From 54bb80251432ff49c967115f8401e7dafc5c57d6 Mon Sep 17 00:00:00 2001 From: Thales Lima Oliveira Date: Tue, 19 Dec 2017 22:00:05 -0200 Subject: Several implementations on math expression block --- Project/fparser/docs/fparser.html | 1841 +++++++++++++++++++++++++++++++++++++ 1 file changed, 1841 insertions(+) create mode 100644 Project/fparser/docs/fparser.html (limited to 'Project/fparser/docs/fparser.html') 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 @@ + + + + + + Function Parser for C++ v4.5.2 : Documentation + + + +

Function Parser for C++ v4.5.2

+ +

Authors: Juha Nieminen +(http://iki.fi/warp/), +Joel Yliluoma +(http://iki.fi/bisqwit/). + +

The usage license of this library is located at the end of this file. + +

Table of contents:

+ + + + +

What's new

+ +

What's new in v4.5.2 +

+ + + + + +

Preface

+ +

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. + +

For example, a function like "sin(sqrt(x*x+y*y))" can be +parsed from a string (either std::string or a C-style string) +and then evaluated with different values of x and y. +This library can be useful for evaluating user-inputted functions, or in +some cases interpreting mathematical expressions in a scripting language. + +

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. + +

Different numerical types are supported: double, + float, long double, long int, + std::complex (of types double, + float and long double), + 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.) + + + + +

Usage

+ +

To use the FunctionParser class, you have to include +"fparser.hh" in your source code files which use the +FunctionParser class. + +

If you are going to use the MPFR version of the library, you need to +include "fparser_mpfr.hh". If you are going to use the GMP +version of the library, you need to include "fparser_gmpint.hh". +(Note that support for these special parser versions needs to be specified +with preprocessor macros. See the documentation +below for details.) + +

When compiling, you have to compile fparser.cc and +fpoptimizer.cc 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). + +

If you are going to use the MPFR or the GMP versions of the library, +you also need to add mpfr/MpfrFloat.cc or +mpfr/GmpInt.cc files to your project, respectively. Otherwise +they should not be added to the project. + +

Note that part of the library source code is inside several +.inc files inside the extrasrc subdirectory +(these files contain auto-generated C++ code), provided in the library +package. These files are used by fparser.cc 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 extrasrc subdirectory. + +

Simple usage example of the library: + +

+    FunctionParser fp;
+    fp.Parse("sqrt(x*x + y*y)", "x,y");
+    double variables[2] = { 1.5, 2.9 };
+    double result = fp.Eval(variables);
+
+ + + +

Parser types

+ +

Different versions of the function parser class are supported, using + different floating point or integral types for function evaluation. + +

All the classes other than the default one, FunctionParser, + need to be enabled at compile time by defining a preprocessor macro + (specified below) either in the fpconfig.hh 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.) + +

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. + +

Currently the Optimize() method works only for the + FunctionParser, FunctionParser_f and + FunctionParser_ld classes. For the other types it can be + called but it does nothing. + +

+

+

FunctionParser

+
+

This is the default class, which uses double as its + numerical type. This is the only class enabled by default. +

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 FP_DISABLE_DOUBLE_TYPE. +

+ +

FunctionParser_f

+
+

This parser uses float as its numerical type. +

The FP_SUPPORT_FLOAT_TYPE preprocessor macro needs to be + defined for this class to be enabled. +

+ +

FunctionParser_ld

+
+

This parser uses long double as its numerical type. +

The FP_SUPPORT_LONG_DOUBLE_TYPE preprocessor macro needs + to be defined for this class to be enabled. +

Note that the FP_USE_STRTOLD preprocessor macro should + also be defined when using this version of the parser if the compiler + supports the (C99) function strtold(). (See + documentation below.) +

+ +

FunctionParser_li

+
+

This parser uses long int as its numerical type. +

The FP_SUPPORT_LONG_INT_TYPE preprocessor macro needs + to be defined for this class to be enabled. +

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 abs(), eval(), + if(), min() and max(), besides + basic arithmetic operators, except for the power operator). +

+ +

FunctionParser_cd, FunctionParser_cf, + FunctionParser_cld

+
+

These parsers use std::complex<double>, + std::complex<float> and + std::complex<long double> as their numerical type, + respectively. +

