <td><code>OUT_OF_MEMORY</code></td> - <td>"Not enough memory"</td> -</tr><tr> - <td><code>UNEXPECTED_ERROR</code></td> - <td>"An unexpected error occurred. Please make a full bug report to the - author"</td> -</tr><tr> - <td><code>INVALID_VARS</code></td> - <td>"Syntax error in parameter 'Vars' given to FunctionParser::Parse()"</td> -</tr><tr> - <td><code>ILL_PARAMS_AMOUNT</code></td> - <td>"Illegal number of parameters to function"</td> -</tr><tr> - <td><code>PREMATURE_EOS</code></td> - <td>"Syntax error: Premature end of string"</td> -</tr><tr> - <td><code>EXPECT_PARENTH_FUNC</code></td> - <td>"Syntax error: Expecting ( after function"</td> -</tr><tr> - <td><code>UNKNOWN_IDENTIFIER</code></td> - <td>"Syntax error: Unknown identifier"</td> -</tr><tr> - <td><code>NO_FUNCTION_PARSED_YET</code></td> - <td>"(No function has been parsed yet)"</td> -</tr> -</table> - - -<hr> -<a name="longdesc_Eval"></a> -<pre> -double Eval(const double* Vars); -</pre> - -<p>Evaluates the function given to <code>Parse()</code>. -The array given as parameter must contain the same amount of values as -the amount of variables given to <code>Parse()</code>. Each value corresponds -to each variable, in the same order. - -<p>Return values: -<ul> - <li>On success returns the evaluated value of the function given to - <code>Parse()</code>. - <li>On error (such as division by 0) the return value is unspecified, - probably 0. -</ul> - -<p>Example: - -<p><code>double Vars[] = {1, -2.5};</code><br> -<code>double result = parser.Eval(Vars);</code> - - -<hr> -<a name="longdesc_EvalError"></a> -<pre> -int EvalError(void) const; -</pre> - -<p>Used to test if the call to <code>Eval()</code> succeeded. - -<p>Return values: - -<p>If there was no error in the previous call to <code>Eval()</code>, -returns <code>0</code>, else returns a positive value as follows: -<ul> - <li>1: division by zero - <li>2: sqrt error (sqrt of a negative value) - <li>3: log error (logarithm of a negative value) - <li>4: trigonometric error (asin or acos of illegal value) - <li>5: maximum recursion level in <code>eval()</code> reached -</ul> - - -<hr> -<a name="longdesc_Optimize"></a> -<pre> -void Optimize(); -</pre> - -<p>This method can be called after calling the <code>Parse()</code> method. -It will try to simplify the internal bytecode so that it will evaluate faster -(it tries to reduce the amount of opcodes in the bytecode). - -<p>For example, the bytecode for the function <code>"5+x*y-25*4/8"</code> will -be reduced to a bytecode equivalent to the function <code>"x*y-7.5"</code> (the -original 11 opcodes will be reduced to 5). Besides calculating constant -expressions (like in the example), it also performs other types of -simplifications with variable and function expressions. - -<p>This method is quite slow and the decision of whether to use it or -not should depend on the type of application. If a function is parsed -once and evaluated millions of times, then calling <code>Optimize()</code> -may speed-up noticeably. However, if there are tons of functions to parse -and each one is evaluated once or just a few times, then calling -<code>Optimize()</code> will only slow down the program. - -<p>Also, if the original function is expected to be optimal, then calling -<code>Optimize()</code> would be useless. - -<p>Note: Currently this method does not make any checks (like -<code>Eval()</code> does) and thus things like <code>"1/0"</code> will cause -undefined behaviour. (On the other hand, if such expression is given to the -parser, <code>Eval()</code> will always give an error code, no matter what -the parameters.) If caching this type of errors is important, a work-around -is to call <code>Eval()</code> once before calling <code>Optimize()</code> -and checking <code>EvalError()</code>. - -<p>If the destination application is not going to use this method, -the compiler constant <code>FP_SUPPORT_OPTIMIZER</code> can be undefined in -<code>fpconfig.hh</code> to make the library smaller (<code>Optimize()</code> -can still be called, but it will not do anything). - -<p>(If you are interested in seeing how this method optimizes the opcode, -you can call the <code>PrintByteCode()</code> method before and after the -call to <code>Optimize()</code> to see the difference.) - - -<hr> -<a name="longdesc_AddConstant"></a> -<pre> -bool AddConstant(const std::string& name, double value); -</pre> - -<p>This method can be used to add constants to the parser. Syntactically - constants are identical to variables (ie. they follow the same naming - rules and they can be used in the function string in the same way as - variables), but internally constants are directly replaced with their - value at parse time. - -<p>Constants used by a function must be added before calling -<code>Parse()</code> for that function. Constants are preserved between -<code>Parse()</code> calls in the current FunctionParser instance, so -they don't need to be added but once. (If you use the same constant in -several instances of FunctionParser, you will need to add it to all the -instances separately.) - -<p>Constants can be added at any time and the value of old constants can -be changed, but new additions and changes will only have effect the next -time <code>Parse()</code> is called. (That is, changing the value of a constant -after calling <code>Parse()</code> and before calling <code>Eval()</code> -will have no effect.) - -<p>The return value will be <code>false</code> if the '<code>name</code>' of -the constant was illegal, else <code>true</code>. If the name was illegal, -the method does nothing. - -<p>Example: <code>parser.AddConstant("pi", 3.1415926535897932);</code> - -<p>Now for example <code>parser.Parse("x*pi", "x");</code> will be identical -to the call <code>parser.Parse("x*3.1415926535897932", "x");</code> - - -<hr> -<a name="longdesc_AddUnit"></a> -<pre> -bool AddUnit(const