CODEWITHSUNDEEP
coutputmath.h
Shubham Bansal
Shubham Bansal

Reputation: 81

How can pow() function of C output the exact value of 2^1023 without any precision loss?

How does the following program print the exact value of 2^1023 without having any precision loss in C language?

#include <stdio.h>
#include<math.h>
int main()
{
// Printing the value of 2 ^1023
printf("%.0f",pow(2,1023));

return 0;
}

Output: 89884656743115795386465259539451236680898848947115328636715040578866337902750481566354238661203768010560056939935696678829394884407208311246423715319737062188883946712432742638151109800623047059726541476042502884419075341171231440736956555270413618581675255342293149119973622969239858152417678164812112068608

Upvotes: 1

Views: 334

Answers (1)

user2371524
user2371524

Reputation:

Powers of two require only a single bit of precision. The mantissa will be just 1 (which is equivalent to two to the power of zero).

Think about it: This is because the base of a binary representation is 2. In a base 10 that you're used to as a human, any power of ten needs only a single digit, e.g. 1000000 = 1 * 10^6.

Your exponent of 1023 has 10 bits in binary notation (11 1111 1111), so as long as the representation of a double on your implementation has at least 11 bits (one more is needed for the sign) for the exponent, it's no surprise this number can be represented exactly.

Upvotes: 9

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