***   my corrections to

      SUBROUTINE UPDATC(IPASC,FLAGMU)

C-----------------------------------------------------------------------
C  UPDAT(ES PARTICLE PARAMETERS IN A) C(URVED ATMOSPHERE)
C
C  IN THE CASE THE HORIZONTAL COMPONENT OF THE TRACK IS TO LONG (> 20KM)
C  THE PARTICLE TRACK IS CHOPPED IN SEVERAL SHORTER TRACKS.
C  FOR EACH OF THESE CHOPPED TRACKS SUBR. UPDATE IS CALLED.
C  THIS SUBROUTINE IS CALLED FROM AAMAIN, BOX3, AND MUTRAC.
C  ARGUMENTS:
C   IPASC  = 0  TRANSPORT LEADS TO END OF RANGE OF PARTICLE
C            1  TRANSPORT LEADS TO OBSERVATION LEVEL
C   FLAGMU      FLAG INDICATING THE TRACKING OF MUONS
C
C  DESIGN  : F. SCHROEDER UNI WUPPERTAL
C-----------------------------------------------------------------------

***   added in the variables section:

      DOUBLE PRECISION PI2, SINTHE, COSPHI, SINPHI, SINTHENEW, MYSINPHI,
     *     MYCOSPHI, MYPHI, PRICOSPHI, PRISINPHI, PRICOSTH, PRISINTH

***   then in the body statement
*       COSTHENEW = COSTHE*COSDIF - SIGNE*SINDIF*SQRT(1.D0-COSTHE**2)
***   is replaced with

        SINTHE=SQRT(1.D0-COSTHE**2)
        COSPHI=COS(PHI)
        SINPHI=SIN(PHI)
        PRICOSPHI=COS(PRMPAR(4))
        PRISINPHI=SIN(PRMPAR(4))
        PRICOSTH=COS(PRMPAR(3))
        PRISINTH=SIN(PRMPAR(3))

        COSTHENEW = MAX(MIN(COSTHE*COSDIF - SIGNE*SINDIF*SINTHE*
     *       (COSPHI*PRICOSPHI+SINPHI*PRISINPHI), 1.D0), -1.D0)
        SINTHENEW = SQRT(1.D0-COSTHENEW**2)

        IF ( SINTHENEW.NE.0.D0 ) THEN

        MYSINPHI=(PRICOSPHI*PRICOSPHI*(COSDIF-1)+1)*SINTHE*COSPHI+
     *       (PRICOSPHI*PRISINPHI*(COSDIF-1))*SINTHE*SINPHI+
     *       (PRICOSPHI*SINDIF)*COSTHE

        MYCOSPHI=(PRISINPHI*PRICOSPHI*(COSDIF-1))*SINTHE*COSPHI+
     *       (PRISINPHI*PRISINPHI*(COSDIF-1)+1)*SINTHE*SINPHI+
     *       (PRISINPHI*SINDIF)*COSTHE

        MYSINPHI = MAX(MIN(MYSINPHI/SINTHENEW, 1.D0), -1.D0)
        MYCOSPHI = MAX(MIN(MYCOSPHI/SINTHENEW, 1.D0), -1.D0)

        MYPHI=ACOS(MYCOSPHI)
        PI2=ACOS(-1.0)*2.D0

        IF ( MYSINPHI.LT.0.D0 ) THEN
        MYPHI=PI2-MYPHI
        ENDIF

        IF ( MYPHI.GT.PI2 ) THEN
        MYPHI=MYPHI-PI2
        ENDIF

        ENDIF

***   similar changes can be done in NRANGC, PRANGC, THICKC, ELECTR, PHOTON