Cmath in c

The abs() function in C++ returns the absolute value of the argument. It is defined in the cmath header file.Mathematically, abs(num) = |num|.Example#include #include using namespace std;int main() { // get absolute value of -5.5 cout return 0;}// Output: 5.5Syntax of abs()The syntax of the abs() function is:abs(double num);abs() ParametersThe abs() function takes the following parameter: num - a floating point number whose absolute value is returned. It can be of the following types: double float long double abs() Return ValueThe abs() function returns: the absolute value of num i.e. |num|abs() PrototypesThe prototypes of abs() as defined in the cmath header file are:double abs(double num);float abs(float num);long double abs(long double num);// for integral typesdouble abs(T num);Note: The cmath abs() function is identical to the fabs() function.Example 1: C++ abs()#include #include using namespace std;int main() { double num = -87.91, result; result = abs(num); cout Outputabs(-87.91) = |-87.91| = 87.91Example 2: C++ abs() for Integral Types#include #include using namespace std;int main() { int num = -101; double result; result = abs(num); cout Outputabs(-101) = |-101| = 101

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Which is familiar to Pascal/Delphi programmers, is defined as a synonym for "long double" in OptiVec for C/C++. As Visual C++ does not support 80-bit reals, we define extended as "double" in the OptiVec versions for that compiler.b) Delphi only:The data type Float, which is familiar to C/C++ programmers, is defined as a synonym for Single. We prefer to have the letters defining the real-number data types in alphabetical proximity: "D" for Double, "E" for Extended, and "F" for Float. The letters "G" and "H" are already reserved for Great (128-bit real) and Half (16-bit real). For historical reasons (dating back to the development of Turbo Pascal), the various integer data types have a somewhat confusing nomenclature in Delphi. In order to make the derived function prefixes compatible with the C/C++ versions of OptiVec, we define a number of synonyms, as described in the following table:typeDelphi namesynonymderived prefix8 bit signedShortIntByteIntVBI_8 bit unsignedByteUByteVUB_16 bit signed SmallInt VSI_16 bit unsigned WordUSmallVUS_32 bit signed LongInt VLI_32 bit unsigned ULongVUL_64 bit signed Int64QuadIntVQI_64 bit unsigned (x64 version only!)UInt64UQuadVUQ_16/32 bit signedInteger VI_16/32 bit unsignedCardinalUIntVU_To have a Boolean data type available which is of the same size as Integer, we define the type IntBool. It is equivalent to LongBool in Delphi. You will see the IntBool type as the return value of many mathematical VectorLib functions. 2.2 Complex NumbersAs described in greater detail for CMATH, OptiVec supports complex numbers both in cartesian and polar format. If you use only the vectorized complex functions (but not the scalar functions of CMATH), you need not explicitly include CMATH. In this case, the following complex data types are defined in for C/C++: typedef struct { float Re, Im; } fComplex;typedef struct { double Re, Im; } dComplex;typedef struct { extended Re, Im; } eComplex;typedef struct { float Mag, Arg; } fPolar;typedef struct { double Mag, Arg; } dPolar;typedef struct { extended Mag, Arg; } ePolar;The corresponding definitions for Pascal/Delphi are contained in the unit VecLib:type fComplex = record Re, Im: Float; end;type dComplex = record Re, Im: Double; end;type eComplex = record Re, Im: Extended; end;type fPolar = record Mag, Arg: Float; end;type dPolar = record Mag, Arg: Double; end;type ePolar = record Mag, Arg: Extended; end;If, for example, a complex number z is declared as "fComplex z;", the real and imaginary parts of z are available as z.Re and z.Im, resp. Complex numbers are initialized either by setting the constituent parts separately to the desired value, e.g., z.Re = 3.0; z.Im = 5.7;p.Mag = 4.0; p.Arg = 0.7;(of course, the assignment operator is := in Pascal/Delphi).Alternatively, the same initialization can be accomplished by thefunctions fcplx or fpolr:C/C++:z = fcplx( 3.0, 5.7 );p = fpolr( 4.0, 0.7 );Pascal/Delphi:fcplx( z,

