Foreword
Why are we having these discussions about floating-point type, numbers & arithmetic? Simple. We count in base 10, but the machine count in base 2.
BigDecimal - Need for an exact representation (not approximation)
If you are using BigDecimal
, this means that you want an exact representation of 0.1
and other negative powers of ten (usually you would be dealing with money or arithmetic involving decimals).
Double means trouble (where BigDecimal is concerned)
Then, if you are finding yourself having to manipulate double
(or float) values using BigDecimal
, then you are in double trouble, because it is impossible to represent 0.1
as a double in base 2. The machine "stores" doubles(IEEE-754 standard for floating-point arithmetic) as base 2. Here is a good write-up of what's really happening if you are interested.). Duncan's answer illustrates what i am trying to say, of what to do and not do.
Any programming language that you think can store 0.1 accurately is actually not. It is just an approximation.
System.out.println(0.1d);
//Prints 0.1 or so you think ;-)
//If you are not convinced, try this:
double x = 1.1; double y = 1.0;
if (x-y == 0.1) {// print true } else {// print false}
//or perhaps this:
double amount1 = 2.15;
double amount2 = 1.10;
System.out.println("Difference: " + (amount1 - amount2));
Examples
double smallD = 0.0001;
double smallDNoScientificNotation = 0.001; //>= 10E-3
double normalD = 10.345678;
double bigDNoScientificNotation = 1234567.123456789; //<=10E7
double bigD = 56_789_123_456_789.123456789;
//double
System.out.println(smallD); //1.0E-4, computerized scientific notation, this is how Double toString works
System.out.println(smallDNoScientificNotation); //0.001, OK
System.out.println(normalD); //10.345678, OK
System.out.println(bigDNoScientificNotation); //1234567.123456789, OK
System.out.println(bigD); //5.6789123456789125E13, computerized scientific notation, this is how Double toString works
//new BigDecimal(double): not OK, don't use! Attempting to representing the base-2 representation as accurately as possible
System.out.println(new BigDecimal(smallD)); //0.000100000000000000004792173602385929598312941379845142364501953125
System.out.println(new BigDecimal(smallDNoScientificNotation)); //0.001000000000000000020816681711721685132943093776702880859375
System.out.println(new BigDecimal(normalD)); //10.34567799999999948568074614740908145904541015625
System.out.println(new BigDecimal(bigDNoScientificNotation)); //1234567.12345678894780576229095458984375
System.out.println(new BigDecimal(bigD)); //56789123456789.125
//BigDecimal.valueOf (Dont use if the range is >= 10E-3, >= 10E7), under the hood it's using Double.toString
System.out.println(BigDecimal.valueOf(smallD)); //0.00010 - notice the extra 0, stemming from 1.0E-4
System.out.println(BigDecimal.valueOf(smallDNoScientificNotation)); //0.001
System.out.println(BigDecimal.valueOf(normalD)); //10.345678
System.out.println(BigDecimal.valueOf(bigDNoScientificNotation)); //1234567.123456789
System.out.println(BigDecimal.valueOf(bigD)); //56789123456789.125 //loss of accuracy
Computerized scientific notation - more here.
BONUS 1 - Pitfalls
Here
BONUS 2 - Effective Java 3rd edition (Joshua Bloch)
Item 60: Avoid float or double if exact answers are required
The float and double types are particularly ill-suited for monetary calculations because it is impossible to represent 0.1 (or any other negative power of ten) as a float or double exactly.
:
There are, however, two disadvantages to using BigDecimal: it's a lot less convenient than using a primitive arithmetic type, and it's a lot slower. The latter disadvantage is irrelevant if you're solving a single short problem, but the former may annoy you.
:
An alternative to using BigDecimal is to use int or long, depending on the amounts involved, and to keep track of the decimal point yourself. In this example, the obvious approach is to do all computation in cents.
Extra reading for the mathematically inclined ;-)
What Every Computer Scientist Should Know About Floating-Point Arithmetic