I'm attempting to truncate a series of double-precision values in C#. The following value fails no matter what rounding method I use. What is wrong with this value that causes both of these methods to fail? Why does even Math.Round fail to correctly truncate the number? What method can be used instead to correctly truncate such values?
The value :
double value = 0.61740451388888251;
Method 1:
return Math.Round(value, digits);
Method 2:
double multiplier = Math.Pow(10, decimals)
return Math.Round(value * multiplier) / multiplier;
Fails even in VS watch window!
Double is a floating binary point type. They are represented in binary system (like 11010.00110). When double is presented in decimal system it is only an approximation as not all binary numbers have exact representation in decimal system. Try for example this operation:
double d = 3.65d + 0.05d;
It will not result in 3.7 but in 3.6999999999999997. It is because the variable contains a closest available double.
The same happens in your case. Your variable contains closest available double.
For precise operations double/float is not the most fortunate choice.
Use double/float when you need fast performance or you want to operate on larger range of numbers, but where high precision is not required. For instance, it is perfect type for calculations in physics.
For precise decimal operations use, well, decimal.
Here is an article about float/decimal: http://csharpindepth.com/Articles/General/FloatingPoint.aspx
If you need a more exact representation of the number you might have to use the decimal type, which has more precision but smaller range (it's usually used financial calculations).
More info on when to use each here: https://stackoverflow.com/a/618596/1373170
According to this online tool which gives the binary representation of doubles, the two closest double values to 0.62 are:
6.19999999999999995559107901499E-1 or 0x3FE3D70A3D70A3D7
link
6.20000000000000106581410364015E-1 or 0x3FE3D70A3D70A3D8
link
I'm not sure why neither of these agree with your value exactly, but like the others said, it is likely a floating point representation issue.
I think you are running up against the binary limit of a double-precision float (64 bits). From http://en.wikipedia.org/wiki/Double-precision_floating-point_format, a double only gives between 15-17 significant digits.
Related
Let's say we have the following simple code
string number = "93389.429999999993";
double numberAsDouble = Convert.ToDouble(number);
Console.WriteLine(numberAsDouble);
after that conversion numberAsDouble variable has the value 93389.43. What can i do to make this variable keep the full number as is without rounding it? I have found that Convert.ToDecimal does not behave the same way but i need to have the value as double.
-------------------small update---------------------
putting a breakpoint in line 2 of the above code shows that the numberAsDouble variable has the rounded value 93389.43 before displayed in the console.
93389.429999999993 cannot be represented exactly as a 64-bit floating point number. A double can only hold 15 or 16 digits, while you have 17 digits. If you need that level of precision use a decimal instead.
(I know you say you need it as a double, but if you could explain why, there may be alternate solutions)
This is expected behavior.
A double can't represent every number exactly. This has nothing to do with the string conversion.
You can check it yourself:
Console.WriteLine(93389.429999999993);
This will print 93389.43.
The following also shows this:
Console.WriteLine(93389.429999999993 == 93389.43);
This prints True.
Keep in mind that there are two conversions going on here. First you're converting the string to a double, and then you're converting that double back into a string to display it.
You also need to consider that a double doesn't have infinite precision; depending on the string, some data may be lost due to the fact that a double doesn't have the capacity to store it.
When converting to a double it's not going to "round" any more than it has to. It will create the double that is closest to the number provided, given the capabilities of a double. When converting that double to a string it's much more likely that some information isn't kept.
See the following (in particular the first part of Michael Borgwardt's answer):
decimal vs double! - Which one should I use and when?
A double will not always keep the precision depending on the number you are trying to convert
If you need to be precise you will need to use decimal
This is a limit on the precision that a double can store. You can see this yourself by trying to convert 3389.429999999993 instead.
The double type has a finite precision of 64 bits, so a rounding error occurs when the real number is stored in the numberAsDouble variable.