IntroductionThe tan() function in C++ is part of the cmath library, used to calculate the tangent of an angle given in radians. This mathematical function is widely used in fields such as engineering, physics, and computer graphics for performing trigonometric calculations precisely.In this article, you will learn how to effectively use the tan() function in C++. The examples provided will demonstrate how to calculate the tangent for both specific angles and dynamically during runtime, along with handling specific mathematical considerations such as angles that yield undefined tangent values.Utilizing tan() in C++Calculating Tangent of a Specific AngleInclude the cmath library to access the tan() function.Define an angle in radians.Calculate the tangent of the angle using tan(). cpp #include #include int main() { double angle = M_PI / 4; // 45 degrees double tangent = std::tan(angle); std::cout "The tangent of 45 degrees is: " tangent std::endl; return 0;} This code calculates the tangent of 45 degrees (π/4 radians). The output should approximate 1, as the tangent of 45 degrees equals 1.Handling Angles with Undefined TangentUnderstand that the tangent function has undefined values at odd multiples of π/2 (90 degrees, 270 degrees, etc.).Check if the angle is an odd multiple of π/2 before calling tan().Provide an appropriate response or handling mechanism for these cases. cpp #include #include #include int main() { double angle = M_PI / 2; // 90 degrees if (fmod(angle, M_PI / 2) == 0 && (int)(angle / (M_PI / 2)) % 2 != 0) { std::cout "The tangent of 90 degrees is undefined." std::endl; } else { double tangent = std::tan(angle); std::cout "The tangent of the angle is: " tangent std::endl; } return 0;} In this example, the code checks if angle is an odd multiple of π/2, where the tangent function is classically undefined. If it is, it outputs a message indicating so; otherwise, it calculates the tangent.Dynamic Tangent CalculationPrompt the user to input an angle.Calculate and display the tangent of the entered angle. cpp #include #include int main() { double angle; std::cout "Enter an angle in radians: "; std::cin >> angle; double tangent = std::tan(angle); std::cout "The tangent of " angle " radians is: " tangent std::endl; return 0;} This program takes an angle in radians from the user and calculates its tangent, which is then displayed. This approach allows for dynamic calculation based on user input.ConclusionUsing the tan() function from the cmath library in C++ enables precise

Matplotlib-cppWelcome to matplotlib-cpp, possibly the simplest C++ plotting library.It is built to resemble the plotting API used by Matlab and matplotlib.UsageComplete minimal example:#include "matplotlibcpp.h"namespace plt = matplotlibcpp;int main() { plt::plot({1,3,2,4}); plt::show();}g++ minimal.cpp -std=c++11 -I/usr/include/python2.7 -lpython2.7Result:A more comprehensive example:namespace plt = matplotlibcpp;int main(){ // Prepare data. int n = 5000; std::vector x(n), y(n), z(n), w(n,2); for(int i=0; i#include "matplotlibcpp.h"#include cmath>namespace plt = matplotlibcpp;int main(){ // Prepare data. int n = 5000; std::vectordouble> x(n), y(n), z(n), w(n,2); for(int i=0; iat(i) = i*i; y.at(i) = sin(2*M_PI*i/360.0); z.at(i) = log(i); } // Set the size of output image to 1200x780 pixels plt::figure_size(1200, 780); // Plot line from given x and y data. Color is selected automatically. plt::plot(x, y); // Plot a red dashed line from given x and y data. plt::plot(x, w,"r--"); // Plot a line whose name will show up as "log(x)" in the legend. plt::named_plot("log(x)", x, z); // Set x-axis to interval [0,1000000] plt::xlim(0, 1000*1000); // Add graph title plt::title("Sample figure"); // Enable legend. plt::legend(); // Save the image (file format is determined by the extension) plt::save("./basic.png");}g++ basic.cpp -I/usr/include/python2.7 -lpython2.7Result:Alternatively, matplotlib-cpp also supports some C++11-powered syntactic sugar:#include "matplotlibcpp.h"using namespace std;namespace plt = matplotlibcpp;int main(){ // Prepare data. int n = 5000; // number of data points vector x(n),y(n); for(int i=0; i#include cmath>#include "matplotlibcpp.h"using namespace std;namespace plt = matplotlibcpp;int main(){ // Prepare data. int n = 5000; // number of data points vectordouble> x(n),y(n); for(int i=0; idouble t = 2*M_PI*i/n; x.at(i) = 16*sin(t)*sin(t)*sin(t); y.at(i) = 13*cos(t) - 5*cos(2*t) - 2*cos(3*t) - cos(4*t); }