%MM% v0.2a - a full-featured WinNT math macro
Posted: 08 Aug 2018 06:54
Hiya guys! Been awhile since I dropped by, but I just wanted to share my latest little goodie... and hopefully find a few interested testers. ^_^
%MM% is a math macro that contains all of the functionality of my previous large, slow, and over-bloated Math.cmd utility, except for functions and decimal rounding. Instead, I was able to add unary ops (~ ' -), bitwise ops (| ^ &), logical ops (||,|&,&&), compound assignments (+= -= *= /= @= $= |= ^= &= <<= >>=) and conditional/ternary if (?:). Although it's naturally much smaller I still had to struggle to keep it under the maximum size (it currently has about 350 characters to spare). It's also noticeably faster (although I've yet to do a comparison) not only because of the lack of CALLs, but also because all math is performed on groups of eight digits instead of just one. Please give it a try and post any operational or computational issues you may find.
If you run it as-is, it will display the help, run a sample Nth-Root convergence formula, and allow you to enter sample expressions for testing. I've only tested it on my Win7 x64 machine, I don't have access to any others.
Edit 2018/08/08: I had totally forgotten the no-space method of inserting comments in macros (saw it while poking around the forum) so I've updated the post with a heavily commented/verbosely-cluttered version. No version# change as I only added comments and didn't alter a single character of code. After repeatedly handing it many difficult and increasingly unnecessarily herculean tasks, I currently have it finding the 999,999th root of 999,999 to 32 decimal accuracy starting at 1.005... sure it's been running for nearly 3 days now, but I've no doubt that it'll finally make it! ^_^
Edit 2018/08/09: Cleaned up v0.1 again and re-posted. Changed %# to %= for comments, replaced tabs with %= =%, and removed the DelayedExpansion duality. No code has changed, it just looks different. Also, I chose not to employ DB's fix for the endless-loop effect because I like to know when something's broken, it's better if I actually fix it. ^_^
Incidentally, that 999,999th root is on guess#517 and counting... any day now.
Edit 2018/08/17: I've just posted v0.2 with (hopefully) some improvements (v0.1 can conveniently be found archived on the post below this one). All ops from SET/A are now supported with bitwise ops being passed directly to SET/A which treats values above 2147483647 as 2147483647 and below -2147483648 as -2147483648. Due to the size of the macro, expressions are limited to ~350 characters, so I've also added the ability to save longer expressions to a variable (%$MM%) which can be passed into the macro by invoking it without any parameters. I haven't tested it too extensively, so I'm expecting to correct at least a glitch or two (if not more). Please post if you try it and encounter any issues.
Edir 2018/08/18: Reading through the comments I had forgotten about the endless-loop issue in the demo. I've corrected that by extending the maxDecimal by +2 during process and reducing back down before final truncation (+1 would probably be sufficient, but perhaps +2 will better approximate rounding). I also took the opportunity to minimize the size as much as I could by reducing all possible variables to single characters, added a few comments and posted v0.2a
%MM% is a math macro that contains all of the functionality of my previous large, slow, and over-bloated Math.cmd utility, except for functions and decimal rounding. Instead, I was able to add unary ops (~ ' -), bitwise ops (| ^ &), logical ops (||,|&,&&), compound assignments (+= -= *= /= @= $= |= ^= &= <<= >>=) and conditional/ternary if (?:). Although it's naturally much smaller I still had to struggle to keep it under the maximum size (it currently has about 350 characters to spare). It's also noticeably faster (although I've yet to do a comparison) not only because of the lack of CALLs, but also because all math is performed on groups of eight digits instead of just one. Please give it a try and post any operational or computational issues you may find.
Code: Select all
:: %MM% is a WinNT batch macro that performs mathematical and relational
:: operations on large integers and decimals. It will accept either numerals
:: or variables as operands, supports the parsing of multiple complex in-line
:: expressions, and provides the following operators in order of precedence:
:: |( ) Grouping
:: Highest | ' LogicalNot | ~ BitwiseNot | - Negative
:: | $ PowerOf
:: | * Multiply | / Division | @ Modulo
:: | + Addition | - Subtraction
:: | << LeftShift | >> RightShift
:: |<=> 3-way Comparison
:: | < LessThan | > GreaterThan | <= LessOrEqual | >= GreaterOrEqual
:: | ## IsEqualTo | <> NotEqualTo
:: | & BitwiseAnd > ^ BitwiseXor > | BitwiseOr
:: | && LogicalAnd > |& LogicalXor > || LogicalOr
:: | ?: TernaryIf
:: Lowest | = += -= *= /= @= $= |= ^= &= <<= >>= Equals/Compound Assignment
:: | ;, Expression Separators
::
:: Relation & Logical ops return both value and ERRORLEVEL of 1=True, 0=False.
:: 3-way Comparison operator returns 1 if n1>n2, 0 if n1=n2, or -1 if n1<n2.
:: TernaryIf(?:) = boolean ? returnIfBoolean<>0 : returnIfBoolean==0.
:: Bitwise ops are passed to SET/A, which allows signed 32-bit integers only.
:: Modulo(@) is integer only. PowerOf($) exponent is integer and positive only.
:: Variables may contain 0-9, A-z, []_ only, and first letter can't be 0-9.
:: If a variable's value is undefined or non-numerical, it's treated as 0.
