CS151, Class 8: Numbers

Overview:
* Types in Scheme
* Numeric Types in Scheme
* Lab
* Reflection

Administrivia:
* Feel free to use computers during my 10:00-10:50 class and my
  3:15-4:05 class.
* Read "Defining Procedures in Scheme"
* Have a good weekend.

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Types in Scheme

* Almost every computer language assigns a "type" to values
* "Type" says what kind of information the value is:
  symbol, number, procedure
* Why do we have types?
  + Permits it the computer to understand underlying "bits"
  + Helps programmers "do the right thing"
* Many kinds of numbers in Scheme
  + Exact / Inexact
    Precisely represented / Probably approximated
  + Integer, Rational, Real, Complex
* Lots of built-in numeric procedures
  + sqrt, expt, + , -, *, /
  + quotient, remainder, mod, numerator, denominator, ...
* Predicates for checking kinds of numbers
  + integer? rational? real? complex?
  + even? odd?
  + exact? inexact?


REFLECTION
* "1.507 times 10 to the fifteenth power"
  1.507e15
* "as an exact number"
  #e1.507e15
* Alternatively ...
  (* 1507 (expt 10 12))
* #e can only go in front of numbers, not expressions
* What does (round (+ i 1/2)) do for integer i?
* Quotient and remainder:
* What is (numerator 1.3)
  1 + XXXXX/(expt 2 52) 

> (inexact->exact #i13/10)
1 1351079888211149/4503599627370496

Isn't that thrilling?