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| author | Thales Lima Oliveira <thaleslima.ufu@gmail.com> | 2017-12-31 18:00:25 -0200 |
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| committer | GitHub <noreply@github.com> | 2017-12-31 18:00:25 -0200 |
| commit | 0c0280cfcf540f943fd2dbfdf7ac0304ea96a465 (patch) | |
| tree | 51c89fc8155dcc447743dc89a1ab5ce36acc72cf /Project/fparser/docs/fparser.html | |
| parent | c8193665975686fb8a344bee3dc94914a3d3558a (diff) | |
| parent | dbe0b112622f8e91fa3e44a6b6e1aa7e230d3ded (diff) | |
| download | PSP.git-0c0280cfcf540f943fd2dbfdf7ac0304ea96a465.tar.gz PSP.git-0c0280cfcf540f943fd2dbfdf7ac0304ea96a465.tar.xz PSP.git-0c0280cfcf540f943fd2dbfdf7ac0304ea96a465.zip | |
Merge pull request #43 from Thales1330/wip/math-expr-control-block
Wip math expr control block
Diffstat (limited to 'Project/fparser/docs/fparser.html')
| -rw-r--r-- | Project/fparser/docs/fparser.html | 1841 |
1 files changed, 1841 insertions, 0 deletions
diff --git a/Project/fparser/docs/fparser.html b/Project/fparser/docs/fparser.html new file mode 100644 index 0000000..eb94d19 --- /dev/null +++ b/Project/fparser/docs/fparser.html @@ -0,0 +1,1841 @@ +<!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++ v4.5.2 : Documentation</title> +</head> + +<body> +<h1>Function Parser for C++ v4.5.2 </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 v4.5.2 + <ul> + <li>Fixed several optimizer bugs. + <li>Fixed compilation problems with Visual Studio 2013 and gcc. + </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> |