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library-> ErrorHandler NearEqual speed_test SpeedTest time_test NumericType CheckNumericType SimpleVector CheckSimpleVector nan pow_int Poly LuDetAndSolve RombergOne RombergMul Runge45 Rosen34 OdeErrControl OdeGear OdeGearControl BenderQuad opt_val_hes LuRatio CppAD_vector thread_alloc memory_leak

NumericType-> NumericType.cpp

Headings-> Type Requirements Default Constructor Constructor From Integer Copy Constructor Assignment Operators Example Exercise

Definition of a Numeric Type
Type Requirements
A NumericType is any type that satisfies the requirements below. The following is a list of some numeric types: int, float, double, AD<double>, AD< AD<double> >. The routine CheckNumericType can be used to check that a type satisfies these conditions.

Default Constructor
The syntax
     NumericType x;
creates a NumericType object with an unspecified value.

Constructor From Integer
If i is an int, the syntax
     NumericType x(i);
creates a NumericType object with a value equal to i where i can be const.

Copy Constructor
If x is a NumericType object the syntax
     NumericType y(x);
creates a NumericType object y with the same value as x where x can be const.

Assignment
If x and y are NumericType objects, the syntax
     x = y
sets the value of x equal to the value of y where y can be const. The expression corresponding to this operation is unspecified; i.e., it could be void and hence
     x = y = z
may not be legal.

Operators
Suppose x, y and z NumericType objects where x and y may be const. In the result type column, NumericType can be replaced by any type that can be used just like a NumericType object.

Operation	Description	Result Type
+x	unary plus	NumericType
-x	unary minus	NumericType
x +  y	binary addition	NumericType
x -  y	binary subtraction	NumericType
x *  y	binary multiplication	NumericType
x /  y	binary division	NumericType
z += y	computed assignment addition	unspecified
z -= y	computed assignment subtraction	unspecified
z *= y	computed assignment multiplication	unspecified
z /= y	computed assignment division	unspecified

Example
The file NumericType.cpp contains an example and test of using numeric types. It returns true if it succeeds and false otherwise. (It is easy to modify to test additional numeric types.)

Exercise

1. List three operators that are not supported by every numeric type but that are supported by the numeric types int, float, double.
2. Which of the following are numeric types: std::complex<double>, std::valarray<double>, std::vector<double> ?

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Input File: omh/numeric_type.omh