Numbers in Javascript

Relevant links

• Flanagan’s book, section 3.1.
• MDN’s reference for Numbers
• MDN’s reference for the Math object
• IEEE 754 standard (optional)
• The group working on the standard (optional)
• Wikipedia page on IEEE 754 standard (optional)

Numbers in Javascript

• Unlike most languages, in Javascript there is only one type of numbers, namely 64-bit floating point numbers defined in the IEEE 754 standard.
• Certain operations (e.g. bitwise) are performed treating the numbers as 32-bit integers instead.
• Number literals are much like in other languages. You can use 0x for hexadecimals.
• Avoid using octal literals (those starting with a 0).
• The Math object contains a number of useful functions. Refer to the MDN documentation for these functions for details. As practice, learn how to do the following: (avoid functions tagged as “experimental”):
  • Raising to a power (so compute for example \(3^{2.2}\). Should get about \(11.2\))
  • Maximum/Minimum (compute for example the maximum between 2, -3 and 1e2)
  • Random numbers
    • Ask the system to generate a random number between 0 and 1
    • Obtain a random integer between 0 and 4 as follows:
      • Start with a random number between 0 and 1
      • Multiply it by 5
      • Use the floor function to round it down
  • Learn how to round numbers up, and also what the normal round would do
  • Logarithm and exponentials if you have time
  • Trigonometric functions if you have time
• The Math object also contains a number of mathematical constants (pi, e).
• The Number object contains constants for the largest integer, as well as Infinity and NaN (not a number).
• Arithmetic operations never raise errors, instead producing either Infinity, -Infinity or NaN.
• NaN in particular is a very unusual value. It represents a numeric value that is indeterminate.
  • So it is a number, even though it stands for “not a number”.
  • You can see that by typing typeof NaN.
  • NaN is not equal to any value, including itself.
  • You can see that by trying NaN == NaN.
  • Number.isNaN can be used to check if a number is actually NaN.
• Some behavior to watch out for (try to explain it): Number.MAX_VALUE == Number.MAX_VALUE + 1.
• Make sure to read about rounding errors, that are unavoidable whenever you do floating point arithmetic.