PROGRAM series2
!
! Author:  Br. David Carlson
!
! Date:  December 31, 1999
!
! Revised:  May 2, 2004
!
! This program prints out partial sums for a series, stopping when no further
! change is found by adding on another term (or when a set number of terms
! have been added -- to prevent an infinite loop).  The particular series
! used is the well-known series for sin(x).

IMPLICIT NONE

REAL::x, xsquared, term, sum, sumold
INTEGER::n, count

WRITE (*, 20)
20 FORMAT (1X, 'Program to investigate a series')

WRITE (*, *) 'Enter an angle in radians: '
READ (*, *) x

sum = 0.0
count = 0
n = 1
term = x
xsquared = x * x

WRITE (*, 50)
50 FORMAT (' ', T5, 'count', T15, 'term', T35, 'partial sum')

DO 
   count = count + 1
   sumold = sum
   sum = sum + term
   WRITE (*, 100) count, term, sum
   IF ((sum == sumold) .OR. (count == 200)) THEN
      EXIT
   END IF
   term = -term * xsquared / ((n + 1) * (n + 2))
   n = n + 2
END DO

100 FORMAT (' ', T5, I3, T15, E16.8, T35, E16.8)

WRITE (*, 200) SIN(x)
200 FORMAT (1X, 'The built-in sine function gives: ', E16.8)

END PROGRAM