The preprocessor macros to enable them are + FP_SUPPORT_COMPLEX_DOUBLE_TYPE, + FP_SUPPORT_COMPLEX_FLOAT_TYPE and + FP_SUPPORT_COMPLEX_LONG_DOUBLE_TYPE. +

If FunctionParser_cld is used, the + FP_USE_STRTOLD macro should also be defined if the compiler + supports the strtold() function. +

+ +

FunctionParser_mpfr

+
+

This parser uses MpfrFloat as its numerical type. +

The FP_SUPPORT_MPFR_FLOAT_TYPE preprocessor macro needs + to be defined for this class to be enabled. +

Note that to use this version of the parser, + "fparser_mpfr.hh" needs to be included. +

MpfrFloat 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 + mpfr/MpfrFloat.hh file (see that file for info about + the public interface of the class). +

If this class is enabled, mpfr/MpfrFloat.cc + 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 + "-lgmp -lmpfr".) +

+ +

FunctionParser_gmpint

+
+

This parser uses GmpInt as its numerical type. +

The FP_SUPPORT_GMP_INT_TYPE preprocessor macro needs + to be defined for this class to be enabled. +

Note that to use this version of the parser, + "fparser_gmpint.hh" needs to be included. +

GmpInt 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 + mpfr/GmpInt.hh file (see that file for info about + the public interface of the class). +

If this class is enabled, mpfr/GmpInt.cc + needs to be compiled into the project, as well as the GMP library. +

This version of the class also uses a reduced version of the syntax, + like the long int version. +

Note: 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. +

+
+ +

Note that these different classes are completely independent and + instances of different classes cannot be given to each other using the + AddFunction() method. Only objects of the same type can + be given to that method. + +

The rest of the documentation assumes that FunctionParser + (which uses the double type) is used. The usage of the other + classes is identical except that double is replaced with the + correspondent type used by that class. (In other words, whenever the + rest of this documentation uses the type keyword 'double', + the correspondent type should be used instead, when using another version + of the class.) + + + +

Configuring the compilation

+ +

There is a set of precompiler options in the fpconfig.hh 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 +-D option in gcc), and thus it's not necessary to modify this +file. + +

+

FP_USE_STRTOLD : (Default off)

+

If FunctionParser_ld or FunctionParser_cld + are used, this preprocessor macro should be defined if the compiler + supports the (C99) function strtold(). 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 strtold() will also be automatically used + if __cplusplus indicates that C++11 is in use. +

+ +

FP_SUPPORT_CPLUSPLUS11_MATH_FUNCS : (Default off)

+

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.) + +

FP_SUPPORT_OPTIMIZER : (Default on)

+

If you are not going to use the Optimize() method, you + can comment this line out to speed-up the compilation a bit, as + well as making the binary a bit smaller. (Optimize() can + still be called, but it will not do anything.) + +

You can also disable the optimizer by specifying the + FP_NO_SUPPORT_OPTIMIZER precompiler constant in your + compiler settings. +

+ +

FP_USE_THREAD_SAFE_EVAL : (Default off)

+

Define this precompiler constant to make Eval() + thread-safe. Refer to the thread safety + section later in this document for more information. + Note that defining this may make Eval() slightly slower. +

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. +

+ +

FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA : (Default off)

+

This is like the previous, but makes Eval() use the + alloca() function (instead of std::vector). + This will make it faster, but the alloca() + function is not standard and thus not supported by all compilers. +

+
+ + + + +

Copying and assignment

+ +

The class implements a safe copy constructor and assignment operator. + +

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. + +

This means that copying/assigning is a very fast operation, and if + the copies are never modified then actual data copying never happens + either. + +

The Eval() and EvalError() methods of the +copy can be called without the internal data being copied. + +

Calling Parse(), Optimize() or the user-defined +constant/function adding methods will cause a deep-copy. + + + + +

Short descriptions of FunctionParser methods

+ +
+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);
+
+ +

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. + +

+
+void setDelimiterChar(char);
+
+ +

Sets an ending delimiter character for the function string. (See the + long description for more details.) + +