:: To display result use "echo#=" in the expression, where #=num of linefeeds.
:: The result of each expression is always returned in the variable %MM_%.
:: IF ERRORLEVEL 1 IF %MM_%==0 then an error has occurred.
::
:: Constants: set these prior to invoking the macro, default if undefined.
:: SET $M#= # of asterisks, tildes, and equal-signs to scan for, default is 16.
:: if insufficient macro will fail without warning, ERRORLEVEL=MM_=0.
:: SET $MD= the maximum number of decimals to return, 2 if undefined.
:: macro is most efficient when $MD+2 is a multiple of 8.
:: SET $MM= expression to execute if %MM% is invoked without parameters. Line
:: input is limited to ~350 characters, use this to input up to ~8000.
::
::
@ECHO OFF
SET $M#=
SET $MD=
SET $MM=
:: setup macro
(SET \n=^^^
%= This defines an escaped Line Feed - DO NOT ALTER =%
)
SET MM=FOR %%# IN (1 2)DO IF %%#==2 (%= 'v0.2a 2018/08/18 =%%\n%
%= =%FOR %%A IN (D G N T U U1 U2 X Y)DO SET $%%A=%= '$ is used as prefix on all first-tier variables as these can't be passed into the macro, clear intitial values =%%\n%
%= =%SET $Y=4096 2048 1024 512 256 128 64 32 16 8 4 2 1%= 'binary regression for sizeOf/trailingZeros functions =%%\n%
%= =%SET $Z=0000000000000000%= 'create constants, 9-digit controls, 4096 zeros, operator-precedence table =%%\n%
%= =%FOR %%A IN (1 2 3 4)DO SET $%%A=%%A00000000^&SET $Z=!$Z!!$Z!!$Z!!$Z!%\n%
%= =%FOR %%A IN ("( ," ": )" "T # +# -# \# /# @# $# |# {# &# <<# >>#" "||" "|&" "&&" "|" { "&" "## <>" "< > ># <#" "<#>" "<< >>" "+ -" "\ / @" $ "' } `")DO SET/A $T+=1^&SET "$O!$T!= %%~A "%\n%
%= =%IF "!$MD!"=="" SET $MD=2%= '$MD/maxDecimal=maximum #of decimals to return =%%\n%
%= =%IF "!$M#!"=="" SET $M#=16%= '$M#=maximum# of asterisks/equal-signs/tildes allowed in input, else macro will fail without warning and MM_=ERRORLEVEL=0, be sure to set this value high enough for your usage =%%\n%
%= =%IF "!$P: =!"==";" SET $P=;!$MM!%= 'if no input (or only spaces), copy parameters from variable $MM =%%\n%
%= =%SET "$P=!$P:^={!"%= 'replace ^ carets(problem char#1) with { left-brace =%%\n%
%= =%SET $P=!$P:^"= !%= 'remove double-quotes =%%\n%
%= =%SET $P=!$P:\=/!%= 'assume \ backslash is / forwardslash(division), \ backslash is then used for * multiplication =%%\n%
%= =%SET $P=!$P:,=;!%= 'assume all expression separators are ; semi-colons, commas are then used as ? ternary-open =%%\n%
%= =%SET $P=!$P:?= , ! %= 'replace ? question-marks(problem char#2) with , commas =%%\n%
%= =%FOR %%A IN (+ - / @ $ # : ' { "&" "|" "<" ">" "(" ")" ";")DO SET "$P=!$P:%%~A= %%~A !"%\n%
%= =%FOR /L %%A IN (0,1,!$M#!)DO (%= 'separate all other operators from operands =%%\n%
%= =%FOR /F "tokens=1* delims=*" %%B IN ("!$P!")DO IF "%%C" NEQ "" SET "$P=%%B \ %%C"%= 'replace * asterisks(problem char#3) with \ backslash =%%\n%
%= =%FOR /F "tokens=1* delims==" %%B IN ("!$P!")DO IF "%%C" NEQ "" SET "$P=%%B # %%C"%= 'replace = equal-signs(problem char#4) with # hashmark =%%\n%
%= =%FOR /F "tokens=1* delims=~" %%B IN ("!$P!")DO IF "%%C" NEQ "" SET "$P=%%B } %%C"%= 'replace ~ tilde(problem char#5) with } right-brace =%%\n%
%= =%SET $P=!$P: = !)%= 'reduce double-spaces, replace numeric negation(-) with ` and remove unary(+), reassemble multi-char operators =%%\n%
%= =%FOR %%A IN (+ - \ / @ $ # : ' { } "&" "|" ">" "<" "(" ";" ",")DO SET "$P=!$P: %%~A - = %%~A ` !"^&SET "$P=!$P: %%~A + = %%~A !"%\n%
%= =%FOR %%A IN ("< <=<<" "> >=>>" "< >=<>" "< #=<#" "# >=#>" "> #=>#" "# #=##" "+ #=+#" "- #=-#" "\ #=\#" "/ #=/#" "@ #=@#" "$ #=$#" "| #=|#" "& #=&#" "{ #={#" "& &=&&" "| &=|&" "| |=||" "{ {={" "{ {={")DO SET "$P=!$P:%%~A!"%\n%
