A new version that does exponents and lots of other neat things. Update

from the original author of math.sed.

Submitted by:	K S Braunsdorf <sed@ksb.npcguild.org>

2 files changed, 670 insertions, 118 deletions

diff --git a/tools/regression/usr.bin/sed/math.sed b/tools/regression/usr.bin/sed/math.sed
index 8e7bf51..cdd18d6 100644
--- a/tools/regression/usr.bin/sed/math.sed
+++ b/tools/regression/usr.bin/sed/math.sed
@@ -1,24 +1,28 @@
+# This is ksb's infamous sed calculator.		(ksb@sa.fedex.com)
 #
-#	@(#)math.sed	8.1 (Berkeley) 6/6/93
+# $FreeBSD$
 #
-# Addition and multiplication in sed.
-# ++ for a limited time only do (expr) too!!!
+# $Id: math.sed,v 2.5 1998/08/02 13:23:34 ksb Exp ksb $
+# expr ::= (expr) | expr! |
+#	expr ^ expr |
+#	-expr | expr * expr | expr / expr | expr % expr |
+#	expr + expr | expr - expr |
+#	[0-9][0-9]* ;
+# Bugs: some sign combinations don't work, and I got sick of added cases
+# for unary +.  Don't depend on signed math working all the time. -- ksb
 #
-# Kevin S Braunsdorf, PUCC UNIX Group, ksb@cc.purdue.edu.
-#
-# Ex:
-#	echo "4+7*3" | sed -f %f
+# $Compile: echo "4+7*3+2^7/3" | sed -f %f
 
 # make sure the expression is well formed
 s/[ 	]//g
-/[+*\/-]$/{
+/[*\/^%+-]$/{
 	a\
-	poorly formed expression, operator on the end
+	poorly formed expression, dyadic operator on the end
 	q
 }
-/^[+*\/]/{
+/^[*\/^%]/{
 	a\
-	poorly formed expression, leading operator
+	poorly formed expression, leading dyadic operator
 	q
 }
 
@@ -27,12 +31,19 @@ x
 s/^.*/done/
 x
 
-# main loop, process operators (*, + and () )
+# main loop, process operators ((), !, *, /, %, +, and -)
 : loop
-/^\+/{
+# uncomment the print below to follow the "logic" -- ksb
+#p
+/^[+]/{
+	s///
+	b loop
+}
+/^--/{
 	s///
 	b loop
 }
+# eval parenthesised sub expressions first
 /^\(.*\)(\([^)]*\))\(.*\)$/{
 	H
 	s//\2/
@@ -41,21 +52,224 @@ x
 	x
 	b loop
 }
-/^[0-9]*\*/b mul
-/^\([0-9]*\)\+\([0-9+*]*\*[0-9]*\)$/{
-	s//\2+\1/
+# reduce a^b^c -> a^(b^c)
+/\([0-9][0-9]*^\)\([0-9][0-9]*^[0-9][0-9^]*\)/{
+	s//\1(\2)/
+	b loop
+}
+# pull any burried exponents
+/^\(.*[^0-9]\)\([0-9][0-9]*^[0-9][0-9]*\)$/{
+	s//\1(\2)/
+	b loop
+}
+/^\(.*[^0-9]\)\([0-9][0-9]*^[0-9][0-9]*\)\([^0-9].*\)$/{