std::string& name, double value); -</pre> - -<p>In some applications it is desirable to have units of measurement. -A typical example is an application which creates a page layout to be -printed. When printing, distances are usually measured in points -(defined by the resolution of the printer). However, it is often more -useful for the user to be able to specify measurements in other units -such as centimeters or inches. - -<p>A unit is simply a value by which the preceding element is multiplied. -For example, if the printing has been set up to 300 DPI, one inch is -then 300 points (dots). Thus saying eg. <code>"5in"</code> is the same as saying -<code>"5*300"</code> or <code>"1500"</code> (assuming <code>"in"</code> has -been added as a unit with the value 300). - -<p>Note that units are slightly different from a multiplication in -that they have a higher precedence than any other operator (except -parentheses). Thus for example <code>"5/2in"</code> is parsed as -<code>"5/(2*300)"</code>. -(If 5/2 inches is what one wants, it has to be written <code>"(5/2)in"</code>.) - -<p>You can use the <code>AddUnit()</code> method to add a new unit. The -unit can then be used after any element in the function (and will work as -a multiplier for that element). An element is a float literal, a constant, -a variable, a function or any expression in parentheses. When the element -is not a float literal nor an expression in parentheses, there has to naturally -be at least one whitespace between the element and the unit (eg. -<code>"x in"</code>). To change the value of a unit, call -<code>AddUnit()</code> again with the same unit name and the new value. - -<p>Unit names share the same namespace as constants, functions and - variables, and thus should be distinct from those. - -<p>Example: <code>parser.AddUnit("in", 300);</code> - -<p>Now for example the function <code>"5in"</code> will be identical to -<code>"(5*300)"</code>. Other usage examples include <code>"x in"</code>, -<code>"3in+2"</code>, <code>"pow(x,2)in"</code>, <code>"(x+2)in"</code>. - - -<hr> -<a name="longdesc_AddFunction1"></a> -<pre> -bool AddFunction(const std::string& name, - double (*functionPtr)(const double*), - unsigned paramsAmount); -</pre> - -This method can be used to add new functions to the parser. For example, -if you would like to add a function "<code>sqr(A)</code>" which squares the -value of <code>A</code>, you can do it with this method (so that you don't -need to touch the source code of the parser). - -<p>The method takes three parameters: - -<ul> - <li>The name of the function. The name follows the same naming conventions - as variable names. - - <li>A C++ function, which will be called when evaluating the function - string (if the user-given function is called there). The C++ function - must have the form: - <p><code>double functionName(const double* params);</code> - - <li>The number of parameters the function takes. 0 is a valid value - in which case the function takes no parameters (such function - should simply ignore the <code>double*</code> it gets as a parameter). -</ul> - -<p>The return value will be <code>false</code> if the given name was invalid -(either it did not follow the variable naming conventions, or the name was -already reserved), else <code>true</code>. If the return value is -<code>false</code>, nothing is added. - -<p>Example: Suppose we have a C++ function like this: - -<p><code>double Square(const double* p)</code><br> -<code>{</code><br> -<code> return p[0]*p[0];</code><br> -<code>}</code> - -<p>Now we can add this function to the parser like this: - -<p><code>parser.AddFunction("sqr", Square, 1);</code><br> -<code>parser.Parse("2*sqr(x)", "x");</code> - -<p>An example of a useful function taking no parameters is a function - returning a random value. For example: - -<p><code>double Rand(const double*)</code><br> -<code>{</code><br> -<code> return drand48();</code><br -<code>}</code> - -<p><code>parser.AddFunction("rand", Rand, 0);</code> - -<p><em>Important note</em>: If you use the <code>Optimize()</code> method, -it will assume that the user-given function has no side-effects, that is, -it always returns the same value for the same parameters. The optimizer will -optimize the function call away in some cases, making this assumption. -(The <code>Rand()</code> function given as example above is one such -problematic case.) - - -<hr> -<a name="longdesc_AddFunction2"></a> -<pre> -bool AddFunction(const std::string& name, FunctionParser&); -</pre> - -<p>This method is almost identical to the previous <code>AddFunction()</code>, -but instead of taking a C++ function, it takes another FunctionParser -instance. - -<p>There are some important restrictions on making a FunctionParser instance - call another: - -<ul> - <li>The FunctionParser instance given as parameter must be initialized - with a <code>Parse()</code> call before giving it as parameter. That - is, if you want to use the parser <code>A</code> in the parser - <code>B</code>, you must call <code>A.Parse()</code> before you can - call <code>B.AddFunction("name", A)</code>. - - <li>The amount of variables in the FunctionParser instance given as - parameter must not change after it has been given to the - <code>AddFunction()</code> - of another instance. Changing the number of variables will result in - malfunction. - - <li><code>AddFunction()</code> will fail (ie. return <code>false</code>) - if a recursive loop is - formed. The method specifically checks that no such loop is built. - - <li>The FunctionParser instance given as parameter will <em>not</em> be - copied internally, only referenced. Thus the FunctionParser instance - given as parameter must exist for as long as the other FunctionParser - instance uses it. -</ul> - -<p>Example: - -<p><code>FunctionParser f1, f2;</code><br> -<p><code>f1.Parse("x*x", "x");</code><br> -<p><code>f2.AddFunction("sqr", f1);</code> - -<p>This