%= =%SET $R=MM_=%= 'initialize $R=return-variable-queue and feed expressions one-at-a-time into loop =%%\n%
%= =%FOR %%: IN (^"!$P: ;=^" ^"!^")DO IF %%: NEQ "" IF DEFINED $R (SET "$E=(%%~: + 0 )"%= 'begin shunting-yard(ish) parser =%%\n%
%= =%FOR %%A IN (C Q S T V)DO SET $%%A=%= 'small cheat by seeding expression with '( exp + 0 )' to greatly simplify parser =%%\n%
%= =%FOR %%A IN (^"!$E: =^" ^"!^")DO IF %%A NEQ "" IF DEFINED $R (SET/A $O=$K=0%= 'feed ops one-at-a-time into loop =%%\n%
%= =%FOR /F %%B IN ("!$V!")DO SET $K=%%B%= '$K=peek at value on top of $V=precedence-value-of-operator stack =%%\n%
%= =%FOR /L %%B IN (1,1,17)DO IF "!$O%%B!" NEQ "!$O%%B: %%~A =!" SET $O=%%B%= 'find $O=operator-precedence of current op =%%\n%
%= =%IF !$O!==0 (SET $Q=%%~A !$Q!%= 'if no match, then it's an operand, place on top of queue =%%\n%
%= =%)ELSE IF !$O!==3 (IF !$K! GTR 3 SET $R=^&ECHO Assignment error.^>^&2%= 'only ternary, assignments, and parenthesis are allowed below assignments =%%\n%
%= =%)ELSE IF !$O! NEQ 1 IF !$O! LSS 16 IF !$O! LEQ !$K! (SET $T=%= 'if not openParenthesis/openTernary(lowest) nor powerOf/unary(highest) but LEQ top of stack then process stack =%%\n%
%= =%IF "!$S!"=="!$S:(=!" SET $R=^&ECHO Missing open parenthesis.^>^&2%= 'there should always be open-parenthesis in the stack =%%\n%
%= =%FOR %%B IN (^"!$S: =^" ^"!^")DO IF %%B NEQ "" IF DEFINED $R (%= 'feed operators from stack one-at-a-time into loop =%%\n%
%= =%IF !$O! LEQ !$K! (SET/A $C+=1%= '$C=counter for next-queued-variable,if current operator-precedence LEQ top of stack process next operator =%%\n%
%= =%FOR /F "tokens=1-3*" %%C IN ("!$Q!")DO (%= 'pop operands from the top of queue =%%\n%
%= =%IF !$K!==17 (SET $A=%%C %%C^&SET $B=%%D %%E %%F^&IF "%%C"=="" SET $R=%= 'if unary operator =%%\n%
%= =%)ELSE IF %%~B==T (SET $A=%%D %%C %%E^&SET $B=%%F^&IF "%%E"=="" SET $R=%= 'if ternary operator =%%\n%
%= =%)ELSE SET $A=%%D %%C^&SET $B=%%E %%F^&IF "%%D"=="" SET $R=%= 'if binary operator =%%\n%
%= Start Math =%IF DEFINED $R (SETLOCAL%= 'if operands are good,SETLOCAL and start math sequence =%%\n%
%= Capture Operands =%FOR %%I IN (!$A!)DO FOR /F "tokens=* delims=-0123456789." %%J IN ("%%I")DO (SET/A $D+=1%= '$D=counter for operands =%%\n%
%= =%IF "%%J"=="" (SET $N!$D!=%%I)ELSE SET $N!$D!=!%%I!)%= 'determine if number or variable,capture values =%%\n%
%= =%FOR %%I IN (g n n1 n2 n3 u u1 u2 v)DO SET %%I=!$%%I!%= 'now it's OK to use variables other than $, set/clear new values =%%\n%
%= =%SET/A i=1,a=f=f1=q=s11=s12=s21=s22=t=t1=t2=t3=w=0%= 'clear start values =%%\n%
%= =%SET "p=%%~B"%= 'capture current operator-symbol =%%\n%
%= Discover Operands =%FOR /L %%I IN (1,1,!$D!)DO (IF "!n%%I:~0,1!"=="-" SET n%%I=!n%%I:~1!^&SET u%%I=-%= 'separate unary from value =%%\n%
%= =%FOR /F "tokens=* delims=0123456789." %%J IN ("!n%%I!")DO IF "%%J" NEQ "" SET n%%I=!n%%I:%%J=!%= 'remove non-numerical portion of value =%%\n%
%= =%FOR /F "tokens=1-2 delims=." %%J IN ("0!n%%I!")DO FOR /F "tokens=* delims=0" %%L IN ("%%J")DO SET o%%I1=%%L^&SET o%%I2=%%K%\n%
%= =%IF "!o%%I1!"=="" SET o%%I1=0%= 'capture integer+decimal portions of value, remove leading zeros, check for zero =%%\n%
%= =%SET o%%I=!o%%I1!!o%%I2!%= 'set o1/o2/o3=assembled non-padded values =%%\n%
%= =%FOR %%J IN (1 2)DO (SET t=!o%%I%%J!0%= 'find length of integer/decimal portion of each value =%%\n%
%= =%FOR %%K IN (!$Y!)DO IF "!t:~%%K,1!" NEQ "" SET/A s%%I%%J+=%%K^&SET t=!t:~%%K!)%\n%
%= =%SET/A s%%I=s%%I1+s%%I2)%= 'set total length(s=size) of each value, then set padded values(m1=maxIntLength,m2=maxDecLength,n1/n2=padded-values) =%%\n%
