Page 1                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



     NNNNAAAAMMMMEEEE
          ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp,,,, dddd____ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp,,,,
          ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp0000____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp,,,, dddd____ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp0000____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp ----
          GGGGiiiivvvveeeennnn aaaannnn aaaarrrrrrrraaaayyyy ooooffff zzzzoooonnnneeee----aaaavvvveeeerrrraaaaggggeeeedddd ddddiiiiffffffffeeeerrrreeeennnncccceeeessss,,,, DDDDVVVVAAAARRRRLLLL,,,, tttthhhheeeesssseeee
          rrrroooouuuuttttiiiinnnneeeessss iiiinnnntttteeeerrrrppppoooollllaaaatttteeee tttthhhhiiiirrrrdddd----oooorrrrddddeeeerrrr aaaaccccccccuuuurrrraaaatttteeee zzzzoooonnnneeee iiiinnnntttteeeerrrrffffaaaacccceeee
          vvvvaaaalllluuuueeeessss,,,, wwwwiiiitttthhhhoooouuuutttt mmmmoooonnnnoooottttoooonnnniiiicccciiiittttyyyy ccccoooonnnnssssttttrrrraaaaiiiinnnnttttssss oooorrrr ddddiiiissssccccoooonnnnttttiiiinnnnuuuuiiiittttyyyy
          ddddeeeetttteeeeccccttttiiiioooonnnn....



     FFFFOOOORRRRTTTTRRRRAAAANNNN SSSSPPPPEEEECCCCIIIIFFFFIIIICCCCAAAATTTTIIIIOOOONNNN
          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp0000____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp(((( SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF,,,,
          CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF,,,, SSSSMMMMAAAALLLLDDDDVVVV,,,, DDDDVVVVAAAARRRRLLLL,,,, VVVVAAAARRRRLLLL,,,, VVVVAAAARRRRRRRR,,,, UUUUNNNNSSSSMMMMTTTTHHHH,,,, DDDDIIIISSSSCCCCOOOONNNNTTTT,,,,
          NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR ))))
          rrrreeeeaaaallll****4444 SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444  DDDDVVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444   VVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444   VVVVAAAARRRRRRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444 SSSSMMMMAAAALLLLDDDDVVVV((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444  UUUUNNNNSSSSMMMMTTTTHHHH((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 DDDDIIIISSSSCCCCOOOONNNNTTTT((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          iiiinnnntttteeeeggggeeeerrrr****4444 NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR



























          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp(((( DDDDAAAALLLLFFFFAAAACCCC,,,, DDDDAAAARRRRFFFFAAAACCCC,,,,
          FFFFAAAACCCCDDDDAAAA,,,, FFFFCCCCDDDDAAAAZZZZLLLL,,,, FFFFAAAACCCCDDDDAAAALLLL,,,,  FFFFAAAA6666DDDDAAAALLLL,,,, FFFFAAAA6666DDDDAAAARRRR,,,, FFFFLLLLLLLLDDDDAAAALLLL,,,, FFFFLLLLLLLLDDDDAAAARRRR,,,,



     Page 1                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          FFFFRRRRRRRRDDDDAAAALLLL,,,, FFFFRRRRRRRRDDDDAAAARRRR,,,, SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF,,,, CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF,,,, SSSSMMMMAAAALLLLDDDDVVVV,,,, DDDDVVVVAAAARRRRLLLL,,,,
          VVVVAAAARRRRLLLL,,,, VVVVAAAARRRRRRRR,,,, UUUUNNNNSSSSMMMMTTTTHHHH,,,, DDDDIIIISSSSCCCCOOOONNNNTTTT,,,, NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY ))))
          rrrreeeeaaaallll****4444 DDDDAAAALLLLFFFFAAAACCCC((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 DDDDAAAARRRRFFFFAAAACCCC((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444  FFFFAAAACCCCDDDDAAAA((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFCCCCDDDDAAAAZZZZLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFAAAACCCCDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFAAAA6666DDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFAAAA6666DDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFLLLLLLLLDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFLLLLLLLLDDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFRRRRRRRRDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 FFFFRRRRRRRRDDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 SSSSMMMMAAAALLLLDDDDVVVV((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444  FFFFCCCCDDDDAAAAZZZZLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444  FFFFAAAACCCCDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444   DDDDVVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444    VVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444    VVVVAAAARRRRRRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****4444  UUUUNNNNSSSSMMMMTTTTHHHH((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****4444 DDDDIIIISSSSCCCCOOOONNNNTTTT((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          iiiinnnntttteeeeggggeeeerrrr****4444 NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR



























