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5 changed files with 28 additions and 8 deletions
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Project0/src/ciao
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Project0/src/ciao
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@ -79,24 +79,26 @@ fraction add_fractions(fraction frac1, fraction frac2)
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fraction sum_fraction_array(fraction frac_array[], int n) {
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fraction sum_fraction_array(fraction frac_array[], int n) {
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fraction sum = { 0, 1 };
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fraction sum = { 0, 1 };
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print_fraction_array(frac_array, n);
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for (int i = 0; i < n; i++) {
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for (int i = 0; i < n; i++) {
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fraction frac = frac_array[i];
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fraction frac = frac_array[i];
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sum = add_fractions(sum, frac);
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sum = add_fractions(sum, frac);
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print_fraction(sum);
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}
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}
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return sum;
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return sum;
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}
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}
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double sum_fraction_array_approx(fraction frac_array[], int n)
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double sum_fraction_array_approx(fraction frac_array[], int n)
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{
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{
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return fraction2double(sum_fraction_array(frac_array, n));
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double sum = 0;
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for (int i = 0; i < n; i++) {
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sum += fraction2double(frac);
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}
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return sum;
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// the approximation in this function is given by the fact that floating
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// the approximation in this function is given by the fact that floating
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// point numbers cannot represent precisely rational numbers due to the
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// point numbers cannot represent precisely rational numbers due to the
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// fixed size of significant digits they can hold in the mantissa. This
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// fixed size of significant digits they can hold in the mantissa. The
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// implementation minimizes the approximation by computing the sum into a
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// approximation adds up for each fraction to double conversion performed in
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// fraction FIRST before performing the double conversion.
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// the loop
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}
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}
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void fill_fraction_array(fraction frac_array[], int n)
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void fill_fraction_array(fraction frac_array[], int n)
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Project0/src/fraction_summing/fraction_toolbox.o
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Project0/src/fraction_summing/fraction_toolbox.o
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Project0/src/fraction_summing/main
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Project0/src/fraction_summing/main
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@ -1,6 +1,7 @@
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#include <iostream>
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#include <iostream>
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#include <stdio.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdlib.h>
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#include <limits.h>
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#include "fraction_toolbox.hpp"
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#include "fraction_toolbox.hpp"
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@ -70,8 +71,19 @@ static void test_array_functions(int n)
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cout << "Sum of array as double (approx.): " << endl;
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cout << "Sum of array as double (approx.): " << endl;
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cout << sum_fraction_array_approx(a, n) << endl;
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cout << sum_fraction_array_approx(a, n) << endl;
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//TODO: find n for which sum function breaks. Explain what is happening.
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// find n for which sum function breaks. Explain what is happening. n=4448,
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// this is the first number where the numerator overflows and thus
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// erroneoulsly becomes a negative number. The overflow is caused by the
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// sum_fractions function, specifically in the multiplication between
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// denominators. The approximation function doesn't overflow since fractions
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// are first converted into double floating point numbers, thus never
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// calling the sum_fractions functions and performing dangerous fixed size
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// integer multiplications. Additionally, due to the floating point nature
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// of the double type, a sum of doubles will never overflow to something
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// "weird", albeit precision will be lost due to the limited number of
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// significant digits and for larger and larger values the sum will
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// eventually reach the value "+Infinity" due to the fixed exponent size.
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}
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}
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static void test_toolbox(int argc, char* argv[])
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static void test_toolbox(int argc, char* argv[])
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@ -83,7 +95,13 @@ static void test_toolbox(int argc, char* argv[])
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test5();
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test5();
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cout << "\n========== test_array_functions ========= " << endl;
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cout << "\n========== test_array_functions ========= " << endl;
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#if 1
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cout << "Input n: " << endl;
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int n;
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cin >> n;
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#else
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int n = 5;
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int n = 5;
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#endif
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test_array_functions(n);
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test_array_functions(n);
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}
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}
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