This script gradually grew from twenty lines to over 250 AHK code lines. It might not be the best approach, but each time only a few new lines were added, so it was never feasible to start all over for a more general expression parser.

The main point is not providing a standalone calculator, because there are hundreds of free ones available, but to allow evaluating a math expression typed in an editor or word processor. The compiled script can run in a PC, where AHK is not installed. It is easy to add new functions of one variable. Follow the examples of SGN (the sign of its argument), Fib (the n-th Fibonacci number) and FAC (the factorial). Two argument functions are implemented as operators: "9 gcd 6" is the same as it would be in functional form gcd(9,6), which is 3. "4choose2" = 6, the binomial coefficient. Min and Max can be chained: "-1 min 2 min -5" gives -5; "3 max 5 max 2" = max(3,5,2) = 5. Further operators can be easily added to the script.

User variables can be defined and used. They are kept in memory until the script is reloaded, with values assigned before they are used in expressions, like "a:=1; b:=2; a+b". In later evaluated expressions "a" and "b" still have their last assigned values.

User functions (even recursive ones) can also be defined in expressions:

f(x) := x < 2 ? 1 : x*f(x-1)

Here the formal parameter x is not defined as a variable, it is a placeholder for the value given to the function at a call. The function definition also remains in memory until the script is terminated.

As usage examples, two hotkeys obtain the math text from the current document. Ctrl+Win+- replaces the expression with the result, Ctrl+Win+= appends an "=" and the result. If a (multi-line) expression is selected, it gets evaluated. If there is nothing selected, the script searches for the last back-quote in the current line, and uses the text after it, until the insertion point (caret). For example, after pressing Win+Ctrl+= the text

"The area is `125*32"

becomes

"The area is 125*32 = 4000"

If instead you press Win+Ctrl+- at the the original line above, it becomes

"The area is 4000"

There are many features supported in the expressions:

- They can contain HEX (0x1ff), Decimal (123, 1.23e2) and Binary numbers ('1001, first bit = sign),

- arbitrary number of nested parentheses (..)

- variables (a, b), constants (e, pi, inch, foot, mile, ounce, pint, gallon, oz, lb)

- user defined functions

- ternary- (_? _ : _) and logical operators !; ||; &&

- relational operators =,<>; <,>,<=,>=

- special operators: GCD, MIN, MAX, Choose;

- bitwise operators ~; |; ^; &; <<, >>

- arithmetic operators +, - (or #); *, /, \ (or % = mod); ** (or @ = power);

(They are listed in the order of their precedence, from low to high, except the unary operators !,-, + and ~ are of highest precedence. The operators separated by commas are of equal precedence.)

- Functions Abs,Ceil,Exp,Floor,Log,Ln,Round,Sqrt,Sin,Cos,Tan,ASin,ACos,ATan,SGN,Fib,fac

The output format can also be specified.

- If the expression does not contain the format specifier "$", 6 decimal digits are shown in the general form (%0.6g in C), and integers are in decimal

- With ${k}: k (optional integer) decimal digits are shown after the decimal point, in case of floating point result

- With ${k}e or ${k}g: k decimal digits are shown of floating point results, in exponential or general scientific form, respectively

- With $x or $h: Rounded results are shown Hex

- With $b{W}: Rounded results are shown in binary form (LS W-bits; W="": first bit is sign: "1000" = -8, "0111" = 7)

There are no precision limitations in version 1.1 or later. All intermediate results are computed and stored in full 64-bit accuracy.

The ternary operator "condition ? exp1 : exp2" is implemented as two low precedence operators: "a ? b" (which returns "b" if "a" is true, that is nonempty and nonzero. It evaluates to the empty string if "a" is false, that is empty or 0. The other operator "b : c" returns "c" if "b" is the empty string, otherwise it returns "b". (It can also be used to set default values to uninitialized variables.) This saves time, because only the one of "b" or "c" is computed, which is returned. It also helps avoiding arithmetic errors, like in "x=0 ? 0 : 1/x". Here 1/x is not computed if x=0.

