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Re-using existing functions in C++

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• Problem Solving with Computer Programs
  • The easiest way to solve a new problem is to re-use an existing function AS IS

  • Functionality-based modular programming can improve the opportunity for (complete or partial) re-use.

  • Most of the time, the solution obtain by RE-USE is NOT the optimal solution... but often, you can "lived with the result"

  • If you cannot live with a solution based on re-using existing software (low performance), it is then necessary to develop a new algorithm from scratch....

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• Re-using an existing function example: Integrating with Rectangle Rule to given precision
  • Problem Description:

    Find an approximate a definite integral of a function f(x) such that the error is approximately EPS

  • How to estimate error in the Rectangle Rule result

    A common method to estimate error in numerical methods is using finer step size:

    Compute V1 = Integrate function f(x) with step size h Compute V2 = Integrate function f(x) again with step size h' = 0.5*h Estimated error is approximately Abs(V1 - V2)

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• How to RE-USE "RectangleRule()" in this problem
  • Fact: We have already written a function

            RectangleRule(f, a, b, N)

    that computes the estimate integral for step size h = (b-a)/N

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  • Finding an integral with error estimation:

    Inputs: function f interval a, b precision EPS N = 1; V1 = RectangleRule(f, a, b, N); // Last estimate N = 2*N; V2 = RectangleRule(f, a, b, N); // New estimate // Keep doing it as long as the error exceeds threshold.... while ( abs(V2 - V1) > EPS ) { V2 = V1; // Remember the last estimate N = 2*N; V2 = RectangleRule(f, a, b, N); // Compute NEW estimate }

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    Here, we will again use the technique to define/declare a function that has another function as parameter.

    The material was discussed here: click here

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  • Implementation:

    extern RectangleRule(float (float), float, float, int); float RectangleRule_Prec(float f(float), float a, float b, float EPS) { /* ------------------------------ "Local" Variables ------------------------------ */ int N; float V1, V2; // Successive estimates N = 1; V1 = RectangleRule(f, a, b, N); // Use RectangleRule() N = 2*N; V2 = RectangleRule(f, a, b, N); // Use RectangleRule() again while ( abs(V2 - V1) > EPS ) { V1 = V2; N = 2*N; V2 = RectangleRule(f, a, b, N); } return(V2); }

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  • Example Program: (Build new function using an existing function) -----

    1. Here is the RectangleRule_Prec(f, a, b, N) function implementing the precision-driven Rectangle Rule: click here

    2. This program uses the RectangleRule(f, a, b, N) function: click here

    3. And you need a function f(x) to integrate: click here

    4. Finally, you need a driver program to run the function: click here

    5. Compilation commands:

        CC -c rect-rule4.C
        CC -c rect-rule-prec.C
        CC -c rect-rule-func.C
        CC -c rect-rule2b.C
        CC -o rect-rule4 rect-rule4.o rect-rule-prec.o \
       	rect-rule-func.o rect-rule2b.o
       
       OR less efficient (but easier to type):
       
        CC -o rect-rule4 rect-rule4.C rect-rule-prec.C \
               rect-rule-func.C rect-rule2b.C