+	s//\1(\2)\3/
+	b loop
+}
+/^\([0-9][0-9]*^[0-9][0-9]*\)\([^0-9].*\)$/{
+	s//(\1)\2/
+	b loop
+}
+/^\([-]*[0-9]*\)^0*$/{
+	s//1/
+	b loop
+}
+/^\([-]*[0-9]*\)^0*1$/{
+	s//\1/
+	b loop
+}
+/^\([-]*[0-9]*\)^-[0-9]*$/{
+	s//0/
+	b loop
+}
+/^\([-]*\)\([0-9]*\)^\([0-9][0-9]*[13579]\)$/{
+	s//\1\2*((\2*\2)^(\3\/2))/
+	b loop
+}
+/^[-]*\([0-9]*\)^\([0-9][0-9]*[02468]\)$/{
+	s//(\1*\1)^(\2\/2)/
+	b loop
+}
+# single digit powers (2  3,9  4,6,8   5,7
+/^[-]*\([0-9]*\)^0*2$/{
+	s//(\1*\1)/
+	b loop
+}
+/^\([-]*\)\([0-9]*\)^0*\([39]\)$/{
+	s//\1(\2*(\2*\2))^(\3\/3)/
+	b loop
+}
+/^[-]*\([0-9]*\)^0*\([468]\)$/{
+	s//(\1*\1)^(\2\/2)/
+	b loop
+}
+# 5 7 
+/^\([-]*[0-9]*\)^\([0-9]*\)$/{
+	s//\1*(\1^(\2-1))/
+	b loop
+}
+# reduce all number factorials
+/^0*[01]!/{
+	s//1/
+	b loop
+}
+/\([*+-/%^]\)0*[01]!/{
+	s//\11/
+	b loop
+}
+/\([0-9]*\)!/{
+	s//(\1-1)!*\1/
+	b loop
+}
+# sign simplifications
+/^-\([0-9]*\)\([*/%]\)-\([0-9]*\)$/{
+	s//\1\2\3/
+	b loop
+}
+/^\([0-9]*\)\([*/%]\)-\([0-9]*\)$/{
+	s//-\1\2\3/
+	b loop
+}
+/^-\([0-9][0-9]*\)[+]*-\([0-9][0-9]*\)$/{
+	s//\1+\2/
+	x
+	s/\(.*\)/()-@@\1/
+	x
+	b loop
+}
+/^-\([0-9]*\)[+]\([0-9]\)*$/{
+	s//\2-\1/
+	b loop
+}
+/^-.*[-+*/%].*/{
+	H
+	s/^-//
+	x
+	s/^\(.*\)\n-.*$/()-@@\1/
+	x
+	b loop
+}
+# can we simplify multiplications
+/^\([0-9]*\)\([*][0-9]*[1-9]\)00*$/{
+	H
+	s//\1\2/
+	x
+	s/^\(.*\)\n[0-9]*[*][0-9]*[1-9]\(00*\)$/()@\2@\1/
+	x
+	b loop
+}
+/^\([0-9][1-9]*\)00*\([*][0-9]*\)$/{
+	H
+	s//\1\2/
+	x
+	s/^\(.*\)\n[0-9][1-9]*\(00*\)[*][0-9]*$/()@\2@\1/
+	x
+	b loop
+}
+# can we simplify division (20/30 -> 2/3)
+/^\([0-9][0-9]*\)0\([/%]\)\([0-9][0-9]*\)0$/{
+	s//\1\2\3/
 	b loop
 }
-/^[0-9]*\+/{
+# n/1 -> n
+/^0*\([0-9][0-9]*\)0[/]0*1$/{
+	s//\1/
+	b loop
+}
+# n%2 -> last_digit(n)%2 (same for 1, BTW) N.B. NO LOOP
+/^[0-9]*\([0-9]\)%0*\([12]\)$/{
+	s//\1%\2/
+}
+# move any mul/divs to the front via parans
+/^\([0-9+]*\)\([-+]\)\([0-9]*[*/][0-9*/]*\)/{
+	s//\1\2(\3)/
+	b loop
+}
+# can we div or mul
+/^[0-9]*[*][0-9]*$/{
+	b mul
+}
+/^[0-9]*[/%]0*$/{
+	i\
+divide by zero
+	d
+}
+/^[0-9]*[/%][0-9]*$/{
+	H
+	s/\([0-9]\).*[/%]/\1-/
+	x
+	s/^\(.*\)\n\([0-9]\)\([0-9]*\)\([/%]\)\([0-9]*\).*$/.\4\3q0r\2-\5@\1/