+
+static double epsilon();
+static void setEpsilon(double);
+
+ +

Setter and getter for the epsilon value used with comparison operators. + +

+
+const char* ErrorMsg(void) const;
+
+ +

Returns an error message corresponding to the error in +Parse(), or an empty string if no such error occurred. + +

+
+ParseErrorType GetParseErrorType() const;
+
+ +

Returns the type of parsing error which occurred. Possible return types + are described in the long description. + +

+
+double Eval(const double* Vars);
+
+ +

Evaluates the function given to Parse(). + +

+
+int EvalError(void) const;
+
+ +

Returns 0 if no error happened in the previous call to +Eval(), else an error code >0. + +

+
+void Optimize();
+
+ +

Tries to optimize the bytecode for faster evaluation. + +

+
+bool AddConstant(const std::string& name, double value);
+
+ +

Add a constant to the parser. Returns false if the name of +the constant is invalid, else true. + +

+
+bool AddUnit(const std::string& name, double value);
+
+ +

Add a new unit to the parser. Returns false if the name of +the unit is invalid, else true. + +

+
+bool AddFunction(const std::string& name,
+                 double (*functionPtr)(const double*),
+                 unsigned paramsAmount);
+
+ +

Add a user-defined function to the parser (as a function pointer). +Returns false if the name of the function is invalid, else +true. + +

+
+bool AddFunction(const std::string& name, FunctionParser&);
+
+ +

Add a user-defined function to the parser (as a FunctionParser +instance). Returns false if the name of the function is invalid, +else true. + +

+
+bool RemoveIdentifier(const std::string& name);
+
+ +

Removes the constant, unit or user-defined function with the specified +name from the parser. + +

+
+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);
+
+ +

Like Parse(), 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. + + + +

Long descriptions of FunctionParser methods

+ +
+ +
+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);
+
+ +

Parses the given function (and compiles it to internal format). +Destroys previous function. Following calls to Eval() will evaluate +the given function. + +

The strings given as parameters are not needed anymore after parsing. + +

Parameters: + + + + + + + + + + + +
FunctionString containing the function to parse.
VarsString containing the variable names, separated by commas.
+ Eg. "x,y", "VarX,VarY,VarZ,n" or + "x1,x2,x3,x4,__VAR__". +
useDegrees(Optional.) Whether to use degrees or radians in + trigonometric functions. (Default: radians)
+ +

If a char* is given as the Function parameter, +it must be a null-terminated string. + +

Variables can have any size and they are case sensitive (ie. +"var", "VAR" and "Var" are +different 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 'Vars' string. Function names are not legal +variable names. + +

Using longer variable names causes no overhead whatsoever to the +Eval() method, so it's completely safe to use variable names +of any size. + +

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. + +

Return values: + +

+ +

Example: parser.Parse("3*x+y", "x,y"); + + +

+ +
+void setDelimiterChar(char);
+
+ +

By default the parser expects the entire function string to be valid +(ie. the entire contents of the given std::string, or a C string +ending in the null character '\0'). + +

If a delimiter character is specified with this function, then if it's +encountered at the outermost parsing level by the Parse() +function, and the input function has been valid so far, Parse() +will return an index to this character inside the input string, but rather +than set an error code, FP_NO_ERROR will be set. + +

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. + +

For example, suppose you are writing an interpreter for a scripting + language, which can have commands like this: + +

let MyFunction(x,y) = { sin(x*x+y*y) } // A 2-dimensional function + +

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 '}' as +the delimiter character and then simply give a pointer to the character +which comes after the '{'. If all goes well, the +Parse() function will return an index to the '}' +character (from the given starting point) and GetParseErrorType() +will return FP_NO_ERROR. You can use the return +value (if it's not -1) to jump forward in the string to the +delimiter character. + +

Note that a null character ('\0') or the end of the +std::string (if one was given) will still be a valid end of +the function string even if a delimiter character was specified. (In this +case Parse() will return -1 if there was no error, +as usual.) + +

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 '}', +'"', ']', etc). + + +

+ +
+static double epsilon();
+static void setEpsilon(double);
+
+ +

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: + +

+ + +
+ +
+const char* ErrorMsg(void) const;
+
+ +

Returns a pointer to an error message string corresponding to the error +caused by Parse() (you can use this to print the proper error +message to the user). If no such error has occurred, returns an empty string. + + +

