The modulo operator (%) gives a different result for different .NET versions in C#

Question

I am encrypting the user's input for generating a string for password. But a line of code gives different results in different versions of the framework. Partial code with value of key pressed by user:

Key pressed: 1. Variable ascii is 49. Value of 'e' and 'n' after some calculation:

e = 103, 
n = 143,

Math.Pow(ascii, e) % n

Result of above code:

• In .NET 3.5 (C#)

  Math.Pow(ascii, e) % n
  

  gives 9.0.

• In .NET 4 (C#)

  Math.Pow(ascii, e) % n
  

  gives 77.0.

Math.Pow() gives the correct (same) result in both versions.

What is the cause, and is there a solution?

Answer 1

Math.Pow works on double-precision floating-point numbers; thus, you shouldn't expect more than the first 15–17 digits of the result to be accurate:

All floating-point numbers also have a limited number of significant digits, which also determines how accurately a floating-point value approximates a real number. A Double value has up to 15 decimal digits of precision, although a maximum of 17 digits is maintained internally.

However, modulo arithmetic requires all digits to be accurate. In your case, you are computing 49¹⁰³, whose result consists of 175 digits, making the modulo operation meaningless in both your answers.

To work out the correct value, you should use arbitrary-precision arithmetic, as provided by the BigInteger class (introduced in .NET 4.0).

int val = (int)(BigInteger.Pow(49, 103) % 143);   // gives 114

Edit: As pointed out by Mark Peters in the comments below, you should use the BigInteger.ModPow method, which is intended specifically for this kind of operation:

int val = (int)BigInteger.ModPow(49, 103, 143);   // gives 114