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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