mirror of
https://github.com/opnsense/src.git
synced 2026-05-28 04:12:45 -04:00
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>
This commit is contained in:
Sean Kelly
parent
cff5a08d74
commit
528d980cc0
2 changed files with 678 additions and 126 deletions
|
|
@ -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
|
||||
}
|
||||
/^[0-9]*\+/{
|
||||
# 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
|
||||
|
|
@ -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
|
||||
/^0*1\*/{
|
||||
s///
|
||||
/^00*\*.*/{
|
||||
s//0/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)0\*/{
|
||||
s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
|
||||
b mul
|
||||
/^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
|
||||
}
|
||||
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 leading
|
||||
}
|
||||
/^\([0-9*]*\)[+]=/{
|
||||
s//\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9*]*\)\+=/{
|
||||
s//\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)\+\([0-9*+]*\)\+=/{
|
||||
s//\2+\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)0\+\([0-9]*\)\([0-9]\)=/{
|
||||
/^\([0-9]*\)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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
}
|
||||
/^[0-9]*\+/{
|
||||
# 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
|
||||
|
|
@ -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
|
||||
/^0*1\*/{
|
||||
s///
|
||||
/^00*\*.*/{
|
||||
s//0/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)0\*/{
|
||||
s/^\([0-9]*\)0\*\([0-9]*\)/\1*\20/
|
||||
b mul
|
||||
/^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
|
||||
}
|
||||
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 leading
|
||||
}
|
||||
/^\([0-9*]*\)[+]=/{
|
||||
s//\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9*]*\)\+=/{
|
||||
s//\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)\+\([0-9*+]*\)\+=/{
|
||||
s//\2+\1/
|
||||
b loop
|
||||
}
|
||||
/^\([0-9]*\)0\+\([0-9]*\)\([0-9]\)=/{
|
||||
/^\([0-9]*\)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
|
||||
|
|
|
|||
Loading…
Reference in a new issue