There is, however, a little difference between this implementation and the true ternary operator "a ? b : c". In Monster if "a" is true, "b" is returned by the "?" operator. If it happens to be empty (an error in an arithmetic expression), the following ":" operator does not know if "a" was false or this error occurred, and returns "c", instead of the empty "b". It was easy to change this behavior (e.g. "?" could return a special, non-numeric character when "a" is false and ":" checks for this character), but then we'd loose the "default value" function of the ":" operator "x:0".

Function names are internally enclosed by ' characters, operators are enclosed by « and » characters, to prevent problems when their names happen to be the prefix or postfix of another name (like tan/atan/at).

Please report bugs! Regular expressions are heavily used, and they are notoriously difficult to read (and to get them right).

; MONSTER Version 1.2 to EVALUATE ARITHMETIC EXPRESSIONS in strings (needs AHK 1.0.48+) ; Containing HEX, Signed Binary ('11 = -1, '011 = 3), scientific numbers (1.2e+5) ; Assignments :=, preceding an expression. E.g: a:=1; b:=2; a+b ; User defined functions: f(x) := expr; ; AHK Functions Abs|Ceil|Exp|Floor|Log|Ln|Round|Sqrt|Sin|Cos|Tan|ASin|ACos|ATan ; Predefined functions: SGN|Fib|Fac (sign, Fibonacci numbers, Factorials) ; '(',')'; Variables; Predefined operators GCD,MIN,MAX,Choose (2-parameter functions) ; Predefined constants: e, pi, inch, foot, mile, ounce, pint, gallon, oz, lb; ; Logic operators: !, ||, &&; ternary operator: (_?_:_); ; Relations: =,<>; <,>,<=,>= ; Binary operators: ~; |, ^, &, <<, >> ; Arithmetic operators: +, -; *, /, \ (or % = mod); ** (or @ = power) ; Output FORMAT: $x,$h: Hex; $b{W}: W-bit binary; ; ${k}: k-digit fixpoint, ${k}e,${k}g: k-digit scientific (Default $6g) #SingleInstance Force #NoEnv SetBatchLines -1 Process Priority,,High xe := 2.718281828459045, xpi := 3.141592653589793 ; referenced as "e", "pi" xinch := 2.54, xfoot := 30.48, xmile := 1.609344 ; [cm], [cm], [Km] xounce := 0.02841, xpint := 0.5682, xgallon := 4.54609 ; liters xoz := 28.35, xlb := 453.59237 ; gramms /* -test cases MsgBox % Eval("1e1") ; 10 MsgBox % Eval("0x1E") ; 30 MsgBox % Eval("ToBin(35)") ; 100011 MsgBox % Eval("$b 35") ; 0100011 MsgBox % Eval("'10010") ; -14 MsgBox % Eval("2>3 ? 9 : 7") ; 7 MsgBox % Eval("$2E 1e3 -50.0e+0 + 100.e-1") ; 9.60E+002 MsgBox % Eval("fact(x) := x < 2 ? 1 : x*fact(x-1); fact(5)") ; 120 MsgBox % Eval("f(ab):=sqrt(ab)/ab; y:=f(2); ff(y):=y*(y-1)/2/x; x := 2; y+ff(3)/f(16)") ; 6.70711 MsgBox % Eval("x := qq:1; x := 5*x; y := x+1") ; 6 [if y empty, x := 1...] MsgBox % Eval("x:=-!0; x<0 ? 2*x : sqrt(x)") ; -2 MsgBox % Eval("tan(atan(atan(tan(1))))-exp(sqrt(1))") ; -1.71828 MsgBox % Eval("---2+++9 + ~-2 --1 -2*-3") ; 15 MsgBox % Eval("x1:=1; f1:=sin(x1)/x1; y:=2; f2:=sin(y)/y; f1/f2") ; 1.85082 MsgBox % Eval("Round(fac(10)/fac(5)**2) - (10 choose 5) + Fib(8)") ; 21 MsgBox % Eval("1 min-1 min-2 min 2") ; -2 MsgBox % Eval("(-1>>1<=9 && 3>2)<<2>>1") ; 2 MsgBox % Eval("(1 = 1) + (2<>3 || 2 < 1) + (9>=-1 && 3>2)") ; 3 MsgBox % Eval("$b6 -21/3") ; 111001 MsgBox % Eval("$b ('1001 << 5) | '01000") ; 