+	x
+	b loop
+}
+/^\([0-9]*[*/%][0-9]*\)\(.*\)/{
+	H
+	s//\1/
+	x
+	s/^\(.*\)\n\([0-9]*[*/][0-9]*\)\(.*\)$/()@\3@\1/
+	x
+	b loop
+}
+# can we add or subtract -- note subtract hold expression for underflow
+/^[0-9]*[+][0-9]*$/{
 	s/$/=/
 	b add
 }
+/^[0-9][0-9]*-[0-9]*$/{
+	H
+	s/$/=/
+	b sub
+}
+/^\([0-9][0-9]*[-+][0-9]*\)\(.*\)/{
+	H
+	s//\1/
+	x
+	s/^\(.*\)\n\([0-9]*[-+][0-9]*\)\(.*\)$/()@\3@\1/
+	x
+	b loop
+}
+# look in hold space for stack to reduce
 x
 /^done$/{
 	x
+	s/^0*\([0-9][0-9]*\)/\1/
 	p
 	d
 }
+# .[/%] numerator q quotient r remainder-divisor @stack
+/^\./{
+	x
+	/^[^-]/{
+		H
+		x
+		s/.\(.\)\([0-9]*\)q\([^r]*\)r\([0-9]*\)-\([0-9]*\)@\(.*\)\n\(.*\)/.\1\2q\3+1r\7-\5@\6/
+		h
+		s/..[0-9]*q[^r]*r\([0-9]*-[0-9]*\)@.*/\1/
+		b loop
+	}
+	/^-/{
+		g
+		/.\(.\)\([0-9]\)\([0-9]*\)q\([^r]*\)r0*\([0-9]*\)-\([^@]*\)@.*/{
+			s//\5\2-\6/
+			x
+			s/.\(.\)\([0-9]\)\([0-9]*\)q\([^r]*\)r0*\([0-9]*\)-\([0-9]*\)@\(.*\)/.\1\3q(\4)*10r\5\2-\6@\7/
+			x
+			b loop
+		}
+# no digits to shift on
+		s/^\.[/]q\([^r]*\)r[^@]*@.*/\1/
+		s/^\.[%]q[^r]*r0*\([0-9][0-9]*\)-[^@]*@.*/\1/
+		/^\./{
+			i\
+divide error
+			q
+		}
+		x
+		s/^\.[/%]q[^r]*r[^@]*@\(.*\)/\1/
+		x
+		b loop
+	}
+}
 /^()/{
 	s///
 	x
@@ -67,73 +281,71 @@ x
 	b loop
 }
 i\
-help, stack problem
+help, stack problem - the hold space
 p
 x
+i\
+and the pat space
 p
+i\
+quit
 q
 
-# turn mul into add until 1*x -> x
+# turn mul into add until 1*x -> x, 0*x -> 0
 : mul
+/^00*\*.*/{
+	s//0/
+	b loop
+}
 /^0*1\*/{
 	s///
+: leading
+	s/^0*\([0-9][0-9]*\)/\1/
 	b loop
 }
-/^\([0-9]*\)0\*/{
-	s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
-	b mul
+s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
+s/^\([0-9]*\)1\*\([0-9]*\)/\1*\20+\2/
+s/^\([0-9]*\)2\*\([0-9]*\)/\1*\20+(\2+\2)/
+s/^\([0-9]*\)3\*\([0-9]*\)/\1*\20+(\2+\2+\2)/
+s/^\([0-9]*\)4\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2)/
+s/^\([0-9]*\)5\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)6\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)7\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)8\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)9\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2+\2+\2)/
