Double Precision

Question

I have a code, and I do not understand it. I am developing an application which precision is very important. but it does not important for .NET, why? I don't know.

double value = 3.5;
MessageBox.Show((value + 1 * Math.Pow(10, -20)).ToString());

but the message box shows: 3.5 Please help me, Thank you.

Answer 1

You can have precision, but it depends on what else you want to do. If you put the following in a Console application:

double a = 1e-20;
Console.WriteLine(" a  = {0}", a);
Console.WriteLine("1+a = {0}", 1+a);

decimal b = 1e-20M;
Console.WriteLine(" b  = {0}", b);
Console.WriteLine("1+b = {0}", 1+b);

You will get

 a  = 1E-20
1+a = 1
 b  = 0,00000000000000000001
1+b = 1,00000000000000000001

But Note that The Pow function, like almost everything in the Math class, only takes doubles:

double Pow(double x, double y);

So you cannot take the Sine of a decimal (other then by converting it to double)

Also see this question.

Answer 2

If you're doing anything where precision is very important, you need to be aware of the limitations of floating point. A good reference is David Goldberg's "What Every Computer Scientist Should Know About Floating-Point Arithmetic".

You may find that floating-point doesn't give you enough precision and you need to work with a decimal type. These, however, are always much slower than floating point -- it's a tradeoff between accuracy and speed.

Answer 3

The precision of a Double is 15 digits (17 digits internally). The value that you calculate with Math.Pow is correct, but when you add it to value it just is too small to make a difference.

Edit:
A Decimal can handle that precision, but not the calculation. If you want that precision, you need to do the calculation, then convert each value to a Decimal before adding them together:

double value = 3.5;
double small = Math.Pow(10, -20);

Decimal result = (Decimal)value + (Decimal)small;

MessageBox.Show(result.ToString());

Answer 4

Or use the Decimal type rather than double.

Answer 5

Double precision means it can hold 15-16 digits. 3.5 + 1e-20 = 21 digits. It cannot be represented in double precicion. You can use another type like decimal.