The most efficient way to implement an integer based power function pow(int, int)

power function in c without pow
pow() function in c
iterative power function
power function in c++
recursive power function
power function using recursion
calculate power function
recursive power function python

What is the most efficient way given to raise an integer to the power of another integer in C?

// 2^3
pow(2,3) == 8

// 5^5
pow(5,5) == 3125

Exponentiation by squaring.

int ipow(int base, int exp)
{
    int result = 1;
    for (;;)
    {
        if (exp & 1)
            result *= base;
        exp >>= 1;
        if (!exp)
            break;
        base *= base;
    }

    return result;
}

This is the standard method for doing modular exponentiation for huge numbers in asymmetric cryptography.

Power Function in C/C++, The most efficient way to implement an integer based power function pow(int, int )?. What is the most efficient way given to raise an integer to� The most efficient way to implement an integer based power function pow(int, int) (17 answers) Closed 5 years ago . I've read that cmath calculates pow(a,b) by performing exp(b*log(a)) .

Note that exponentiation by squaring is not the most optimal method. It is probably the best you can do as a general method that works for all exponent values, but for a specific exponent value there might be a better sequence that needs fewer multiplications.

For instance, if you want to compute x^15, the method of exponentiation by squaring will give you:

x^15 = (x^7)*(x^7)*x 
x^7 = (x^3)*(x^3)*x 
x^3 = x*x*x

This is a total of 6 multiplications.

It turns out this can be done using "just" 5 multiplications via addition-chain exponentiation.

n*n = n^2
n^2*n = n^3
n^3*n^3 = n^6
n^6*n^6 = n^12
n^12*n^3 = n^15

There are no efficient algorithms to find this optimal sequence of multiplications. From Wikipedia:

The problem of finding the shortest addition chain cannot be solved by dynamic programming, because it does not satisfy the assumption of optimal substructure. That is, it is not sufficient to decompose the power into smaller powers, each of which is computed minimally, since the addition chains for the smaller powers may be related (to share computations). For example, in the shortest addition chain for a¹⁵ above, the subproblem for a⁶ must be computed as (a³)² since a³ is re-used (as opposed to, say, a⁶ = a²(a²)², which also requires three multiplies).

Write a program to calculate pow(x,n), Given two numbers base and exponent, pow() function finds x raised to int a;. // Using typecasting for. // integer result. a = ( int )( pow (5, 2) + 0.5); or you want to share more information about the topic discussed above. We use cookies to ensure you have the best browsing experience on our website. The most efficient way to implement an integer based power function pow(int, int) The only two methods that I know is, A single for loop: extremely slow. Rewrite recursively calculate. I wonder is there a faster algorithm than these two? Any bitwise technique are welcome. Thank you. C# demos for the two algorithms:

If you need to raise 2 to a power. The fastest way to do so is to bit shift by the power.

2 ** 3 == 1 << 3 == 8
2 ** 30 == 1 << 30 == 1073741824 (A Gigabyte)

How to Implement a Power Function in Java, Given two integers x and n, write a function to compute xn. Function to calculate x raised to the power y */. public : int power( int x, unsigned int y) incorrect, or you want to share more information about the topic discussed above. How to implement text Auto-complete feature using Ternary Search Tree� The most efficient way to implement an integer based power function pow(int, int) What is the most efficient/elegant way to parse a flat table into a tree? Efficient way to insert a number into a sorted array of numbers? Most efficient way to store thousand telephone numbers

Here is the method in Java

private int ipow(int base, int exp)
{
    int result = 1;
    while (exp != 0)
    {
        if ((exp & 1) == 1)
            result *= base;
        exp >>= 1;
        base *= base;
    }

    return result;
}

Efficiently implement power function, Problem: Write a function in Java to calculate the power of integers. Method Signature: power(int x, int y) The most efficient way to implement an integer based power function pow(int, int) What is the most efficient way given to raise an integer to the power of another integer in C?// 2^3 pow(2,3)== 8// 5^5 pow(5,5)== 3125…

int pow( int base, int exponent)

