COP 3223H Lecture -*- Outline -*-

* Friday problems with C modules

** rational numbers

  This problem is about an abstract data type
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           FOR YOU TO DO

Implement Rational Numbers, as
specified by the following header file.

// rational.h
#ifndef RATIONAL_H
#define RATIONAL_H 1
#include <stdbool.h>
typedef int *ratl;

/* requires: denom != 0;
 * ensures: result is a fresh rational number whose
 *          numerator is num and denominator is denom
 */ 
extern ratl rmake(int num, int denom);

// ensures: result is the numerator of r
extern int numerator(ratl r);

// ensures: result is the denominator of r
extern int denominator(ratl r);

// ensures: result is the sum of x and y
extern ratl radd(ratl x, ratl y);

// ensures: result is the arithmetic inverse of r
extern ratl rnegate(ratl r);

// ensures: result is the product of x and y
extern ratl rmult(ratl x, ratl y);

// requires: the numerator of r is not 0
// ensures: result is the multiplicative inverse of r
extern ratl rinverse(ratl r);

// ensures: result is true just when r1 and r2 are mathematically equal
extern bool requals(ratl r1, ratl r2);
#endif
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           DESIGN DECISIONS

- How to represent rationals?




- How does the representation relate to the mathematical rationals?




- Any other possibilities?




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     ... rep as arrays with 2 elements
        0 is numerator
        1 is denominator

     ... rep[0] is the numerator, rep[1] is the demominator

     ... yes, lots. For example:
         - same idea but with an invariant to keep the fraction in
           lowest terms (so denominator doesn't divide the numerator)
     represent num/denom as
        2^{num} * 3^{denom}

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            IMPLEMENTING RMAKE


#include "rational.h"

#define ELEMS 2

ratl rmake(int num, int denom) {





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      Q: How can we return our representation for a rational?
      Can't return a locally declared array, get dangling pointers
      Have to allocate the array on the heap

    ... // needed for malloc
    #include <stdlib.h>
    #define ELEMS 2

    ratl rat = (ratl)malloc(sizeof(int[ELEMS]));
    rat[0] = num;
    rat[1] = denom;
    return rat;
}

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            FOR YOU TO DO

Implement the following functions:

// ensures: result is the numerator of r
extern int numerator(ratl r);

// ensures: result is the denominator of r
extern int denominator(ratl r);

// ensures: result is the sum of x and y
extern ratl radd(ratl x, ratl y);

// ensures: result is the arithmetic inverse of r
extern ratl rnegate(ratl r);

// ensures: result is the product of x and y
extern ratl rmult(ratl x, ratl y);

// requires: the numerator of r is not 0
// ensures: result is the multiplicative inverse of r
extern ratl rinverse(ratl r);

// ensures: result is true just when r1 and r2 are mathematically equal
extern bool requals(ratl r1, ratl r2);

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** complex numbers
   Could do something similar with complex numbers