+ +
+ParseErrorType GetParseErrorType() const;
+
+ +

Returns the type of parse error which occurred. + +

This method can be used to get the error type if ErrorMsg() +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. + +FunctionParser::ParseErrorType is an enumerated type inside +the class (ie. its values are accessed like +"FunctionParser::SYNTAX_ERROR"). + +

The possible values for FunctionParser::ParseErrorType are listed below, +along with their equivalent error message returned by the +ErrorMsg() method: + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
FP_NO_ERRORIf no error occurred in the previous call to Parse().
SYNTAX_ERROR"Syntax error"
MISM_PARENTH"Mismatched parenthesis"
MISSING_PARENTH"Missing ')'"
EMPTY_PARENTH"Empty parentheses"
EXPECT_OPERATOR"Syntax error: Operator expected"
OUT_OF_MEMORY"Not enough memory"
UNEXPECTED_ERROR"An unexpected error occurred. Please make a full bug report to the + author"
INVALID_VARS"Syntax error in parameter 'Vars' given to FunctionParser::Parse()"
ILL_PARAMS_AMOUNT"Illegal number of parameters to function"
PREMATURE_EOS"Syntax error: Premature end of string"
EXPECT_PARENTH_FUNC"Syntax error: Expecting ( after function"
UNKNOWN_IDENTIFIER"Syntax error: Unknown identifier"
NO_FUNCTION_PARSED_YET"(No function has been parsed yet)"
+ + +

+ +
+double Eval(const double* Vars);
+
+ +

Evaluates the function given to Parse(). +The array given as parameter must contain the same amount of values as +the amount of variables given to Parse(). Each value corresponds +to each variable, in the same order. + +

Return values: +

+ +

Example: + +

double Vars[] = {1, -2.5};
+double result = parser.Eval(Vars); + + +

+ +
+int EvalError(void) const;
+
+ +

Used to test if the call to Eval() succeeded. + +

Return values: + +

If there was no error in the previous call to Eval(), +returns 0, else returns a positive value as follows: +

+ + +
+ +
+void Optimize();
+
+ +

This method can be called after calling the Parse() 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). + +

For example, the bytecode for the function "5+x*y-25*4/8" will +be reduced to a bytecode equivalent to the function "x*y-7.5" (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. + +

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 Optimize() +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 +Optimize() will only slow down the program. + +

Also, if the original function is expected to be optimal, then calling +Optimize() would be useless. + +

Note: Currently this method does not make any checks (like +Eval() does) and thus things like "1/0" will cause +undefined behaviour. (On the other hand, if such expression is given to the +parser, Eval() 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 Eval() once before calling Optimize() +and checking EvalError(). + +

If the destination application is not going to use this method, +the compiler constant FP_SUPPORT_OPTIMIZER can be undefined in +fpconfig.hh to make the library smaller (Optimize() +can still be called, but it will not do anything). + +

(If you are interested in seeing how this method optimizes the opcode, +you can call the PrintByteCode() method before and after the +call to Optimize() to see the difference.) + + +

+ +
+bool AddConstant(const std::string& name, double value);
+
+ +

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. + +

Constants used by a function must be added before calling +Parse() for that function. Constants are preserved between +Parse() 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.) + +

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 Parse() is called. (That is, changing the value of a constant +after calling Parse() and before calling Eval() +will have no effect.) + +

The return value will be false if the 'name' of +the constant was illegal, else true. If the name was illegal, +the method does nothing. + +

Example: parser.AddConstant("pi", 3.1415926535897932); + +

Now for example parser.Parse("x*pi", "x"); will be identical +to the call parser.Parse("x*3.1415926535897932", "x"); + + +

+ +
+bool AddUnit(const std::string& name, double value);
+
+ +

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. + +

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. "5in" is the same as saying +"5*300" or "1500" (assuming "in" has +been added as a unit with the value 300). + +

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 "5/2in" is parsed as +"5/(2*300)". +(If 5/2 inches is what one wants, it has to be written "(5/2)in".) + +

You can use the AddUnit() 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. +"x in"). To change the value of a unit, call +AddUnit() again with the same unit name and the new value. + +

