COSC 1306COMPUTER SCIENCE AND PROGRAMMING FLOATINGPOINT NUMBERS JehanFranois

COSC 1306—COMPUTER SCIENCE AND PROGRAMMING FLOATING-POINT NUMBERS Jehan-François Pâris jfparis@uh. edu

Floating point numbers • Three main differences with integer numbers – Cannot handle well extremely large or extremely small values – Limited precision • Can manipulate trillions of dollars but results are not exact to the cent – Must specify number of decimals

Limited precision # precision. py """ floating-point computations can be inaccurate """ alpha = 5 E 9 delta = 5 E-9 beta = alpha + delta gamma = beta - alpha print ('delta = ' + str(delta) + ' but gamma = ' + str(gamma))

The output delta = 5 e-9 but gamma = 0. 0 • Why? – Computations are carried out with a limited number of significant bits • Result has a limited number of significant digits • Be careful when computing very small differences between two numbers

Note • Limitations on floating point number size and precision are – Hardware dependent – Shared by most programming languages • Unlike Python, most programming languages do not support arbitrary-size integers

Displaying floating point numbers • Easiest way to specify number of decimal places is string interpolation – 'Answer is %. nf ' %x does two things • It inserts the value of x inside the string • It specifies that the string representation of x should have n decimal places

Example (I) • pi = 3. 1415917 print('pi equals %. 1 f‘ % pi ) print('pi equals %. 2 f' % pi ) print('pi equals %. 3 f' % pi ) print('pi equals %. 4 f' % pi )

Example (II) • Program prints pi equals 3. 142 pi equals 3. 1416 • Values are nicely rounded

Converting o. F into o. C (I) #F 2 CF. py """converts fahrenheit degrees into celsius degrees """ fahrenheit =float(input('Enter a temperature in degrees Fahrenheit: ')) celsius = (fahrenheit - 32)*5/9 print('%. 1 f degrees F equals %. 1 f degrees C' %(fahrenheit, celsius))

Converting o. F into o. C r (II) • Output is Enter a temperature in degrees Fahrenheit: 100. 0 degrees F equals 37. 8 degrees C

More about string interpolation • Can interpolate – Floating-point numbers in scientific notation • >>> c = 300000 >>> print('c = %. 3 e km/s'% c) c = 3. 000 e+05 km/s – Integers using %d – Strings using %s

Example (I) • # interpolate. py """ silly demo """ name = input("What's your name? ") nclasses=int(input('How many classes are you taking? ')) print ('%s is taking %d classe(s)' %(name, nclasses))

Example (II) • Output is: What's your name? Bill How many classes are you taking? 5 Bill is taking 5 classe(s)

Using the proper quotes • We had to use double quotes (") in name = input("What's your name? ") because the string contained an apostrophe (') • we could have "escaped" the apostrophe as in name = input('What's your name? ')

More escapes • Escape sequence Meaning ' Apostrophe " Double quote \ Backslash n Newline r Carriage return • (See page 86)

Escaping the percent sign • Not required in normal strings >>> print("Use the %. 3 f format") Use the %. 3 f format • Required when we use string interpolation >>> print("Use %%. 3 f to print %. 3 f" % 3. 1416) Use %. 3 f to print 3. 142

Boolean type • Two values: – True and False • Created as – Result of a comparison: ==, !=, >, >=, <, <= – Conversion using bool(…) function • Zero values and anything empty converts into a False • Anything else converts into a True value

Examples >>> a = 3 >>> b = 5 >>> p = (a < b) >>> q = (b <= a) >>> print("p = " + str(p) + “ and q = " +str(q)) p = True and q = False

Boolean operations (I) • AND: – True if both operands are true a b F F T F a and b F F F This is called a truth table

Boolean operations (II) • OR: – True unless both operands are false a F F T T b F T a or b F T T T

Boolean operations (III) • NOT: – True if operand is false a not a F T T F

Boolean operations (IV) • Equality/Mutual Implication: – True when both operands are equal – Represented by a == sign a F F T T b a==b F T T F F F T T

Boolean operations (V) • Inequality/Exclusive OR (XOR): – True when operands are not equal – Represented by a != sign a b a!=b F F T T F T F T T F

Notes • XOR is used for – Generating parity bits – Hardware hashing

Examples • Assuming P is True and q is False >>> p or q True >>> p and q False >>> not p False >>> p != q True

Variables and objects • Variables point to objects – Integers – Strings – Floating-point numbers

What is an object? • Short for data object • Example: dates – Cannot add two dates but can compute their difference – Can initialize date – Can compute weekday(date) – Special date today() – Multiple ways to convert a date into a string

Definition • An object is an instance of a specific class on which class-specific operations called methods are defined • So if an object is of the type date, we will define – A method to initialize a date – A method pr a function to compute the difference of two dates –…

String methods • These methods never modify the string they apply to! • See pages 90 to 95 of text – Do not memorize them (yet) please! • One example – s. capitalize(): capitalizes the first letter of the string and converts all other letters to lower case

Examples (I) >>> a = 'bill' >>> a. capitalize() 'Bill' >>> b = 'Bill' >>> b. capitalize() 'Bill'

Examples (II) >>> c = 'b. ILL' >>> c. capitalize() 'Bill' >>> d ='Billy Bob' >>> d. capitalize() 'Billy bob‘

Better but not perfect – s. title(): capitalizes the first letter of each word in the string and converts all other letters to lower case as in the title case • Defines words in a very crude fashion