+/^0*\*[0-9]*[+]*\(.*\)/{
+	s//\1/
+	b loop
 }
-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
-/^\+\([0-9+*]*\)=/{
+/^[+]\([0-9+*]*\)=/{
 	s//\1/
-	b loop
+	b leading
 }
-/^\([0-9*]*\)\+=/{
+/^\([0-9*]*\)[+]=/{
 	s//\1/
 	b loop
 }
-/^\([0-9]*\)\+\([0-9*+]*\)\+=/{
-	s//\2+\1/
-	b loop
-}
-/^\([0-9]*\)0\+\([0-9]*\)\([0-9]\)=/{
+/^\([0-9]*\)0[+]\([0-9]*\)\([0-9]\)=/{
 	s//\1+\2=\3/
 	b add
 }
-/^\([0-9]*\)\([0-9]\)\+\([0-9]*\)0=/{
+/^\([0-9]*\)\([0-9]\)[+]\([0-9]*\)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/^\([0-9]*\)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/
@@ -157,7 +369,71 @@ s/1=\([0-9]*\)$/2=\1/
 	s/2_/3/
 	s/1_/2/
 	s/0_/1/
-	s/\+_/+1/
+	s/[+]_/+1/
 	/_/b inc
 }
 b add
+
+# get rid of a sub term until /-0*=/ or underflow
+: sub
+/^\([0-9]*\)-0*=/{
+	s//\1/
+	x
+	s/\(.*\)\n.*$/\1/
+	x
+	b leading
+}
+/^-\([0-9].*\)=/{
+: under
+	g
+	s/.*\n\([0-9]*\)-\([0-9]*\).*/-(\2-\1)/
+	x
+	s/\(.*\)\n.*/\1/
+	x
+	b loop
+}
+/^\([0-9]*\)\([0-9]\)-\([0-9]*\)0=/{
+	s//\1-\3=\2/
+	b sub
+}
+s/1=/0=/
+s/2=/1=/
+s/3=/2=/
+s/4=/3=/
+s/5=/4=/
+s/6=/5=/
+s/7=/6=/
+s/8=/7=/
+s/9=/8=/
+
+s/^\([0-9]*\)1-/\1_-/
+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/^\([0-9]*\)0-/\1'9-/
+s/_/0/
+
+: scarry
+/0'/{
+	s//'9/
+	b scarry
+}
+/^'/{
+	b under
+}
+s/1'/0/
+s/2'/1/
+s/3'/2/
+s/4'/3/
+s/5'/4/
+s/6'/5/
+s/7'/6/
+s/8'/7/
+s/9'/8/
+
+b sub
diff --git a/usr.bin/sed/TEST/math.sed b/usr.bin/sed/TEST/math.sed
index 8e7bf51..cdd18d6 100644
--- a/usr.bin/sed/TEST/math.sed
+++ b/usr.bin/sed/TEST/math.sed
@@ -1,24 +1,28 @@
+# This is ksb's infamous sed calculator.		(ksb@sa.fedex.com)
 #
-#	@(#)math.sed	8.1 (Berkeley) 6/6/93
+# $FreeBSD$
 #
-# Addition and multiplication in sed.
-# ++ for a limited time only do (expr) too!!!
+# $Id: math.sed,v 2.5 1998/08/02 13:23:34 ksb Exp ksb $
+# expr ::= (expr) | expr! |
+#	expr ^ expr |
+#	-expr | expr * expr | expr / expr | expr % expr |
+#	expr + expr | expr - expr |
+#	[0-9][0-9]* ;
+# Bugs: some sign combinations don't work, and I got sick of added cases
+# for unary +.  Don't depend on signed math working all the time. -- ksb
 #
-# Kevin S Braunsdorf, PUCC UNIX Group, ksb@cc.purdue.edu.