%= =%FOR %%I IN (1 2)DO SET/A"m%%I=(s1%%I+7)/8*8"^&IF !s2%%I! GTR !s1%%I! SET/A"m%%I=(s2%%I+7)/8*8"%\n%
%= =%FOR %%I IN (1 2)DO FOR /F "tokens=1*" %%J IN ("!m1! !m2!")DO SET n%%I=!$Z!!o%%I1!^&SET t=!o%%I2!!$Z!^&SET n%%I=!n%%I:~-%%J!!t:~0,%%K!%\n%
%= =%IF "!n1!" GTR "!n2!" (SET q=1)ELSE IF "!n1!" LSS "!n2!" SET q=-1%= 'determine q=3-way compare=if abs(n1) GTR abs(n2) =%%\n%
%= Compound Assignment =%FOR %%I IN (+ - \ / @ $ { "|" "&" "<<" ">>")DO IF %%B=="%%~I#" SET y=%%D^&SET "p=%%~I"%= 'check for compound assignments, if found, correct op and set y=return variable =%%\n%
%= =%SET/A d=m2,h=m1+m2,z=$MD+2%= 'd=decimalPlace=max padded fractional length,h=maxLength of padded int + fraction values =%%\n%
%= =%IF !p!==+ IF "!u2!" NEQ "!u1!" SET u2=!u1!^&SET p=-%\n%
%= =%IF !p!==- IF "!u2!" NEQ "!u1!" SET u2=!u1!^&SET p=+%= 'only add/subtract values with matching unaries =%%\n%
%= (`)Negative =%IF !p!==` SET n=!n1!^&IF "!u1!"=="" SET u=-%= 'negative - numeric negation =%%\n%
%= (#)Assignment =%IF !p!==# SET y=%%D^&SET u=!u2!^&SET n=!n2!%= 'assignment - set y=return variable=operand2,u=unary of answer=same as value2,n=final answer=same as value2 =%%\n%
%= (T)Ternary If =%IF !p!==T SET u=!u1!^&SET n=!n1!^&IF !o3! EQU 0 SET u=!u2!^&SET n=!n2!%= 'ternary - set u=n=value1, if third-value=0, set u=n=value2 =%%\n%
%= (+)Addition =%IF !p!==+ (SET u=!u1!%= 'addition - group values by 8 digits, add values, collect carry, assemble n=answer =%%\n%
%= =%FOR /L %%I IN (8,8,!h!)DO SET/A t=1!n1:~-%%I,8!+1!n2:~-%%I,8!+w,w=t/$3^&SET n=!t:~1!!n!%\n%
%= =%SET n=!w!!n!)%= 'collect carry =%%\n%
%= (-)Subtraction =%IF !p!==- (%= 'subtraction - only subtract lesser from greater, if n1>=n2 set u=u1=unary of value1, else swap n1 with n2 and set u=negative if u1=positive, then same procedure as addition without the carry =%%\n%
%= =%IF !q! GEQ 0 (SET u=!u1!)ELSE SET t=!n1!^&SET n1=!n2!^&SET n2=!t!^&IF "!u1!"=="" SET u=-%\n%
%= =%IF !q! NEQ 0 FOR /L %%I IN (8,8,!h!)DO SET/A t=3!n1:~-%%I,8!-1!n2:~-%%I,8!+w,w=t/$2-1^&SET n=!t:~1!!n!)%\n%
%= =%IF "!n!"=="" SET d=0%= 'above operations require d=m2, all others require d=0, if n="" then no operations have been performed =%%\n%
%= (@)Modulo =%IF !p!==@ SET p=/^&SET f1=1%= 'modulo - set op=division and f1/MODflag=1 =%%\n%
%= (/)Division =%IF !p!==/ (SET/A s11+=s22,s12-=s22%= 'division+modulo - set s11/size1_int+=size2_dec,s12/size1_dec-=size2_dec =%%\n%
%= =%IF !s12! LSS 0 SET s12=0%= 'if size1_dec<0 set to 0 =%%\n%
%= =%SET/A s1=s11+s12,j=s11+z%= 's1/length_of_value1=size1_int+size1_dec,j/#of divisions=size1+$maxDecimal =%%\n%
%= =%SET w=!$Z!%= 'w=remainder=$zeros =%%\n%
%= =%SET o1=0!o1!!$Z!%= 'o1/non-padded value1=lead0~o1~$zeros =%%\n%
%= =%IF !f1!==1 SET j=0%= 'above will move decimalPlace and set j=#of divisions, if f1/MODflag=1 set j=0 because integer only =%%\n%
%= =%IF !j! LSS !s1! SET/A j=s1%= 'if j LSS s1/size1=length of value1 then j=size1 ie. no fraction/integer only =%%\n%
%= =%IF "!u1!" NEQ "!u2!" SET u=-%= 'if unaries don't match answer is negative =%%\n%
%= =%FOR %%I IN (!h!)DO SET n2=!$Z!!o2!^&SET n2=!n2:~-%%I!%= 'set n2/divisor=corrected/padded value2 =%%\n%
%= =%IF !q!==0 (SET n=1)ELSE IF !n2! EQU 0 (SET g=X^&ECHO Divide by zero error.^>^&2%\n%
%= =%)ELSE IF !o1! NEQ 0 FOR /L %%I IN (1,1,!j!)DO (SET t=0%= 'reset t/answer digit=0 and d/decimalPlace+=1 if GTR lengthOfDividend =%%\n%
%= =%IF %%I GTR !s11! SET/A d+=1%= 'add next digit from dividend to remainder and crop to maxSize for comparison with divisor =%%\n%
%= =%FOR %%J IN (!h!)DO SET w=!w!!o1:~%%I,1!^&SET w=!w:~-%%J!%\n%
