-# $OpenBSD: math.sed,v 1.1 2008/10/10 14:33:34 millert Exp $
+# This is ksb's infamous sed calculator. (ksb@sa.fedex.com)
#
-# from: @(#)math.sed 8.1 (Berkeley) 6/6/93
+# $FreeBSD: head/usr.bin/sed/tests/math.sed 228975 2011-12-30 00:04:11Z uqs $
#
-# Addition and multiplication in sed.
-# ++ for a limited time only do (expr) too!!!
+# $Id: math.sed,v 1.2 2015/05/10 01:45:12 millert Exp $
+# 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
}
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/
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 buried 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
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/
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
projects / openbsd / commitdiff