slides.md

---
marp: true
title: Introduction to structured programming with Fortran
author: P.Y. Barriat
backgroundImage: url('assets/back.png')
_backgroundImage: url('assets/garde.png')
footer: 09/11/2023 | Introduction to structured programming with Fortran
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paginate: true
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---

Introduction to structured programming with `Fortran`<!--fit-->
===

https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran

![h:150](assets/fortran_logo.png)

### Pierre-Yves Barriat

##### November 09, 2023

###### CISM/CÉCI Training Sessions

---

# Fortran : shall we start ?

- You already know one computer language ?
- You understand the very basic programming concepts :
  - What is a variable, an assignment, function call, etc. ?
  - Why do I have to compile my code ?
  - What is an executable ?
- You (may) already know some Fortran ?
- How to proceed from old Fortran, to much more modern languages like Fortran 90/2003 ?

---

# Why to learn Fortran ?

* Because of the execution `speed` of a program
* Well suited for numerical computations :
more than 45% of scientific applications are in Fortran
* `Fast` code : compilers can optimize well
* Optimized `numerical libraries` available
* Fortran is a `simple` langage and it is (kind-of) `easy to learn`

---

# Fortran is simple

- **We want to get our science done! Not learn languages!**
* How easy/difficult is it really to learn Fortran ?
* The concept is easy:
*variables, operators, controls, loops, subroutines/functions*

* **Invest some time now, gain big later!**

---

# History

**FOR**mula **TRAN**slation
> invented 1954-8 by John Backus and his team at IBM

- FORTRAN 66 (ISO Standard 1972)
- FORTRAN 77 (1978)
- Fortran 90 (1991)
- Fortran 95 (1997)
- Fortran 2003 (2004) → `"standard" version`
- Fortran 2008 (2010)
- Fortran 2018 (11/2018)

---

# Starting with Fortran 77

- Old Fortran provides only the absolute minimum !
- Basic features
  > data containers (integer, float, ...), arrays, basic operators, loops, I/O, subroutines and functions
- But this version has flaws
  > no dynamic memory allocation, old & obsolete constructs, "spaghetti" code, etc.
- Is that enough to write code ?

---

# Fortran 77 → Fortran >90

- If Fortran 77 is so simple, why is it then so difficult to write good code ?
- Is simple really better ?
  > ⇒ Using a language allows us to express our thoughts (on a computer)
- A more sophisticated language allows for more complex thoughts
- More language elements to get organized
  > ⇒ Fortran 90/95/2003 (recursive, OOP, etc)

---

# How to Build a FORTRAN Program

FORTRAN is a compiled language (like C) so the source code (what you write) must be converted into machine code before it can be executed (e.g. Make command)

![h:350](assets/build_fortran.png)

> Fortran 77 source code [hello_world.f](https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/src/master/src/00_hello_world.f)

---

# FORTRAN 77 Format

This version requires a fixed format for programs

![h:300](assets/f77_format.png)

- max length variable names is 6 characters
- alphanumeric only, must start with a letter
- character strings are case sensitive

---

# FORTRAN >90 Format

Versions >90 relaxe these requirements:

- comments following statements (`!` delimiter)
- long variable names (31 characters)
- containing only letters, digits or underscore
- max row length is 132 characters
- can be max 39 continuation lines
- if a line is ended with ampersand (`&`), the line continues onto the next line
- semicolon (`;`) as a separator between statements on a single line

---

# Program Organization

Most `FORTRAN` programs consist of a main program and one or more subprograms

There is a fixed order:

```Fortran90
Heading
Declarations
Variable initializations
Program code
Format statements

Subprogram definitions
(functions & subroutines)
```

---

# Data Type Declarations

Basic data types are :

- `INTEGER` : integer numbers (+/-)
- `REAL` : floating point numbers
- `DOUBLE PRECISION` : extended precision floating point
- `CHARACTER*n` : string with up to **n** characters
- `LOGICAL` : takes on values `.TRUE.` or `.FALSE.`

---

# Data Type Declarations

`INTEGER` and `REAL` can specify number of bytes to use

- Default is: `INTEGER*4` and `REAL*4`
- `DOUBLE PRECISION` is same as `REAL*8`

Arrays of any type must be declared:

