In [1]:

    

#include <cmath>
#include <iostream>
#include <limits>

using namespace std;


    

    
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In [2]:

    

double epsilon = numeric_limits<double>::epsilon();


    

    
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(double) 0.000000

In [3]:

    

double x[2] = {1, 1};


    

    
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(double [2]) { 1.000000, 1.000000 }

In [5]:

    

double normNaive(double* x) {
    double normSquared = 0;
    for (int i = 0; i < 2; i++)
        normSquared += x[i] * x[i];
    return sqrt(normSquared);
}


    

    
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In [6]:

    

cout << normNaive(x) << endl;


    

    




1.41421






    
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(std::__1::basic_ostream &) @0x7fffcfcfa660

In [7]:

    

double normBetter(double* x, int n) {
    double maxElement = epsilon;
    double normSquared = 0;
    
    for (int i=0; i < n; i++) {
        maxElement = max(maxElement, fabs(x[i]));
    }
    
    for (int i=0; i < n; i++) {
        double scaled = x[i] / maxElement;
        normSquared += scaled * scaled;
    }
    
    return sqrt(normSquared) * maxElement;
}


    

    
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In [8]:

    

cout << normBetter(x, 2) << endl;


    

    




1.41421






    
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(std::__1::basic_ostream &) @0x7fffcfcfa660

In [9]:

    

normBetter(x, 2);


    

    
Out[9]:





(double) 1.414214

In [20]:

    

normBetter((double[3]){1,2,3}, 3);


    

    
Out[20]:





(double) 3.741657

In [18]:

    

normBetter((double[4]){1,2,3,4}, 4);


    

    
Out[18]:





(double) 5.477226

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