Unit names share the same namespace as constants, functions and + variables, and thus should be distinct from those. + +

Example: parser.AddUnit("in", 300); + +

Now for example the function "5in" will be identical to +"(5*300)". Other usage examples include "x in", +"3in+2", "pow(x,2)in", "(x+2)in". + + +

+ +
+bool AddFunction(const std::string& name,
+                 double (*functionPtr)(const double*),
+                 unsigned paramsAmount);
+
+ +This method can be used to add new functions to the parser. For example, +if you would like to add a function "sqr(A)" which squares the +value of A, you can do it with this method (so that you don't +need to touch the source code of the parser). + +

The method takes three parameters: + +

+ +

The return value will be false if the given name was invalid +(either it did not follow the variable naming conventions, or the name was +already reserved), else true. If the return value is +false, nothing is added. + +

Example: Suppose we have a C++ function like this: + +

double Square(const double* p)
+{
+    return p[0]*p[0];
+} + +

Now we can add this function to the parser like this: + +

parser.AddFunction("sqr", Square, 1);
+parser.Parse("2*sqr(x)", "x"); + +

An example of a useful function taking no parameters is a function + returning a random value. For example: + +

double Rand(const double*)
+{
+    return drand48();
} + +

parser.AddFunction("rand", Rand, 0); + +

Important note: If you use the Optimize() 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 Rand() function given as example above is one such +problematic case.) + + +

+ +
+bool AddFunction(const std::string& name, FunctionParser&);
+
+ +

This method is almost identical to the previous AddFunction(), +but instead of taking a C++ function, it takes another FunctionParser +instance. + +

There are some important restrictions on making a FunctionParser instance + call another: + +

+ +

Example: + +

FunctionParser f1, f2;
+

f1.Parse("x*x", "x");
+

f2.AddFunction("sqr", f1); + +

This version of the AddFunction() 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). + +

+ +
+template<typename DerivedWrapper>
+bool AddFunctionWrapper(const std::string& name, const DerivedWrapper&,
+                        unsigned paramsAmount);
+
+ +

See section on specialized function objects. + +

+ +
+bool RemoveIdentifier(const std::string& name);
+
+ +

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 +true, else nothing will be done and the return value will be +false. + +

(Note: If you want to remove everything from an existing +FunctionParser instance, simply assign a fresh instance to it, ie. like +"parser = FunctionParser();") + +

+ +
+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);
+
+ +

These functions work in the same way as the Parse() function, +but the variables in the input function string are deduced automatically. The +parameters are: + +

+ +

As with Parse(), the return value will be -1 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. + + + +

Specialized function objects

+ +

The AddFunction() 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 boost::function or other similar specialized stateful +function objects instead of raw function pointers. This library provides a +mechanism to achieve this. + +

Creating and adding a specialized function object

+ +

In order to create a specialized function object, create a class derived +from the FunctionParser::FunctionWrapper class. This class +declares a virtual function named callFunction that the derived +class must implement. For example: + +

+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];
+    }
+};
+
+ +

You can then add an instance of this class to FunctionParser +using the AddFunctionWrapper() method, which works like +AddFunction(), but takes a wrapper object instead of a function +pointer as parameter. For example: + +

+MyFunctionWrapper wrapper;
+parser.AddFunctionWrapper("funcName", wrapper, 1);
+
+ +

Note that FunctionParser 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 +FunctionParser instance. Hence the above could also be written as: + +

+parser.AddFunctionWrapper("funcName", MyFunctionWrapper(), 1);
+
+ +

Note that this also means that the wrapper class must have a working +copy constructor. + +

Also note that if the FunctionParser instance is copied, all +the copies will share the same function wrapper objects given to the original. + +

Retrieving specialized function objects

+ +

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 +AddFunctionWrapper(). 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 GetFunctionWrapper() 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. + +

Note that the returned pointer will be of type +FunctionParser::FunctionWrapper. In order to get a pointer to +the actual derived type, the calling code should perform a +dynamic_cast, for example like this: + +

+MyFunctionWrapper* wrapper =
+    dynamic_cast<MyFunctionWrapper*>
+    (parser.GetFunctionWrapper("funcName"));
+
+if(!wrapper) { /* oops, the retrieval failed */ }
+else ...
+
+ +

