Download presentation

Presentation is loading. Please wait.

Published byGustavo Burnell Modified over 4 years ago

1
Structure and Interpretation of Computer Programs* Section 2.4 – 2.5 Presenter: Xiang Zhang 05/04/2010 1 * Harold A., Gerald J. S., Julie S.. Structure and Interpretation of Computer Programs.

2
Topics Last Session Data Abstraction Today Multiple Representations for Abstract Data Data-Directed Programming Generic Operations 2

3
A Running Example – Complex Number System* y x Two Possible Representations for Complex Numbers The rectangular representation: (real, imaginary) The polar representation: (magnitude, angle) One representation can be derived from another * Taken from the book Structure and Interpretation of Computer Programs Real Imaginary r z = x + iy = r e iA A 3

4
A Running Example – Complex Number System* * Taken from the book Structure and Interpretation of Computer Programs Elementary Operators Addition: z 1 + z 2 Real-part(z 1 + z 2 ) = Real-part(z 1 ) + Real-part(z 2 ) Imaginary-part(z 1 + z 2 ) = Imaginary-part(z 1 ) + Imaginary-part(z 2 ) Subtraction Replace - for + in addition Multiplication Magnitude(z 1 * z 2 ) = Magnitude(z 1 ) * Magnitude (z 2 ) Angle(z 1 * z 2 ) = Angle(z 1 ) + Angle(z 2 ) Division Replace / for * and - for + in multiplication 4

5
A Running Example – Complex Number System* * Taken from the book Structure and Interpretation of Computer Programs Rectangular Representation Polar Representation add-complex sub-complex mul-complex div-complex Programs that use complex numbers Generic Operators real-part imag-part magnitude angle 5

6
Dispatching on Type Use Type to Distinguish Representations Example Code for the real-part procedure 3 4 rectangular (rectangular (3 4)) 6

7
The Weakness of Dispatch on Type Rectangular Polar add-complex sub-complex mul-complex div-complex Programs that use complex numbers real-part imag-part magnitude angle …… X (cases for other representations) 7

8
Data-directed Programming 8 Rectangular Polar add-complex sub-complex mul-complex div-complex Programs that use complex numbers real-part imag-part magnitude angle …… X Proc Table Query Register OperatorRectangularPolar… real-partreal-part-recreal-part-po… imag-partimag-part-recimag-part-po… mag-partmag-part-recmag-part-po… ang-partang-part-recang-part-po…

9
A Unified Arithmetic System 9 Rational arithmetic add sub mul div Programs that use rational numbers, complex numbers, and ordinary numbers Rect Polar Complex Arithmetic Ordinary Arithmetic Proc Table Query Register OperatorRationalComplexOrdinary addrat-addcomplex-add+ subrat-subcomplex-sub- mulrat-mulcomplex-mul* divrat-divcomplex-div/

10
Operate on Different Types - Coercion Supertype and subtype relations An integer is a rational number A rational number is a complex number … 10

11
11 Rational arithmetic add sub mul div Programs that use rational numbers, complex numbers, and ordinary numbers Rect Polar Complex Arithmetic Ordinary Arithmetic Proc Table Query Register ComplexRationalOrdinary ComplexN/A RationalRat->ComN/A OrdinaryOrd->ComOrd->RatN/A Operate on Different Types - Coercion Coercion Table Query

12
Summary Dispatch on Type Data-directed Programming Data Coercion 12

Similar presentations

OK

EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 17: 1) Sinusoidal Source 2) Complex Numbers.

EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 17: 1) Sinusoidal Source 2) Complex Numbers.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on diode as rectifier tube Ppt on relations and functions for class 11th biology Download ppt on islands of india Ppt on computer based information system Ppt on operating systems Powerpoint ppt on patient safety goals Ppt on fire training Ppt on ministry of corporate affairs ontario Ppt on the art of war summary Ppt on electrical power transmission system