- `DIMENSION A(3,5)` - declares a 3 x 5 array
- `CHARACTER*30 NAME(50)` - directly declares a `character` array with 30 `character` strings in each element

---

# Implicit vs Explicit Declarations

By default, an implicit type is assumed depending on the first letter of the variable name:

- `A-H, O-Z` define REAL variables
- `I-N` define INTEGER variables

Can use the IMPLICIT statement:

```fortran
IMPLICIT REAL (A-Z) 
```

> makes all variables REAL if not declared

---

# Implicit vs Explicit Declarations

```fortran
IMPLICIT CHARACTER*2 (W)
```

> makes variables starting with W be 2-character strings

```fortran
IMPLICIT DOUBLE PRECISION (D)
```

> makes variables starting with D be double precision

**Good habit**: force explicit type declarations

```fortran
IMPLICIT NONE
```

> user must explicitly declare all variable types

---

# Assignment Statements

**Old** assignment statement: `<label>` `<variable>` = `<expression>`

- `<label>` : statement label number (1 to 99999)
- `<variable>` : FORTRAN variable
(max 6 characters, alphanumeric only for standard FORTRAN 77)

**Expression**:

- Numeric expressions: `VAR = 3.5*COS(THETA)`
- Character expressions: `DAY(1:3) = 'TUE'`
- Relational expressions: `FLAG = ANS .GT. 0`
- Logical expressions: `FLAG = F1 .OR. F2`

---

# Numeric Expressions

Arithmetic operators: precedence: `**` *(high)* → `-` *(low)*

|   Operator   | Function        |
| ------------ | --------------- |
|     `**`     |  exponentiation |
|     `*`     |  multiplication |
|     `/`     |  division |
|     `+`     |  addition |
|     `-`     |  subtraction |

---

# Numeric Expressions

Numeric expressions are up-cast to the highest data type in the expression according to the precedence:

*(low)* logical → integer → real → complex *(high)*

and smaller byte size *(low)* to larger byte size *(high)*

## Examples:

> Fortran 77 source code [01_arith.f](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/01_arith.f)
> Fortran 77 source code [02_sphere.f](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/02_sphere.f)

---

# Character Expressions

Only built-in operator is **Concatenation** defined by `//`

```fortran
'ILL'//'-'//'ADVISED'
```

`character` arrays are most commonly encountered

- treated like any array (indexed using : notation)
- fixed length (usually padded with blanks)

---

# Character Expressions

Example:

```fortran
CHARACTER FAMILY*16
FAMILY = ‘GEORGE P. BURDELL’

PRINT*,FAMILY(:6)
PRINT*,FAMILY(8:9)
PRINT*,FAMILY(11:)
PRINT*,FAMILY(:6)//FAMILY(10:)
```

```fortran
GEORGE
P.
BURDELL
GEORGE BURDELL
```

---

# Relational Expressions

Two expressions whose values are compared to determine whether the relation is true or false

- may be numeric (common) or non-numeric

`character`  strings can be compared

- done character by character
- shorter string is padded with blanks for comparison

---

# Relational Expressions

|   Operator   | Relationship        |
| ------------ | --------------- |
|     `.LT.` or `<`    |  less than |
|     `.LE.` or `<=`    |  less than or equal to |
|     `.EQ.` or `==`    |  equal to |
|     `.NE.` or `/=`    |  not equal to |
|     `.GT.` or `>`    |  greater than |
|     `.GE.` or `>=`    |  greater than or equal to |

---

# Logical Expressions

Consists of one or more logical operators and logical, numeric or relational operands

- values are `.TRUE.` or `.FALSE.`
- need to consider overall operator precedence

> can combine logical and integer data with logical operators but this is tricky (**avoid!**)

