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#!/bin/sed -nf # dc.sed - an arbitrary precision RPN calculator # Created by Greg Ubben <gsu@romulus.ncsc.mil> early 1995, late 1996 # # Dedicated to MAC's memory of the IBM 1620 ("CADET") computer. # @(#)GSU dc.sed 1.1 06-Mar-1999 [non-explanatory] # # Examples: # sqrt(2) to 10 digits: echo "10k 2vp" | dc.sed # 20 factorial: echo "[d1-d1<!*]s! 20l!xp" | dc.sed # sin(ln(7)): echo "s(l(7))" | bc -c /usr/lib/lib.b | dc.sed # hex to base 60: echo "60o16i 6B407.CAFE p" | dc.sed # tests most of dc.sed: echo 16oAk2vp | dc.sed # # To debug or analyze, give the dc Y command as input or add it to # embedded dc routines, or add the sed p command to the beginning of # the main loop or at various points in the low-level sed routines. # If you need to allow [|~] characters in the input, filter this # script through "tr '|~' '\36\37'" first (or use dc.pl). # # Not implemented: ! \ # But implemented: K Y t # !< !> != fractional-bases # SunOS limits: 199/199 commands (though could pack in 10-20 more) # Limitations: scale <= 999; |obase| >= 1; input digits in [0..F] # Completed: 1am Feb 4, 1997 s/^/|P|K0|I10|O10|?~/ : next s/|?./|?/ s/|?#[ -}]*/|?/ /|?!*[lLsS;:<>=]\{0,1\}$/N /|?!*[-+*/%^<>=]/b binop /^|.*|?[dpPfQXZvxkiosStT;:]/b binop /|?[_0-9A-F.]/b number /|?\[/b string /|?l/b load /|?L/b Load /|?[sS]/b save /|?c/ s/[^|]*// /|?d/ s/[^~]*~/&&/ /|?f/ s//&[pSbz0<aLb]dSaxsaLa/ /|?x/ s/$[^~]*~$$.*|?x$~*/\2\1/ /|?[KIO]/ s/.*|$[KIO]$$[^|]*$.*|?\1/\2~&/ /|?T/ s/\.*0*~/~/ # a slow, non-stackable array implementation in dc, just for completeness # A fast, stackable, associative array implementation could be done in sed # (format: {key}value{key}value...), but would be longer, like load & save. /|?;/ s/|?;$[^{}]$/|?~[s}s{L{s}q]S}[S}l\1L}1-d0>}s\1L\1l{xS\1]dS{xL}/ /|?:/ s/|?:$[^{}]$/|?~[s}L{s}L{s}L}s\1q]S}S}S{[L}1-d0>}S}l\1s\1L\1l{xS\1]dS{x/ /|?[ ~ cdfxKIOT]/b next /|?\n/b next /|?[pP]/b print /|?k/ s/^$[0-9]\{1,3\}$$[.~].*|K$[^|]*/\2\1/ /|?i/ s/^$-\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}$$~.*|I$[^|]*/\2\1/ /|?o/ s/^$-\{0,1\}[1-9][0-9]*\.\{0,1\}[0-9]*$$~.*|O$[^|]*/\2\1/ /|?[kio]/b pop /|?t/b trunc /|??/b input /|?Q/b break /|?q/b quit h /|?[XZz]/b count /|?v/b sqrt s/.*|?$[^Y]$.*/\1 is unimplemented/ s/\n/\\n/g l g b next : print /^-\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}~.*|?p/!b Print /|O10|/b Print # Print a number in a non-decimal output base. Uses registers a,b,c,d. # Handles fractional output bases (O<-1 or O>=1), unlike other dc's. # Converts the fraction correctly on negative output bases, unlike # UNIX dc. Also scales the fraction more accurately than UNIX dc. # s,|?p,&KSa0kd[[-]Psa0la-]Sad0>a[0P]sad0=a[A*2+]saOtd0>a1-ZSd[[[[ ]P]sclb1\ !=cSbLdlbtZ[[[-]P0lb-sb]sclb0>c1+]sclb0!