Examples (I) >>> s = 'bi. LLy Bob' >>> s. title() 'Billy Bob' >>> s ='jehan-francois' >>> s. title() 'Jehan-Francois' >>> s. title()

Examples >>> s = "dean's list" >>> s. title() "Dean'S List" >>> s "dean's list" >>>

Dollars into bills revisited (I) # dollars 2 bills. py """ This program prompts repeatedly for a value in dollars and converts it into its equivalents in twenty, ten, five and one dollar bills. It terminates when the user enters a zero value """

Dollars into bills revisited (II) # amount is the dollar amount we enter # ntwentys is number of $20 bills we need # ntens is number of $10 bills we need # nfives is number of $5 bills we need # nones is number of $1 bills we need # outstr is our output string

Dollars into bills revisited (III) amount = int(input("Enter an integer amount of dollars: ")) while amount != 0 : outstr = '$' + str(amount) + ' is same as ' ntwentys = amount // 20 if ntwentys != 0 : outstr = outstr + str(ntwentys) + ' $20 bill(s) ' temp = amount % 20 ntens = temp // 10 if ntens != 0 :

Dollars into bills revisited (IV) temp = temp % 10 nfives = temp // 5 if nfives != 0 : outstr = outstr + 'and ' + str(nfives) + ' $5 bill(s) ' nones = temp % 5 if nones != 0 : outstr = outstr + 'and ' + str(nones) + ' $1 bill(s) ' outstr. replace('as and', 'as') print(outstr) amount = int(input("Enter an integer amount of dollars: "))

Outputs Enter an integer amount of dollars: 20 $20 is same as 1 $20 bill(s) Enter an integer amount of dollars: 7 $7 is same as 1 $5 bill(s) and 2 $1 bill(s) Enter an integer amount of dollars: 35 $35 is same as 1 $20 bill(s) and 1 $10 bill(s) and 1 $5 bill(s) Enter an integer amount of dollars: 0 Goodbye!

Useful shorthand • Can replace Ø a = a + … by a += … Ø b = b – … by b –= … Ø c = c * … by c *= … • Cannot use i++, i --, ++i , --i constructs of C Ø++i read as +(+i) = i Ø--i read as –(–i) • Does not work!

Examples (I) >>> i=1 >>> i += 1 >>> print(i) 2 >>> i++ Syntax. Error: invalid syntax >>> ++i 2

Examples (II) • In the preceding program we could have written outstr += str(ntwentys) + ' $20 bill(s) ' … outstr += 'and ' + str(ntens) + ' $10 bill(s) ' … outstr += 'and ' + str(nfives) + ' $5 bill(s) ' …

Operator precedence (I) • Recall the rules of precedence of arithmetic and algebra • From highest to lowest – Exponentiation (**) – Unary + and – – Multiplication, divisions and remainder (*, / , //, %) – Addition and subtraction (+ and -)

Operator precedence (II) • Python extends these rules to other operators • From highest to lowest – All arithmetic operations – All comparison operators (==, !=, <, …) – Boolean not – Boolean and (like multiplication) – Boolean or (like addition)

Examples • x**2*2 + 4*x is same as ((x**2)*2) +( 4*x) • (x + 3)/4 + 2 is same as ((x + 3)/4) + 2

Examples • Allows us to write if a < b and c < d : for if (a < b) and (c < d ): • Allows us to write a and b or not c for (a and b ) or (not c)

A common sense rule • Some expressions such as a*x**2 + b*x + c do not need parentheses • Nobody has ever been fired for writing if (a < b) and (c < d ): or even (a and b ) or (not c) • It is always better to play safe!

How our programs are translated • Our programs are not written in machine language – Cannot be directly executed by any computer – Must be first translated • Two approaches –Compiled languages –Interpreted languages

Compiled languages (I) • Programs written in Fortran, C, C++ and so on go to a program that translates them into directly executable code – The compiler • Doing gcc myprogram. c –o myprogram produces an executable file called myprogram that can run anytime

Compiled languages (II) C program C compiler Executable

Advantages • The executable can run on any computer with – Same CPU instruction set – Same—or compatible—operating system • We can sell copies of the executable without revealing the secrets of our program

Intellectual Property Issues (I) • Law protects programs in two ways – They can be trade secrets • Protection ends once secret is revealed. – The can be copyrighted • Only protects expressions of an idea • Others can write a program doing the same things are your program

Intellectual Property Issues (II) • Selling C programs or Python programs is a very risky proposition – Invites imitators • Best solution is – Selling copies of executables • Properly obfuscated – Keeping source code secret

Interpreted languages (I) • Languages like Basic, Perl, Python and Ruby are not compiled – Translated into bytecode before being executed – Bytecode is interpreted by the language interpreter

Interpreted languages (II) Python Program Bytecode Python Interpreter: translates program into bytecode then executes it

Advantages • Platform independence: – Bytecode can run on any platform for which there is an interpreter • Dynamic typing: – Same variable can refer to a string then an integer then … • Smaller executable sizes

Disadvantages • Portability limitations : – Bytecode will not run on any machine on which the interpreter was not installed. • Speed: – Bytecode is not optimized for a specific architecture – Just-in-time compilation introduces delays

A partial solution • In many cases, speed is not an issue outside of loops than get executed thousands of times • Loops inside other loops • Can rewrite code for these inner loops in C and include this code into a Python program – Use Python C API

Neither fish nor fowl • Java is compiled – Like Fortran, C, … into bytecode – Like Perl and Python • Bytecode is executed by Java Virtual Machine