%= =%IF "!w!" GEQ "!n2!" FOR /L %%J IN (1,1,9)DO IF "!w!" GEQ "!n2!" (SET/A t+=1,t2=0%\n%
%= =%SET t3=!w!%= 'if w/remainder GTR n2/divisor then w-=n2 until it's not, t=answer digit=#of subtractions until w LSS n2 =%%\n%
%= =%SET w=%\n%
%= =%FOR /L %%K IN (8,8,!h!)DO SET/A t1=3!t3:~-%%K,8!-1!n2:~-%%K,8!+t2,t2=t1/$2-1^&SET w=!t1:~1!!w!)%\n%
%= =%SET n=!n!!t!)%= 'add t=answer digit to n/quotient/final answer =%%\n%
%= =%IF !f1!==1 SET u=!u1!^&SET n=!w!)%= 'if f1/MODflag=1 set u=unary of dividend,n/answer=w/integer remainder =%%\n%
%= ($)Power Of =%IF !p!==$ (SET p=\^&SET u2=%= 'powerOf - set op=multiply, check for integer/0/1 exponent =%%\n%
%= =%IF !s22! NEQ 0 SET o2=0^&SET g=X^&ECHO Non-integer exponent.^>^&2%\n%
%= =%IF !o1! LEQ 1 SET o2=0%= 'i=o2=0 will effectively cancel multiplication routine =%%\n%
%= =%SET/A i=o2,a=i/3+1,t=i%%2,n=o2=s2=1%= 'set i=exponent,a=#of loop iterations,t=even/odd exponent,answer=non-padded value2=length of value2=1 =%%\n%
%= =%IF !t!==0 SET u1=)%= 'if exponent is even clear unary of value1, as answer will be positive =%%\n%
%= (\)Multiplication =%IF !p!==\ (IF "!u1!" NEQ "!u2!" SET u=-%= 'multiplication+powerOf - if unaries don't match answer is negative =%%\n%
%= =%FOR /L %%H IN (0,1,!a!)DO IF !i! NEQ 0 (SET/A t2=i%%2,i/=2%= 'if exponent NEQ 0 capture odd/even and halve exponent =%%\n%
%= =%IF !t2!==1 (SET n=%= 'n/answer=NULL =%%\n%
%= =%SET n2=0000000!o2!%= 'n2=0000000non-padded value2 =%%\n%
%= =%SET/A"d=s12+s22,h=(s2+7)/8*8"%= 'set decimalPlace=size1_dec+size2_dec,maxSize=largest group of 8 =%%\n%
%= =%FOR /L %%I IN (1,1,!h!)DO SET _%%I=0%= 'clear carry columns =%%\n%
%= =%FOR /L %%I IN (1,1,!s1!)DO (SET/A w=t1=0,c=%%I%= 'multiply each digit of o1 by n2 grouped by 8 =%%\n%
%= =%FOR /L %%J IN (8,8,!h!)DO SET/A t=!o1:~-%%I,1!,t=t*1!n2:~-%%J,8!+w-t*$1,w=t/$1,_!c!+=t%%$1,c+=8%\n%
%= =%SET _!c!=!w!)%= 'collect carry into the next column =%%\n%
%= =%FOR /L %%I IN (1,1,!c!)DO SET/A _%%I+=t1,t1=_%%I/10^&SET n=!_%%I:~-1!!n!%\n%
%= =%SET n=!t1!!n!)%= 'add all columns together, attach remainder to product =%%\n%
%= =%IF !i! NEQ 0 (SET n1=%= 'if exponent NEQ 0 square n1 by setting n2=n1 and repeating as above saving product in n1 =%%\n%
%= =%SET n2=0000000!o1!%\n%
%= =%SET/A"s12*=2,s22=d,h=(s1+7)/8*8"%\n%
%= =%FOR /L %%I IN (1,1,!h!)DO SET _%%I=0%\n%
%= =%FOR /L %%I IN (1,1,!s1!)DO (SET/A w=t1=0,c=%%I%\n%
%= =%FOR /L %%J IN (8,8,!h!)DO SET/A t=!o1:~-%%I,1!,t=t*1!n2:~-%%J,8!+w-t*$1,w=t/$1,_!c!+=t%%$1,c+=8%\n%
%= =%SET _!c!=!w!)%\n%
%= =%FOR /L %%I IN (1,1,!c!)DO SET/A _%%I+=t1,t1=_%%I/10^&SET n1=!_%%I:~-1!!n1!%\n%
%= =%SET n1=!t1!!n1!^&SET n2=!n!%= 'n1=new square,n2=current answer, remove leading zeros =%%\n%
%= =%FOR %%I IN (1 2)DO FOR /F "tokens=* delims=0" %%J IN ("!n%%I!")DO (SET o%%I=%%J%\n%
%= =%SET/A s%%I=0,t=s%%I2-z%= 'clear size,set t=size#_dec - $maxDecimal =%%\n%
%= =%IF !t! GTR 0 FOR %%K IN (!t!)DO SET/A s%%I2=z^&SET o%%I=!o%%I:~0,-%%K!%\n%
%= =%SET t=!o%%I!0%= 'crop values to $maxDecimal,determine new length =%%\n%
%= =%FOR %%K IN (!$Y!)DO IF "!t:~%%K,1!" NEQ "" SET/A s%%I+=%%K^&SET t=!t:~%%K!))))%\n%
%= Relational Ops =%IF DEFINED u1 (IF DEFINED u2 (SET/A q*=-1)ELSE SET q=-1)ELSE IF DEFINED u2 SET q=1%= 'q=abs(n1)>abs(n2), correct using unaries u1+u2 =%%\n%
%= =%IF !p!==## IF !q!==0 SET f=1%= 'relational operators =%%\n%
%= =%IF %%B==">" IF !q! GTR 0 SET f=1%= 'f=flag=only set to 1(true) by logic and relational operators =%%\n%
%= =%IF %%B=="<" IF !q! LSS 0 SET f=1%\n%
%= =%IF %%B==">#" IF !q! GEQ 0 SET f=1%\n%
%= =%IF %%B=="<#" IF !q! LEQ 0 SET f=1%\n%
