↜ Back to index Introduction to Numerical Analysis 1

We start with a review of what you learned in your first year classes 情報・計算科学基礎 and 計算科学.

Fortran knowledge (Fortran知識)

You need a working Fortran compiler: gfortran

From the class Computational science (計算科学) you should already know most of the Fortran language that we will be using:

• basic arithmetic: 1 + 2, x = sqrt(2.0), x**2, …

• comments (コメント): Anything on a line after ! is ignored.

  implicit none
  ! this is a comment
  real x      ! comment on a line with code
  end

• program end: end

• variable declaration (変数宣言)

  integer i            ! integer variable
  real x               ! single precision real variable 単精度実数変数

• printing to standard output (標準出力)

  write(*,*) 'hello'
  print *, 'hello'        ! I prefer this

• reading from standard input (キーボード入力)

  read *, x, i            ! user can input values for x, i
                          ! separated by space, comma (,) or Enter

• if condition (条件分岐)

  if (1 < 2) then         ! can also be (1 .lt. 2)
      print *, 'true'
  else 
      print *, 'false'
  end if

• do loops (ループ)

  do i=1,5
      print *, 'square of ', i, ' is ', i**2
  end do

• built-in functions: abs, cos, sin, mod, …

I prefer using the free-form Fortran style that does not require 6 spaces at the beginning of each line. The file extension (拡張子) must be .f90.

For details see Fortran cheatsheet.

Why do we need to compile Fortran code?

Let us consider the program that computes a factorial (階乗) of an input number.

! Program that computes a factorial
implicit none
integer i, n, f

print *, "Enter n"
read *, n

f = 1

do i = 1,n
    f = f * i
end do

print *, "Factorial of ", n, " = ", f

end

We can only run a Fortran program after we compile it. In the terminal (Cygwin for example):

$ gfortran fact.f90
$ ./a.exe 
 Enter n
5
 Factorial of            5  =          120

(Advanced) What is in the file a.exe?

Let us try to print it out:

$ cat a.exe

You will see a lot of strange characters in the output. The file a.exe is a binary file that does not contain text but contains a sequence of numbers that represent the instructions for your computer, specifically the CPU (central processing unit). This is a chip that reads a sequence of simple instructions from the computer memory and performs them one at a time. Some of these instructions read data from memory, some do arithmetic operations on the data and some print stuff to the screen.

We can print out the instructions in a.exe in a readable form using objdump program:

$ objdump -d a.exe


a.exe:     file format elf64-x86-64


Disassembly of section .init:

0000000000001000 <_init>:
    1000:   f3 0f 1e fa             endbr64 
    1004:   48 83 ec 08             sub    $0x8,%rsp
    1008:   48 8b 05 c9 2f 00 00    mov    0x2fc9(%rip),%rax        # 3fd8 <__gmon_start__>
    100f:   48 85 c0                test   %rax,%rax
    1012:   74 02                   je     1016 <_init+0x16>
    1014:   ff d0                   callq  *%rax
    1016:   48 83 c4 08             add    $0x8,%rsp
    101a:   c3                      retq   

...

You can see the instructions for subtraction (sub), addition (add), jumps to other instructions (je: jump if equal) etc. This is what your computer sees when you run the compiled Fortran program.

Exercises (練習問題)

Here are a few exercises for today to review your Fortran knowledge.

print *, "Hello"
end

$ gfortran hello.f90
$ ./a.exe
Hello

$ gfortran hello.f90 -o hello.exe
$ ./hello.exe
Hello

print *, 'The value of cos(2pi) is', cos(2 * pi)
end

x1 = 1.00000
x2 = 2.00000

Test questions

1. How do you compile Fortran program equation.f90?

2. How do you run compiled Fortran program?

3. What is the difference between Fortran programs in a file with extension .f and extension .f90?

4. What does implicit none do?