---

# Logical Expressions

|   F77 Operator  |   >F90 Operator |   Example   | Meaning        |
| --------------- | --------------- | ------------ | --------------- |
|     `.AND.`     |     `&&`     |     `A .AND. B`     |  logical `AND` |
|     `.OR.`      |     `\|\|`      |     `A .OR. B`      |  logical `OR` |
|     `.EQV.`     |     `==`     |     `A .EQV. B`      |  logical equivalence |
|     `.NEQV.`    |     `/=`    |     `A .NEQV. B`      |  logical inequivalence |
|     `.XOR.`     |     `/=`     |     `A .XOR. B`      |  exclusive `OR` (same as `.NEQV.`) |
|     `.NOT.`     |             |     `.NOT. A`      |  logical negation |

---

# Arrays in FORTRAN

Arrays can be multi-dimensional (up to 7 in F77) and are indexed using `( )`:

- `TEST(3)` or `FORCE(4,2)`

> Indices are by default defined as `1...N`

We can specify index range in declaration

- `INTEGER K(0:11)` : `K` is dimensioned from `0-11` (12 elements)

Arrays are stored in column order (1st column, 2nd column, etc) so accessing by **incrementing row index first** usually is **fastest** (see later)

Whole array reference (only in >F90): `K(:)=-8` assigns 8 to all elements in K

> Avoid `K=-8` assignement

---

# Unconditional `GO TO` in F77

This is the only GOTO in FORTRAN 77

- Syntax: `GO TO label`
- Unconditional transfer to labeled statement

```fortran
  10  -code-
      GO TO 30
      -code that is bypassed-
  30  -code that is target of GOTO-
      -more code-
      GO TO 10
```

- **Problem** : leads to confusing *"spaghetti code"* :boom:

---

# `IF ELSE IF` Statement

Basic version:

```fortran
IF (KSTAT.EQ.1) THEN
  CLASS='FRESHMAN'
ELSE IF (KSTAT.EQ.2) THEN
  CLASS='SOPHOMORE'
ELSE IF (KSTAT.EQ.3) THEN
  CLASS='JUNIOR'
ELSE IF (KSTAT.EQ.4) THEN
  CLASS='SENIOR'
ELSE
  CLASS='UNKNOWN'
ENDIF
```

---

# Spaghetti Code in F77 (and before)

Use of `GO TO` and arithmetic `IF`'s leads to bad code that is very hard to maintain

Here is the equivalent of an `IF-THEN-ELSE` statement:

```fortran
  10  IF (KEY.LT.0) GO TO 20
      TEST=TEST-1
      THETA=ATAN(X,Y)
      GO TO 30
  20  TEST=TEST+1
      THETA=ATAN(-X,Y)
  30  CONTINUE
```

Now try to figure out what a complex `IF ELSE IF` statement would look like coded with this kind of simple `IF`...

---

# Loop Statements (old versions)

`DO` loop: structure that executes a specified number of times

*Spaghetti Code Version*

```fortran
      K=2
  10  PRINT*,A(K)
      K=K+2
      IF (K.LE.11) GO TO 10
  20  CONTINUE
```

*F77 Version*

```fortran
      DO 100 K=2,10,2
      PRINT*,A(K)
 100  CONTINUE
```

---

# Loop Statements (>F90)

```fortran
DO K=2,10,2
  WRITE(*,*) A(K)
END DO
```

- `loop_control` can include variables and a third parameter to specify increments, including negative values
- loop always executes ONCE before testing for end condition

```fortran
READ(*,*) R
DO WHILE (R.GE.0) 
  VOL=2*PI*R**2*CLEN
  READ(*,*) R
END DO
```

- Loop will not execute at all if `logical_expr` is not true at start

---

# Comments on Loop Statements

### To exit a loop

- in old versions: use a `GO TO` statement

- in new versions: use an `EXIT` statement
  > you cannot transfer out of multiple nested loops with a single `EXIT` 
  > use named loops if needed : `myloop : do i=1,n` and then `EXIT myloop`

### To skip to next loop cycle

- in new versions **only** : use a `CYCLE` statement

---

# File-Directed Input and Output

Much of early FORTRAN was devoted to reading input data from "cards" and writing to a line printer

Today, most I/O is to and from a file: it requires more extensive I/O capabilities standardized until FORTRAN 77

**I/O** = communication between a program and the outside world

- opening and closing a file with `OPEN` & `CLOSE`
- data reading & writing with `READ` & `WRITE`
- can use **unformatted** `READ` & `WRITE` if no human readable data are involved (much faster access, smaller files)