%= =%IF %%B=="<>" IF !q! NEQ 0 SET f=1%\n%
%= =%IF %%B=="<#>" SET/A n=q%\n%
%= Logical Ops =%IF !p!==' IF !o1! EQU 0 SET f=1%= 'logical operators - not =%%\n%
%= =%IF %%B=="||" IF !o1!!o2! NEQ 0 SET f=1%= 'or =%%\n%
%= =%IF %%B=="&&" IF !o1! NEQ 0 IF !o2! NEQ 0 SET f=1%= 'and =%%\n%
%= =%IF %%B=="|&" IF !o1! NEQ 0 (IF !o2! EQU 0 SET f=1)ELSE IF !o2! NEQ 0 SET f=1%= 'xor =%%\n%
%= =%IF !f!==1 SET n=1^&SET g= 00%= 'if flag1=1 set n=answer=true=1 and ErrLvl=1 =%%\n%
%= Bitwise Ops =%SET o1=!u1!!o1!^&SET o2=!u2!!o2!%= 'bitwise operators =%%\n%
%= =%IF !p!==} SET/A n=~o1%= 'passed directly to SET/A using variables as operands, so it never errors? =%%\n%
%= =%IF !p!=={ SET/A"n=o1^o2"%= 'supports 32-bit signed integers only =%%\n%
%= =%IF %%B=="|" SET/A"n=o1|o2"%= 'values above 2147483647 are treated as 2147483647 =%%\n%
%= =%IF %%B=="&" SET/A"n=o1&o2"%= 'values below -2147483648 are treated as -2147483648 =%%\n%
%= =%IF %%B=="<<" SET/A"n=o1<<o2"%\n%
%= =%IF %%B==">>" SET/A"n=o1>>o2"%\n%
%= =%SET/A z-=2%\n%
%= Finalize Value =%IF !d! NEQ 0 (FOR %%I IN (!d!)DO FOR %%J IN (!z!)DO SET n=!n:~0,-%%I!.!n:~-%%I,%%J!%\n%
%= =%FOR %%I IN (!$Y!)DO IF "!n:~-%%I!"=="!$Z:~-%%I!" SET n=!n:~0,-%%I!%= 'remove trailing zeros =%%\n%
%= =%IF "!n:~-1!"=="." SET n=!n:~0,-1!)%= 'if d GTR 0 answer is decimal, place decimal in n cropping to $maxDecimal, if last character is decimal remove it =%%\n%
%= =%FOR /F "tokens=* delims=0" %%I IN ("!n!")DO SET n=%%I%= 'remove leading zeros =%%\n%
%= =%IF "!n!"=="" SET n=0%= 'if n=NULL set to 0 =%%\n%
%= =%IF !n! NEQ 0 SET n=!u!!n!%= 'if n/answer=non-zero attach unary =%%\n%
%= =%IF "!g!" NEQ "X" IF /I "!y:~0,4!"=="ECHO" (^<NUL SET/P=!n!%= 'if no error check for ECHO command =%%\n%
%= =%FOR /L %%J IN (1,1,!y:~4!)DO ECHO.%\n%
%= =%SET y=)%= 'return values from 2nd-tier SETLOCAL =%%\n%
%= Return Value =%FOR /F "tokens=1-3 delims=;" %%I IN (^""!y!";"!n!";"!g!"^")DO (ENDLOCAL%\n%
%= =%IF %%I NEQ "" SET %%~I=%%~J^&SET $R=!$R!" "%%~I=%%~J%= 'if return variable present SET value and add to return-varible-queue =%%\n%
%= =%SET $_!$C!=%%~J%= 'SET value of current queued variable =%%\n%
%= =%SET $X=%%~K)%= 'SET exitcode =%%\n%
%= Resume Parser =%IF "!$X!"=="X" SET $R=%= 'if exitcode=X then ERROR, clear $R as halt-flag for FOR loops =%%\n%
%= =%SET $Q=$_!$C! !$B!%= 'push newly computed value on top of queue =%%\n%
%= =%)ELSE ECHO Missing operand.^>^&2)%= 'otherwise operand not found =%%\n%
%= =%FOR /F "tokens=2*" %%C IN ("!$V!")DO SET $K=%%C^&SET $V=%%C %%D%= 'pop and peek at the value stack =%%\n%
%= =%)ELSE SET "$T=!$T! %%~B")%= 'rebuild remainder of symbol stack =%%\n%
%= =%SET $S=!$T!)%= 'reset stack to remainder of stack =%%\n%
%= =%IF !$O!==2 (FOR /F "tokens=1*" %%C IN ("!$V!")DO SET $V=%%D%= 'if current op is close parenthesis/ternary =%%\n%
%= =%FOR /F "tokens=1*" %%C IN ("!$S!")DO (SET "$S=%%D"%= 'pop both stacks, check for ternary(push new operator onto stacks) or type mismatch(error if found) =%%\n%
%= =%IF "%%C"=="," (IF %%A==":" (SET $S=T !$S!^&SET $V=3 !$V!)ELSE SET $R=^&ECHO Missing ternary close.^>^&2)ELSE IF %%A==":" SET $R=^&ECHO Missing ternary open.^>^&2)%\n%
%= =%)ELSE IF !$O! GTR 0 SET "$S=%%~A !$S!"^&SET $V=!$O! !$V!)%= 'else if current op is not an operand, push to top of stacks =%%\n%
%= =%IF DEFINED $R (SET $S= !$S!%= 'if no errors check for empty stack and single item in operand queue =%%\n%
%= =%IF "!$S: =!" NEQ "" (SET $R=^&ECHO Missing close parenthesis.^>^&2%='if symbol stack is not empty =%%\n%
%= =%)ELSE FOR /F "tokens=1*" %%A IN ("!$Q!")DO (%\n%