version of the <code>AddFunction()</code> method can be useful to -eg. chain user-given functions. For example, ask the user for a function F1, - and then ask the user another function F2, but now the user can - call F1 in this second function if he wants (and so on with a third - function F3, where he can call F1 and F2, etc). - -<hr> -<a name="longdesc_AddFunction3"></a> -<pre> -template<typename DerivedWrapper> -bool AddFunctionWrapper(const std::string& name, const DerivedWrapper&, - unsigned paramsAmount); -</pre> - -<p>See section on <a href="#functionobjects">specialized function objects</a>. - -<hr> -<a name="longdesc_RemoveIdentifier"></a> -<pre> -bool RemoveIdentifier(const std::string& name); -</pre> - -<p>If a constant, unit or user-defined function with the specified name -exists in the parser, it will be removed and the return value will be -<code>true</code>, else nothing will be done and the return value will be -<code>false</code>. - -<p>(Note: If you want to remove <em>everything</em> from an existing -FunctionParser instance, simply assign a fresh instance to it, ie. like -"<code>parser = FunctionParser();</code>") - -<hr> -<a name="longdesc_ParseAndDeduceVariables"></a> -<pre> -int ParseAndDeduceVariables(const std::string& function, - int* amountOfVariablesFound = 0, - bool useDegrees = false); -int ParseAndDeduceVariables(const std::string& function, - std::string& resultVarString, - int* amountOfVariablesFound = 0, - bool useDegrees = false); -int ParseAndDeduceVariables(const std::string& function, - std::vector<std::string>& resultVars, - bool useDegrees = false); -</pre> - -<p>These functions work in the same way as the <code>Parse()</code> function, -but the variables in the input function string are deduced automatically. The -parameters are: - -<ul> - <li><code>function</code>: The input function string, as with - <code>Parse()</code>. - <li><code>amountOfVariablesFound</code>: If non-null, the amount of found - variables will be assigned here. - <li><code>resultVarString</code>: The found variables will be written to - this string, in the same format as accepted by the <code>Parse()</code> - function. The variable names will be sorted using the <code><</code> - operator of <code>std::string</code>. - <li><code>resultVars</code>: The found variables will be written to this - vector, each element being one variable name. They will be sorted using - the <code><</code> operator of <code>std::string</code>. (The amount - of found variables can be retrieved, rather obviously, with the - <code>size()</code> method of the vector.) - <li><code>useDegrees</code>: As with <code>Parse()</code>. -</ul> - -<p>As with <code>Parse()</code>, the return value will be <code>-1</code> if -the parsing succeeded, else an index to the location of the error. None of -the specified return values will be modified in case of error. - -<!-- -------------------------------------------------------------------- --> -<a name="functionobjects"></a> -<h3>Specialized function objects</h3> - -<p>The <code>AddFunction()</code> method can be used to add a new user-defined -function to the parser, its implementation being called through a C++ function -pointer. Sometimes this might not be enough, though. For example, one might -want to use <code>boost::function</code> or other similar specialized stateful -function objects instead of raw function pointers. This library provides a -mechanism to achieve this. - -<h4>Creating and adding a specialized function object</h4> - -<p>In order to create a specialized function object, create a class derived -from the <code>FunctionParser::FunctionWrapper</code> class. This class -declares a virtual function named <code>callFunction</code> that the derived -class must implement. For example: - -<pre> -class MyFunctionWrapper: - public FunctionParser::FunctionWrapper -{ - public: - virtual double callFunction(const double* values) - { - // Perform the actual function call here, like: - return someFunctionSomewhere(values); - - // In principle the result could also be - // calculated here, like for example: - return values[0] * values[0]; - } -}; -</pre> - -<p>You can then add an instance of this class to <code>FunctionParser</code> -using the <code>AddFunctionWrapper()</code> method, which works like -<code>AddFunction()</code>, but takes a wrapper object instead of a function -pointer as parameter. For example: - -<pre> -MyFunctionWrapper wrapper; -parser.AddFunctionWrapper("funcName", wrapper, 1); -</pre> - -<p>Note that <code>FunctionParser</code> will internally create a copy of -the wrapper object, managing the lifetime of this copy, and thus the object -given as parameter does not need to exist for as long as the -<code>FunctionParser</code> instance. Hence the above could also be written as: - -<pre> -parser.AddFunctionWrapper("funcName", MyFunctionWrapper(), 1); -</pre> - -<p>Note that this also means that the wrapper class must have a working -copy constructor. - -<p>Also note that if the <code>FunctionParser</code> instance is copied, all -the copies will share the same function wrapper objects given to the original. - -<h4>Retrieving specialized function objects</h4> - -<p>As noted, the library will internally make a copy of the wrapper object, -and thus it will be separate from the one which was given as parameter to -<code>AddFunctionWrapper()</code>. In some cases it may be necessary to -retrieve this wrapper object (for example to read or change its state). -This can be done with the <code>GetFunctionWrapper()</code> method, which -takes the name of the function and returns a pointer to the wrapper object, -or null if no such object exists with that name. - -<p>Note that the returned pointer will be of type -<code>FunctionParser::FunctionWrapper</code>. In order to get a pointer to -the actual derived type, the calling code should perform a -<code>dynamic_cast</code>, for example like this: - -<pre> -MyFunctionWrapper* wrapper = - dynamic_cast<MyFunctionWrapper*> - (parser.GetFunctionWrapper("funcName")); - -if(!wrapper) { /* oops, the retrieval failed */ } -else ... -</pre> - -<p>(Using dynamic cast rather than a static cast adds safety because if you -accidentally try to downcast to the wrong type, the pointer will become null.) - -<p>The calling code is free to modify the object in any way it wants, but it -must not delete it (because <code>FunctionParser</code> itself handles this). - - -<!