<c[0P1+dld>c]scdld>cscSdLbP]q]Sb\ [t[1P1-d0<c]scd0<c]ScO_1>bO1!<cO[16]<bOX0<b[[q]sc[dSbdA>c[A]sbdA=c[B]sbd\ B=c[C]sbdC=c[D]sbdD=c[E]sbdE=c[F]sb]xscLbP]~Sd[dtdZOZ+k1O/Tdsb[.5]*[.1]O\ X^*dZkdXK-1+ktsc0kdSb-[Lbdlb*lc+tdSbO*-lb0!=aldx]dsaxLbsb]sad1!>a[[.]POX\ +sb1[SbO*dtdldx-LbO*dZlb!<a]dsax]sadXd0<asbsasaLasbLbscLcsdLdsdLdLak[]pP, b next : Print /|?p/s/[^~]*/&\ ~&/ s/$.*|P$$[^|]*$/\ \2\1/ s/$[^~]*$\n$[^~]*$$.*|P$/\1\3\2/ h s/~.*// /./{ s/.//; p; } # Just s/.//p would work if we knew we were running under the -n option. # Using l vs p would kind of do \ continuations, but would break strings. g : pop s/[^~]*~// b next : load s/$.*|?.$$.$/\20~\1/ s/^$.$0$.*|r\1\([^~|]*$~\)/\1\3\2/ s/.// b next : Load s/$.*|?.$$.$/\2\1/ s/^$.$$.*|r\1$$[^~|]*~$/|\3\2/ /^|/!i\ register empty s/.// b next : save s/$.*|?.$$.$/\2\1/ /^$.$.*|r\1/ !s/$.$.*|/&r\1|/ /|?S/ s/$.$.*|r\1/&~/ s/$.$$[^~]*~$$.*|r\1$[^~|]*~\{0,1\}/\3\2/ b next : quit t quit s/|?[^~]*~[^~]*~/|?q/ t next # Really should be using the -n option to avoid printing a final newline. s/.*|P$[^|]*$.*/\1/ q : break s/[0-9]*/&;987654321009;/ : break1 s/^$[^;]*$$[1-9]$$0*$$[^1]*\2\(.$[^;]*\3$9*$.*|?.\)[^~]*~/\1\5\6\4/ t break1 b pop : input N s/|??$.*$$\n.*$/|?\2~\1/ b next : count /|?Z/ s/~.*// /^-\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}$/ s/[-.0]*$[^.]*$\.*/\1/ /|?X/ s/-*[0-9A-F]*\.*$[0-9A-F]*$.*/\1/ s/|.*// /~/ s/[^~]//g s/./a/g : count1 s/a\{10\}/b/g s/b*a*/&a9876543210;/ s/a.\{9\}$.$.*;/\1/ y/b/a/ /a/b count1 G /|?z/ s/\n/&~/ s/\n[^~]*// b next : trunc # for efficiency, doesn't pad with 0s, so 10k 2 5/ returns just .40 # The X* here and in a couple other places works around a SunOS 4.x sed bug. s/$[^.~]*\.*$$.*|K\([^|]*$\)/\3;9876543210009909:\1,\2/ : trunc1 s/^$[^;]*$$[1-9]$$0*$$[^1]*\2\(.$[^:]*X*\3$9*$[^,]*\),$[0-9]$/\1\5\6\4\7,/ t trunc1 s/[^:]*:$[^,]*$[^~]*/\1/ b normal : number s/$.*|?$$_\{0,1\}[0-9A-F]*\.\{0,1\}[0-9A-F]*$/\2~\1~/ s/^_/-/ /^[^A-F~]*~.*|I10|/b normal /^[-0.]*~/b normal s:$[^.~]*$\.*$[^~]*$:[Ilb^lbk/,\1\2~0A1B2C3D4E5F1=11223344556677889900;.\2: : digit s/^$[^,]*$,$-*$$[0-F]$$[^;]*\(.$\3[^1;]*$1*$\)/I*+\1\2\6\5~,\2\4/ t digit s:...$[^/]*.$$[^,]*$[^.]*$.*|?.$:\2\3KSb[99]k\1]SaSaXSbLalb0<aLakLbktLbk: b next : string /|?[^]]*$/N s/$|?[^]]*$\[$[^]]*$]/\1|{\2|}/ /|?\[/b string s/$.*|?$|{$.*$|}/\2~\1[/ s/|{/[/g s/|}/]/g b next : binop /^[^~|]*~[^|]/ !i\ stack empty //!b next /^-\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}~/ !s/[^~]*$.*|?!*[^!=<>]$/0\1/ /^[^~]*~-\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}~/ !s/~[^~]*$.*|?!*[^!=<>]$/~0\1/ h /|?\*/b mul /|?\//b div /|?%/b rem /|?^/b exp /|?[+-]/ s/^$-*$$[^~]*~$$-*$$[^~]*~$.*|?$-\{0,1\}$.*/\2\4s\3o\1\3\5/ s/$[^.~]*$$[^~]*~[^.~]*$$.*$/<\1,\2,\3|=-~.0,123456789<></ /^<$[^,]*,[^~]*$\.*0*~\1\.