CSE 232 Spring 2012

Computer Project #4 -- Mathematical Functions

Assignment Overview:

  This assignment focuses on the design, implementation and testing of C++
  functions which support mathematical operations on floating point values.
  You will develop two C++ source code modules (a library module and a driver
  module), as described below.

  It is worth 40 points (4% of course grade) and must be completed no later
  than 11:59 PM on Thursday, February 9.

Assignment Specifications:

  1) The library module will consist of the following functions:

    double absolute( double X );
    double modulo( double X, double Y );
    double factorial( unsigned N );
    double power( double X, unsigned N );
    double sine( double X );
    double cosine( double X );

  Function "absolute" will return the absolute value of its argument.

  Function "modulo" will return the remainder of the division of X by Y.

  Function "factorial" will return the factorial of N.

  Function "power" will return the value of X raised to the Nth power.

  Function "sine" will return the sine of X, where X is measured in radians.

  Function "cosine" will return the cosine of X, where X is measured in
  radians.

  2) The functions in the library module will not perform any operations on
  input or output streams.

  3) The functions in the library module will include appropriate error
  processing.

  a) Function "modulo" will return the "double" value Not-A-Number for all
  error conditions.

  b) Functions "factorial" and  "power" will return the "double" value
  Infinity for all error conditions.

  c) Functions "sine" and "cosine" will return the "double" value Not-A-Number
  for all error conditions.

  4) The functions in the library module will not use the following
  mathematical functions (declared in "cmath"):  "fabs", "fmod", "pow", "sin"
  and "cos".

  5) Your computation of the sine and cosine will use the power series
  approximation method (described below).



  6) The driver module will consist of function "main" and any auxiliary
  functions that directly support "main".  The driver module will demonstrate
  that each function in the library module is implemented correctly.

  All output displayed by the driver module will be appropriately formatted
  and labeled.

  Your driver module will not be interactive.  If your driver module accepts
  any input, you will supply that input in a text file named "proj04.tests".

Assignment Deliverables:

  The deliverables for this assignment include the following files:

    proj04.makefile    -- your makefile which produces "proj04"
    proj04.library.cpp -- your implementation of the library module
    proj04.driver.cpp  -- your implementation of the driver module
    proj04.tests       -- your test cases (if needed by your driver module)

  Be sure to use the specified file names, and to submit your files for
  grading via the "handin" program.

Assignment Notes:

  1) For your convenience, the following file is available:

    /user/cse232/Projects/project04.library.h

  That file contains the declarations for the functions which are part of the
  library module.

  Any source code file which uses the library module should contain the
  following preprocessor directive:

    #include "/user/cse232/Projects/project04.library.h"

  2) One method for computing the sine of a value is to approximate the value
  using a power series.  Using "!" to represent the factorial function:

                    3          5          7          9
    sine(X) = X - (X / 3!) + (X / 5!) - (X / 7!) + (X / 9!) - ....

  An individual term in this power series can be expressed as:

        k  2k+1
    (-1)  X
    -----------
      (2k+1)!

  where "k" represents the position in the power series (k = 0, 1, 2, ....).

  Similarly, the cosine of a value can be approximated using the following
  power series:

                      2          4          6          8
    cosine(X) = 1 - (X / 2!) + (X / 4!) - (X / 6!) + (X / 8!) - ....

  Expand each power series approximation until you reach a term whose absolute
  value is less than a specified epsilon (which is defined to be 1.0e-8 for
  this project).  That term should not be included in the approximate value of
  the power series.