A solution that would work for your example is to use the decimal type instead, which has 128 bit precision. However, the same problem arises with a smaller difference.
For arbitrary large numbers, the System.Numerics.BigInteger object from the .NET Framework 4.0 supports arbitrary precision for integers. However you will need a 3rd party library to use arbitrary large real numbers.
You could truncate the decimal places to the amount of digits you need, not exceeding double precision.
For instance, this will truncate to 5 decimal places, getting 93389.42999. Just replace 100000 for the needed value
string number = "93389.429999999993";
decimal numberAsDecimal = Convert.ToDecimal(number);
var numberAsDouble = ((double)((long)(numberAsDecimal * 100000.0m))) / 100000.0;
Convert.ToDouble is adding zeros and 1 like in this picture:
Why it is turning from 21.62 to 21.620000000000001 ?
Is this about floating point issue?
Double (and Float) are floating-point types, and in a binary system will have some imprecision.
If you need more precise comparisons use decimal instead. If you're just doing calculations double should be fine. If you need to compare doubles for absolute equiality then compare the absolute value of the difference to some small constant:
if (a == b) // not reliable for floating point
{
....
}
double EPSILON = 0.0000001;
if (Math.Abs(a-b) < EPSILON)
{
....
}
The floating point numbers have some problems of approximation.
This is because decimal fraction like 0,00001 can't be represented exactly on a binary system (where fractional numbers are represented in module q/p).
The problem is intrinsic.
In short, yes; between any two bases (in this case, 2 and 10), there are always values that can expressed w/ a finite number of "decimal" (binimal?) places in one that cannot in the other.
Rounding errors like this are common in almost every high level programming language. In Java, to get around this you use a class called BigDecimal if you need guaranteed accuracy. Otherwise, you can just write a method that rounds a decimal to the nearest place you need.
In the example below the number 12345678.9 loses accuracy when it's converted to a string as it becomes 1.234568E+07. I just need a way to preserve the accuracy for large floating point numbers. Thanks.
Single sin1 = 12345678.9F;
String str1 = sin1.ToString();
Console.WriteLine(str1); // displays 1.234568E+07
If you want to preserve decimal numbers, you should use System.Decimal. It's as simple as that. System.Single is worse than System.Double in that as per the documentation:
By default, a Single value contains only 7 decimal digits of precision, although a maximum of 9 digits is maintained internally.
You haven't just lost information when you've converted it to a string - you've lost information in the very first line. That's not just because you're using float instead of double - it's because you're using a floating binary point number.
The decimal number 0.1 can't be represented accurately in a binary floating point system no matter how big you make the type...
See my articles on floating binary point and floating decimal point for more information. Of course, it's possible that you should be using double or even float and just not caring about the loss of precision - it depends on what you're trying to represent. But if you really do care about preserving decimal digits, then use a decimal-based type.
You can't. Simple as that. In memory your number is 12345679. Try the code below.
Single sin1 = 12345678.9F;
String str1 = sin1.ToString("r"); // Shows "all" the number
Console.WriteLine(sin1 == 12345679); // true
Console.WriteLine(str1); // displays 12345679
Technically r means (quoting from MSDN) round-trip: Result: A string that can round-trip to an identical number. so in reality it isn't showing all the decimals. It's only showing all the decimals needed to distinguish it from other possible values of Single. If you want to show all the decimals use F20.
If you want more precision use double or better use decimal. float has the precision that it has. As we say in Italy "Non puoi spremere sangue da una rapa" (You can't squeeze blood from a turnip)
You could also write an IFormatProvider for your purpose - but the precision doesn't get any better unless you use a different type.
this article may help - http://www.csharp-examples.net/string-format-double/
I came across following issue while developing some engineering rule value engine using eval(...) implementation.