-#
-# Ex:
-#	echo "4+7*3" | sed -f %f
+# $Compile: echo "4+7*3+2^7/3" | sed -f %f
 
 # make sure the expression is well formed
 s/[ 	]//g
-/[+*\/-]$/{
+/[*\/^%+-]$/{
 	a\
-	poorly formed expression, operator on the end
+	poorly formed expression, dyadic operator on the end
 	q
 }
-/^[+*\/]/{
+/^[*\/^%]/{
 	a\
-	poorly formed expression, leading operator
+	poorly formed expression, leading dyadic operator
 	q
 }
 
@@ -27,12 +31,19 @@ x
 s/^.*/done/
 x
 
-# main loop, process operators (*, + and () )
+# main loop, process operators ((), !, *, /, %, +, and -)
 : loop
-/^\+/{
+# uncomment the print below to follow the "logic" -- ksb
+#p
+/^[+]/{
+	s///
+	b loop
+}
+/^--/{
 	s///
 	b loop
 }
+# eval parenthesised sub expressions first
 /^\(.*\)(\([^)]*\))\(.*\)$/{
 	H
 	s//\2/
@@ -41,21 +52,224 @@ x
 	x
 	b loop
 }
-/^[0-9]*\*/b mul
-/^\([0-9]*\)\+\([0-9+*]*\*[0-9]*\)$/{
-	s//\2+\1/
+# reduce a^b^c -> a^(b^c)
+/\([0-9][0-9]*^\)\([0-9][0-9]*^[0-9][0-9^]*\)/{
+	s//\1(\2)/
+	b loop
+}
+# pull any burried exponents
+/^\(.*[^0-9]\)\([0-9][0-9]*^[0-9][0-9]*\)$/{
+	s//\1(\2)/
+	b loop
+}
+/^\(.*[^0-9]\)\([0-9][0-9]*^[0-9][0-9]*\)\([^0-9].*\)$/{
+	s//\1(\2)\3/
+	b loop
+}
+/^\([0-9][0-9]*^[0-9][0-9]*\)\([^0-9].*\)$/{
+	s//(\1)\2/
+	b loop
+}
+/^\([-]*[0-9]*\)^0*$/{
+	s//1/
+	b loop
+}
+/^\([-]*[0-9]*\)^0*1$/{
+	s//\1/
+	b loop
+}
+/^\([-]*[0-9]*\)^-[0-9]*$/{
+	s//0/
+	b loop
+}
+/^\([-]*\)\([0-9]*\)^\([0-9][0-9]*[13579]\)$/{
+	s//\1\2*((\2*\2)^(\3\/2))/
+	b loop
+}
+/^[-]*\([0-9]*\)^\([0-9][0-9]*[02468]\)$/{
+	s//(\1*\1)^(\2\/2)/
+	b loop
+}
+# single digit powers (2  3,9  4,6,8   5,7
+/^[-]*\([0-9]*\)^0*2$/{
+	s//(\1*\1)/
+	b loop
+}
+/^\([-]*\)\([0-9]*\)^0*\([39]\)$/{
+	s//\1(\2*(\2*\2))^(\3\/3)/
+	b loop
+}
+/^[-]*\([0-9]*\)^0*\([468]\)$/{
+	s//(\1*\1)^(\2\/2)/
+	b loop
+}
+# 5 7 
+/^\([-]*[0-9]*\)^\([0-9]*\)$/{
+	s//\1*(\1^(\2-1))/
+	b loop
+}
+# reduce all number factorials
+/^0*[01]!/{
+	s//1/
+	b loop
+}
+/\([*+-/%^]\)0*[01]!/{
+	s//\11/
+	b loop
+}
+/\([0-9]*\)!/{
+	s//(\1-1)!*\1/
+	b loop
+}
+# sign simplifications
+/^-\([0-9]*\)\([*/%]\)-\([0-9]*\)$/{
+	s//\1\2\3/
+	b loop
+}
+/^\([0-9]*\)\([*/%]\)-\([0-9]*\)$/{
+	s//-\1\2\3/
+	b loop
+}
+/^-\([0-9][0-9]*\)[+]*-\([0-9][0-9]*\)$/{
+	s//\1+\2/
+	x
+	s/\(.*\)/()-@@\1/
+	x
+	b loop
+}
+/^-\([0-9]*\)[+]\([0-9]\)*$/{
