!**********************************************************************************************************************************
!  ISROUND
!
!  Statistical rounding function.
!
!  Given a positive real number X of the form I.F, where I is the integer part and F is the fractional part,
!  round the result to integer I with probablility 1-F, or to integer I+1 with probability F.
!
!  This version returns an INTEGER result.
!
!  The random number generator should be initialized by calling RANDOM_SEED in the main program.
!**********************************************************************************************************************************

      FUNCTION ISROUND (X) RESULT (IY)

      IMPLICIT NONE

      DOUBLE PRECISION, INTENT(IN) :: X
      INTEGER :: IY
      INTEGER :: I
      REAL :: XRAND
      DOUBLE PRECISION :: X1, F
      LOGICAL :: NEG


      NEG = X .LT. 0.0D0                                                            ! save sign of original X, in case X is negative
      X1 = ABS(X)                                                                   ! X1 = |X|

      I = INT(X1)                                                                   ! I = integer part of X1
      F = X1 - I                                                                    ! F = fractional part of X1

      CALL RANDOM_NUMBER (XRAND)                                                    ! random number between 0 and 1

      IF (XRAND .GT. F) THEN                                                        ! with probability 1-F..
         IY = I                                                                     ! round down
      ELSE                                                                          ! with probability F..
         IY = I+1                                                                   ! round up
      END IF

      IF (NEG) IY = -IY                                                             ! restore original sign

      RETURN

      END FUNCTION ISROUND