100101000 MsgBox % Eval("$0 194*lb/1000") ; 88 [Kg] MsgBox % Eval("$x ~0xfffffff0 & 7 | 0x100 << 2") ; 0x407 MsgBox % Eval("- 1 * (+pi -((3%5))) +pi+ 1-2 + e-ROUND(abs(sqrt(floor(2)))**2)-e+pi $9") ; 3.141592654 MsgBox % Eval("(20+4 GCD abs(2**4)) + (9 GCD (6 CHOOSE 2))") ; 11 t := A_TickCount Loop 1000 r := Eval("x:=" A_Index/1000 ";atan(x)-exp(sqrt(x))") ; simulated plot t := A_TickCount - t MsgBox Result = %r%`nTime = %t% ; -1.93288: ~400 ms [on Inspiron 9300] */ ^#-:: ; Replace selection or `expression with result ^#=:: ; Append result to selection or `expression ClipBoard = SendInput ^c ; copy selection ClipWait 0.5 If (ErrorLevel) { SendInput +{HOME}^c ; copy, keep selection to overwrite (^x for some apps) ClipWait 1 IfEqual ErrorLevel,1, Return If RegExMatch(ClipBoard, "(.*)(``)(.*)", y) SendInput % "{RAW}" y1 . (A_ThisHotKey="^#=" ? y3 . " = " : "") . Eval(y3) } Else SendInput % "{RAW}" . (A_ThisHotKey="^#=" ? ClipBoard . " = " : "") . Eval(ClipBoard) Return Eval(x) { ; non-recursive PRE/POST PROCESSING: I/O forms, numbers, ops, ";" Local FORM, FormF, FormI, i, W, y, y1, y2, y3, y4 FormI := A_FormatInteger, FormF := A_FormatFloat SetFormat Integer, D ; decimal intermediate results! RegExMatch(x, "\$(b|h|x|)(\d*[eEgG]?)", y) FORM := y1, W := y2 ; HeX, Bin, .{digits} output format SetFormat FLOAT, 0.16e ; Full intermediate float precision StringReplace x, x, %y% ; remove $.. Loop If RegExMatch(x, "i)(.*)(0x[a-f\d]*)(.*)", y) x := y1 . y2+0 . y3 ; convert hex numbers to decimal Else Break Loop If RegExMatch(x, "(.*)'([01]*)(.*)", y) x := y1 . FromBin(y2) . y3 ; convert binary numbers to decimal: sign = first bit Else Break x := RegExReplace(x,"(^|[^.\d])(\d+)(e|E)","$1$2.$3") ; add missing '.' before E (1e3 -> 1.e3) ; literal scientific numbers between ‘ and ’ chars x := RegExReplace(x,"(\d*\.\d*|\d)([eE][+-]?\d+)","‘$1$2’") StringReplace x, x,`%, \, All ; % -> \ (= MOD) StringReplace x, x, **,@, All ; ** -> @ for easier process StringReplace x, x, +, ±, All ; ± is addition x := RegExReplace(x,"(‘[^’]*)±","$1+") ; ...not inside literal numbers StringReplace x, x, -, ¬, All ; ¬ is subtraction x := RegExReplace(x,"(‘[^’]*)¬","$1-") ; ...not inside literal numbers Loop Parse, x, `; y := Eval1(A_LoopField) ; work on pre-processed sub expressions ; return result of last sub-expression (numeric) If FORM = b ; convert output to binary y := W ? ToBinW(Round(y),W) : ToBin(Round(y)) Else If (FORM="h" or FORM="x") { SetFormat Integer, Hex ; convert output to hex y := Round(y) + 0 } Else { W := W="" ? "0.6g" : "0." . W ; Set output form, Default = 6 decimal places SetFormat FLOAT, %W% y += 0.0 } SetFormat Integer, %FormI% ; restore original formats SetFormat FLOAT, %FormF% Return y } Eval1(x) { ; recursive PREPROCESSING of :=, vars, (..) [decimal, no ";"] Local i, y, y1, y2, y3 ; save function definition: f(x) := expr If RegExMatch(x, "(\S*?)\((.*?)\)\s*:=\s*(.*)", y) { f%y1%__X := y2, f%y1%__F := y3 Return } ; execute leftmost ":=" operator of a := b := ... If RegExMatch(x, "(\S*?)\s*:=\s*(.*)", y) { y := "x" . y1 ; user vars internally start with x to avoid name conflicts Return %y% := Eval1(y2) } ; here: no variable to the left of last ":=" x := RegExReplace(x,"([\)’.