+	s//\2-\1/
+	b loop
+}
+/^-.*[-+*/%].*/{
+	H
+	s/^-//
+	x
+	s/^\(.*\)\n-.*$/()-@@\1/
+	x
+	b loop
+}
+# can we simplify multiplications
+/^\([0-9]*\)\([*][0-9]*[1-9]\)00*$/{
+	H
+	s//\1\2/
+	x
+	s/^\(.*\)\n[0-9]*[*][0-9]*[1-9]\(00*\)$/()@\2@\1/
+	x
+	b loop
+}
+/^\([0-9][1-9]*\)00*\([*][0-9]*\)$/{
+	H
+	s//\1\2/
+	x
+	s/^\(.*\)\n[0-9][1-9]*\(00*\)[*][0-9]*$/()@\2@\1/
+	x
+	b loop
+}
+# can we simplify division (20/30 -> 2/3)
+/^\([0-9][0-9]*\)0\([/%]\)\([0-9][0-9]*\)0$/{
+	s//\1\2\3/
 	b loop
 }
-/^[0-9]*\+/{
+# n/1 -> n
+/^0*\([0-9][0-9]*\)0[/]0*1$/{
+	s//\1/
+	b loop
+}
+# n%2 -> last_digit(n)%2 (same for 1, BTW) N.B. NO LOOP
+/^[0-9]*\([0-9]\)%0*\([12]\)$/{
+	s//\1%\2/
+}
+# move any mul/divs to the front via parans
+/^\([0-9+]*\)\([-+]\)\([0-9]*[*/][0-9*/]*\)/{
+	s//\1\2(\3)/
+	b loop
+}
+# can we div or mul
+/^[0-9]*[*][0-9]*$/{
+	b mul
+}
+/^[0-9]*[/%]0*$/{
+	i\
+divide by zero
+	d
+}
+/^[0-9]*[/%][0-9]*$/{
+	H
+	s/\([0-9]\).*[/%]/\1-/
+	x
+	s/^\(.*\)\n\([0-9]\)\([0-9]*\)\([/%]\)\([0-9]*\).*$/.\4\3q0r\2-\5@\1/
+	x
+	b loop
+}
+/^\([0-9]*[*/%][0-9]*\)\(.*\)/{
+	H
+	s//\1/
+	x
+	s/^\(.*\)\n\([0-9]*[*/][0-9]*\)\(.*\)$/()@\3@\1/
+	x
+	b loop
+}
+# can we add or subtract -- note subtract hold expression for underflow
+/^[0-9]*[+][0-9]*$/{
 	s/$/=/
 	b add
 }
+/^[0-9][0-9]*-[0-9]*$/{
+	H
+	s/$/=/
+	b sub
+}
+/^\([0-9][0-9]*[-+][0-9]*\)\(.*\)/{
+	H
+	s//\1/
+	x
+	s/^\(.*\)\n\([0-9]*[-+][0-9]*\)\(.*\)$/()@\3@\1/
+	x
+	b loop
+}
+# look in hold space for stack to reduce
 x
 /^done$/{
 	x
+	s/^0*\([0-9][0-9]*\)/\1/
 	p
 	d
 }
+# .[/%] numerator q quotient r remainder-divisor @stack
+/^\./{
+	x
+	/^[^-]/{
+		H
+		x
+		s/.\(.\)\([0-9]*\)q\([^r]*\)r\([0-9]*\)-\([0-9]*\)@\(.*\)\n\(.*\)/.\1\2q\3+1r\7-\5@\6/
+		h
+		s/..[0-9]*q[^r]*r\([0-9]*-[0-9]*\)@.*/\1/
+		b loop
+	}
+	/^-/{
+		g
+		/.\(.\)\([0-9]\)\([0-9]*\)q\([^r]*\)r0*\([0-9]*\)-\([^@]*\)@.*/{
+			s//\5\2-\6/
+			x
+			s/.\(.\)\([0-9]\)\([0-9]*\)q\([^r]*\)r0*\([0-9]*\)-\([0-9]*\)@\(.*\)/.\1\3q(\4)*10r\5\2-\6@\7/
+			x
+			b loop
+		}
+# no digits to shift on
+		s/^\.[/]q\([^r]*\)r[^@]*@.*/\1/
+		s/^\.[%]q[^r]*r0*\([0-9][0-9]*\)-[^@]*@.*/\1/
+		/^\./{
+			i\
+divide error
+			q
+		}
+		x
+		s/^\.[/%]q[^r]*r[^@]*@\(.*\)/\1/
+		x
+		b loop
+	}
+}
 /^()/{
 	s///
 	x
@@ -67,73 +281,71 @@ x
 	b loop
 }
 i\
-help, stack problem