          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee dddd____ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp0000____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp(((( SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF,,,,



     Page 2                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF,,,, SSSSMMMMAAAALLLLDDDDVVVV,,,, DDDDVVVVAAAARRRRLLLL,,,, VVVVAAAARRRRLLLL,,,, VVVVAAAARRRRRRRR,,,, UUUUNNNNSSSSMMMMTTTTHHHH,,,, DDDDIIIISSSSCCCCOOOONNNNTTTT,,,,
          NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR ))))
          rrrreeeeaaaallll****8888 SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888  DDDDVVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888   VVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888   VVVVAAAARRRRRRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888 SSSSMMMMAAAALLLLDDDDVVVV((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888  UUUUNNNNSSSSMMMMTTTTHHHH((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 DDDDIIIISSSSCCCCOOOONNNNTTTT((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          iiiinnnntttteeeeggggeeeerrrr****4444 NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR



























          ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee dddd____ppppppppmmmm99998888____ddddiiiifffftttteeeerrrrpppp____ddddiiiissssccccoooonnnntttt____ccccoooommmmpppp(((( DDDDAAAALLLLFFFFAAAACCCC,,,, DDDDAAAARRRRFFFFAAAACCCC,,,,
          FFFFAAAACCCCDDDDAAAA,,,, FFFFCCCCDDDDAAAAZZZZLLLL,,,, FFFFAAAACCCCDDDDAAAALLLL,,,,  FFFFAAAA6666DDDDAAAALLLL,,,, FFFFAAAA6666DDDDAAAARRRR,,,, FFFFLLLLLLLLDDDDAAAALLLL,,,, FFFFLLLLLLLLDDDDAAAARRRR,,,,
          FFFFRRRRRRRRDDDDAAAALLLL,,,, FFFFRRRRRRRRDDDDAAAARRRR,,,, SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF,,,, CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF,,,, SSSSMMMMAAAALLLLDDDDVVVV,,,, DDDDVVVVAAAARRRRLLLL,,,,
          VVVVAAAARRRRLLLL,,,, VVVVAAAARRRRRRRR,,,, UUUUNNNNSSSSMMMMTTTTHHHH,,,, DDDDIIIISSSSCCCCOOOONNNNTTTT,,,, NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY ))))
          rrrreeeeaaaallll****8888 DDDDAAAALLLLFFFFAAAACCCC((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 DDDDAAAARRRRFFFFAAAACCCC((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888  FFFFAAAACCCCDDDDAAAA((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFCCCCDDDDAAAAZZZZLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFAAAACCCCDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFAAAA6666DDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFAAAA6666DDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFLLLLLLLLDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFLLLLLLLLDDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 FFFFRRRRRRRRDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))



     Page 3                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          rrrreeeeaaaallll****8888 FFFFRRRRRRRRDDDDAAAARRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 SSSSMMMMAAAALLLLDDDDVVVV((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888  FFFFCCCCDDDDAAAAZZZZLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888  FFFFAAAACCCCDDDDAAAALLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888   DDDDVVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888    VVVVAAAARRRRLLLL((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888    VVVVAAAARRRRRRRR((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR++++1111))))
          rrrreeeeaaaallll****8888  UUUUNNNNSSSSMMMMTTTTHHHH((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          rrrreeeeaaaallll****8888 DDDDIIIISSSSCCCCOOOONNNNTTTT((((1111----NNNNBBBBDDDDYYYY____LLLL::::NNNNZZZZOOOONNNNEEEESSSS++++NNNNBBBBDDDDYYYY____RRRR))))
          iiiinnnntttteeeeggggeeeerrrr****4444 NNNNZZZZOOOONNNNEEEESSSS,,,, NNNNBBBBDDDDYYYY____LLLL,,,, NNNNBBBBDDDDYYYY____RRRR






























          All of the above routines are functionally similar.  They
          differ only in the type declarations of their arguments and
          whether or not a uniform grid is assumed.  The routines
          ppm98_difterp0_discont_comp and
          d_ppm98_difterp0_discont_comp assume a uniform grid.








