Some of the functions in math.h

Copyright © 2004 by Dorothy L. Nixon. All rights reserved

• Absolute value
• Ceiling and floor
• Exponential
• Logarithm
• Power
• Square root
• Trigonometric functions
• Inverse trignometric functions

For some preliminary information about the use of C++ library functions, see the section on Library functions in the Tutorial on Unix, vi, gcc, and elementary C++ syntax, and review your lecture notes. For an example of the use of one math function in a simple program, see sineDemo.cpp.

• Absolute value

  Given an argument x, the abs function returns |x|.

  Prototypes:

    double abs(double x);                //  C++ only
    float abs(float x);                  //  C++ only
    long double abs(long double x);      //  C++ only
    double fabs(double x);
    float fabs(float x);                 //  C++ only
    long double fabs(long double x);     //  C++ only
    float fabsf(float x);                //  required with C99
    long double fabsl(long double x);    //  required with C99
  

  Examples of use:

    float a = -3;
    float b = abs(a);           // value of b is now 3.0
  
    double p = -5.4;
    double q = abs(p);          // value of q is now 5.4
  
    double z = abs(-100.0);     // value of z is now 100.0
  
    float r;
    cin >> r;
    cout << abs(r) << endl;
  

  
  

• Ceiling and floor

  Given a floating-point argument x, the ceil function returns the lowest integer greater than or equal to x. The floor function returns the highest integer less than or equal to x. The returned value is still of a floating-point type.

  Prototypes:

    double ceil(double x);
    float ceil(float x);                 //  C++ only
    long double ceil(long double x);     //  C++ only
    float ceilf(float x);                //  required with C99
    long double ceill(long double x);    //  required with C99
  
    double floor(double x);
    float floor(float x);                //  C++ only
    long double floor(long double x);    //  C++ only
    float floorf(float x);               //  required with C99
    long double floorl(long double x);   //  required with C99
  

  Examples of use:

     float a = 5.3;
     int m = (int) floor(a);      // value of m is now 5
  
     double b = 10.4;
     long n = (long) ceil(b);     // value of n is now 11
  

  
  

• Exponential

  Given an argument x, the exp function returns the exponential of x, i.e. it returns e to the x power.

  Prototypes:

    double exp(double x);
    float exp(float x);                  //  C++ only
    long double exp(long double x);      //  C++ only
    float expf(float x);                 //  required with C99
    long double expl(long double x);     //  required with C99
  

  Examples of use:

     float a = 0;
     float b = exp(a);            // value of b is now 1
  
     double y = exp(1);           // value of y is now e
     double z = exp(exp(0));      // value of z is now e
  
     cout << exp(2) << endl;      // outputs the square of e
     cout << exp(1+1) << endl;    // outputs the square of e
     cout << exp(1+2) << endl;    // outputs the cube of e
  

  
  

• Logarithm

  Given an argument x, the log function returns the natural (base-e) logarithm of x, and the log10 function returns the base-10 logarithm of x.

  Prototypes:

    double log(double x);
    float log(float x);                  //  C++ only
    long double log(long double x);      //  C++ only
    float logf(float x);                 //  required with C99
    long double logl(long double x);     //  required with C99
  
    double log10(double x);
    float log10(float x);                //  C++ only
    long double log10(long double x);    //  C++ only
    float log10f(float x);               //  required with C99
    long double log10l(long double x);   //  required with C99
  

  Examples of use:

    double a = 100;
    double b = log10(a);            // value of b is now 2
  
    cout << log10(0.001) << endl;   // outputs -3.0
  
    cout << log(exp(2)) << endl;    // outputs 2.0
    cout << exp(log(2)) << endl;    // outputs 2.0
  

  
  

• Power

  Given two arguments x and y, the pow function returns x raised to the y power.

  Prototypes:

    double pow(double x, double y);
    float pow(float x, float y);         //  C++ only
    long double pow(long double x,
                    long double y);      //  C++ only
    double pow(double x, int y);         //  C++ only
    float pow(float x, int y);           //  C++ only
    long double pow(long double x,
                    int y);              //  C++ only
    float powf(float x, float y);        //  required with C99
    long double powl(long double x,
                     long double y);     //  required with C99
  

  Examples of use:

    cout << pow(2, 3) << endl;               // outputs 8.0
    cout << pow(2, -3) << endl;              // outputs 0.125
    cout << log10(pow(10, 3)) << endl;       // outputs 3.0
    cout << pow(10, log10(3)) << endl;       // outputs 3.0
    cout << pow(10, 2 + log10(3)) << endl;   // outputs 300.0
  

  
  

• Square root

  Given an argument x which must be greater than or equal to zero, the sqrt function returns the square root of x.

  Prototypes:

    double sqrt(double x);
    float sqrt(float x);                 //  C++ only
    long double sqrt(long double x);     //  C++ only
    float sqrtf(float x);                //  required with C99
    long double sqrtl(long double x);    //  required with C99
  

  Examples of use: No example provided. You'll be asked to develop an example in the homework.

  
  

• Trigonometric functions

  Given an argument x representing an angle in radians, the cos function returns the cosine of x, the sin function returns the sine of x, and the tan function returns the tangent of x.

  Prototypes:

    double cos(double x);
    float cos(float x);                  //  C++ only
    long double cos(long double x);      //  C++ only
    float cosf(float x);                 //  required with C99
    long double cosl(long double x);     //  required with C99
  
    double sin(double x);
    float sin(float x);                  //  C++ only
    long double sin(long double x);      //  C++ only
    float sinf(float x);                 //  required with C99
    long double sinl(long double x);     //  required with C99
  
    double tan(double x);
    float tan(float x);                  //  C++ only
    long double tan(long double x);      //  C++ only
    float tanf(float x);                 //  required with C99
    long double tanl(long double x);     //  required with C99
  

  Examples of use: For one example in the context of a simple complete program, see sineDemo.cpp.

  
  

• Inverse trignometric functions

  Given an argument x, the acos function returns the angle (in radians) whose cosine is x, in the range 0 to pi radians. The asin function returns the angle whose sine is x, in the range -pi/2 to +pi/2 radians. The atan function returns the angle whose tangent is x, in the range -pi/2, +pi/2 radians.

  Given two arguments x and y, the atan2 function returns the angle whose tangent is y/x, in the full angular range -pi to +pi radians. (This function is handy when converting from rectangular coordinates to polar coordinates.)

  Prototypes:

    double acos(double x);
    float acos(float x);                 //  C++ only
    long double acos(long double x);     //  C++ only
    float acosf(float x);                //  required with C99
    long double acosl(long double x);    //  required with C99
  
    double asin(double x);
    float asin(float x);                 //  C++ only
    long double asin(long double x);     //  C++ only
    float asinf(float x);                //  required with C99
    long double asinl(long double x);    //  required with C99
  
    double atan(double x);
    float atan(float x);                 //  C++ only
    long double atan(long double x);     //  C++ only
    float atanf(float x);                //  required with C99
    long double atanl(long double x);    //  required with C99
  
    double atan2(double y, double x);
    float atan2(float y, float x);       //  C++ only
    long double atan2(long double y,
                      long double x);    //  C++ only
    float atan2f(float y, float x);      //  required with C99
    long double atan2l(long double y,
                       long double x);   //  required with C99
  

  Examples of use: No example provided. Develop some examples on your own, and test them in a simple program, as additional practice for Quiz 1.