CSC161 2010F, Class 14: Operators and Precedence

Overview:
* IEEE Floating Point, Continued.
* C's Wealth of Operators.
* Some Precedence and Other Examples.
* Group Exercise.

Admin:
* Warning: Your class mentor will be unavailable most of next week.
* Don't forget the Town Hall meetings today!  (Noon and 7:30)
* Reading for tomorrow: 3.1-3.3.
* Reminder: Review session Friday!
* Take-home exam distributed Wednesday, due the following Wednesday.
  INDIVIDUAL work.
* Are there questions on Assignment 4?  I know that some of you have 
  questions about stacks.

Questions on Assignment 4

* The algorithm for part 2:
  Start with an "empty" array of some fixed size
  For each remaining value in the input
  * If it's a number, add it to the "end" of the array
  * If you see an operator, remove the parameters from the "end" of the
    array, evaluate the operator, and put the result back in the array.
* What do you mean by "push" and "pop"
  * Pop means "remove from the end"
  * Push means "add to the end"
* Do we know that the input is divided by spaces?
  * No, but you can assume the input is separate strings, so life is
    okay.
* Can we add an extra parameter to rpn that takes the position we
  start at in the array?
  * Yes.
* Why would we want to do that?
  * So that we can ignore the first element of argv
  rpn (size, array_of_strings)
  rpn (size, array_of_strings, start_here)
* Bring more questions tomorrow!

IEEE Floating Point, Continued
* Effectively, exponential notation in binary
  Three parts:
  * Sign
  * Significand
  * Exponent
* Designer of such a notation needs to decide
  * How many bits for each part
  * How to represent each part
  * How to deal with special cases
* Sign: 1 bit
* How should we distribute the remaining 31 bits
  * E.g., 15 bits for significand and 16 bits for exponent
    * If exponent can be positive or negative, the largest possible
      exponent is about 2^15 and the smallest possible exponent is
      about -(2^15)
    * 1/2^15 is the accuracy - about 1/32thousand - four or five significant
      digits
  * The IEEE committee decided
    * 8 bits for the exponent
    * 23 bits for the significand (virtually 24)
* How do you represent each part?
  * Decision for exponent: Excess 127
    So exponent -127 could be represented as 00000000
    And exponent 0 is represented as 01111111
    Smallest legal exponent -126
    Largest legal exponent 127
    Note 00000000 and 11111111 are not legal exponents
  * These are used for other special values
    All 0's: Significand is interpreted as between 0 and 1, permitting us
      to represent 0 (and some other small numbers),
      treat exponent as -127 (0 is therefore all 0's)
    All 1's
      If the significand is all 0's, it's infinity
      Otherwise, it's Not a Number (NaN)

Next Topic: Operations in C

* C provides a lot of operations
  * Two-parameter Arithmetic operations: -, +, *, /, % (modulo)
  * Two-parameter Bitwise operations: |, &, ^ (exclusive or)
  * Two-parameter Binary operations: <<, >>
  * Two-parameter Assignment Operations: =, +=, -=, *=. <<=, /=, %=
  * Two-parameter logical operations: ==, !=, <, <=, >, >=, &&, ||
  * One-parameter Arithmetic operations: -, ++, --, +
    -x means "negate x"
  * One-parameter Bitwise operations: ~
  * One-parameter logical operations: !
* Typical issue with operators: Precedence!
  3 + 4 * 5
  * C does pay attention to precedence

Precedence
* Some examples

Exercise