{   // Does not work for negative exponents. (But that would be leaving the range of int) 
    if (exponent == 0) return 1;  // base case;
    int temp = pow(base, exponent/2);
    if (exponent % 2 == 0)
        return temp * temp; 
    else
        return (base * temp * temp);
}

Power Function In C, Given two integers x and n where n is non-negative, efficiently compute the value of power function pow(x, n) using Divide & Conquer. A simple solution to calculate Expand Search Form Search int x = -2;. unsigned n = 10;. printf(" pow(%d,%d) = %d", x, n, power(x, n));. return 0; newest oldest most voted. Anika. Guest. Output : 0.125000. Write an iterative O(Log y) function for pow(x, y) Modular Exponentiation (Power in Modular Arithmetic) If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org.

Java Program to Calculate the Power of a Number, This article we will tell you how to use Power Function In C to calculate How To Best Utilize Power Function In C? which you can call anytime you want to calculate the power of any integer. 1. 2. 3. 4. 5. 6. 7. 8. 9. int power(int base, int exponent) The pow() function is present in math.h header file. C library function - pow() - The C library function double pow(double x, double y) returns x raised to the power of y i.e. xy.

C++ Program to Calculate Power of a Number, public class Power { public static void main(String[] args) { int base = 3, In this program, we use Java's Math.pow() function to calculate the power of the given� C++ pow() The pow() function computes a base number raised to the power of exponent number.

Raise numbers to a power: here's how to exponentiate , Example 2: Compute power using pow() Function. #include <iostream> #include <cmath> using namespace std; int main() { float base, exponent, result; cout� One such example is pow(5, 2). When assigned to an integer, it outputs 24 on some compilers and works fine for some other compilers. But pow(5, 2) without any assignment to an integer outputs 25. This is because 5 2 (i.e. 25) might be stored as 24.9999999 or 25.0000000001 because the return type is double. When assigned to int, 25.0000000001

Comments
  • When you say "efficiency," you need to specify efficient in relation to what. Speed? Memory usage? Code size? Maintainability?
  • Doesn't C have a pow() function?
  • yes, but that works on floats or doubles, not on ints
  • If you're sticking to actual ints (and not some huge-int class), a lot of calls to ipow will overflow. It makes me wonder if there's a clever way to pre-calculate a table and reduce all the non-overflowing combinations to a simple table lookup. This would take more memory than most of the general answers, but perhaps be more efficient in terms of speed.
  • pow() not a safe function
  • You should probably add a check that "exp" isn't negative. Currently, this function will either give a wrong answer or loop forever. (Depending on whether >>= on a signed int does zero-padding or sign-extension - C compilers are allowed to pick either behaviour).
  • I wrote a more optimized version of this, freely downloadable here: gist.github.com/3551590 On my machine it was about 2.5x faster.
  • @AkhilJain: It's perfectly good C; to make it valid also in Java, replace while (exp) and if (exp & 1) with while (exp != 0) and if ((exp & 1) != 0) respectively.
  • Your function should probably have unsigned exp, or else handle negative exp properly.
  • @ZinanXing Multiplying n times results in more multiplications and is slower. This method saves multiplications by effectively reusing them. E.g., to calculate n^8 the naïve method of n*n*n*n*n*n*n*n uses 7 multiplications. This algorithm instead computes m=n*n, then o=m*m, then p=o*o, where p = n^8, with just three multiplications. With large exponents the difference in performance is significant.
  • @JeremySalwen: As this answer states, binary exponentiation is not in general the most optimal method. There are no efficient algorithms currently known for finding the minimal sequence of multiplications.
  • @EricPostpischil, That depends on your application. Usually we don't need a general algorithm to work for all numbers. See The Art of Computer Programming, Vol. 2: Seminumerical Algorithms
  • There's a good exposition of this exact problem in From Mathematics to Generic Programming by Alexander Stepanov and Daniel Rose. This book should be on the shelf of every software practitioner, IMHO.