     Page 4                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



     AAAARRRRGGGGUUUUMMMMEEEENNNNTTTTSSSS
          DDDDVVVVAAAARRRRLLLL [input]
                    array of differences of zone-averaged values,
                    centered at the left zone interface. For example,
                    if VARAV is an array of zone averages, then
                    DAL(i) = VARAV(i) - VARAV(i-1)
                    Required on the range [1-NBDY_L,NZONES+NBDY_R]


          VVVVAAAARRRRLLLL [output]
                    array of interpolated left interface point values
                    of the variable difference. Values on the range
                    [3-NBDY_L, NZONES+NBDY_R-3] are computed



          VVVVAAAARRRRRRRR [output]
                    array of interpolated right interface point values
                    of the variable difference. Values on the range
                    [3-NBDY_L, NZONES+NBDY_R-3] are computed


          DDDDAAAALLLLFFFFAAAACCCC [input]
                    An array of precomputed grid constants for non-
                    uniform grids. Values on the range [1-
                    NBDY_L,NZONES+NBDY_R] are required, set by a call
                    to [d_]ppm98_interface_factors or
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          DDDDAAAARRRRFFFFAAAACCCC [input]
                    An array of precomputed grid constants for non-
                    uniform grids. Values on the range [1-
                    NBDY_L,NZONES+NBDY_R] are required, set by a call
                    to [d_]ppm98_interface_factors or
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFAAAACCCCDDDDAAAA [input]
                    An array of precomputed grid constants for non-
                    uniform grids. Values on the range [1-
                    NBDY_L,NZONES+NBDY_R] are required, set by a call
                    to [d_]ppm98_interface_factors or
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Required on the range [1-



     Page 5                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



                    NBDY_L,NZONES+NBDY_R]


          FFFFCCCCDDDDAAAAZZZZLLLL [input]
                    An array of precomputed grid constants for non-
                    uniform grids. Values on the range [1-
                    NBDY_L,NZONES+NBDY_R] are required, set by a call
                    to [d_]ppm98_interface_factors or
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFAAAACCCCDDDDAAAALLLL [input]
                    An array of precomputed grid constants for non-
                    uniform grids. Values on the range [1-
                    NBDY_L,NZONES+NBDY_R] are required, set by a call
                    to [d_]ppm98_interface_factors or
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFAAAA6666DDDDAAAALLLL [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFAAAA6666DDDDAAAARRRR [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFLLLLLLLLDDDDAAAALLLL [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]





     Page 6                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          FFFFLLLLLLLLDDDDAAAARRRR [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFRRRRRRRRDDDDAAAALLLL [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]


          FFFFRRRRRRRRDDDDAAAARRRR [input]
                    An array of precomputed grid constants for non-
                    uniform grids, set by a call to
                    [d_]ppm98_interpolation_factors. Routines without
                    this in their calling sequence assume a uniform
                    grid Values are required on the range [1-
                    NBDY_L,NZONES+NBDY_R]



          SSSSMMMMAAAALLLLLLLL____DDDDIIIIFFFF [input]
                    An array of zone centered differences,supplied by
                    the user, of an unspecified quantity.  This
                    differences should be small across
                    disconltinuities of the type the user whishes to
                    steepen.


          CCCCOOOOMMMMPPPPAAAARRRRIIIISSSSOOOONNNN____DDDDIIIIFFFF [input]
                    An array of zone centered differences,supplied by
                    the user, of an unspecified quantity.  This
                    differences should be large (relative to
                    SMALL_DIF) across disconltinuities of the type the
                    user whishes to steepen.