%= =%IF "%%~B" NEQ "" SET $R=^&ECHO Missing operator.^>^&2%= 'if more than one item in queue =%%\n%
%= =%SET MM_=!%%~A!)))%= 'set MM_=final value for expression =%%\n%
%= =%IF "!$R!"=="" SET $R=MM_=^&SET MM_=0^&SET $X= 00%= 'if error set ErrLvl=1 and MM_=0 =%%\n%
%= =%FOR /F "tokens=1-3 delims=;" %%A IN (^""!$R!";"!MM_!";"COLOR!$X!"^")DO (ENDLOCAL%= 'exit macro and return values =%%\n%
%= =%FOR %%: IN (%%A)DO SET %%:%= 'process return-variable-queue =%%\n%
%= =%SET MM_=%%~B%= 'set MM_=final value of last expression =%%\n%
%= =%%%~C)%= 'set ERRORLEVEL=0/1 =%%\n%
)ELSE SETLOCAL EnableDelayedExpansion^&SET $P= ;%= [returnVar[+,-,*,/,@,$,|,^,&,<<,>>]= [ ...]] [boolean ?] ['~-]operand1 [+,-,*,/,@,$,<,>,<#,>#,##,<>,<#>,|,^,&,<<,>>,||,|&,&& operand2] [;exp2 [,exp3 [ ...up to ~300 characters]]] =%
:: Parser Variables:
:: $#= 9-digit control numbers used by +-*/ to stack 8-digits per iteration using SET/A
:: $A= operands that have been pulled from the queue for the current operation
:: $B= remainder of the operand queue
:: $C= variable counter for newly-generated operands, as in SET "$_!$C!=new value"
:: $D= variable counter for the currently-captured operands
:: $E= current expression being parsed, padded with "($E+0)" to simplify the parser
:: $K= precedence value of operator on top of stack
:: $N#= value of each currently-captured operand
:: $O= precedence value of current operator
:: $O#= operator symbols numbered by precedence, used to identify the current operator
:: $P= input parameters, replaced with contents of $MM if empty (or only spaces)
:: $Q= current operand queue
:: $R= return variable queue, list of double-quote separated "variable=value" pairs, also used as a flag to halt macro
:: $S= current operator stack, symbols
:: $T= temp variable
:: $V= current operator stack, precedence values
:: $X= exit code, empty=0, 00=1, X=error
:: $Y= binary regression from 4096 to 1 used to find string-length and remove trailing zeros
:: $Z= 4096 zeros used to pad values to equal lengths, needed for compare, add, and subtract
::
:: Math Variables:
:: a= # of iterations to perform in multiplication/powerOf, starting at 0
:: c= column counter used during multiplication, steps by 8
:: d= decimal position for the final return value
:: f= boolean flags, f=logical/relational op is True, f1=Modulo in Division
:: g= exit code for 2nd-tier SETLOCAL, undefined=0, space00=1, X=error
:: h= maximum size of zero-padded values, always a multiple of 8, used to group SET/A operations together (8x fewer iterations)
:: i= powerOf exponent, initialize i=1 to allow multiplication
:: j= # of divisions to perform, based on position of decimal and $MD=maxDecimal to return
:: m#= maximum size of zero-padded values, always a multiple of 8, 1=integer portion, 2=decimal portion
:: n= final value for the current operation
:: n#= zero-padded values for the current operands, decimal removed
:: o#= non-padded values for the current operands, decimal removed
:: o##= non-padded values, 2nd # is 1=integer portion, 2=decimal portion
:: p= current operand symbol, used to select routine
:: q= 3-way compare of absolute values of n1<=>n2, for subtraction and relational
:: s#= size (length) of the current operands
:: s##= size (length), 2nd # is 1=integer portion, 2=decimal portion
:: t= temp variables, t,t1,t2,t3
:: u= operand unaries (only -), u=current result, u#=current operands
:: w= also a temp variable, changed to a single letter to save ~70 characters
:: y= name of user return variable
:: z= $MD+2 adjusted maxDecimal. Used to increase accuracy of truncated decimal operations, better approximates rounding.