(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.) + +

The calling code is free to modify the object in any way it wants, but it +must not delete it (because FunctionParser itself handles this). + + + + +

FunctionParserBase

+ +

All the different parser types are derived from a templated base class +named FunctionParserBase. 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 FunctionParserBase directly is the easiest way to achieve +this. + +

For example, if you want to make a function that handles more than one +type of parser, it can be done like this: + +

+template<typename Value_t>
+void someFunction(FunctionParserBase<Value_t>& parser)
+{
+    // do something with 'parser' here
+}
+
+ +

Now it's convenient to call that function with more than one type of +parser, for example: + +

+FunctionParser realParser;
+FunctionParser_cd complexParser;
+
+someFunction(realParser);
+someFunction(complexParser);
+
+ +

Another example is a class that inherits from FunctionParser +which also wants to support different numerical types. Such class can be +declared as: + +

+template<typename Value_t>
+class SpecializedParser: public FunctionParserBase<Value_t>
+{
+    ...
+};
+
+ + + +

Syntax

+ + +

Numeric literals

+ +

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). + +

An integer literal can consist solely of numerical digits (possibly with + a preceding unary minus). For example, "12345". + +

If the literal is preceded by the characters "0x", it + will be interpreted as a hexadecimal literal, where digits can also include + the letters from 'A' to 'F' (in either uppercase + or lowercase). For example, "0x89ABC" (which corresponds to the + value 563900). + +

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 "12.34", optionally followed by a + decimal exponent. + +

A decimal exponent consists of an 'E' or 'e', + followed by an optional plus or minus sign, followed by decimal digits, and + indicates multiplication by a power of 10. For example, "1.2e5" + (which is equivalent to the value 120000). + +

If a floating point literal is preceded by the characters "0x" + 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). + +

A binary exponent has the same format as a decimal exponent, except that + 'P' or 'p' is used. A binary exponent indicates + multiplication by a power of 2. For example, "0xA.Bp10" + (which is equivalent to the value 10944). + +

With the complex versions of the library, the imaginary part of a numeric + literal is written as a regular numeric literal with an 'i' + appended, for example "5i". Note that when also specifying + the real part of a complex literal, parentheses should be used to avoid + precedence problems. (For example, "(2+5i) * x" + is not the same thing as "2+5i * x". The latter + would be equivalent to "2 + (5i * x)".) + + +

Identifier names

+ +

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. + +

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. + +

All functions, variables, constants and units must use unique names. + It's not possible to add two different identifiers with the same name. + + + + +

The function string syntax

+ +

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: + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
()expressions in parentheses first
A unita unit multiplier (if one has been added)
A^Bexponentiation (A raised to the power B)
-Aunary minus
!Aunary logical not (result is 1 if int(A) is 0, else 0)
A*B A/B A%Bmultiplication, division and modulo
A+B A-Baddition and subtraction
A=B A<B A<=B
A!=B A>B A>=B		comparison between A and B (result is either 0 or 1)
A&Bresult is 1 if int(A) and int(B) differ from + 0, else 0.
+ 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.
A|Bresult is 1 if int(A) or int(B) differ from 0, + else 0.
+ 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.
+ +

(Note that currently the exponentiation operator is not supported for + FunctionParser_li nor FunctionParser_gmpint. + 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".) + +

Since the unary minus has higher precedence than any other operator, for + example the following expression is valid: x*-y + +

The comparison operators use an epsilon value, so expressions which may +differ in very least-significant digits should work correctly. For example, +"0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1 = 1" should always +return 1, and the same comparison done with ">" or +"<" should always return 0. (The epsilon value can be +configured in the fpconfig.hh file.) +Without epsilon this comparison probably returns the wrong value. + +