Dim first As Double = 1.1
Dim second As Double = 2.2
Dim sum As Double = first + second
If (sum = 3.3) Then
Console.WriteLine("Matched")
Else
Console.WriteLine("Not Matched")
End If
'Above condition returns false because sum's value is 3.3000000000000003 instead of 3.3
It looks like 15th digit is round-tripped. Someone may give better explanation on this pls.
Is Math.Round(...) only solution available OR there is something else also I can attempt?
You are not adding decimals - you are adding up doubles.
Not all doubles can be represented accurately in a computer, hence the error. I suggest reading this article for background (What Every Computer Scientist Should Know About Floating-Point Arithmetic).
Use the Decimal type instead, it doesn't suffer from these issues.
Dim first As Decimal = 1.1
Dim second As Decimal = 2.2
Dim sum As Decimal= first + second
If (sum = 3.3) Then
Console.WriteLine("Matched")
Else
Console.WriteLine("Not Matched")
End If
that's how the double number work in PC.
The best way to compare them is to use such a construction
if (Math.Abs(second - first) <= 1E-9)
Console.WriteLine("Matched")
instead if 1E-9 you can use another number, that would represent the possible error in comparison.
Equality comparisons with floating point operations are always inaccurate because of how fractional values are represented within the machine. You should have some sort of epsilon value by which you're comparing against. Here is an article that describes it much more thoroughly:
http://www.cygnus-software.com/papers/comparingfloats/Comparing%20floating%20point%20numbers.htm
Edit: Math.Round will not be an ideal choice because of the error generated with it for certain comparisons. You are better off determining an epsilon value that can be used to limit the amount of error in the comparison (basically determining the level of accuracy).
A double uses floating-point arithmetic, which is approximate but more efficient. If you need to compare against exact values, use the decimal data type instead.
In C#, Java, Python, and many other languages, decimals/floats are not perfect. Because of the way they are represented (using multipliers and exponents), they often have inaccuracies. See http://www.yoda.arachsys.com/csharp/decimal.html for more info.
From the documentaiton:
http://msdn.microsoft.com/en-us/library/system.double.aspx
Floating-Point Values and Loss of
Precision
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 Double
value contains 15 decimal digits of
precision, although a maximum of 17
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.
In addition, the result of arithmetic
and assignment operations with Double
values may differ slightly by platform
because of the loss of precision of
the Double type. For example, the
result of assigning a literal Double
value may differ in the 32-bit and
64-bit versions of the .NET Framework.
The following example illustrates this
difference when the literal value
-4.42330604244772E-305 and a variable whose value is -4.42330604244772E-305
are assigned to a Double variable.
Note that the result of the
Parse(String) method in this case does
not suffer from a loss of precision.
THis is a well known problem with floating point arithmatic. Look into binary coding for further details.
Use the type "decimal" if that will fit your needs.
But in general, you should never compare floating point values to constant floating point values with the equality sign.
Failing that, compare to the number of places that you want to compare to (e.g. say it is 4 then you would go (if sum > 3.2999 and sum < 3.3001)
I have come across a precision issue with double in .NET I thought this only applied to floats but now I see that double is a float.
double test = 278.97 - 90.46;
Debug.WriteLine(test) //188.51000000000005
//correct answer is 188.51
What is the correct way to handle this? Round? Lop off the unneeded decimal places?
Use the decimal data type. "The Decimal value type is appropriate for financial calculations requiring large numbers of significant integral and fractional digits and no round-off errors."
This happens in many languages and stems from the fact that we cannot usually store doubles or floats precisely in digital hardware. For a detailed explanation of how doubles, floats, and all other floating point values are often stored, look at the various IEEE specs described on wikipedia. For example: http://en.wikipedia.org/wiki/Double_precision
Of course there are other formats, such as fixed-point format. But this imprecision is in most languages, and why you often need to use epsilon tests instead of equality tests when using doubles in conditionals (i.e. abs(x - y) <= 0.0001 instead of x == y).
How you deal with this imprecision is up to you, and depends on your application.