C     This program prompts the user for a real number, N, and then
C     calculates the square root of that number approximately by finding
C     the root of the equation x**2 - N.  The root is found using the
C     bisection technique.
C     
C     To ensure the root is bracketed, the initialize the interval lower
C     and upper bounds to be unity and N, respectively, if the number is
C     greater than one and values of N and unity, respectively, if the
C     number is less than one.  Bisectioning terminates and the root is
C     considered found when, for an interval mid-point c, |f(c,N)| <=
C     |c/10^5|.  The program reports the number of iterations where were
C     required to find the root.
C
C     The user terminates input with control-D at which point the
C     program reports the number of values that were entered.
C
C     John Schneider
C     CptS 203, HW 6
C--------------------------------------------------------------------------
      program sqroot
      real a, b, mid, num
      integer count, count1

C.....
C     a   = lower limit of interval
C     b   = upper limit of interval
C     mid = mid point of interval
C     num = number for which the square root is to be calculated
C
C     count  = count of the number of iterations needed to find root
C     count1 = count of the number of values entered
C.....

      count1 = 0

 10   continue
         print *, 'Enter a positive number.'
         read (5,*,end=30) num

         count1 = count1 + 1

C........
C        Initialize upper and lowever limits of interval that bracket
C        root.
C........
         if (num .gt. 1.0) then
            a = 1.0
            b = num
         else
            a = num
            b = 1.0
         endif

         mid = (a+b)/2.0
         count = 0
         
C........While stopping condition is not met, continue bisectioning.
 20      if (abs(f(mid,num)) .gt. abs(mid*1.e-5)) then
            if (f(a,num)*f(mid,num) .lt. 0.0) then
               b=mid
            else
               a=mid
            endif
            mid = (a+b)/2.0
            count = count + 1
         goto 20
         endif

         print *, 'Square root of number is ',mid,'.'
         print *, 'It took ',count,' iterations to get there.' 
         print *

      goto 10
 30   continue

      print *, 'You entered a total of ',count1,' numbers.  Bye!'

      stop
      end

C.....
C     Function for which we are finding the root.
C.....
      real function f(x,num)
      real x, num
      f = x*x - num
C      print *, 'f = ',f
      return
      end