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Chapter 2 – Data Types

We start now to deal with details of “syntax”

Yes, you need to know syntax

OTOH, it’s in the book, if you can find it.

Prudent Programming Practice:• learn to do it right• don’t push the envelope on the rules• think: 80% get it right, 20% know the rules• sometimes (usually?) vanilla is better

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Data Types

INTEGER : numbers without decimal pointsREAL : numbers with dec points (scientific

notation)COMPLEX : complex numbersCHARACTER : strings of textLOGICAL : either .TRUE. or .FALSE.

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Symbols

Book calls these things “identifiers”

I will probably call these things “variable names” or “symbols”

Lots of fussy rules

Identifiers:• must start with a letter• must be only letters, numerals, or underscore• must be lessequal 31 characters long

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Case Sensitivity

Fortran is NOT, repeat NOT, “case sensitive”

ThisSymbol is the same as THISSYMBOL is the same as thissymbol is the the same as tHiSsYmBoL

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Variables

Declare variables asREAL :: x

INTEGER :: n

Assign values to variables asx = 3.14159

x = 0.314159E01

n = -23

Variables that are declared but not yet assigned a value are undefined (ANSI) although some compilers will assign zero

DO NOT RELY ON INITIAL ASSIGNMENT!!!!

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Equals is NOT “Equals”

Assignment statements are writtenr1 = (-b + SQRT(b**2 – 4.0*a*c))/(2.0*a)

This is not a mathematical “equality” statementThink of this as

“r1 gets the value yada yada”r1(-b + SQRT(b**2 – 4.0*a*c))/(2.0*a)

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Safe Programming Practice

Fortran historically has said that variables beginning with i through n are integers and all else are reals by default

This would let you avoid declaring variables

DO NOT DO THIS! NOT EVER!! NEVER!!!

A vast number of programming errors are typos of variable names

Let the compiler catch these errors.Use the IMPLICIT none

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Safe Programming Practice

Variables can be declared and assigned an initial value all at once.

REAL :: pi = 3.14159

instead ofREAL :: pi

pi = 3.14159

Or they can be declared to be constantsREAL,PARAMETER :: pi = 3.14159

This latter makes illegal any later assignment like

pi = 1.56789

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Issues

DO NOT EVER do the followingREAL :: x = 43.79 ! initial assignment

part 1 code here

x = 23.9

part 2 code here

Either make the variable a parameter and assign it a value once for all time, or else assign it a value with an assignment statement

What’s going to happen the second time you execute the part 1 code? Is that your final answer?

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The End

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Arithmetic and Assignments

Assignments are not “equals”Most expressionsx = some reasonably legal expression

are in fact legal in Fortranbut they may not produce the result you expect

CAUTION: Juxtaposition for multiplication won’t work.

The expression “a times b” must be writtena * b and not a b

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Arithmetic and Assignments

r1 = (-b + SQRT(b**2 – 4.0*a*c))/(2.0*a)

Exp, (mult and div), (add and sub), left to rightProper parentheses on numerators and

denominatorsConstant is 2.0, not just 2All the mults use the *Exp is “star star” and use exponent 2, not 2.0The SQRT calls the Fortran builtin function

SAFE PROGRAMMING: don’t be cute or clever; use spaces and parentheses to make the expression readable

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Arithmetic and Assignments

Don’t be cute or clever; code for correctness and readability

num = -b + SQRT(b**2 – 4.0*a*c)

den = 2.0*a

root = num/den

gets the job done just as well as the one-linerIf the expression is complicated and would take

multiple lines, it is probably better to spread it out

Many errors come from misplaced parenthesesAny decent, modern, compiler will produce code

that is just as efficient

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Integer Arithmetic

If you divide two integers, the fraction is thrown away

4/5 results in 0

14/5 results in 2

(-14)/5 could perhaps be -3 or -2 (rounding down to minus infinity or truncating toward zero)

CHECK YOUR COMPILER if in doubt

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Mixed-Mode Arithmetic

An expression with variables of different types (e.g., integers with reals) is called mixed-mode

Variables are promoted (INTEGER to REAL, specifically) before the expression is evaluated

But be careful! What about

x = (2/3) * 4.0

Would this truncate 2/3 to 0 and then multiply?

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Mixed-Mode Arithmetic

When you really need mixed mode arithmetic, be explicit – use the intrinsic functions such as

INT(expression)

REAL(expression)

so that you can see specifically what you have asked the machine to do

This is sometimes called a cast of one type to another (because that’s what the C language calls it)

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Buell’s Rules

IN ORDER OF IMPORTANCE

1. Get it right2. Know what the problems might be from

being cute, and don’t be cute3. Know where to look up the precise rulesIf you practice 1)-3) religiously, then you can

usually avoid 4)

The compiler/computer will always tell you what it’s going to do if there’s a question.