          SSSSMMMMAAAALLLLDDDDVVVV [input]
                    An array of trivial values of differences of DVARL
                    Values are required on the range [2-
                    NBDY_L,NZONES+NBDY_R]


          UUUUNNNNSSSSMMMMTTTTHHHH [output]



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     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



                    An array of indicator values which ranges from  0
                    for a smooth function to  1  for a zone near a
                    sudden jump which is unresolved on the grid.
                    Values are calculated on the range [2-
                    NBDY_L,NZONES+NBDY_R-2]


          DDDDIIIISSSSCCCCOOOONNNNTTTT [output]
                    array indicating the likelihood of a fiven zone
                    being in a discontinuity.  Ranges from 0 for a
                    continuous function to 1 for discontinuities.
                    Values are calculated on the range [2-
                    NBDY_L,NZONES+NBDY_R-2]



          NNNNZZZZOOOONNNNEEEESSSS [input]
                    the number of (non boundary) zones


          NNNNBBBBDDDDYYYY____LLLL [input]
                    the number of zones set on the left end of the
                    arrays which have been set to accomodate boundary
                    conditions.  This must be at least 2.


          NNNNBBBBDDDDYYYY____RRRR [input]
                    the number of zones set on the right end of the
                    arrays which have been set to accomodate boundary
                    conditions.  This must be at least 3.




     DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
          These routines interpolate third-order accurate point
          values, VARL and VARR at the left- and right-hand zone
          interfaces from an array of zone average differences, DVARL.
          Both  VARL  and  VARR  refer to an assumed vanishing value
          of  VARAV, the zone average. For example, these routines are
          used to interpolate Riemann invariants which are defined
          only by inexact differentials, for which therefore  VARAV
          cannot be provided.  Only the difference  DVARL  is
          available.  When the zone averaged values of a quantity,
          VARAV, are nown, then DVARL  would be defined by:
          DVARL(i) = VARAV(i) - VARAV(i-1)

          A measure of the lack of smoothness of the function  a  is
          also constructed, Where the data are judged unsmooth, a
          further calculation is performed to determine whether or not
          the data are discontinuous.  Where judge discontinuous, and
          interpolation better suited for discontinuities is used



     Page 8                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          rather than one better suited to continuous data (which is
          usually used.)

          In all where the data are judged unsmooth, monotonicity
          constraints are applied.  These constraints are applied by
          resetting the values of VARL or VARR (or both) to obtain a
          monotone interpolation.  Because of this, the interpolation
          may be discontinuous at zone interfaces.The values UNSMTH
          provide an indication of the wellresolved the input data are
          on the grid.  By definition, if the data in the two zones
          surrounding zone I are well represented by the parabolic
          interpolation determined for zone I, the data are smooth and
          well resolved, and UNSMTH=0.0.  As the quality of the fit of
          the parabola decrease, UNSMTH increase to a maximum values
          of 1.  Determined on a zone-byzone basis.

          The unconstrained differences, DVARL, are used to estimate
          the first and third derivatives of the variable centered on
          a zone.  These are then compared, and if the ratio of the
          third to the first derivative is large enough (and
          positive), and if the signs of the second derivatives in
          neighboring zones are opposite, and if the jump in the
          variable between these two neighbor zones is not negligible,
          then a flag is set instructing the code to replace its
          estimates for the left and right interface values by those
          obtained by using monotonized linear interpolation functions
          in the neighbor zones.  This flag is returned as the array
          DISCONT.  Its value ranges from 0 for no detection of
          discontinuity to 1 for zones judged to be with a
          discontinuity.

          A further test is applied before steepening a discontinuity.
          The arrays  SMALL_DIF  and  COMPARISON_DIF  are zone-
          centered differences of user selected variables.  These
          differences are used to determine whether or not a
          particular steep jump in the variable  a  (and passing the
          above test for a discontinuity) )  should be steepened.  The
          interpolation will be steepened if  SMALL_DIF  is small
          compared to  COMPARISON_DIF.  More concretely, the ratio
          (SMALL_DIF / COMPARISON_DIF)  of these differences (assuming
          that they have the same sign, or if they do not, no
          steepening will occur) is computed for candidate zones, and
          steepening is performed if this ratio exceeds the PPMLIB
          internal constant   ppm98_smlrat.  The flag is returned as
          the array DISCONT.


