Why does .Net use a rounding algorithm in String.Format that is inconsistent with the default Math.Round() algorithm?

Question

I've noticed the following inconsistency in C#/.NET. I was wondering why it is so.

Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.04, Math.Round(1.04, 1)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.05, Math.Round(1.05, 1)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.06, Math.Round(1.06, 1)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.14, Math.Round(1.14, 1)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.15, Math.Round(1.15, 1)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.16, Math.Round(1.16, 1)); Console.WriteLine(); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.04, Math.Round(1.04, 1, MidpointRounding.AwayFromZero)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.05, Math.Round(1.05, 1, MidpointRounding.AwayFromZero)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.06, Math.Round(1.06, 1, MidpointRounding.AwayFromZero)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.14, Math.Round(1.14, 1, MidpointRounding.AwayFromZero)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.15, Math.Round(1.15, 1, MidpointRounding.AwayFromZero)); Console.WriteLine("{0,-4:#.0} | {1,-4:#.0}", 1.16, Math.Round(1.16, 1, MidpointRounding.AwayFromZero)); 

Output:

1.0  | 1.0 1.1  | 1.0 1.1  | 1.1 1.1  | 1.1 1.2  | 1.2 1.2  | 1.2  1.0  | 1.0 1.1  | 1.1 1.1  | 1.1 1.1  | 1.1 1.2  | 1.2 1.2  | 1.2 

It appears that the default string formatting behaviour is to round using MidpointRounding.AwayFromZero rather than Math.Round()'s default of MidpointRounding.ToEven.

Answer 1

As a historical note, the original Visual Basic implementation of Format$ also was inconsistent with round-to-even, aka, Banker's Rounding. The original Format$ code was written by Tim Paterson. You might recall that Tim was the author of a little program called QDOS (later known as MS-DOS) that was rather a good seller for a while there.

Perhaps this is yet another case of 25 years of backwards compatibility.

Answer 2

Seems this problem is worse than a "simple" inconsistency:

double dd = 0.034999999999999996;  Math.Round(dd, 2); // 0.03 Math.Round(dd, 2, MidpointRounding.AwayFromZero); // 0.03 Math.Round(dd, 2, MidpointRounding.ToEven); // 0.03  string.Format("{0:N2}", dd); // "0.04" 

This is absolutely bananas. Who knows where the heck it get "0.04" from.