Here Be Dragons
![[pic of dragon]](../images/dragon-right-facing.gif)
![[pic of dragon]](../images/dragon-left-facing.gif)
Fixed Point Oddities
Example of post-increment side effect:
int i = 1;
i = i++ + i + i;
System.output.print( "i = " + i );
Output: i = 5
Example of overflow:
byte b = 100;
b += 100;
System.output.print( "b = " + b );
Output: b = -56
Example of conversion error:
byte b = -100;
char c = (char) b;
int i = c;
System.out.print( "b=" + b + ", c=" + c + "i=" + i );
Output: b=-100, c=ﾜ, i=65436
(FYI: The letter is Japanese Katakana)
Example of division:
int i = 9 / 10;
System.output.print( "i = " + i );
Output: i = 0
Floating Point Oddities
Example of round-off error:
double d1 = 0.1, d2 = 0.3, d3;
d3 = d1 + d1 + d1;
if ( d2 == d3 )
System.out.print( "d2 equals d3" );
else
System.out.print( "d3 - d2 = " + (d3 - d2) );
Output: d3 - d2 = 5.551115123125783E-17
To work around this use fixed point, the
"BigDecimal" class, or code like this:
final double EPSILON = 1E-14;
...
if ( d2 >= d3 - EPSILON && d2 <= d3 + EPSILON )
System.out.print( "d2 equals d3" );
else
System.out.print( "d3 - d2 = " + (d3 - d2) );
Output: d2 equals d3
The similar looking test below isn't
quite the same and should be avoided:
if ( Math.abs(d3 - d2) < EPSILON )
Examples of loss of precision:
final float EPSILON = 0.1f;
float f1 = 50000000.0f;
float f2 = f1 + 2.0f;
if ( f1 >= f2 - EPSILON && f1 <= f2 + EPSILON )
System.out.print( "f1 equals f2" );
else
System.out.print( "f2 - f1 = " + (f2 - f1) );
Output: f1 equals f2
float f3 = f1 + 5.0f + 5.0f + 5.0f + 5.0f;
float f4 = 5.0f + 5.0f + 5.0f + 5.0f + f1;
System.out.printf( "f3 = %,f, f4 = %,f\n", f3, f4 );
Output: f3 = 50,000,016.0, f4 = 50,000,020.0
Logic errors that look like compiler errors:
int a = 1;
a += 0.2;
System.out.println( "a == 1 + 0.2 ==> " + (a == 1 + 0.2) );
System.out.println( "1/10f == 1/10.0 ==> " + (1/10f == 1/10.0) );
System.out.println( "1/10f == 1/10 ==> " + (1/10f == 1/10) );
System.out.println( "1/2f == 1/2.0 ==> " + (1/2f == 1/2.0) );
Output: a == 1 + 0.2 ==> false
1/10f == 1/10.0 ==> false
1/10f == 1/10 ==> false
1/2f == 1/2.0 ==> true
Example of overflow:
double d1 = 1.6e308;
double d2 = d1 * 2.0 / 2.0;
System.out.println( "d1 = " + d1 );
System.out.println( "d2 = " + d2 );
Output: d1 = 1.6E308
d2 = Infinity
Examples of division by zero:
double d1 = 0.0 / 0.0;
double d2 = 0.0 / 0.0;
double d3 = d1;
System.out.println( "d1 = " + d1 );
System.out.println( "d2 = " + d2 );
System.out.println( "d3 = " + d3 );
System.out.println( "d1 == d2 is " + (d1 == d2) );
System.out.println( "d1 == d3 is " + (d1 == d3) );
int i = 1 / 0;
Output: d1 = NaN
d2 = NaN
d3 = NaN
d1 == d2 is false
d1 == d3 is false
java.lang.ArithmeticException: / by zero
at MathOddities.addContent(MathOddities.java:177)
at MathOddities.init(MathOddities.java:22)
at sun.applet.AppletPanel.run(AppletPanel.java:424)
at java.lang.Thread.run(Thread.java:619)
Examples of Negative zero, infinity, and Not a Number:
double d1 = 1.0 / 0.0;
double d2 = -1.0 / 0.0;
double d3 = 0.0 / 1.0;
double d4 = 0.0 / -1.0;
double d5 = -0.0 / 0.0;
System.out.println( "d1 = " + d1 );
System.out.println( "d2 = " + d2 );
System.out.println( "d3 = " + d3 );
System.out.println( "d4 = " + d4 );
System.out.println( d3 == d4 );
System.out.println( "d5 = " + d5 );
System.out.println( "d5 == d5: " + (d5 == d5) );
System.out.println( "Double.isNaN( d5 ) = "
+ Double.isNaN( d5 ) );
Output: d1 = Infinity
d2 = -Infinity
d3 = 0.0
d4 = -0.0
true
d5 = NaN
d5 == d5: false
Double.isNaN( d5 ) = true
Example of BigDecimal error:
BigDecimal zero1 = new BigDecimal("0");
BigDecimal zero2 = new BigDecimal("0.0");
BigDecimal zero3 = zero1.stripTrailingZeros();
System.out.println(zero1.equals(zero2));
System.out.println(zero1.compareTo(zero2));
System.out.println(zero1.equals(zero3));
Output: false
true
true