%! % -*- Mode: Postscript -*- % pst-math.pro --- PostScript header file pst-math.pro % % Author : Christophe JORSSEN % ('libre' is the french word for 'free' if you want to contact me ;-)) % Created the : Sat 20 March 2004 % Last Mod : $Date: 2004/05/08 13:40:15 $ % Version : 1.1 $ % /PI 3.14159265359 def /ENeperian 2.71828182846 def /DegToRad {PI mul 180 div} bind def /RadToDeg {180 mul PI div} bind def /COS {RadToDeg cos} bind def /SIN {RadToDeg sin} bind def /TAN {dup SIN exch COS Div} bind def /tan {dup sin exch cos Div} bind def /ATAN {neg -1 atan 180 sub DegToRad} bind def /ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def /acos {dup dup mul neg 1 add sqrt exch atan} bind def /ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def /asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def /EXP {ENeperian exch exp} bind def /COSH {dup EXP exch neg EXP add 2 div} bind def /SINH {dup EXP exch neg EXP sub 2 div} bind def /TANH {dup SINH exch COSH div} bind def /ACOSH {dup dup mul 1 sub sqrt add ln} bind def /ASINH {dup dup mul 1 add sqrt add ln} bind def /ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def /SINC {dup SIN exch Div} bind def /GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def /GAMMA { 2 dict begin % hv 2007-08-30 /z exch def 1.000000000190015 % p(0) 0 1 5 { % on stack is 0 1 2 3 4 5 dup % n-1 n-1 [ 76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155 0.1208650973866179E-2 -0.5395239384953E-5 ] exch get exch % p(n) n-1 1 add z add div % p(n)/(z+n) add % build the sum } for Pi 2 mul sqrt z div mul z 5.5 add z 0.5 add exp mul Euler z 5.5 add neg exp mul end } bind def /GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015 0 1 5 { [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155 .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get 4 -1 roll 1 add dup 5 1 roll div add} for 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def /BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def /HORNER {aload length dup 2 add -1 roll exch 1 sub { dup 4 1 roll mul add exch } repeat pop } bind def /BESSEL_J0 {dup abs 8 lt { dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER Div} {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER 3 index COS mul exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER 4 -1 roll SIN mul 3 -1 roll mul neg add mul} ifelse} bind def /BESSEL_Y0 {dup 8 lt { dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER Div exch dup ln exch BESSEL_J0 .636619772 mul mul add} {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER 3 index SIN mul exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER 4 -1 roll COS mul 3 -1 roll mul add mul} ifelse} bind def /BESSEL_J1 {dup abs 8 lt { dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER Div} {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER 3 index COS mul exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul} ifelse} bind def /BESSEL_Y1 {dup 8 lt { dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add} {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER 3 index SIN mul exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER 4 -1 roll COS mul 3 -1 roll mul add mul} ifelse} bind def % En cours... /BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div { mul 3 -1 roll mul 2 index sub pstack} for } ifelse } ifelse } bind def % END pst-math.pro