The class supports these functions: + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
abs(A)Absolute value (magnitude) of A. + With real numbers, if A is negative, returns -A otherwise returns A. + With complex numbers, equivalent to hypot(real(x),imag(x)).
acos(A)Arc-cosine of A. Returns the angle, measured in radians, whose cosine is A.
acosh(A)Same as acos() but for hyperbolic cosine.
arg(A)Phase angle of complex number A. Equivalent to atan2(imag(x),real(x)).
asin(A)Arc-sine of A. Returns the angle, measured in radians, whose sine is A.
asinh(A)Same as asin() but for hyperbolic sine.
atan(A)Arc-tangent of (A). Returns the angle, measured in radians, + whose tangent is A.
atan2(A,B)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.
atanh(A)Same as atan() but for hyperbolic tangent.
cbrt(A)Cube root of A. Returns a solution to expression pow(x,3)=A.
conj(A)Complex conjugate of A. Equivalent to real(x) - 1i*imag(x) or polar(abs(x),-arg(x)).
ceil(A)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.
cos(A)Cosine of A. Returns the cosine of the angle A, where A is + measured in radians.
cosh(A)Same as cos() but for hyperbolic cosine.
cot(A)Cotangent of A. Equivalent to 1/tan(A).
csc(A)Cosecant of A. Equivalent to 1/sin(A).
eval(...)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 if() to avoid + infinite recursion.
exp(A)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.
exp2(A)Base 2 exponential of A. Equivalent to pow(2,A).
floor(A)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.
hypot(A,B)Euclidean distance function. Equivalent to sqrt(A^2+B^2).
if(A,B,C)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 eval() in them.
imag(A)Return the imaginary part of complex number A. Equivalent to abs(A)*sin(arg(A)).
int(A)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.
log(A)Natural (base e) logarithm of A. Returns the solution to expression exp(x)=A.
log2(A)Base 2 logarithm of A. Equivalent to log(A)/log(2).
log10(A)Base 10 logarithm of A.
max(A,B)If A>B, the result is A, else B.
min(A,B)If A<B, the result is A, else B.
polar(A,B)Returns a complex number from magnitude A, phase angle B (in radians). + Equivalent to real(A)*(cos(real(B))+1i*sin(real(B))).
pow(A,B)Exponentiation (A raised to the power B).
real(A)Return the real part of complex number A. Equivalent to abs(A)*cos(arg(A)).
sec(A)Secant of A. Equivalent to 1/cos(A).
sin(A)Sine of A. Returns the sine of the angle A, where A is + measured in radians.
sinh(A)Same as sin() but for hyperbolic sine.
sqrt(A)Square root of A. Returns a solution to expression pow(x,2)=A.
tan(A)Tangent of A. Returns the tangent of the angle A, where A + is measured in radians.
tanh(A)Same as tan() but for hyperbolic tangent.
trunc(A)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.
+ +

(Note that for FunctionParser_li and + FunctionParser_gmpint only the functions + abs(), eval(), if(), + min() and max() are supported.) + +

Examples of function string understood by the class: + +

"1+2"
+"x-1"
+"-sin(sqrt(x^2+y^2))"
+"sqrt(XCoord*XCoord + YCoord*YCoord)"
+ +

An example of a recursive function is the factorial function: + +"if(n>1, n*eval(n-1), 1)" + +

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). + +

Also note that even though the maximum recursion level of +eval() 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 eval() is disabled by default. It can be enabled +in the fpconfig.hh file. + + + + +

Inline variables

+ +

The function syntax supports defining new variables inside the function +string itself. This can be done with the following syntax: + +

"<variable name> := <expression>; <function>" + +

For example: + +

"length := sqrt(x*x+y*y); 2*length*sin(length)" + +

(Spaces around the ':=' operator are optional.) + +

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. + +

The variable name must be an unused identifier (in other words, not an +existing function, variable or unit name). + +

The <function> part can have further inline variable +definitions, and thus it's possible to have any amount of them, for example: + +