-- -------------------------------------------------------------------- --> -<a name="base"></a> -<h3>FunctionParserBase</h3> - -<p>All the different parser types are derived from a templated base class -named <code>FunctionParserBase</code>. In normal use it's not necessary to -directly refer to this base class in the calling code. However, if the calling -code also needs to be templated (with respect to the numerical type), then -using <code>FunctionParserBase</code> directly is the easiest way to achieve -this. - -<p>For example, if you want to make a function that handles more than one -type of parser, it can be done like this: - -<pre> -template<typename Value_t> -void someFunction(FunctionParserBase<Value_t>& parser) -{ - // do something with 'parser' here -} -</pre> - -<p>Now it's convenient to call that function with more than one type of -parser, for example: - -<pre> -FunctionParser realParser; -FunctionParser_cd complexParser; - -someFunction(realParser); -someFunction(complexParser); -</pre> - -<p>Another example is a class that inherits from <code>FunctionParser</code> -which also wants to support different numerical types. Such class can be -declared as: - -<pre> -template<typename Value_t> -class SpecializedParser: public FunctionParserBase<Value_t> -{ - ... -}; -</pre> - - -<!-- -------------------------------------------------------------------- --> -<h2>Syntax</h2> - -<a name="literals"></a> -<h3>Numeric literals</h3> - -<p>A numeric literal is a fixed numerical value in the input function string - (either a floating point value or an integer value, depending on the parser - type). - -<p>An integer literal can consist solely of numerical digits (possibly with - a preceding unary minus). For example, "<code>12345</code>". - -<p>If the literal is preceded by the characters "<code>0x</code>", it - will be interpreted as a hexadecimal literal, where digits can also include - the letters from '<code>A</code>' to '<code>F</code>' (in either uppercase - or lowercase). For example, "<code>0x89ABC</code>" (which corresponds to the - value 563900). - -<p>A floating point literal (only supported by the floating point type parsers) - may additionally include a decimal point followed by the decimal part of the - value, such as for example "<code>12.34</code>", optionally followed by a - decimal exponent. - -<p>A decimal exponent consists of an '<code>E</code>' or '<code>e</code>', - followed by an optional plus or minus sign, followed by decimal digits, and - indicates multiplication by a power of 10. For example, "<code>1.2e5</code>" - (which is equivalent to the value 120000). - -<p>If a floating point literal is preceded by the characters "<code>0x</code>" - it will be interpreted in hexadecimal. A hexadecimal floating point - literal consists of a hexadecimal value, with an optional decimal point, - followed optionally by a binary exponent in base 10 (in other words, the - exponent is not in hexadecimal). - -<p>A binary exponent has the same format as a decimal exponent, except that - '<code>P</code>' or '<code>p</code>' is used. A binary exponent indicates - multiplication by a power of 2. For example, "<code>0xA.Bp10</code>" - (which is equivalent to the value 10944). - -<p>With the complex versions of the library, the imaginary part of a numeric - literal is written as a regular numeric literal with an '<code>i</code>' - appended, for example "<code>5i</code>". Note that when also specifying - the real part of a complex literal, parentheses should be used to avoid - precedence problems. (For example, "<code>(2+5i) * x</code>" - is not the same thing as "<code>2+5i * x</code>". The latter - would be equivalent to "<code>2 + (5i * x)</code>".) - -<a name="identifiers"></a> -<h3>Identifier names</h3> - -<p>An identifier is the name of a function (internal or user-defined), - variable, constant or unit. New identifiers can be specified with the - functions described in the earlier subsections in this document. - -<p>The name of an identifier can use any alphanumeric characters, the - underscore character and any UTF8-encoded unicode character, excluding - those denoting whitespace. - The first character of the name cannot be a numeric digit, though. - -<p>All functions, variables, constants and units must use unique names. - It's not possible to add two different identifiers with the same name. - - -<!-- -------------------------------------------------------------------- --> -<a name="functionsyntax"></a> -<h3>The function string syntax</h3> - -<p>The function string understood by the class is very similar (but not -completely identical in all aspects) to mathematical expressions in the -C/C++ languages. -Arithmetic float expressions can be created from float literals, variables -or functions using the following operators in this order of precedence: - -<p><table border=2> - <tr> - <td><code>()</code></td> - <td>expressions in parentheses first</td> - </tr><tr> - <td><code>A unit</code></td> - <td>a unit multiplier (if one has been added)</td> - </tr><tr> - <td><code>A^B</code></td> - <td>exponentiation (A raised to the power B)</td> - </tr><tr> - <td><code>-A</code></td> - <td>unary minus</td> - </tr><tr> - <td><code>!A</code></td> - <td>unary logical not (result is 1 if <code>int(A)</code> is 0, else 0)</td> - </tr><tr> - <td><code>A*B A/B A%B</code></td> - <td>multiplication, division and modulo</td> - </tr><tr> - <td><code>A+B A-B</code></td> - <td>addition and subtraction</td> - </tr><tr> - <td><code>A=B A<B A<=B<br>A!