Floating Point

Objectives

1. Gain a basic understanding of the floating point type.
2. Discuss floating point operations.
3. Understand common problems with floating point.
4. Discuss the Math library.

Notes

• I like making long notes, but short videos.
  • So I will probably turn this into 4-5 videos.
• Sources
  • Again, we will use section 2.5 of the book.
  • And the Oracle documentation.
• Floating Point type.
  • reference.
    • This is quite technical.
  • Floating point numbers are numbers with
    • A decimal point (3.14)
    • Or in scientific notation
      • Very small: 2.9834 x 10 ^-12
      • Very large: 9.856 x 10³⁴
    • There are two floating point types in java
      • float, a 32 bit number.
      • double, a 64 bit number.
    • These both conform to IEEE 754 (Institute of Electrical and Electronic Engineers) standard number 754.
      • This is an old technical standard, but works well.
      • And we will NOT discuss it here.
  • Literals
    • All literals are double unless they end with a f
    • 0.1f, 1.0e-1f or 1.0E-1f are all acceptable.
    • So are 3e23f
    • 3f is acceptable as well.
    • I can place a d at the end to form a double.
    • There are more rules for literals, but we will skip them.
  • Printing
    • Remember, %3.2f prints two decimal points.
    • And will rounded up.
    • %E and %e are used for scientific notation.
• Floating point operations.
  • +,-,*,/ as you would expect.
    • Don't divide by 0.
    • Produces Infinity.
  • % exists but I would not use it.
  • ++ and -- as with integers.
  • +=, -=, ...
• The Math Library
  • There is a mathematics library for java.
  • Reference
  • Some constant definitions (Math.PI, Math.E)
  • MANY functions.
• Problems :
  • We have seen 1/0 produces infinity
    • There is also negative infinity
    • And 0.0f/0.0f produce nan
  • We can't represent all numbers between any two floats.
  • Look at Math.pow(2.0, 63.0);

    • double y;
      y = Math.pow(2.0,63.0);
      System.out.printf("%.0f\n",y);
                   

    • Real: 9223372036854775808
    • Comp: 9223372036854776000
    • Why
      • This is the scoreboard problem all over again.
      • We just ran out of digits, but this time we "put the error on the right."
      • This is a precision error.: the difference between a computed approximation and the exact result.
• In conclusion:
  • Choose double,
    • Reduces the chance/impact of overflow, precision errors.
    • floats might be slightly faster than doubles
    • But you are working in java, so use a double.
  • Always be careful however, especially when dealing with very precise quantities.