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+#
+# from: @(#)math.sed 8.1 (Berkeley) 6/6/93
+# $NetBSD: math.sed,v 1.3 1997/01/09 20:21:36 tls Exp $
+#
+# Addition and multiplication in sed.
+# ++ for a limited time only do (expr) too!!!
+#
+# Kevin S Braunsdorf, PUCC UNIX Group, ksb@cc.purdue.edu.
+#
+# Ex:
+# echo "4+7*3" | sed -f %f
+
+# make sure the expression is well formed
+s/[ ]//g
+/[+*\/-]$/{
+ a\
+ poorly formed expression, operator on the end
+ q
+}
+/^[+*\/]/{
+ a\
+ poorly formed expression, leading operator
+ q
+}
+
+# fill hold space with done token
+x
+s/^.*/done/
+x
+
+# main loop, process operators (*, + and () )
+: loop
+/^\+/{
+ s///
+ b loop
+}
+/^\(.*\)(\([^)]*\))\(.*\)$/{
+ H
+ s//\2/
+ x
+ s/^\(.*\)\n\(.*\)(\([^()]*\))\(.*\)$/()\2@\4@\1/
+ x
+ b loop
+}
+/^[0-9]*\*/b mul
+/^\([0-9]*\)\+\([0-9+*]*\*[0-9]*\)$/{
+ s//\2+\1/
+ b loop
+}
+/^[0-9]*\+/{
+ s/$/=/
+ b add
+}
+x
+/^done$/{
+ x
+ p
+ d
+}
+/^()/{
+ s///
+ x
+ G
+ s/\(.*\)\n\([^@]*\)@\([^@]*\)@\(.*\)/\2\1\3/
+ x
+ s/[^@]*@[^@]*@\(.*\)/\1/
+ x
+ b loop
+}
+i\
+help, stack problem
+p
+x
+p
+q
+
+# turn mul into add until 1*x -> x
+: mul
+/^0*1\*/{
+ s///
+ b loop
+}
+/^\([0-9]*\)0\*/{
+ s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
+ b mul
+}
+s/^\([0-9]*\)1\*/\10*/
+s/^\([0-9]*\)2\*/\11*/
+s/^\([0-9]*\)3\*/\12*/
+s/^\([0-9]*\)4\*/\13*/
+s/^\([0-9]*\)5\*/\14*/
+s/^\([0-9]*\)6\*/\15*/
+s/^\([0-9]*\)7\*/\16*/
+s/^\([0-9]*\)8\*/\17*/
+s/^\([0-9]*\)9\*/\18*/
+s/\*\([0-9*]*\)/*\1+\1/
+b mul
+
+# get rid of a plus term until 0+x -> x
+: add
+/^\+\([0-9+*]*\)=/{
+ s//\1/
+ b loop
+}
+/^\([0-9*]*\)\+=/{
+ s//\1/
+ b loop
+}
+/^\([0-9]*\)\+\([0-9*+]*\)\+=/{
+ s//\2+\1/
+ b loop
+}
+/^\([0-9]*\)0\+\([0-9]*\)\([0-9]\)=/{
+ s//\1+\2=\3/
+ b add
+}
+/^\([0-9]*\)\([0-9]\)\+\([0-9]*\)0=/{
+ s//\1+\3=\2/
+ b add
+}
+/^\([0-9]*\)0\+\([0-9*+]*\)\+\([0-9]*\)\([0-9]\)=/{
+ s//\1+\2+\3=\4/
+ b add
+}
+/^\([0-9]*\)\([0-9]\)\+\([0-9*+]*\)\+\([0-9]*\)0=/{
+ s//\1+\3+\4=\2/
+ b add
+}
+s/^\([0-9]*\)1\+/\10+/
+s/^\([0-9]*\)2\+/\11+/
+s/^\([0-9]*\)3\+/\12+/
+s/^\([0-9]*\)4\+/\13+/
+s/^\([0-9]*\)5\+/\14+/
+s/^\([0-9]*\)6\+/\15+/
+s/^\([0-9]*\)7\+/\16+/
+s/^\([0-9]*\)8\+/\17+/
+s/^\([0-9]*\)9\+/\18+/
+
+s/9=\([0-9]*\)$/_=\1/
+s/8=\([0-9]*\)$/9=\1/
+s/7=\([0-9]*\)$/8=\1/
+s/6=\([0-9]*\)$/7=\1/
+s/5=\([0-9]*\)$/6=\1/
+s/4=\([0-9]*\)$/5=\1/
+s/3=\([0-9]*\)$/4=\1/
+s/2=\([0-9]*\)$/3=\1/
+s/1=\([0-9]*\)$/2=\1/
+/_/{
+ s//_0/
+ : inc
+ s/9_/_0/
+ s/8_/9/
+ s/7_/8/
+ s/6_/7/
+ s/5_/6/
+ s/4_/5/
+ s/3_/4/
+ s/2_/3/
+ s/1_/2/
+ s/0_/1/
+ s/\+_/+1/
+ /_/b inc
+}
+b add