=B A>B A>=B</code></td> - <td>comparison between A and B (result is either 0 or 1)</td> - </tr><tr> - <td><code>A&B</code></td> - <td>result is 1 if <code>int(A)</code> and <code>int(B)</code> differ from - 0, else 0.<br> - Note: Regardless of the values, both operands are always - evaluated. However, if the expression is optimized, it may - be changed such that only one of the operands is evaluated, - according to standard shortcut logical operation semantics.</td> - </tr><tr> - <td><code>A|B</code></td> - <td>result is 1 if <code>int(A)</code> or <code>int(B)</code> differ from 0, - else 0.<br> - Note: Regardless of the values, both operands are always - evaluated. However, if the expression is optimized, it may - be changed such that only one of the operands is evaluated, - according to standard shortcut logical operation semantics.</td> - </tr> -</table> - -<p>(Note that currently the exponentiation operator is not supported for - <code>FunctionParser_li</code> nor <code>FunctionParser_gmpint</code>. - With the former the result would very easily overflow, making its - usefulness questionable. With the latter it could be easily abused to - make the program run out of memory; think of a function like - "10^10^10^100000".) - -<p>Since the unary minus has higher precedence than any other operator, for - example the following expression is valid: <code>x*-y</code> - -<p>The comparison operators use an epsilon value, so expressions which may -differ in very least-significant digits should work correctly. For example, -<code>"0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1 = 1"</code> should always -return 1, and the same comparison done with "<code>></code>" or -"<code><</code>" should always return 0. (The epsilon value can be -configured in the <code>fpconfig.hh</code> file.) -Without epsilon this comparison probably returns the wrong value. - -<p>The class supports these functions: - -<p><table border=2> -<tr> - <td><code>abs(A)</code></td> - <td>Absolute value (magnitude) of A. - With real numbers, if A is negative, returns -A otherwise returns A. - With complex numbers, equivalent to <code>hypot(real(x),imag(x))</code>.</td> -</tr><tr> - <td><code>acos(A)</code></td> - <td>Arc-cosine of A. Returns the angle, measured in radians, whose cosine is A.</td> -</tr><tr> - <td><code>acosh(A)</code></td> - <td>Same as acos() but for hyperbolic cosine.</td> -</tr><tr> - <td><code>arg(A)</code></td> - <td>Phase angle of complex number A. Equivalent to <code>atan2(imag(x),real(x))</code>.</td> -</tr><tr> - <td><code>asin(A)</code></td> - <td>Arc-sine of A. Returns the angle, measured in radians, whose sine is A.</td> -</tr><tr> - <td><code>asinh(A)</code></td> - <td>Same as asin() but for hyperbolic sine.</td> -</tr><tr> - <td><code>atan(A)</code></td> - <td>Arc-tangent of (A). Returns the angle, measured in radians, - whose tangent is A.</td> -</tr><tr> - <td><code>atan2(A,B)</code></td> - <td>Principal arc-tangent of A/B, using the signs of the - two arguments to determine the quadrant of the result. - Returns the solution to the two expressions - hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B. - The return value is in range -pi to pi, inclusive.</td> -</tr><tr> - <td><code>atanh(A)</code></td> - <td>Same as atan() but for hyperbolic tangent.</td> -</tr><tr> - <td><code>cbrt(A)</code></td> - <td>Cube root of A. Returns a solution to expression pow(x,3)=A.</td> -</tr><tr> - <td><code>conj(A)</code></td> - <td>Complex conjugate of A. Equivalent to <code>real(x) - 1i*imag(x)</code> or <code>polar(abs(x),-arg(x))</code>.</td> -</tr><tr> - <td><code>ceil(A)</code></td> - <td>Ceiling of A. Returns the smallest integer not smaller than A. - Rounds up to the next higher integer. E.g. -2.9, -2.5 and -2.1 are - rounded to -2.0, and 2.9, 2.5 and 2.1 are rounded to 3.0.</td> -</tr><tr> - <td><code>cos(A)</code></td> - <td>Cosine of A. Returns the cosine of the angle A, where A is - measured in radians.</td> -</tr><tr> - <td><code>cosh(A)</code></td> - <td>Same as cos() but for hyperbolic cosine.</td> -</tr><tr> - <td><code>cot(A)</code></td> - <td>Cotangent of A. Equivalent to <code>1/tan(A)</code>.</td> -</tr><tr> - <td><code>csc(A)</code></td> - <td>Cosecant of A. Equivalent to <code>1/sin(A)</code>.</td> -</tr><tr> - <td><code>eval(...)</code></td> - <td>This a recursive call to the function to be evaluated. The - number of parameters must be the same as the number of parameters - taken by the function. Must be called inside <code>if()</code> to avoid - infinite recursion.</td> -</tr><tr> - <td><code>exp(A)</code></td> - <td>Exponential of A. Returns the value of e raised to the power - A where e is the base of the natural logarithm, i.e. the - non-repeating value approximately equal to 2.71828182846.</td> -</tr><tr> - <td><code>exp2(A)</code></td> - <td>Base 2 exponential of A. Equivalent to <code>pow(2,A)</code>.</td> -</tr><tr> - <td><code>floor(A)</code></td> - <td>Floor of A. Returns the largest integer not greater than A. Rounds - down to the next lower integer. - E.g. -2.9, -2.5 and -2.1 are rounded to -3.0, - and 2.9, 2.5 and 2.1 are rounded to 2.0.</td> -</tr><tr> - <td><code>hypot(A,B)</code></td> - <td>Euclidean distance function. Equivalent to <code>sqrt(A^2+B^2)</code>.</td> -</tr><tr> - <td><code>if(A,B,C)</code></td> - <td>If int(A) differs from 0, the return value of this function is B, - else C. Only the parameter which needs to be evaluated is - evaluated, the other parameter is skipped; this makes it safe to - use <code>eval()</code> in them.</td> -</tr><tr> - <td><code>imag(A)</code></td> - <td>Return the imaginary part of complex number A. Equivalent to <code>abs(A)*sin(arg(A))</code>.