Code in Depth

Floating Point Numbers

• Operations

Single one  =  1;
Single three =  3;
Single x  =  one / three;
Double result = 3 * x ;
result ==  ?

Answers?
== 1.0, < 1.0, > 1.0 Math.Round(result, 7) == 1

What if? Single result = 3 * x ;

Reason: Base2 airthmatic

• Example 2

Double  x  =  .1;
Double  result  =  10  *  x ;
Double   result2  =  x  + x  + x + x + x + x  + x  + x + x + x;

result == result2 ?
Console.WriteLine( "{0}  - {1}" ,  result,  result2)
Console.WriteLine( "{0:R}  - {1:R}" ,  result,  result2)

Reason: Can't be held exactly in Base 2 system so there is a rounding error

• Division

Int maxDiscountPercent   =  30;
Int markupPercent  =  20;
Int niceFactor  =  30;
Double  discount  =   maxDiscountPercent   * ( markupPercent  /  niceFactor) ;
discount  ?

== 0

Reason: Integer division in C# truncates the value to nearest integer. So 20 / 30 becomes Zero

Error Code:

Int x = 9, int y = 10; int z = 100;
decimal interim = x / y;
Decimal result = z / interim ;

• Divide By Zero

Int zero   =  0;
Int three  =  3;
Int result  = 3  / 0;

-- Int, Decimal => Throws exception
-- Single / Double => They can hold Infinity (Double.PositiveInfinity , Double.NegativeInfinity)

• Rounding

Math.Round(3.5);       ==> 4
Math.Round(4.5);       ==> 4

Reason: .Net rounds mid-point number to the nearest Even digit -> Banker's rounding

Math.Round(4.5, MidpointRounding.AwayFromZero);     ==> 5

• Top Of Type

Int top  =  int.MaxValue;
Int next = top + 1;

-- Int => Airthmatic overflow is not turned ON by default =>  Value rolls over to minimum value
-- Decimal => overflow exception
-- Single, Double => Infinity is supported => top + 1 is same as top.

Learnings:

• Single [Base2-32bit] , Double [Base2-64bit] & Decimal [Base10-128bit]
• Use "fuzzy" comparisons for Single & Double Data Types
• Base 10 & Base 2 rounds differently
• Avoid data Conversions between fractional type
• Decimal performance is 10 times slower than Single & Double
• Decimal for money, Double for everything else