3.5 0, , and NaN

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	Java Number Cruncher: The Java Programmer's Guide to Numerical Computing By Ronald  Mak
	Table of Contents
	Chapter  3.   The Floating-Point Standard

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3.5 ±0, ± , and NaN

Program 3 C3 tabulates the results of the floating-point additive and multiplicative operations involving positive or negative 0, positive or negative infinity, Not-a-Number, and a "regular" floating-point values such as -1.0 and 1.0. See Listing 3-3a.

Listing 3-3a Zero, infinity, and Not-a-Number.

 package numbercruncher.program3_3; import numbercruncher.mathutils.AlignRight; /**  * PROGRAM 3-3: Zero, Infinity, and Not-a-Number  *  * Investigate the results of floating-point arithmetic  * involving zero, infinity, and NaN.  */ public class ZeroInfinityNaN {     public static void main(String args[])     {         AlignRight ar = new AlignRight();         float operands[] = {             -0f, +0f, -1f, 1f,             Float.NEGATIVE_INFINITY, Float.POSITIVE_INFINITY, Float.NaN,         };         ar.print("x", 10); ar.print("y", 10); ar.print("", 2);         ar.print("x+y", 10); ar.print("x-y", 10);         ar.print("x*y", 10); ar.print("x/y", 10); ar.print("x%y", 10);         ar.underline();         for (int i = 0; i < operands.length; ++i) {             for (int j = 0; j < operands.length; ++j) {                 float x = operands[i];                 float y = operands[j];                 ar.print(x, 10); ar.print(y, 10); ar.print("", 2);                 ar.print(x+y, 10); ar.print(x-y, 10);                 ar.print(x*y, 10); ar.print(x/y, 10); ar.print(x%y, 11);                 ar.println();             }         }     } } 

Output:

 x         y        x+y       x-y       x*y       x/y       x%y ------------------------------------------------------------------------       -0.0      -0.0       -0.0       0.0       0.0       NaN        NaN       -0.0       0.0        0.0      -0.0      -0.0       NaN        NaN       -0.0      -1.0       -1.0       1.0       0.0       0.0       -0.0       -0.0       1.0        1.0      -1.0      -0.0      -0.0       -0.0       -0.0 -Infinity  -Infinity  Infinity       NaN       0.0       -0.0       -0.0  Infinity   Infinity -Infinity       NaN      -0.0       -0.0       -0.0       NaN        NaN       NaN       NaN       NaN        NaN        0.0      -0.0        0.0       0.0      -0.0       NaN        NaN        0.0       0.0        0.0       0.0       0.0       NaN        NaN        0.0      -1.0       -1.0       1.0      -0.0      -0.0        0.0        0.0       1.0        1.0      -1.0       0.0       0.0        0.0        0.0 -Infinity  -Infinity  Infinity       NaN      -0.0        0.0        0.0  Infinity   Infinity -Infinity       NaN       0.0        0.0        0.0       NaN        NaN       NaN       NaN       NaN        NaN       -1.0      -0.0       -1.0      -1.0       0.0  Infinity        NaN       -1.0       0.0       -1.0      -1.0      -0.0 -Infinity        NaN       -1.0      -1.0       -2.0       0.0       1.0       1.0       -0.0       -1.0       1.0        0.0      -2.0      -1.0      -1.0       -0.0       -1.0 -Infinity  -Infinity  Infinity  Infinity       0.0       -1.0       -1.0  Infinity   Infinity -Infinity -Infinity      -0.0       -1.0       -1.0       NaN        NaN       NaN       NaN       NaN        NaN        1.0      -0.0        1.0       1.0      -0.0 -Infinity        NaN        1.0       0.0        1.0       1.0       0.0  Infinity        NaN        1.0      -1.0        0.0       2.0      -1.0      -1.0        0.0        1.0       1.0        2.0       0.0       1.0       1.0        0.0        1.0 -Infinity  -Infinity  Infinity -Infinity      -0.0        1.0        1.0  Infinity   Infinity -Infinity  Infinity       0.0        1.0        1.0       NaN        NaN       NaN       NaN       NaN        NaN  -Infinity      -0.0  -Infinity -Infinity       NaN  Infinity        NaN  -Infinity       0.0  -Infinity -Infinity       NaN -Infinity        NaN  -Infinity      -1.0  -Infinity -Infinity  Infinity  Infinity        NaN  -Infinity       1.0  -Infinity -Infinity -Infinity -Infinity        NaN  -Infinity -Infinity  -Infinity       NaN  Infinity       NaN        NaN  -Infinity  Infinity        NaN -Infinity -Infinity       NaN        NaN  -Infinity       NaN        NaN       NaN       NaN       NaN        NaN   Infinity      -0.0   Infinity  Infinity       NaN -Infinity        NaN   Infinity       0.0   Infinity  Infinity       NaN  Infinity        NaN   Infinity      -1.0   Infinity  Infinity -Infinity -Infinity        NaN   Infinity       1.0   Infinity  Infinity  Infinity  Infinity        NaN   Infinity -Infinity        NaN  Infinity -Infinity       NaN        NaN   Infinity  Infinity   Infinity       NaN  Infinity       NaN        NaN   Infinity       NaN        NaN       NaN       NaN       NaN        NaN        NaN      -0.0        NaN       NaN       NaN       NaN        NaN        NaN       0.0        NaN       NaN       NaN       NaN        NaN        NaN      -1.0        NaN       NaN       NaN       NaN        NaN        NaN       1.0        NaN       NaN       NaN       NaN        NaN        NaN -Infinity        NaN       NaN       NaN       NaN        NaN        NaN  Infinity        NaN       NaN       NaN       NaN        NaN        NaN       NaN        NaN       NaN       NaN       NaN        NaN 

Program 3 C3 uses a useful class AlignRight in package numbercruncher. mathutils for printing text and numbers right-aligned in columns . The class is shown in Listing 3-3b.

Listing 3-3b Utility class AlignRight for printing text and numbers right-aligned in columns.

 package numbercruncher.mathutils; /**  * Print text and numbers right-aligned in columns.  */ public class AlignRight {     /** line size */   private int lineSize;     /**      * Constructor.      */     public AlignRight() {}     /**      * Print text right-aligned in the column.      * @param text the text to print      * @param width the column width      */     public void print(String text, int width)     {         int padding = width - text.length();         while (- padding >= 0) System.out.print(" ");         System.out.print(text);         lineSize += width;     }     /**      * Print an integer value right-aligned in the column.      * @param value the value to print      * @param width the column width      */     public void print(int value, int width)     {         print(Integer.toString(value), width);     }     /**      * Print a float value right-aligned in the column.      * @param value the value to print      */     public void print(float value, int width)     {         print(Float.toString(value), width);     }     /**      * Print a double value right-aligned in the column.      * @param value the value to print      * @param width the column width      */     public void print(double value, int width)     {         print(Double.toString(value), width);     }     /**      * Print a line.      */     public void println()     {         System.out.println();         lineSize = 0;     }     /**      * Print an underline.      */     public void underline()     {         System.out.println();         for (int i = 0; i < lineSize; ++i) System.out.print("-");         System.out.println();         lineSize = 0;     } } 

Some floating-point comparisons are a bit tricky. -0.0 is always equal to +0.0, and so the value of the relational expression - 0.0 < + 0.0 is false. - Infinity is not equal to + Infinity. Finally, NaN is never equal to another number, not even to another NaN.

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