Have computers started storing 0.1 correctly?

While learning about floating point arithmetic, I came across something, I quote: 'a float/double can't store 0.1 precisely".

There is a question on SO pointing the same thing and accepted answer is also very convincing. However I thought of trying it out on my own computer, so I wrote following program as below

double a = 0.1;

if (a == 0.1)
{
Console.WriteLine("True");
}
else
{
Console.WriteLine("False");
}

Console.Read();


and console printed True. Shocking to as I was already convinced with something else. Can anyone tell me what's going on with floating point arithmetic? Or I just got a computer that store numeric values as base 10?

True

1 Answer
1

Your program is only checking whether the compiler is approximating 0.1 in the same way twice, which it does.

The value of a isn't 0.1, and you're not checking whether it is 0.1. You're checking whether "the closest representable value to 0.1" is equal to "the closest representable value to 0.1".

a

Your code is effectively compiled to this:

double a = 0.1000000000000000055511151231257827021181583404541015625;

if (a == 0.1000000000000000055511151231257827021181583404541015625)
{
Console.WriteLine("True");
}
else
{
Console.WriteLine("False");
}


... because 0.1000000000000000055511151231257827021181583404541015625 is the double value that's closest to 0.1.

double

There are still times you can see some very odd effects. While double is defined to be a 64-bit IEEE-754 number, the C# specification allows intermediate representations to use higher precision. That means sometimes the simple act of assigning a value to a field can change results - or even casting a value which is already double to double.

double

double

double

In the question you refer to, we don't really know how the original value is obtained. The question states:

I've a double variable called x. In the code, x gets assigned a value of 0.1

x

x

We don't know exactly how it's assigned a value of 0.1, and that detail is important. We know the value won't be exactly 0.1, so what kind of approximation has been involved? For example, consider this code:

using System;

class Program
{
static void Main()
{
SubtractAndCompare(0.3, 0.2);
}

static void SubtractAndCompare(double a, double b)
{
double x = a - b;
Console.WriteLine(x == 0.1);
}
}


The value of x will be roughly 0.1, but it's not the exact same approximation as "the closest double value to 0.1". In this case it happens to be slightly less than 0.1 - the value is exactly 0.09999999999999997779553950749686919152736663818359375, which isn't equal to 0.1000000000000000055511151231257827021181583404541015625... so the comparison prints False.

x

double

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