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Floating-Point (i.e. REAL) Arithmetic

Remember “significant digits” from science?0.01 * 0.01 = 0.00

because 0.01 * 0.01 = 0.0001 but we have only allowed two significant digits

Similar rules apply with computers and Fortran

The machine will calculate a number as a result

Only you will know whether the result makes sense

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Computer Arithmetic

Digital logic normally works in on or off mode

So computers work in binary arithmetic

Some effort must be made to deal with conversion from binary to decimal and back again

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Computer Arithmetic

Numbers are represented as a finite set of digits in binary

Fractions, base n, have terminating representations only if the prime divisors of the denominator are divisors of n

½ = 0.5, 1/5 = 0.2, 1/16 = 0.0625, 1/20 = 0.05

all terminate, but 1/3 = 0.33333… does not

Binary is even more restrictive: denominators must be powers of 2

Even 1/10 does not have a terminating rep in binary

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IEEE 754 Standard

(Virtually) all floating point arithmetic is now done using the IEEE 754 standard—this specifies what the results of floating point arithmetic should be

Prior to 754, chaos reigned

The IBM 360 couldn’t multiply by 1.0 correctly

Every machine had its little quirks

Cray: Do you want the right answer? Or do you want an answer fast?

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IEEE 754

Floating point is always slightly inaccurate due to finite precision and to representation in binary

One of the demands of IEEE 754 is that the result of a numerical operation should be the closest representable number to the number that would be the result if there were infinite precision

If you check compiler options, they will have many IEEE 754 possibilities, because accurate means slow, and some of the accuracy issues are mostly for debugging purposes

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32-Bit Floating Point Numbers

1 bit for sign

8 bits for exponent in excess 127 notation(2**128 ~ 10**38)

23 bits for mantissa with an implied leftmost 1(2**24 = 16777216 ~ 10**7)

So we get 6 for sure, and sometimes 7, decimal places of accuracy

The dynamic range is about 10**(-38) to 10**38

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64-Bit Floating Point Numbers

1 bit for sign

11 bits for exponent in excess 1023

52 bits for mantissa with an implied leftmost 1(2**53 ~ 9*(10**15))

So we get 15 for sure, and sometimes 16, decimal places of accuracy

The dynamic range is about 10**300

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32-Bit Integers

Smallest integer is -2**31

Largest integer is 2**31 – 1 = 2147483647

So we get 9 for sure, and sometimes 10, decimal places of accuracy

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64-Bit Integers

Smallest integer is -2**63

Largest integer is 2**63 – 1 = 9 223 372 036 854 775 807

So we get 18 for sure, and sometimes 19, decimal places of accuracy

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Numbers in General

Fortran used to have only 32-bit and 64-bit numbers.

Now you can specify exactly what accuracy you want

However, we will concentrate on 32 bits and 64 bits because most machines deal in those numbers and thus most code is written for these sizes

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The End

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Fortran Requirements

Used to be “fixed format” card punching• Columns 1-5 for statement numbers• Column 6 to indicate continuation• Columns 7-72 for statements• Columns 73-80 for card sequence numbersFortran 90 can be “free format”• Ampersand (&) indicates continuation• Statement numbers not needed (except for FORMAT)

• Spaces (after the first space) don’t count except in a FORMAT string

aware of the old rules in case you see old code

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Coding Standards

INDENT!!!!!Use meaningful variable namesDull, boring, and correct is ok.Clever, fancy, and incorrect is not ok.Be consistent—this will help you find bugsDeclare variables by type, in alpha order?Sort subroutines in alpha order?Open and close structures with comments or

labels

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What’s In a Program?

Header

Specification/declaration statements

Executable statements

Subprograms

End of program statement

“Hello, world” program

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Header and Trailer

All programs start with a

PROGRAM this_is_the_program_name

Statement and they should all end with an

END PROGRAM this_is_the_program_name

statement

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Subprograms

Not everything should be done “in line” in a program.

Subprograms perform specific tasks

“Modular” programs are more readable and more likely to be correct

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Specification/Declaration

All symbols have a meaning in the program (variable names, function names, etc.)

In the specification/declaration section we tell the compiler the context in which we will be using the symbols.

E.g., an integer variable

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Executable

In the executable section of the program are the statements that actually perform the computation

“Hello, world” program

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Input and Output

PRINT *, list of variables

WRITE(6,*) list of variables

WRITE(6,nn) list of variables

nn FORMAT(format statement here)

The first two are “free format” and the last pair is a specifically formatted output statement

By default, “unit 5” is stdin for reading and “unit 6” is stdout for writing

CAVEAT: Fortran reads an entire line with each READ

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Input and Output

With free format output, (the *), you get scientific notation if needed, adequate default precision, etc., with little programming hassle

But you don’t get columns lined up neatly

The purpose of the FORMAT statement is to let you specify the precision and widths so that columnar output looks pretty

We’ll get to formatting later

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Pages 100 ff

These pages detail the Fortran up till now

Study them carefully

Pages 105ff contain hints, good ideas, etc.

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The End