Floating Point Types

• In general, floating point types have the same problem as integers.
  • Limited representation
• But in addition
  • How many numbers are between 1 and 2 as rationals or reals?
  • Because the representation of floating points is discrete, there is a a gap between any two floating point numbers.
  • And they can suffer round off error.
• A quick aside
  • We can change the way cout works with stream manipulators
  • We will discuss some of these
  • But there are quite a few.
  • We will discuss this later, but I need one right now.
• setprecision
  • A reference for:
    • setprecision
    • precision
  • Note, this requires

    • #include <iomanip> 

  • The same as cout.precision()
  • With no argument returns the current precision.

  •  int oldPrecision {cout.precision()}; 

  • With an argument sets the precision.

  • cout << setprecision(15);
    ...
    cout.precision(oldPrecision); 

  • I also used fixed which shows all of the zeros following a number up to the precision.
  • This is reset with defaultfloat
• fixed
  • Controls some aspects of how floating point numbers are printed.
  • Other options are
    • scientific
    • defaultfloat
    • hexfloat
  • This has an impact on precision.
• take a look at floatDemo.cpp
• Floats are stored in scientific notion.
  • They can hold really big integers $2.12\times 10^{234}$
  • Or really small numbers $1.68 \times 10^{-193}$
  • But they will not always be accurate.
• We will want to make sure we need floats when we use them.