---

# `READ` Statement

Syntax: `READ(dev_no, format_label) variable_list`

```fortran
      READ(105,1000) A,B,C
 1000 FORMAT(3F12.4)
```

> device numbers 1-7 are defined as standard I/O devices

- each `READ` reads one line of data 
  > any remaining data in a line is dropped if not translated in `variable_list`

- `variable_list` can include implied `DO` such as :
  `READ(105,1000)(A(I),I=1,10)`

---

# `READ` Statement - cont'd

- input items can be integer, real or character
- characters must be enclosed in `' '` (or `" "`)
- input items are separated by commas
- input items must agree in type with variables in `variable_list`
- each `READ` processes a new record (line)

```fortran
INTEGER K
REAL(8) A,B
! reads one line and look for floating point values for A & B and an integer for K
OPEN(105,FILE='path_to_existing_file')
READ(105,*) A,B,K
```

---

# `WRITE` Statement

Syntax: `WRITE(dev_no, format_label) variable_list`

```fortran
      WRITE(*,1000) A,B,KEY
 1000 FORMAT(F12.4,E14.5,I6)
```

```fortran
|----+----o----+----o----+----o----+----|
    1234.5678  -0.12345E+02    12
```

- device number `*` is by default the screen (or *standard output* - also 6)
- each `WRITE` produces one or more output lines as needed to write out `variable_list` using `format` statement
- `variable_list` can include implied `DO`

---

# `FORMAT` Statement

|   data type  |   format descriptors |   example   |
| --------------- | --------------- | ------------ |
|     `integer`     |     `iw`     |     `write(*,'(i5)') int`     |
|     `real` (*decimal*)      |     `fw.d`      |     `write(*,'(f7.4)') x`      |
|     `real` (*exponential*)     |     `ew.d`     |     `write(*,'(e12.3)') y`      |
|     `character`    |     `a, aw`    |     `write(*,'(a)') string`      |
|     `logical`     |     `lw`     |     `write(*,'(l2)') test`      |
|     spaces & tabs     |     `wx` & `tw`     |     `write (*,'(i3,2x,f6.3)') i, x`      |
|     linebreak     |     `/`     |     `write (*,'(f6.3,/,f6.3)') x, y`      |

---

# `OPEN` & `CLOSE` example (>F90)

Once opened, file is referred to by an assigned device number (a unique id)

```fortran
character(len=*) :: x_name
integer          :: ierr, iSize, guess_unit
logical          :: itsopen, itexists
!
inquire(file=trim(x_name), size=iSize, number=guess_unit, opened=itsopen, exist=itexists)
if ( itsopen ) close(guess_unit, status='delete')
!
open(902,file=trim(x_name),status='new',iostat=ierr)
!
if (iSize <= 0 .OR. .NOT.itexists) then
  open(902,file=trim(x_name),status='new',iostat=ierr)
  if (ierr /= 0) then
    ...
    close(902)
  endif
  ...
endif
```

---

# Examples

Fortran 77 source code [03_histogram.f](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/03_histogram.f) 

Fortran 90 source code [03_histogram.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/03_histogram.f90)

Fortran 90 source code [04_plot.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/04_plot.f90)

---

# `NAMELIST`

It is possible to pre-define the structure of input and output data using `NAMELIST` in order to make it easier to process with `READ` and `WRITE` statements

- Use `NAMELIST` to define the data structure
- Use `READ` or `WRITE` with reference to `NAMELIST` to handle the data in the specified format

> This is not part of standard F77 but it is included in >F90

---

# `NAMELIST` - cont'd

On input, the `NAMELIST` data must be structured as follows:

```fortran
&INPUT
  THICK=0.245,
  LENGTH=12.34,
  WIDTH=2.34,
  DENSITY=0.0034
/
```

> Fortran 90 source code [05_namelist.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/05_namelist.f90)
> Namelist file [05_namelist.def](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/05_namelist.def)

---

# Internal `WRITE` Statement

Internal `WRITE` does same as `ENCODE` in F77 : **a cast to string**

```fortran
INTEGER*4 J,K
CHARACTER*50 CHAR50
DATA J,K/1,2/
...
WRITE(CHAR50,*) J,K
```