</td> -</tr><tr> - <td><code>int(A)</code></td> - <td>Rounds A to the closest integer. Equidistant values are rounded away from - zero. E.g. -2.9 and -2.5 are rounded to -3.0; -2.1 is rounded to -2.0, - and 2.9 and 2.5 are rounded to 3.0; 2.1 is rounded to 2.0.</td> -</tr><tr> - <td><code>log(A)</code></td> - <td>Natural (base e) logarithm of A. Returns the solution to expression exp(x)=A.</td> -</tr><tr> - <td><code>log2(A)</code></td> - <td>Base 2 logarithm of A. Equivalent to <code>log(A)/log(2)</code>.</td> -</tr><tr> - <td><code>log10(A)</code></td> - <td>Base 10 logarithm of A.</td> -</tr><tr> - <td><code>max(A,B)</code></td> - <td>If A>B, the result is A, else B.</td> -</tr><tr> - <td><code>min(A,B)</code></td> - <td>If A<B, the result is A, else B.</td> -</tr><tr> - <td><code>polar(A,B)</code></td> - <td>Returns a complex number from magnitude A, phase angle B (in radians). - Equivalent to <code>real(A)*(cos(real(B))+1i*sin(real(B)))</code>.</td> -</tr><tr> - <td><code>pow(A,B)</code></td> - <td>Exponentiation (A raised to the power B).</td> -</tr><tr> - <td><code>real(A)</code></td> - <td>Return the real part of complex number A. Equivalent to <code>abs(A)*cos(arg(A))</code>.</td> -</tr><tr> - <td><code>sec(A)</code></td> - <td>Secant of A. Equivalent to <code>1/cos(A)</code>.</td> -</tr><tr> - <td><code>sin(A)</code></td> - <td>Sine of A. Returns the sine of the angle A, where A is - measured in radians.</td> -</tr><tr> - <td><code>sinh(A)</code></td> - <td>Same as sin() but for hyperbolic sine.</td> -</tr><tr> - <td><code>sqrt(A)</code></td> - <td>Square root of A. Returns a solution to expression pow(x,2)=A.</td> -</tr><tr> - <td><code>tan(A)</code></td> - <td>Tangent of A. Returns the tangent of the angle A, where A - is measured in radians.</td> -</tr><tr> - <td><code>tanh(A)</code></td> - <td>Same as tan() but for hyperbolic tangent.</td> -</tr><tr> - <td><code>trunc(A)</code></td> - <td>Truncated value of A. Returns an integer corresponding to the value - of A without its fractional part. - E.g. -2.9, -2.5 and -2.1 are rounded to -2.0, - and 2.9, 2.5 and 2.1 are rounded to 2.0.</td> -</tr> -</table> - -<p>(Note that for <code>FunctionParser_li</code> and - <code>FunctionParser_gmpint</code> only the functions - <code>abs()</code>, <code>eval()</code>, <code>if()</code>, - <code>min()</code> and <code>max()</code> are supported.) - -<p>Examples of function string understood by the class: - -<p><code>"1+2"</code><br> -<code>"x-1"</code><br> -<code>"-sin(sqrt(x^2+y^2))"</code><br> -<code>"sqrt(XCoord*XCoord + YCoord*YCoord)"</code><br> - -<p>An example of a recursive function is the factorial function: - -<code>"if(n>1, n*eval(n-1), 1)"</code> - -<p>Note that a recursive call has some overhead, which makes it a bit slower - than any other operation. It may be a good idea to avoid recursive functions - in very time-critical applications. Recursion also takes some memory, so - extremely deep recursions should be avoided (eg. millions of nested recursive - calls). - -<p>Also note that even though the maximum recursion level of -<code>eval()</code> is limited, it is possible to write functions which -never reach that level but still take enormous amounts of time to evaluate. -This can sometimes be undesirable because it is prone to exploitation, -which is why <code>eval()</code> is disabled by default. It can be enabled -in the <code>fpconfig.hh</code> file. - - -<!-- -------------------------------------------------------------------- --> -<a name="inlinevars"></a> -<h3>Inline variables</h3> - -<p>The function syntax supports defining new variables inside the function -string itself. This can be done with the following syntax: - -<p><code>"<variable name> := <expression>; <function>"</code> - -<p>For example: - -<p><code>"length := sqrt(x*x+y*y); 2*length*sin(length)"</code> - -<p>(Spaces around the '<code>:=</code>' operator are optional.) - -<p>The obvious benefit of this is that if a long expression needs to be -used in the function several times, this allows writing it only once and -using a named variable from that point forward. - -<p>The variable name must be an unused identifier (in other words, not an -existing function, variable or unit name). - -<p>The <code><function></code> part can have further inline variable -definitions, and thus it's possible to have any amount of them, for example: - -<p><code>"A := x^2; B := y^2; C := z^2; sqrt(A+B+C)"</code> - -<p>The expressions in subsequent inline variable definitions can use any -of the previous inline variables. It is also possible to redefine an inline -variable. For example: - -<p><code>"A := x^2; A := 2*A; sqrt(A)"</code> - - -<!-- -------------------------------------------------------------------- --> -<a name="whitespace"></a> -<h3>Whitespace</h3> - -<p>Arbitrary amounts of whitespace can optionally be included between - elements in the function string. - The following unicode characters are interpreted as whitespace: -<table> - <tr> - <th>Character number</th> - <th>Character name</th> - <th>UTF-8 byte sequence</th> - </tr> - <tr><td>U+0009</td><td>HORIZONTAL TABULATION </td><td>09</td></tr> - <tr><td>U+000A</td><td>LINE FEED </td><td>0A</td></tr> - <tr><td>U+000B</td><td>VERTICAL TABULATION </td><td>0B</td></tr> - <tr><td>U+000D</td><td>CARRIAGE RETURN </td><td>0D</td></tr> - <tr><td>U+0020</td><td>SPACE </td><td>20</td></tr> - <tr><td>U+00A0</td><td>NO-BREAK SPACE </td><td>C2 A0</td></tr> - <tr><td>U+2000</td><td>EN QUAD </td><td>E2 80 80</td></tr> - <tr><td>U+2001</td><td>EM QUAD </td><td>E2 80 81</td></tr> - <tr><td>U+2002</td><td>EN SPACE </td><td>E2 80 82</td></tr> - <tr><td>U+2003</td><td>EM SPACE </td><td>E2 80 83</td></tr> - <tr><td>U+2004</td><td>THREE-PER-EM SPACE </td><td>E2 80 84</td></tr> - <tr><td>U+2005</td><td>FOUR-PER-EM SPACE </td><td>E2 80 85</td></tr> - <tr><td>U+2006</td><td>SIX-PER-EM SPACE </td><td>E2 80 86</td></tr> - <tr><td>U+2007</td><td>FIGURE SPACE </td><td>E2 80 87</td></tr> - <tr><td>U+2008</td><td>PUNCTUATION SPACE </td><td>E2 80 88</td></tr> - <tr><td>U+2009</td><td>THIN SPACE </td><td>E2 80 89</td></tr> - <tr><td>U+200A</td><td>HAIR SPACE </td><td>E2 80 8A</td></tr> - <tr><td>U+200B</td><td>ZERO WIDTH SPACE </td><td>E2 80 8B</td></tr> - <tr><td>U+202F</td><td>NARROW NO-BREAK SPACE </td><td>E2 80 AF</td></tr> - <tr><td>U+205F</td><td>MEDIUM MATHEMATICAL SPACE</td><td>E2 81 9F</td></tr> - <tr><td>U+3000</td><td>IDEOGRAPHIC SPACE </td><td>E3 80 80</td></tr> -</table> - -<!