hw0: EX2 done

Project0/src/fraction_summing/fraction_toolbox.cpp

@@ -20,46 +20,90 @@ void print_fraction_array(fraction frac_array[], int n)
 
 fraction square_fraction(fraction frac)
 {
-    //TODO: implement function 2
+    struct fraction square = {
+        .num = frac.num * frac.num;
+        .denom = frac.denom * frac.denom;
+    };
+    return square;
 }
 
-//TODO: implement function 3
+void square_fraction_inplace(fraction& frac)
-
+{
+    frac.num *= frac.num;
+    frac.denom *= frac.denom;
+}
 
 double fraction2double(fraction frac)
 {
-    //TODO: implement function 4
+    return (double) frac.num / (double) frac.denom;
 }
 
 int gcd(int a, int b)
 {
-    //TODO: implement function 5
+    return b == 0 ? a : gcd(b, a % b);
 }
 
-//TODO: implement function 6
+int gcd(fraction frac) {
-
+    int a = frac.num, b = frac.denom;
+    while (b != 0) {
+        int t = b;
+        b = a % b;
+        a = t;
+    }
+    return a;     
+}
 
 void reduce_fraction_inplace(fraction & frac)
 {
-    //TODO: implement function 7
+    // the called function is the one implementing the iterative algorithm
+    // because gcd is called with one argument of type fraction (the reference
+    // is implicitly copied and passed by value), matching the signature of the
+    // iterative implementation
+    int g = gcd(frac);
 
-    //TODO: add short comment to explain which of the gcd() functions your code is calling
+    frac.num /= g;
+    frac.denom /= g;
 }
 
 fraction add_fractions(fraction frac1, fraction frac2)
 {
-    //TODO: implement function 8
+    int g = gcd(frac1.denom, frac2.denom);
+
+    {
+        int fac1 = frac1.denom / g;
+        frac1.num *= fac1;
+        frac1.denom *= fac1;
+    }
+
+    {
+        int fac2 = frac2.denom / g;
+        frac2.num *= fac2;
+        frac2.denom *= fac2;
+    }
+
+    struct fraction total = {
+        .num = frac1.num + frac2.num;
+        .denom = g;
+    };
+    return total;    
 }
 
 double sum_fraction_array_approx(fraction frac_array[], int n)
 {
-    //TODO: implement function 9
+    struct fraction sum = { .num = 0, .denom = 0 };
-    
+    for (int i = 0; i < n; i++) {
-    //TODO: add short comment to explain why this function is approximate
+        struct fraction frac = frac_array[i];
+        sum = add_fractions(sum, frac);
     }
 
-//TODO: implement function 10
+    return fraction2double(sum);
 
+    // the approximation in this function is given by the fact that floating
+    // point numbers cannot represent precisely rational numbers due to the
+    // fixed size of significant digits they can hold in the mantissa. This
+    // implementation minimizes the approximation by computing the sum into a
+    // fraction FIRST before performing the double conversion.
+}
 
 void fill_fraction_array(fraction frac_array[], int n)
 {

Project0/src/fraction_summing/fraction_toolbox.hpp

@@ -1,6 +1,9 @@
 #include <iostream>
 
-//TODO: implement fraction datatype
+struct fraction {
+    int num;
+    int denom;
+}
 
 void print_fraction(fraction frac);
 
@@ -8,7 +11,7 @@ void print_fraction_array(fraction frac_array[], int n);
 
 fraction square_fraction(fraction frac);
 
-//TODO: add function declaration for function 3
+void square_fraction_inplace(fraction& frac);
 
 double fraction2double(fraction frac);