Floating Point Numbers

• Floating point numbers are the other basic number type.
  • Numbers with values to the right of the decimal point 3.15
  • Really small numbers $1.0 \times 10^{-20}$
  • Really big numbers $1.0 \times 10^{30}$
• Floating point types
  • float is the standard and what you should use unless there is a justification for more.
  • double is potentially bigger than a float
  • long double is potentially bigger than a double.
  • There is no unsigned.
• Floating point literals
  • reference.
  • 1.0, if you don't include the .0 the compiler will make it an integer type.
  • 1.0e12, 1.0e-12
  • These are all doubles by default.
  • 12.032l is a long double.
  • -3.3e-11f is a float.
• Output
  • The stream attempts to present the number in the best format for the size.
  • See the first part of floatDemo.cpp
• There are a few useful I/O manipulators
  • showpoint: forces floating point numbers to have a decimal point, even if they are integers.
  • fixed, scientific, defaultfloat : set the format for the number (reference.
  • setprecision(n) : set the number of digits to display. (reference.
• Input
  • We can read in many formats.
  • 1 // as an int followed by a space
  • 1.02
  • .023
  • 1.0e2
  • 1.0e-4
  • We might encounter roundoff error.
• A quick look at the limits:
  • Remember #include <limits>
  • Remember: numeric_limits<type> :min(), (max)
• Weird floating point stuff
  • Overflow and Underflow.
  • The GAP: the space between any two numbers.
  • Roundoff error is when the result falls into the gap, the answer is not correct.