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Calculate Pow() and Log() without using java.math

Posted on 2007-11-19
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Last Modified: 2010-05-18
Hi there,
I needed to do some mathematics in an exercice but I am not allowed to use the java.math class, I need to calculate the power Pow() and logarithm log()  with a custom base, base 10 would work as well.
thank you so much!
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Question by:zorfael
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10 Comments
 
LVL 17

Expert Comment

by:CSecurity
ID: 20311776
You can use this POW function:

Example 8
 
double pow(double a, double b)
{
    // true if base is greater than 1
    boolean gt1 = (Math.sqrt((a-1)*(a-1)) <= 1)? false:true;
         
    int oc = -1; // used to alternate math symbol (+,-)
    int iter = 20; // number of iterations
    double p, x, x2, sumX, sumY;
        
    // is exponent a whole number?
    if( (b-Math.floor(b)) == 0 )
    {
        // return base^exponent
        p = a;
        for( int i = 1; i < b; i++ )p *= a;
        return p;
    }
        
    x = (gt1)?
            (a /(a-1)): // base is greater than 1
            (a-1); // base is 1 or less
                
    sumX = (gt1)?
            (1/x): // base is greater than 1
            x; // base is 1 or less
        
    for( int i = 2; i < iter; i++ )
    {
        // find x^iteration
        p = x;
        for( int j = 1; j < i; j++)p *= x;
            
        double xTemp = (gt1)?
                (1/(i*p)): // base is greater than 1
                (p/i); // base is 1 or less
            
        sumX = (gt1)?
                (sumX+xTemp): // base is greater than 1
                (sumX+(xTemp*oc)); // base is 1 or less
                    
        oc *= -1; // change math symbol (+,-)
    }
        
    x2 = b * sumX;
        
    sumY = 1+x2; // our estimate
                
    for( int i = 2; i <= iter; i++ )
    {
        // find x2^iteration
        p = x2;
        for( int j = 1; j < i; j++)p *= x2;
            
        // multiply iterations (ex: 3 iterations = 3*2*1)
        int yTemp = 2;
        for( int j = i; j > 2; j-- )yTemp *= j;
            
        // add to estimate (ex: 3rd iteration => (x2^3)/(3*2*1) )
        sumY += p/yTemp;
    }
        
    return sumY; // return our estimate
}

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0
 
LVL 17

Accepted Solution

by:
CSecurity earned 800 total points
ID: 20311777
And easier one:

 public static int pow(int arg, int times){
int ret = 1;
for ( int i = 1 ; i <= times ; i++ ) {
ret = ret * arg;
}
return ret;
}

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0
 
LVL 9

Assisted Solution

by:brunoguimaraes
brunoguimaraes earned 1200 total points
ID: 20311791
public long pow(int x, int y) {

        long r = 1;

        for (int i = 0; i < y; i++) {
            r = r * x;
        }
        return r;
    }

   // base 2 log
    public int log(int x) {

        int r = 0;
        while ((x >> r) != 0) {
            r++;
        }
        return r - 1;
    }
0
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LVL 2

Author Comment

by:zorfael
ID: 20317154
Thank you for your effort however the "Math" class can never be mentioned and Pow() should work with numbers like 0.53232333 for example and I can't pass a number like that as "int". the Log() function should be base 10 or custom base. In fact I need Pow() to calculate Exponential, Sin, Cosine, if you guys had those functions as well that would be great but with just the Pow() my numbers will come out good because they do if I use math.pow().
any other solutions?
thank you so much
0
 
LVL 2

Author Comment

by:zorfael
ID: 20317276
actually I made it to work with double numbers using brunoguimaraes solution but I still need a logarithm function that would the same value as the function below but whithout using the Math class:

public double Log(double a, double base)
{
   double x;
   x = math.log10(a)/math.log(base)
}

any ideas?
return x;
}
0
 
LVL 2

Author Comment

by:zorfael
ID: 20317280
CSecurity Pow() solution works just like brunoguimaraes's solution when updated to use double instead of int.
0
 
LVL 17

Expert Comment

by:CSecurity
ID: 20318356
My first example was in Double base itself:

double pow(double a, double b)
0
 
LVL 2

Author Comment

by:zorfael
ID: 20318863
sure, however you referenced "Math" on your code:
"Math.sqrt"
I can't use that but that's not the problem right now as I got that figured out,
I need to calculate the Logarithm in a custom base now, any ideas?
thank you!
0
 
LVL 9

Assisted Solution

by:brunoguimaraes
brunoguimaraes earned 1200 total points
ID: 20319086
Try the code below. The greater the decimalplace parameter is, the greater the precision.
public static double log(double x, int base, int decimalplace) {
        
        int integer_value = 0;
        
        while (x < 1) {
            integer_value--; 
            x = x * base;
        }
        
        while (x >= base) {
            integer_value++;
            x = x / base;
        }
        double decimal_fraction = 0.0;
        double partial = 1.0;
        
        x = pow(x, 10);
        
        while (decimalplace > 0) {
            
            partial = partial / 10;
            int digit = 0;
            
            while (x >= base) {
                  digit++;
                  x = x / base;
            }
            decimal_fraction = decimal_fraction + digit * partial;
 
            x = pow(x, 10);
            decimalplace--;
        }
        return integer_value + decimal_fraction;
    }

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LVL 2

Author Closing Comment

by:zorfael
ID: 31409916
thank you all!
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