          In order to interpolate a point value at the left edge of
          zone I, data are required for two zones to the left of zone
          I and two zones to the right.  It follows that the first two
          elements and two elements of the output arrays VARL, VARR,
          UNSMTH, and DISCONT cannot be set.  It will be assumed that



     Page 9                                          (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



          all NZONES  of the array DVARL passed to the routine are
          valid and may be used.








     HHHHIIIINNNNTTTTSSSS
          +o    The required problem boundary conditions may be
               enforced by setting appropriate values of the first two
               elements and last three elements of DVARL.


          +o    If needed, the precomputed grid factors can be set by a
               call to [d_ppm98_interpolation_factors.  These grid
               factors need be computed only once.


          +o    For smooth, well resolved data,  use
               [d_]ppm98_difterp0_interface.


          +o    For discontinuity detetion without the additional
               comparison test, use [d_]ppm98_difterp0_discontinuity.


          +o    For interpolating without discontinuity detection, use
               [d_]ppm98_difterp0_mono, or [d_]ppm98_difterp0_mono.


          +o    On uniform grids use [d_]ppm98_difterp0_discont_comp.


          +o    On nonuniform grids use [d_]ppm98_difterp_discont_comp.


          +o    monotonicity constraints, which will clip extrema, are
               applied only where UNSMTH is non zero.


          +o    The sensitivity of the "unsmooth" calculation is
               governed by the PPMLIB internal constants ppm98_crterr
               and ppm98_ferrfc.


          +o    The sensitivity of the discontinuity detection
               calculation is governed by the PPMLIB internal
               constants ppm98_stpner, ppm98_crtrat, and ppm98_smlrat,
               and indirectly by those governing the "unsmooth"



     Page 10                                         (printed 3/30/99)






     PPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVVPPPPPPPPMMMM99998888IIIINNNNTTTTEEEERRRRPPPP0000____DDDDIIIISSSSCCCCOOOONNNNTTTT____CCCCOOOOMMMMPPPP((((JJJJAAAANNNN  1111999999999999))))



               calculation.


          +o    The above internal constants may be examined and set by
               PPPPPPPPMMMM99998888____PPPPRRRRIIIINNNNTTTT____CCCCOOOONNNNSSSSTTTTAAAANNNNTTTTSSSS,,,, PPPPPPPPMMMM99998888____SSSSEEEETTTT____CCCCOOOONNNNSSSSTTTTAAAANNNNTTTTSSSS,,,, aaaannnndddd
               PPPPPPPPMMMM99998888____RRRREEEESSSSEEEETTTT____CCCCOOOONNNNSSSSTTTTAAAANNNNTTTTSSSS....



     BBBBUUUUGGGGSSSS
          +o

     SSSSEEEEEEEE AAAALLLLSSSSOOOO
          PPM98_INTERFACE_FACTORS, PPM98_INTERFACE_FACTORS,
          PPM98_INTERPOLATION_FACTORS, PPM98_INTERPOLATION_FACTORS,
          PPM98_INTERP_MONO, PPM98_INTERP_DISCONTINUITY,
          PPM98_INTERP_DISCONT_COMP, PPM98_MONO_PARABOLA
          PPM98_PRINT_CONSTANTS, PPM98_SET_CONSTANTS,
          PPM98_RESET_CONSTANTS




     AAAAUUUUTTTTHHHHOOOORRRRSSSS
          PPPPaaaauuuullll RRRR.... WWWWooooooooddddwwwwaaaarrrrdddd paul@lcse.umn.edu
          BBBB.... KKKKeeeevvvviiiinnnn EEEEddddggggaaaarrrr  bke@lcse.umn.edu
          Department of Astronomy
          University of Minnesota
          Minneapolis, MN 55455 USA


























     Page 11                                         (printed 3/30/99)