+help, stack problem - the hold space
 p
 x
+i\
+and the pat space
 p
+i\
+quit
 q
 
-# turn mul into add until 1*x -> x
+# turn mul into add until 1*x -> x, 0*x -> 0
 : mul
+/^00*\*.*/{
+	s//0/
+	b loop
+}
 /^0*1\*/{
 	s///
+: leading
+	s/^0*\([0-9][0-9]*\)/\1/
 	b loop
 }
-/^\([0-9]*\)0\*/{
-	s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
-	b mul
+s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
+s/^\([0-9]*\)1\*\([0-9]*\)/\1*\20+\2/
+s/^\([0-9]*\)2\*\([0-9]*\)/\1*\20+(\2+\2)/
+s/^\([0-9]*\)3\*\([0-9]*\)/\1*\20+(\2+\2+\2)/
+s/^\([0-9]*\)4\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2)/
+s/^\([0-9]*\)5\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)6\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)7\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)8\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2+\2)/
+s/^\([0-9]*\)9\*\([0-9]*\)/\1*\20+(\2+\2+\2+\2+\2+\2+\2+\2+\2)/
+/^0*\*[0-9]*[+]*\(.*\)/{
+	s//\1/
+	b loop
 }
-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
-/^\+\([0-9+*]*\)=/{
+/^[+]\([0-9+*]*\)=/{
 	s//\1/
-	b loop
+	b leading
 }
-/^\([0-9*]*\)\+=/{
+/^\([0-9*]*\)[+]=/{
 	s//\1/
 	b loop
 }
-/^\([0-9]*\)\+\([0-9*+]*\)\+=/{
-	s//\2+\1/
-	b loop
-}
-/^\([0-9]*\)0\+\([0-9]*\)\([0-9]\)=/{
+/^\([0-9]*\)0[+]\([0-9]*\)\([0-9]\)=/{
 	s//\1+\2=\3/
 	b add
 }
-/^\([0-9]*\)\([0-9]\)\+\([0-9]*\)0=/{
+/^\([0-9]*\)\([0-9]\)[+]\([0-9]*\)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/^\([0-9]*\)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/
@@ -157,7 +369,71 @@ s/1=\([0-9]*\)$/2=\1/
 	s/2_/3/
 	s/1_/2/
 	s/0_/1/
-	s/\+_/+1/
+	s/[+]_/+1/
 	/_/b inc
 }
 b add
+
+# get rid of a sub term until /-0*=/ or underflow
+: sub
+/^\([0-9]*\)-0*=/{
+	s//\1/
+	x
+	s/\(.*\)\n.*$/\1/
+	x
+	b leading
+}
+/^-\([0-9].*\)=/{
+: under
+	g
+	s/.*\n\([0-9]*\)-\([0-9]*\).*/-(\2-\1)/
+	x
+	s/\(.*\)\n.*/\1/
+	x
+	b loop
+}
+/^\([0-9]*\)\([0-9]\)-\([0-9]*\)0=/{
+	s//\1-\3=\2/
+	b sub
+}
+s/1=/0=/
+s/2=/1=/
+s/3=/2=/
+s/4=/3=/
+s/5=/4=/
+s/6=/5=/
+s/7=/6=/
+s/8=/7=/
+s/9=/8=/
+
+s/^\([0-9]*\)1-/\1_-/
+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/^\([0-9]*\)0-/\1'9-/
+s/_/0/
+
+: scarry
+/0'/{
+	s//'9/
+	b scarry
+}
+/^'/{
+	b under
+}
+s/1'/0/
+s/2'/1/
+s/3'/2/
+s/4'/3/
+s/5'/4/
+s/6'/5/
+s/7'/6/
+s/8'/7/
+s/9'/8/
+
+b sub