float representation

Question

Hello everyone In my knowledge float could only be represented by 7 decimal bits. But why in debugger I can see more than 7 decimal bits? (in my sample Result2 is of 9 bits other than 7 why?) [Code] float TotalBonus = 199.321F; float Worker1 = 100F; float Worker2 = 300F; // Result1 49.83025 float float Result1 = TotalBonus * Worker1 / (Worker1 + Worker2); // Result2 149.490753 float float Result2 = TotalBonus * Worker2 / (Worker1 + Worker2); [/Code] thanks in advance George

George George · Answer

Thanks Ryan! Great reply! 3 more comments. 1. maintained internally -- internally you mean something like Visual Studio debugger? And this is why I see 9 digits in debugger? 2. Two floating-point numbers that appear equal for a particular precision might not compare equal because their least significant digits are different. -- what means least significant digits? Could you show me a sample float-point and what parts are least significant digits please? From the link I can not find the answer. :-) 3. A mathematical or comparison operation that uses a floating-point number might not yield the same result if a decimal number is used because the floating-point number might not exactly approximate the decimal number. -- I am totally confused. Does it mean something like this? float a = something; float b = somethingelse; float result1 = b + a; decimal result2 = (decimal) b + (decimal) a; result1 and result2 are different? :-) regards George

Ryan Alford · Answer

I will give you the same response that I gave in your CodeGuru thread.... ____________________________________________________________ wow....this was really hard. straight from the MSDN http://msdn.microsoft.com/en-us/library/system.single.aspx Remember that a floating-point number can only approximate a decimal number and that the precision of a floating-point number determines how accurately that number approximates a decimal number. By default a Single value contains only 7 decimal digits of precision although a maximum of 9 digits is maintained internally. The precision of a floating-point number has several consequences : Two floating-point numbers that appear equal for a particular precision might not compare equal because their least significant digits are different. A mathematical or comparison operation that uses a floating-point number might not yield the same result if a decimal number is used because the floating-point number might not exactly approximate the decimal number. A value might not roundtrip if a floating-point number is involved. A value is said to roundtrip if an operation converts an original floating-point number to another form an inverse operation transforms the converted form back to a floating-point number and the final floating-point number is equal to the original floating-point number. The roundtrip might fail because one or more least significant digits are lost or changed in a conversion. now how much longer are we going to have to spoon feed you the answers to your questions?

Brandon Lewis · Answer

Just use double it can represent just about as many as you want. Its like a long decimal. You don't hardly see anyone using float because its restricted like that.

George George · Answer

Thanks. I understand how IEEE represents a float number. In more precise I do not think float has enough significand to represent 9 decimal digits it has only 7. Any ideas? http://en.wikipedia.org/wiki/Floating_point#Implementation_in_actual_computers:_IEEE_floating-point regards George

Brandon Lewis · Answer

Didnt you ask this on CodeGuru? For shame! haha. I saw this question and I think it was somewhat answered though... I have never used float. Just short decimal and double.