Results:

```fortran
CHAR50='    1     2'
```

---

# Internal `READ` Statement

Internal `READ` does same as `DECODE` in F77 : **a cast from string**

```fortran
INTEGER K
REAL A,B
CHARACTER*80 REC80
DATA REC80/'1.2, 2.3, -5'/
...
READ(REC80,*) A,B,K
```

Results:

```fortran
A=1.2, B=2.3, K=-5
```

---

# Structured programming

Structured programming is based on subprograms (functions and subroutines) and control statements (like `IF` statements or loops) :

- structure the control-flow of your programs (e.g. give up the `GO TO`)
- improved readability
- lower level aspect of coding in a smart way

It is a **programming paradigm** aimed at improving the quality, clarity, and access time of a computer program

---

# Functions and Subroutines

Subprograms allow **structured coding** 

  `FUNCTION`: returns single explicit function value for given function arguments
  > it's also a variable → so must be declared !

  `SUBROUTINE`: any values returned must be returned through the arguments
  > no explicit subroutine value is returned !

* Subprograms are not recursive in F77

* Subprograms use a separate namespace (variables are local)

* Variables stored in `COMMON` may be shared between namespaces

---

#  Functions and Subroutines - cont'd

Subprograms must (should) include at least one `RETURN`

`FUNCTION` example:

```fortran
REAL FUNCTION AVG3(A,B,C)
AVG3=(A+B+C)/3
RETURN
END
```

Use:

```fortran
AV = WEIGHT*AVG3(A1,F2,B2)
```

> `FUNCTION` type is implicitly defined as REAL

---

# Functions and Subroutines - cont'd

Subroutine is invoked using the `CALL` statement

```fortran
SUBROUTINE AVG3S(A,B,C,AVERAGE)
AVERAGE=(A+B+C)/3
RETURN
END
```

Use:

```fortran
CALL AVG3S(A1,F2,B2,AVR)
RESULT = WEIGHT*AVR
```

Any returned values must be returned through argument list

---

# Arguments

Arguments in subprogram are `dummy` arguments 
> arguments used in invocation are called "actual" or "real"

- passed by **reference** (memory address) if given as *symbolic*
  > the subprogram can then alter the actual argument value since it can access it by reference

- passed by **value** if given as *literal* (so cannot be modified)

```fortran
CALL AVG3S(A1,3.4,C1,QAV)
```

> 2nd argument is passed by value and others by reference


---

# Arguments - cont'd

Arguments used in invocation (by calling program) may be *variables*, *array names*, *literals*, *expressions* or *function names*

Using symbolic arguments (variables or array names) is the **only way** to return a value (result) from a  `SUBROUTINE`

It is considered **BAD coding practice**, but functions can return values by changing the value of arguments
> this type of use should be strictly **avoided** !

---

# Arguments - cont'd

The `INTENT` keyword (>F90) increases readability and enables better compile-time error checking

```fortran
SUBROUTINE AVG3S(A,B,C,AVERAGE)
  IMPLICIT NONE
  REAL, INTENT(IN)    :: A, B
  REAL, INTENT(INOUT) :: C        ! default
  REAL, INTENT(OUT)   :: AVERAGE
  
  A = 10                          ! Compilation error
  C = 10                          ! Correct
  AVERAGE=(A+B+C)/3               ! Correct
END
```

> compiler uses `INTENT` for error checking and optimization

---

# `FUNCTION` versus Array

`REMAINDER(4,3)` could be a 2D array or it could be a reference to a function

If the name, including arguments, **matches an array declaration**, then it is taken to be an array, **otherwise**, it is assumed to be a `FUNCTION`

Be careful about `implicit` versus `explicit` type declarations with `FUNCTION`

```fortran
PROGRAM MAIN
  INTEGER REMAINDER
  ...
  KR = REMAINDER(4,3)
  ...
END

INTEGER FUNCTION REMAINDER(INUM,IDEN)
  ...
END
```

<!-- _footer: "" -->

---

# Arrays with Subprograms

Arrays must be passed by reference to subprogram 

How do you tell subprogram how large the array is ?
> answer varies with FORTRAN version and vendor (dialect)...