-- -------------------------------------------------------------------- --> -<h2>Miscellaneous</h2> - -<a name="fpaccuracy"></a> -<h3>About floating point accuracy</h3> - -<p>Note that if you are using <code>FunctionParser_ld</code> or -<code>FunctionParser_cld</code> and you want calculations to be as accurate -as the <code>long double</code> type allows, you should pay special attention -to floating point literals in your own code. For example, this is a very -typical mistake: - -<pre>FunctionParser_ld parser; -parser.AddConstant("pi", 3.14159265358979323846);</pre> - -<p>The mistake might not be immediately apparent. The mistake is that a -literal of type <code>double</code> is passed to the <code>AddConstant()</code> -function even though it expects a value of type <code>long double</code>. -In most systems the latter has more bits of precision than the former, which -means that the value will have its least-significant bits clipped, -introducing a rounding error. The proper way of making the above calls is: - -<pre>FunctionParser_ld parser; -parser.AddConstant("pi", 3.14159265358979323846L);</pre> - -<p>The same principle should be used everywhere in your own code, if you are -using the <code>long double</code> type. - -<p>This is especially important if you are using the <code>MpfrFloat</code> -type (in which case its string-parsing constructor or its -<code>ParseValue()</code> or <code>parseString()</code> member functions -should be used instead of using numerical literals). - -<a name="evaluationchecks"></a> -<h3>About evaluation-time checks</h3> - -<p><code>FunctionParser::Eval()</code> will perform certain sanity -checks before performing certain operations. For example, before calling the -<code>sqrt</code> function, it will check if the parameter is negative, and -if so, it will set the proper error code instead of calling the function. -These checks include: - -<ul> - <li>Division by (the exact value of) zero. - <li>Square root of a negative value. - <li>Logarithm of a non-positive value. - <li>Arcsine or arccosine of a value not in the range [-1, 1]. (This includes - hyperbolic versions of the functions.) -</ul> - -<p>However, the library <em>can not</em> guarantee that it will catch all -possible floating point errors before performing them, because this is -impossible to do with standard C++. For example, dividing a very large -value by a value which is very close to zero, or calculating the logarithm -of a very small value may overflow the result, as well as multiplying two -very large values. Raising a negative number to a non-integral power may -cause a <em>NaN</em> result, etc. - -<p>As a rule of thumb, the library will (by default) detect invalid operations -if they are invalid for a range of values. For example, square root is undefined -for all negative values, and arc sine is undefined only values outside the range -[-1, 1]. In general, operations which are invalid for only one single value -(rather than a contiguous range of values) will not be detected (division by -the exact value of zero is an exception to this rule) nor will -overflow/underflow situations. - -<p>The library cannot guarantee that floating point -errors will never happen during evaluation. This can make the library to -return the floating point values <em>inf</em> and <em>NaN</em>. Moreover, -if floating point errors cause an interrupt in the target computer -architecture and/or when using certain compiler settings, this library -cannot guarantee that it will never happen. - -<p>Note that the optimizer never performs any sanity checks. - - -<!-- -------------------------------------------------------------------- --> -<a name="threadsafety"></a> -<h3>About thread safety</h3> - -<p>None of the member functions of the FunctionParser class are thread-safe. -Most prominently, the <code>Eval()</code> function is not thread-safe. -(In other words, the <code>Eval()</code> function of a single FunctionParser -instance cannot be safely called simultaneously by two threads.) - -<p>There are ways to use this library in a thread-safe way, though. If each -thread uses its own FunctionParser instance, no problems will obviously -happen. Note, however, that if these instances need to be a copy of a given -FunctionParser instance (eg. one where the user has entered a function), -a deep copy of this instance has to be performed for each thread. By -default FunctionParser uses shallow-copying (copy-on-write), which means -that a simple assignment of copy construction will not copy the data itself. -To force a deep copy you can all the <code>ForceDeepCopy()</code> function on -each of the instances of each thread after the assignment or copying has been -done. - -<p>Another possibility is to compile the FunctionParser library so that -its <code>Eval()</code> function will be thread-safe. (This can be done by -defining the <code>FP_USE_THREAD_SAFE_EVAL</code> or the -<code>FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA</code> -precompiler constant.) As long as only one thread calls the other functions -of FunctionParser, the other threads can safely call the <code>Eval()</code> -of this one instance. - -<p>Note, however, that compiling the library like this can make -<code>Eval()</code> slightly slower. (The <code>alloca</code> version, if -supported by the compiler, will not be as slow.) - -<p>Also note that the MPFR and GMP versions of the library cannot be - made thread-safe, and thus this setting has no effect on them. - - -<!