A Glance at Numbers

Numbers

• SmallInteger, Integer,
  • 4, 2r100 (4 in base 2), 3r11 (4 in base 3)
• Automatic coercion
  • 1 + 2.3 -> 3.3
  • 1 class -> SmallInteger
  • 1 class maxVal class -> SmallInteger
  • (1 class maxVal + 1) class -> LargePositiveInteger
• Fraction, Float
  • 3/4, 2.4e7
  • (1/3) + (2/3) -> 1
  • 1000 factorial / 999 factorial -> 1000
  • 2/3 + 1 -> (5/3)

Numbers

Small Integers are Real Objects

• Small ints are real objects: instance of class SmallInteger
• No need for boxing or unboxing

	1 class
	> SmallInteger

• Operations on small integers are plain messages (no exception to the rule)

Small integers are optimized

But small integers are heavily optimized

• Small integers encoded on 30 bits
• The pointer itself is the small integer

    2 raisedTo: 30  
    > 1073741823

    SmallInteger maxVal
    > 1073741823

Automatic Coercion

What is the largest small integer?

	1 class maxVal
	> 1073741823

What is the smallest large integer?

	1 class maxVal +1
	> 1073741824

	(1 class maxVal + 1) class
	> LargePositiveInteger

Fun With Numbers

Fun With Large Numbers

factorial is not optimized

1000 factorial numberOfDigits
> 2568 

100000 factorial numberOfDigits
> 456574 

• Takes some seconds :)

Fraction

Fraction

• denominator, numerator, ....
• Can handle large numbers

1000 factorial / 999 factorial
> 1000

Messages Sent to Objects

• Operations on numbers are plain messages
• No exceptions

	(1 / 3) + (2 / 3)
	>1

	2 / 3 + 1
	> 5 / 3

• Numbers are objects
• Mathematical operations are messages sent to objects

Message Limits

• There is no notion of precedence

2 * 3 + 5
> 11

2 + 3 * 5 
> 25 !!!

• Use parenthesis to enforce precedence

2 + (3 * 5)
> 11

Points

• A point has an x and y
• Points are created using the message @ or x:y:

10 @ 100
(10 @ 100) x
> 10
(10 @ 100) y
>100

Alternative

Point new x: 100 y: 100

Class written in a functional way: Most Point methods are returning new points

Rectangles

• Geometric and expected operations
• areasOutside:, expandBy:, insetBy:, intersect:

Rectangle left: 10 right: 100 top: 20  bottom: 40
> (10@20) corner: (100@40)

Rectangle origin: 20@20	corner: 100@200

Margins

• Delta to apply to a rectangle
• Useful for GUI
• Encodes 4 numbers, expressed in 3 different ways
  • a number (same space all around)
  • two numbers (same left/right and top/bottom)
  • four numbers
• Used to compute the extended (or inner) rectangle

Summary

• Numbers are real objects
• Automatic coercion
• Number can be infinitely large
• Abstractions are built on top: Point, Rectangle, Margin