*0*~/ s/</=/ : cmp1 s/^$<[^,]*$$[0-9]$,$[^,]*$$[0-9]$,/\1,\2\3,\4/ t cmp1 /^<$[^~]*$$[^~]$[^~]*~\1$.$.*|=.*\3.*\2/ s/</>/ /|?/{ s/^$[<>]$$-[^~]*~-.*\1$$.$/\3\2/ s/^$.$$.*|?!*$\1/\2!\1/ s/|?![^!]$.$/&l\1x/ s/[^~]*~[^~]*~$.*|?$!*.$.*$|=.*/\1\2/ b next } s/$-*$\1|=.*/;9876543210;9876543210/ /o-/ s/;9876543210/;0123456789/ s/^>$[^~]*~$$[^~]*~$s$-*$$-*o\3\(-*$\)/>\2\1s\5\4/ s/,$[0-9]*$\.*$[^,]*$,$[0-9]*$\.*$[0-9]*$/\1,\2\3.,\4;0/ : right1 s/,$[0-9]$$[^,]*$,;*$[0-9]$$[0-9]*$;*0*/\1,\2\3,\4;0/ t right1 s/.$[^,]*$,~$.*$;0~s$-*$o-*/\1~\30\2~/ : addsub1 s/$.\{0,1\}$$~[^,]*$$[0-9]$$\.*$,$[^;]*$$;\([^;]*\(\3[^;]*$\).*X*\1$.*$\)/\2,\4\5\9\8\7\6/ s/,$[^~]*~$.\{10\}$.$[^;]\{0,9\}$[^;]\{0,1\}$[^;]*/,\2\1\3/ # could be done in one s/// if we could have >9 back-refs... /^~.*~;/!b addsub1 : endbin s/.$[^,]*$,$[0-9.]*$.*/\1\2/ G s/\n[^~]*~[^~]*// : normal s/^$-*$0*$[0-9.]*[0-9]$[^~]*/\1\2/ s/^[^1-9~]*~/0~/ b next : mul s/$-*$$[0-9]*$\.*$[0-9]*$~$-*$$[0-9]*$\.*$[0-9]*$.*|K$[^|]*$.*/\1\4\2\5.!\3\6,|\2<\3~\5>\6:\7;9876543210009909/ : mul1 s/![0-9]$[^<]*$<$[0-9]\{0,1\}$$[^>]*$>$[0-9]\{0,1\}$/0!\1\2<\3\4>/ /![0-9]/ s/$:[^;]*$$[1-9]$$0*$$[^0]*\2\(.$.*X*\3$9*$\)/\1\5\6\4/ /<~[^>]*>:0*;/!t mul1 s/$-*$\1$[^>]*$.*/;\2^>:9876543210aaaaaaaaa/ : mul2 s/$[0-9]~*$^/^\1/ s/<$[0-9]*$$.*[~^]$$[0-9]*$>/\1<\2>\3/ : mul3 s/>$[0-9]$$.*\1.\{9\}\(a*$\)/\1>\2;9\38\37\36\35\34\33\32\31\30/ s/$;[^<]*$$[0-9]$<$[^;]*$.*\2[0-9]*$.*$/\4\1<\2\3/ s/a[0-9]/a/g s/a\{10\}/b/g s/b\{10\}/c/g /|0*[1-9][^>]*>0*[1-9]/b mul3 s/;/a9876543210;/ s/a.\{9\}$.$[^;]*$[^,]*$[0-9]$[.!]*$,/\2,\1\3/ y/cb/ba/ /|<^/!b mul2 b endbin : div # CDDET /^[-.0]*[1-9]/ !i\ divide by 0 //!b pop s/$-*$$[0-9]*$\.*$[^~]*~-*$$[0-9]*$\.*$[^~]*$/\2.\3\1;0\4.\5;0/ : div1 s/^\.0$[^.]*$\.;*$[0-9]$$[0-9]*$;*0*/.\1\2.\3;0/ s/^$[^.]*$$[0-9]$\.$[^;]*;$0*$[0-9]*$$[0-9]$\./\1.\2\30\4.\5/ t div1 s/~$-*$\1$-*$;0*$[^;]*[0-9]$[^~]*/~123456789743222111~\2\3/ s/$.\(.$[^~]*\)[^9]*\2.\{8\}$.$[^~]*/\3~\1/ s,|?.,&SaSadSaKdlaZ+LaX-1+[sb1]Sbd1>bkLatsbLa[dSa2lbla*-*dLa!=a]dSaxsakLasbLb*t, b next : rem s,|?%,&Sadla/LaKSa[999]k*Lak-, b next : exp # This decimal method is just a little faster than the binary method done # totally in dc: 1LaKLb [kdSb*LbK]Sb [[.5]*d0ktdSa<bkd*KLad1<a]Sa d1<a kk* /^[^~]*\./i\ fraction in exponent ignored s,[^-0-9].*,;9d**dd*8*d*d7dd**d*6d**d5d*d*4*d3d*2lbd**1lb*0, : exp1 s/$[0-9]$;$.*\1\([d*]*$[^l]*$[^*]*$$\**$\)/;dd*d**d*\4\3\5\2/ t exp1 G s,-*.\{9\}$[^9]*$[^0]*0.$.*|?.$,\2~saSaKdsaLb0kLbkK*+k1\1LaktsbkLax, s,|?.,&SadSbdXSaZla-SbKLaLadSb[0Lb-d1lb-*d+K+0kkSb[1Lb/]q]Sa0>a[dk]sadK<a[Lb], b next : sqrt # first square root using sed: 8k2v at 1:30am Dec 17, 1996 /^-/i\ square root of negative number /^[-0]/b next s/~.*// /^\./ s/0$[0-9]$/\1/g /^\./ !s/[0-9][0-9]/7/g G s/\n/~/ s,|?.,&K1+k KSbSb[dk]SadXdK<asadlb/lb+[.5]*[sbdlb/lb+[.5]*dlb>a]dsaxsasaLbsaLatLbk K1-kt, b next # END OF GSU dc.sed