- when an array element, e.g. `A(1)`, is used in a subprogram invocation , it is passed as a reference (address), just like a simple variable

- when an array is used by name in a subprogram invocation, it is passed as a reference to the entire array.
  > the array must be appropriately dimensioned (and this can be tricky...)

---

# Data layout in multi-dimensional arrays

- always increment the left-most index of multi-dimensional arrays in the innermost loop (i.e. fastest)
- **column major** ordering in Fortran vs. **row major** ordering in C
- a compiler (with sufficient optimization flags) may re-order loops automatically

```fortran
do j=1,M
  do i=1,N ! innermost loop
    y(i) = y(i)+ a(i,j)*x(j) ! left-most index is i
  end do
end do
```

---

# Arrays - dynamic allocation

Using `ALLOCATABLE` on declaration, and using `ALLOCATE` and `DEALLOCATE` later

```fortran
integer :: m, n
integer, allocatable :: idx(:)
real, allocatable :: mat(:,:)
m = 100 ; n = 200
allocate( idx(0:m-1))
allocate( mat(m, n))
...
deallocate(idx , mat)
```

It exists many array intrinsic functions
> SIZE, SHAPE, SUM, ANY, MINVAL, MAXLOC, RESHAPE, DOT_PRODUCT, TRANSPOSE, WHERE, FORALL, etc

---

# `COMMON` & `MODULE` Statement

A variable declared in a `Main` program can be made accessible to subprograms

- `COMMON` statement allows variables to have a more extensive scope
  > can group into **labeled** `COMMON`

- with > F90, it's better to use a `MODULE` subprogram
  > this can be selective (don't have to share all everywhere) with `ONLY`

> Fortran 77 source code [06_common.f](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/06_common.f)
> Fortran 90 source code [06_module.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/06_module.f90)

---

# Hands-on

Fortran 90 source code [07_plot_newton.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/07_plot_newton.f90)

Fortran 90 source code [07_newton.f90](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/07_newton.f90)

Text file [08_ChristmasTree.txt](https://forge.uclouvain.be/barriat/learning-fortran/-/blob/master/src/08_ChristmasTree.txt)

---

# Modular programming (>F90)

Modular programming is about separating parts of programs into independent and interchangeable modules :

- improve testability
- improve maintainability
- re-use of code
- higher level aspect of coding in a smart way
- *separation of concerns*

The principle is that making significant parts of the code independent, replaceable and independently testable makes your programs **more maintainable**

---

# Data Type Declarations

FORTRAN >90 allows user derived types

```fortran
TYPE my_variable
  character(30)           :: name
  integer                 :: id
  real(8)                 :: value
  integer, dimension(3,3) :: dimIndex
END TYPE variable

type(my_variable) var
var%name = "salinity"
var%id   = 1
```

---

# Subprograms type

`MODULE` are subprograms that allow modular coding and data encapsulation

The interface of a subprogram type is **explicit** or **implicit**

Several types of subprograms:

- `intrinsic`: explicit - defined by Fortran itself (trignonometric functions, etc)
- `module`: explicit - defined with `MODULE` statement and used with `USE`
- `internal`: explicit - defined with `CONTAINS` statement inside (sub)programs
- `external`: implicit (but can be manually (re)defined explicit) - e.g. **libraries**

Differ with the **scope**: what data and other subprograms a subprogram can access

---

# `MODULE` type

```fortran
MODULE example
  IMPLICIT NONE
  INTEGER, PARAMETER :: index = 10
  REAL(8), SAVE      :: latitude
CONTAINS
  FUNCTION check(x) RESULT(z)
  INTEGER :: x, z
  ...
  END FUNCTION check
END MODULE example
```

```fortran
PROGRAM myprog
  USE example, ONLY: check, latitude
  IMPLICIT NONE
  ...
  test = check(a)
  ...
END PROGRAM myprog
```

<!-- _footer: "" -->

<!-- Notes for presenter. -->
<!-- 
```fortran
module subs

contains

subroutine asub (i, control)