-- -------------------------------------------------------------------- --> -<a name="tipsandtricks"></a> -<h3>Tips and tricks</h3> - -<h4>Add constants automatically to all parser objects</h4> - -<p>Often the same constants (such as <em>pi</em> and <em>e</em>) and other -user-defined identifiers (such as units) are always used in all the -<code>FunctionParser</code> objects throughout the program. It would be -troublesome to always have to manually add these constants every time a -new parser object is created. - -<p>There is, however, a simple way to always add these user-defined identifiers -to all instances. Write a class like this: - -<pre> - class ParserWithConsts: public FunctionParser - { - public: - ParserWithConsts() - { - AddConstant("pi", 3.14159265358979323846); - AddConstant("e", 2.71828182845904523536); - } - }; -</pre> - -<p>Now instead of using <code>FunctionParser</code>, always use -<code>ParserWithConsts</code>. It will behave identically except that the -constants (and possibly other user-defined identifiers) will always be -automatically defined. (Objects of this type even survive -<a href="http://en.wikipedia.org/wiki/Object_slicing">slicing</a>, so -they are completely safe to use anywhere.) - - -<!-- -------------------------------------------------------------------- --> -<a name="contact"></a> -<h3>Contacting the author</h3> - -<p>Any comments, bug reports, etc. should be sent to warp@iki.fi - - -<!-- -------------------------------------------------------------------- --> -<!-- -<a name="algorithm"></a> -<h2>The algorithm used in the library</h2> - -<p>The whole idea behind the algorithm is to convert the regular infix -format (the regular syntax for mathematical operations in most languages, -like C and the input of the library) to postfix format. The postfix format -is also called stack arithmetic since an expression in postfix format -can be evaluated using a stack and operating with the top of the stack. - -<p>For example: - -<p><table border=2> -<tr><th>infix</th> <th>postfix</th></tr> -<tr><td><code>2+3</code></td><td><code>2 3 +</code></td></tr> -<tr><td><code>1+2+3</code></td><td><code>1 2 + 3 +</code></td></tr> -<tr><td><code>5*2+8/2</code></td><td><code>5 2 * 8 2 / +</code></td></tr> -<tr><td><code>(5+9)*3</code></td><td><code>5 9 + 3 *</code></td></tr> -</table> - -<p>The postfix notation should be read in this way: - -<p>Let's take for example the expression: <code>5 2 * 8 2 / +</code> -<ul> - <li>Put 5 on the stack - <li>Put 2 on the stack - <li>Multiply the two values on the top of the stack and put the result on - the stack (removing the two old values) - <li>Put 8 on the stack - <li>Put 2 on the stack - <li>Divide the two values on the top of the stack - <li>Add the two values on the top of the stack (which are in this case - the result of 5*2 and 8/2, that is, 10 and 4). -</ul> - -<p>At the end there's only one value in the stack, and that value is the -result of the expression. - -<p>Why stack arithmetic? - -<p>The last example above can give you a hint. - In infix format operators have precedence and we have to use parentheses to -group operations with lower precedence to be calculated before operations -with higher precedence. - This causes a problem when evaluating an infix expression, specially -when converting it to byte code. For example in this kind of expression: - <code>(x+1)/(y+2)</code> -we have to calculate first the two additions before we can calculate the -division. We have to also keep counting parentheses, since there can be -a countless amount of nested parentheses. This usually means that you -have to do some type of recursion. - -<p>The simplest and mostefficient way of calculating this is to convert it -to postfix notation. - The postfix notation has the advantage that you can make all operations -in a straightforward way. You just evaluate the expression from left to -right, applying each operation directly and that's it. There are no -parentheses to worry about. You don't need recursion anywhere. - You have to keep a stack, of course, but that's extremely easily done. -Also you just operate with the top of the stack, which makes it very easy. -You never have to go deeper than 2 items in the stack. - And even better: Evaluating an expression in postfix format is never -slower than in infix format. All the contrary, in many cases it's a lot -faster (eg. because all parentheses are optimized away). - The above example could be expressed in postfix format: - <code>x 1 + y 2 + /</code> - -<p>The good thing about the postfix notation is also the fact that it can -be extremely easily expressed in bytecode form. - You only need a byte value for each operation, for each variable and -to push a constant to the stack. - Then you can interpret this bytecode straightforwardly. You just interpret -it byte by byte, from the beginning to the end. You never have to go back, -make loops or anything. - -<p>This is what makes byte-coded stack arithmetic so fast. ---> - - -<!-- -------------------------------------------------------------------- --> -<a name="license"></a> -<h2>Usage license</h2> - -<p>Copyright © 2003-2011 Juha Nieminen, Joel Yliluoma - -<p>This Library is distributed under the - <a href="http://www.gnu.org/copyleft/lesser.html">Lesser General Public - License</a> (LGPL) version 3. - -</body> -</html> diff --git a/fparser/docs/gpl.txt b/fparser/docs/gpl.txt deleted file mode 100644 index 94a9ed0..0000000 --- a/fparser/docs/gpl.txt +++ /dev/null @@ -1,674 +0,0 @@ - GNU GENERAL PUBLIC LICENSE - Version 3, 29 June 2007 - - Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. 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