::
:mm_help
TITLE Press ENTER to skip...
SET base=1
SET "EKO=<NUL SET/P="
FOR %%# IN ($MD last root guess cnt xx)DO SET %%#=
FOR /F "usebackq tokens=* delims=:" %%# IN ("%~f0")DO IF "%%#"=="" (SET base=)ELSE IF DEFINED base ECHO. %%#
ECHO example: NthRoot convergence (((root-1)*guess)+(base/guess$(root-1)))/root
SET /P "base=enter a base to find the root of (positive decimal): "
IF DEFINED base SET /P "root=enter the NthRoot to find (positive integer): "
IF DEFINED root SET /P "$MD=enter the accuracy (# of decimal places): "
IF DEFINED $MD SET /P "guess=enter your best guess (positive decimal): "
IF NOT DEFINED guess SET $MD=& ECHO. & ECHO okay, maybe try some expressions? max decimal is 8. & GOTO :mm_h2
ECHO. & ECHO Finding %root%th root of %base% to %$MD% decimals starting at %guess%
ECHO guess=(((%root%-1)*%guess%)+(%base%/%guess%$(%root%-1)))/%root%
TITLE Finding %root%th root of %base% to %$MD% decimals starting at %guess%
:mm_h1
SET /A cnt+=1
SET last=%guess%
%EKO%guess#%cnt%=
%MM% "echo1=guess=(((root-1)*guess)+(base/guess$(root-1)))/root,guess<>last"
IF ERRORLEVEL 1 IF %MM_% NEQ 0 ( GOTO :mm_h1 )ELSE ECHO Error : Abort & GOTO :mm_h2
ECHO. & ECHO checking:
%EKO%guess$%root%=
%MM% cnt-=1,echo1=guess$root
ECHO That's %$MD% decimals of accuracy in %cnt% trys.
ECHO.
ECHO now, try some expressions. max decimal is %$MD%.
:mm_h2
TITLE Press ENTER to exit...
SET xx=
SET/P xx=
IF NOT DEFINED xx (IF "!!"=="" ENDLOCAL) & TITLE & EXIT /B 0
%MM% %xx%
IF ERRORLEVEL 1 ( IF %MM_%==0 ( ECHO Error : MM_=%MM_%
)ELSE ECHO True : MM_=%MM_%
)ELSE ECHO False : MM_=%MM_%
GOTO :mm_h2Edit 2018/08/08: I had totally forgotten the no-space method of inserting comments in macros (saw it while poking around the forum) so I've updated the post with a heavily commented/verbosely-cluttered version. No version# change as I only added comments and didn't alter a single character of code. After repeatedly handing it many difficult and increasingly unnecessarily herculean tasks, I currently have it finding the 999,999th root of 999,999 to 32 decimal accuracy starting at 1.005... sure it's been running for nearly 3 days now, but I've no doubt that it'll finally make it! ^_^
Edit 2018/08/09: Cleaned up v0.1 again and re-posted. Changed %# to %= for comments, replaced tabs with %= =%, and removed the DelayedExpansion duality. No code has changed, it just looks different. Also, I chose not to employ DB's fix for the endless-loop effect because I like to know when something's broken, it's better if I actually fix it. ^_^
Incidentally, that 999,999th root is on guess#517 and counting... any day now.
Edit 2018/08/17: I've just posted v0.2 with (hopefully) some improvements (v0.1 can conveniently be found archived on the post below this one). All ops from SET/A are now supported with bitwise ops being passed directly to SET/A which treats values above 2147483647 as 2147483647 and below -2147483648 as -2147483648. Due to the size of the macro, expressions are limited to ~350 characters, so I've also added the ability to save longer expressions to a variable (%$MM%) which can be passed into the macro by invoking it without any parameters. I haven't tested it too extensively, so I'm expecting to correct at least a glitch or two (if not more). Please post if you try it and encounter any issues.
Edir 2018/08/18: Reading through the comments I had forgotten about the endless-loop issue in the demo. I've corrected that by extending the maxDecimal by +2 during process and reducing back down before final truncation (+1 would probably be sufficient, but perhaps +2 will better approximate rounding). I also took the opportunity to minimize the size as much as I could by reducing all possible variables to single characters, added a few comments and posted v0.2a
I find this thread really intriguing. I have read everything here, and I'm struggling to understand basic usage (as if applied to a batch script) and in what cases would this be more practical than set /a?
That doesn't look right 