"A := x^2; B := y^2; C := z^2; sqrt(A+B+C)" + +

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: + +

"A := x^2; A := 2*A; sqrt(A)" + + + + +

Whitespace

+ +

Arbitrary amounts of whitespace can optionally be included between + elements in the function string. + The following unicode characters are interpreted as whitespace: + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Character numberCharacter nameUTF-8 byte sequence
U+0009HORIZONTAL TABULATION 09
U+000ALINE FEED 0A
U+000BVERTICAL TABULATION 0B
U+000DCARRIAGE RETURN 0D
U+0020SPACE 20
U+00A0NO-BREAK SPACE C2 A0
U+2000EN QUAD E2 80 80
U+2001EM QUAD E2 80 81
U+2002EN SPACE E2 80 82
U+2003EM SPACE E2 80 83
U+2004THREE-PER-EM SPACE E2 80 84
U+2005FOUR-PER-EM SPACE E2 80 85
U+2006SIX-PER-EM SPACE E2 80 86
U+2007FIGURE SPACE E2 80 87
U+2008PUNCTUATION SPACE E2 80 88
U+2009THIN SPACE E2 80 89
U+200AHAIR SPACE E2 80 8A
U+200BZERO WIDTH SPACE E2 80 8B
U+202FNARROW NO-BREAK SPACE E2 80 AF
U+205FMEDIUM MATHEMATICAL SPACEE2 81 9F
U+3000IDEOGRAPHIC SPACE E3 80 80
+ + +

Miscellaneous

+ + +

About floating point accuracy

+ +

Note that if you are using FunctionParser_ld or +FunctionParser_cld and you want calculations to be as accurate +as the long double type allows, you should pay special attention +to floating point literals in your own code. For example, this is a very +typical mistake: + +

FunctionParser_ld parser;
+parser.AddConstant("pi", 3.14159265358979323846);
+ +

The mistake might not be immediately apparent. The mistake is that a +literal of type double is passed to the AddConstant() +function even though it expects a value of type long double. +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: + +

FunctionParser_ld parser;
+parser.AddConstant("pi", 3.14159265358979323846L);
+ +

The same principle should be used everywhere in your own code, if you are +using the long double type. + +

This is especially important if you are using the MpfrFloat +type (in which case its string-parsing constructor or its +ParseValue() or parseString() member functions +should be used instead of using numerical literals). + + +

About evaluation-time checks

+ +

FunctionParser::Eval() will perform certain sanity +checks before performing certain operations. For example, before calling the +sqrt 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: + +

+ +

However, the library can not 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 NaN result, etc. + +

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. + +

The library cannot guarantee that floating point +errors will never happen during evaluation. This can make the library to +return the floating point values inf and NaN. 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. + +

Note that the optimizer never performs any sanity checks. + + + + +

About thread safety

+ +

None of the member functions of the FunctionParser class are thread-safe. +Most prominently, the Eval() function is not thread-safe. +(In other words, the Eval() function of a single FunctionParser +instance cannot be safely called simultaneously by two threads.) + +

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 ForceDeepCopy() function on +each of the instances of each thread after the assignment or copying has been +done. + +

Another possibility is to compile the FunctionParser library so that +its Eval() function will be thread-safe. (This can be done by +defining the FP_USE_THREAD_SAFE_EVAL or the +FP_USE_THREAD_SAFE_EVAL_WITH_ALLOCA +precompiler constant.) As long as only one thread calls the other functions +of FunctionParser, the other threads can safely call the Eval() +of this one instance. + +

Note, however, that compiling the library like this can make +Eval() slightly slower. (The alloca version, if +supported by the compiler, will not be as slow.) + +

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. + + + + +

Tips and tricks

+ +

Add constants automatically to all parser objects

+ +

Often the same constants (such as pi and e) and other +user-defined identifiers (such as units) are always used in all the +FunctionParser objects throughout the program. It would be +troublesome to always have to manually add these constants every time a +new parser object is created. + +

There is, however, a simple way to always add these user-defined identifiers +to all instances. Write a class like this: + +

+    class ParserWithConsts: public FunctionParser
+    {
+     public:
+        ParserWithConsts()
+        {
+            AddConstant("pi", 3.14159265358979323846);
+            AddConstant("e", 2.71828182845904523536);
+        }
+    };
+
+ +

Now instead of using FunctionParser, always use +ParserWithConsts. 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 +slicing, so +they are completely safe to use anywhere.) + + + + +

Contacting the author

+ +

Any comments, bug reports, etc. should be sent to warp@iki.fi + + + + + + + + +

Usage license

+ +

Copyright © 2003-2011 Juha Nieminen, Joel Yliluoma + +

This Library is distributed under the + Lesser General Public + License (LGPL) version 3. + + + -- cgit