Comparing double values in C

Question

I ve a double variable called x  In the code  x gets assigned a value of 0 1 and I check it in an  if  statement comparing x and 0 1  if  x  0 1    ----     Unfortunately it does not enter the if statement   Should I use Double or double  What s the reason behind this  Can you suggest a solution for this

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Taking a tip from the Java code base  try using  CompareTo and test for the zero comparison   This assumes the  CompareTo function takes in to account floating point equality in an accurate manner   For instance   System Math PI CompareTo System Math PI     0   This predicate should return true

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As a general rule   Double representation is good enough in most cases but can miserably fail in some situations  Use decimal values if you need complete precision  as in financial applications    Most problems with doubles doesn t come from direct comparison  it use to be a result of the accumulation of several math operations which exponentially disturb the value due to rounding and fractional errors  especially with multiplications and divisions    Check your logic  if the code is   x   0 1  if  x    0 1    it should not fail  it s to simple to fail  if X value is calculated by more complex means or operations it s quite possible the ToString method used by the debugger is using an smart rounding  maybe you can do the same  if that s too risky go back to using decimal    if  x ToString       0 1

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Comparing floating point number can t always be done precisely because of rounding  To compare   x     1    the computer really compares   x -  1  vs 0   Result of sybtraction can not always be represeted precisely because of how floating point number are represented on the machine  Therefore you get some nonzero value and the condition evaluates to false   To overcome this compare  Math Abs x-  1  vs some very small threshold   like 1E-9

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Exact comparison of floating point values is know to not always work due to the rounding and internal representation issue   Try imprecise comparison   if  x  gt   0 099  amp  amp  x  lt   0 101        The other alternative is to use the decimal data type

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Floating point number representations are notoriously inaccurate because of the way floats are stored internally  E g  x may actually be 0 0999999999 or 0 100000001 and your condition will fail  If you want to determine if floats are equal you need to specify whether they re equal to within a certain tolerance   I e    if Math Abs x - 0 1   lt  tol          Do something

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Double  called float in some languages  is fraut with problems due to rounding issues  it s good only if you need approximate values   The Decimal data type does what you want   For reference decimal and Decimal are the same in  NET C   as are the double and Double types  they both refer to the same type  decimal and double are very different though  as you ve seen    Beware that the Decimal data type has some costs associated with it  so use it with caution if you re looking at loops etc

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From the documentation       Precision in Comparisons   The Equals method should be used with caution  because two apparently equivalent values can be unequal due to the differing precision of the two values  The following example reports that the Double value  3333 and the Double returned by dividing 1 by 3 are unequal            Rather than comparing for equality  one recommended technique involves defining an acceptable margin of difference between two values  such as  01  of one of the values   If the absolute value of the difference between the two values is less than or equal to that margin  the difference is likely to be due to differences in precision and  therefore  the values are likely to be equal  The following example uses this technique to compare  33333 and 1 3  the two Double values that the previous code example found to be unequal    So if you really need a double  you should use the techique described on the documentation  If you can  change it to a decimal  It  will be slower  but you won t have this type of problem

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Adding onto Valentin Kuzub s answer above   we could use a single method that supports providing nth precision number   public static bool EqualsNthDigitPrecision this double value  double compareTo  int precisionPoint    gt      Math Abs value - compareTo   lt  Math Pow 10  -Math Abs precisionPoint      Note  This method is built for simplicity without added bulk and not with performance in mind

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Double and double are identical   For the reason  see http   www yoda arachsys com csharp floatingpoint html   In short  a double is not an exact type and a minute difference between  x  and  0 1  will throw it off

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To compare floating point  double or float types  use the specific method of CSharp  if  double1 CompareTo double2   gt  0           double1 is greater than double2   if  double1 CompareTo double2   lt  0           double1 is less than double2   if  double1 CompareTo double2     0           double1 equals double2     https   docs microsoft com en-us dotnet api system double compareto view netcore-3 1

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You need a combination of Math Abs on X-Y and a value to compare with   You can use following Extension method approach   public static class DoubleExtensions               const double  3   0 001          const double  4   0 0001          const double  5   0 00001          const double  6   0 000001          const double  7   0 0000001           public static bool Equals3DigitPrecision this double left  double right                        return Math Abs left - right   lt   3                     public static bool Equals4DigitPrecision this double left  double right                        return Math Abs left - right   lt   4                           Since you rarely call methods on double except ToString I believe its pretty safe extension   Then you can compare x and y like   if x Equals4DigitPrecision y

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double and Double are the same  double is an alias for Double  and can be used interchangeably   The problem with comparing a double with another value is that doubles are approximate values  not exact values  So when you set x to 0 1 it may in reality be stored as 0 100000001 or something like that    Instead of checking for equality  you should check that the difference is less than a defined minimum difference  tolerance   Something like    if  Math Abs x - 0 1   lt  0 0000001

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Use decimal  It doesn t have this  problem

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It s a standard problem due to how the computer stores floating point values  Search here for  floating point problem  and you ll find tons of information   In short     a float double can t store 0 1 precisely  It will always be a little off   You can try using the decimal type which stores numbers in decimal notation  Thus 0 1 will be representable precisely     You wanted to know the reason   Float double are stored as binary fractions  not decimal fractions  To illustrate   12 34 in decimal notation  what we use  means  1   101   2   100   3   10-1   4   10-2  The computer stores floating point numbers in the same way  except it uses base 2  10 01 means   1   21   0   20   0   2-1   1   2-2  Now  you probably know that there are some numbers that cannot be represented fully with our decimal notation  For example  1 3 in decimal notation is 0 3333333     The same thing happens in binary notation  except that the numbers that cannot be represented precisely are different  Among them is the number 1 10  In binary notation that is 0 000110011001100      Since the binary notation cannot store it precisely  it is stored in a rounded-off way  Hence your problem

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number of digits to be compared     public int n   12     n 1 because b a tends to 1 with n leading digits public double MyEpsilon   get      Math Pow 10  - n 1      public bool IsEqual double a  double b           Avoiding division by zero     if  Math Abs a  lt   double Epsilon    Math Abs b   lt   double Epsilon          return Math Abs a - b   lt    double Epsilon          Comparison     return Math Abs 1 0 - a   b   lt    MyEpsilon      Explanation  The main comparison function done using division a b which should go toward 1  But why division  it simply puts one number as reference defines the second one  For example  a   0 00000012345 b   0 00000012346 a b   0 999919002 b a   1 000081004  a b -1   8 099789405475458e-5  1- b a    8 100445524503848e-5    or  a 12345 10 8 b 12346 10 8  a b   0 999919002 b a   1 000081004  a b -1   8 099789405475458e-5  1- b a    8 100445524503848e-5    by division we get rid of trailing or leading zeros  or relatively small numbers  that pollute our judgement of number precision  In the example  the comparison is of order 10 -5  and we have 4 number accuracy  because of that in the beginning code I wrote comparison with 10  n 1  where n is number accuracy

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1  Should i use Double or double      Double and double is the same thing  double is just a C  keyword working as alias for the class System Double The most common thing is to use the aliases  The same for string  System String   int System Int32   Also see Built-In Types Table  C  Reference

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