Math.cmd [/An|/Dn|/Mn|/Rn|/Sn|/Un|/H|/?] In-line_Math_Expression [;...]   v0.2

Full-featured expression parser written in 100% native WinNT batch script.
Supports functions, assignments, numbers to thousands of decimal places,
and provides the following full range of operators in order of precedence:

Highest : $ Exponent : & NthRoot
        : * Multiply : / Divide : @ Modulus
        : + Addition : - Subtraction
        : <=> Raw Compare (returns 1=greater, -1=less, 0=equals)
        : < LessThan : > GreaterThan : <= LessOrEqual : >= GreaterOrEqual
        : ## EqualTo : <> NotEqualTo (comparisons return 1=true, 0=false)
Lowest  : = Equals (assignment)      : ; Expression Separator

Operations are left-to-right, except for '$ &' which are right associative.
'<>^&' must be wrapped in double-quotes. If needed, # can always replace =.

Operands may be digits and/or variables and expressions can be of any size.
Result of the operation is always returned in the user variable {math}.
Up to 32 return variables may be assigned (eg. var1=var2=x*y+(var3=z-1)).

ECHO[n] may be used as a returnVariable to echo result with [n] line feeds.
{math*} and {_math*} are reserved variable names and should not be used.

------  Many standard functions are available for use in expressions  ------

             abs(num) returns the absolute value of num
avg(num1,num2[,numX]) returns the average value of a given list of values
            ceil(num) returns the nearest integer not less than num
       dim(num1,num2) returns the positive difference between num1 and num2
         e(#decimals) returns the constant 'e' to given number of decimals
            fact(num) returns the factorial of int(num)
           floor(num) returns the nearest integer not greater than num
       gcd(num1,num2) returns the greatest common divisor of two values
if(cond,true[,false]) returns {true} if cond <> 0, {false} or 0 if cond = 0
             int(num) returns the nearest integer with magnitude <= num
       lcm(num1,num2) returns the least common multiple of two values
max(num1,num2[,numX]) returns the largest of the given list of values
min(num1,num2[,numX]) returns the smallest of the given list of values
        nth(base,exp) returns the exp-th root of the given base value
        pi(#decimals) returns the constant 'pi' to given number of decimals
        pow(base,exp) returns the given base raised to the power of exp
            sign(num) returns 1 if num > 0, 0 if num = 0, or -1 if num < 0

The left parenthesis is part of the function name, no white-space is allowed.
Functions may have an unlimited number of parameters and are easily mod-able,
simply follow the pattern in the script and add the name to the function list.

-----  If operation is successful the following ErrorLevel is returned  -----
 -1 Negative\LessThan   : 0 Zero\EqualTo\False : 1 Positive\GreaterThan\True

----  If operation is unsuccessful the following ErrorLevel is returned  ----
 2 Non-numeric operand  :  3 Missing operand         : 4 Missing operator
 5 Unsupported operator :  6 Unbalanced parenthesis  : 7 Divide by zero error
 8 Non-integer radical  :  9 Negative root undefined : 10 Function parameter
11 Assignment error     : 12 Negative factorial

---  Environment Variables shown with /Command Switch and Default Values  ---
 _MATH_ABSOLUTE_VALUE /A0 0=respect negative input, 1=all input is positive
    _MATH_MAX_DECIMAL /D9 9=maximum number of decimal places to return
  _MATH_MODULUS_UNARY /M0 0=dividend, 1=divisor, 2=always positive
    _MATH_ROUND_UP_ON /R5 5=round up on this value or greater, 0=truncate
    _MATH_SHOW_RESULT /S0 0=never, 1=if no assignment, 2=expression, 3=both
     _MATH_SHOW_UNARY /U0 0=negative only, 1=both, 2=none (absolute value)

     /?, /H, or a lack of math expression will display this help screen.

If numbers are small enough SET /A is used for fast decimal arithmetic. The 
script keeps track of decimal and unary adding them back to the result, but
when adding 9+, dividing by 9+, subtracting 10+, or multiplying by 10+ digits
batch routines and recursive calls are used, which are exponentially slower.

Examples:
math.cmd /d15 echo = 245850922 / 78256779
Returns '3.141592653589793' in variable {math} + echo to the screen (no LF).

math.cmd result=a1+100/(b1-4)*3
Parses {a1} + ((100 / ({b1} - 4)) * 3) and places answer in {result}.
Variable assignments must always begin a block (eg. after left parenthesis).

math.cmd /d256 /r0 /a1 echo1=answer=myVarName
Returns the absolute value in {myVarName} truncated to 256 decimals using
variable {answer} and echos the value (1 LF). 32 return variables are allowed.

math.cmd "a1=avg(n1,n2,n3,n4); a2=avg(n5,n6,n7,n8); highAvg=if(a1 > a2,a1,a2)"
Returns the average of the two lists in {a1} and {a2} and returns the greater
of the two averages in {highAvg}. Note the quotes are required for '<>^&'.

math.cmd "value1 >= value2" && GOTO :false || GOTO :true
Returns ERRORLEVEL=1 if true, 0 if false. Provides a full range of comparison
operators and can evaluate numbers of virtually any size (large or small).

math.cmd guess = (((root - 1) * guess) + (base / (guess $ (root - 1)))) / root
Computes the {root} of {base} number through convergence starting at {guess}.
Run in a loop, gets more accurate each time. Very slow, start with best guess.

math.cmd v0.2 2017/09/21 written by CirothUngol.
Inspired by Brian Williams' Big Math batch utilities.
http://www.robvanderwoude.com/battech_math.php

v0.2 2017/09/21
     Replaced functions for removing leading and trailing zeros with macros.
     Replaced all error GOTOs and exit GOTOs with macros.
     Added ';' as an expression separator, now supports multiple expressions.
     Changed SHOW_RESULT to display only if no assignment, emulates SET /A.
     Increased number of allowed return variables from 9 to 32.
     Fixed macros to load correctly before or after the SETLOCAL.

v0.1 2017/09/15
     Initial release on DOStips.