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Diffstat (limited to 'text_cmds/sed/TEST/math.sed')
| -rw-r--r-- | text_cmds/sed/TEST/math.sed | 439 |
1 files changed, 439 insertions, 0 deletions
diff --git a/text_cmds/sed/TEST/math.sed b/text_cmds/sed/TEST/math.sed new file mode 100644 index 0000000..c3ecc64 --- /dev/null +++ b/text_cmds/sed/TEST/math.sed @@ -0,0 +1,439 @@ +# This is ksb's infamous sed calculator. (ksb@sa.fedex.com) +# +# $FreeBSD: src/usr.bin/sed/TEST/math.sed,v 1.2 2004/05/01 02:15:58 smkelly Exp $ +# +# $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 +# +# $Compile: echo "4+7*3+2^7/3" | sed -f %f + +# make sure the expression is well formed +s/[ ]//g +/[*\/^%+-]$/{ + a\ + poorly formed expression, dyadic operator on the end + q +} +/^[*\/^%]/{ + a\ + poorly formed expression, leading dyadic operator + q +} + +# fill hold space with done token +x +s/^.*/done/ +x + +# 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 + s/^\(.*\)\n\(.*\)(\([^()]*\))\(.*\)$/()\2@\4@\1/ + x + b loop +} +# 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 +} +# 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 + G + s/\(.*\)\n\([^@]*\)@\([^@]*\)@\(.*\)/\2\1\3/ + x + s/[^@]*@[^@]*@\(.*\)/\1/ + x + b loop +} +i\ +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, 0*x -> 0 +: mul +/^00*\*.*/{ + s//0/ + b loop +} +/^0*1\*/{ + s/// +: leading + s/^0*\([0-9][0-9]*\)/\1/ + b loop +} +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 +} +b mul + +# get rid of a plus term until 0+x -> x +: add +/^[+]\([0-9+*]*\)=/{ + s//\1/ + b leading +} +/^\([0-9*]*\)[+]=/{ + s//\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 +} +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 + +# 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 |