FORTRAN characteristics; compute π

Characteristics of FORTRAN

1. The name comes from FORmula TRANslation; it was the first widely used high-level language (IBM, 1957).
2. It is designed for scientific and engineering calculation, with strong numerical and mathematical support (real, double precision and complex types).
3. It is a compiled language, so programs run fast.
4. The syntax is simple and close to mathematical formulas (A = B*C + D).
5. It has good array handling and many built-in (intrinsic) functions.
6. It supports modular programming with functions and subroutines, and has formatted input/output.
7. FORTRAN 77 uses a fixed-form layout (columns 1–72); later versions (90 and above) have free form, modules and pointers.
8. It is standardised and portable, and has a large library of tested scientific code.

Program: π by the series π = 4 (1 − 1/3 + 1/5 − 1/7 + …) for 25 terms

The K-th term is (−1)^(K+1) / (2K − 1). (-1.0)**(K+1) gives the alternating sign.

      PROGRAM PIVAL
      REAL S, PI
      INTEGER K
      S = 0.0
      DO 10 K = 1, 25
         S = S + (-1.0)**(K+1) / (2.0*K - 1.0)
   10 CONTINUE
      PI = 4.0 * S
      WRITE(*,20) PI
   20 FORMAT(' PI = ', F10.6)
      STOP
      END

Result: with 25 terms the program gives about 3.181577 (calculated separately). The series converges slowly, so 25 terms give only one correct decimal place; the true value is 3.141593.