\w]\s+|[\)’])([a-z_A-Z]+)","$1«$2»") ; op -> «op» x := RegExReplace(x,"\s+") ; remove spaces, tabs, newlines x := RegExReplace(x,"([a-z_A-Z]\w*)\(","'$1'(") ; func( -> 'func'( to avoid atan|tan conflicts x := RegExReplace(x,"([a-z_A-Z]\w*)([^\w'»’]|$)","%x$1%$2") ; VAR -> %xVAR% x := RegExReplace(x,"(‘[^’]*)%x[eE]%","$1e") ; in numbers %xe% -> e x := RegExReplace(x,"‘|’") ; no more need for number markers Transform x, Deref, %x% ; dereference all right-hand-side %var%-s Loop { ; find last innermost (..) If RegExMatch(x, "(.*)\(([^\(\)]*)\)(.*)", y) x := y1 . [email protected](y2) . y3 ; replace (x) with value of x Else Break } Return [email protected](x) } [email protected](x) { ; EVALUATE PRE-PROCESSED EXPRESSIONS [decimal, NO space, vars, (..), ";", ":="] Local i, y, y1, y2, y3, y4 If x is number ; no more operators left Return x ; execute rightmost ?,: operator RegExMatch(x, "(.*)(\?|:)(.*)", y) IfEqual y2,?, Return [email protected](y1) ? [email protected](y3) : "" IfEqual y2,:, Return ((y := [email protected](y1)) = "" ? [email protected](y3) : y) StringGetPos i, x, ||, R ; execute rightmost || operator IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) || [email protected](SubStr(x,3+i)) StringGetPos i, x, &&, R ; execute rightmost && operator IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) && [email protected](SubStr(x,3+i)) ; execute rightmost =, <> operator RegExMatch(x, "(.*)(?<![\<\>])(\<\>|=)(.*)", y) IfEqual y2,=, Return [email protected](y1) = [email protected](y3) IfEqual y2,<>, Return [email protected](y1) <> [email protected](y3) ; execute rightmost <,>,<=,>= operator RegExMatch(x, "(.*)(?<![\<\>])(\<=?|\>=?)(?![\<\>])(.*)", y) IfEqual y2,<, Return [email protected](y1) < [email protected](y3) IfEqual y2,>, Return [email protected](y1) > [email protected](y3) IfEqual y2,<=, Return [email protected](y1) <= [email protected](y3) IfEqual y2,>=, Return [email protected](y1) >= [email protected](y3) ; execute rightmost user operator (low precedence) RegExMatch(x, "i)(.*)«(.*?)»(.*)", y) If IsFunc(y2) Return %y2%([email protected](y1),[email protected](y3)) ; predefined relational ops StringGetPos i, x, |, R ; execute rightmost | operator IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) | [email protected](SubStr(x,2+i)) StringGetPos i, x, ^, R ; execute rightmost ^ operator IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) ^ [email protected](SubStr(x,2+i)) StringGetPos i, x, &, R ; execute rightmost & operator IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) & [email protected](SubStr(x,2+i)) ; execute rightmost <<, >> operator RegExMatch(x, "(.*)(\<\<|\>\>)(.*)", y) IfEqual y2,<<, Return [email protected](y1) << [email protected](y3) IfEqual y2,>>, Return [email protected](y1) >> [email protected](y3) ; execute rightmost +- (not unary) operator RegExMatch(x, "(.*[^!\~±¬\@\*/\\])(±|¬)(.*)", y) ; lower precedence ops already handled IfEqual y2,±, Return [email protected](y1) + [email protected](y3) IfEqual y2,¬, Return [email protected](y1) - [email protected](y3) ; execute rightmost */% operator RegExMatch(x, "(.*)(\*|/|\\)(.*)", y) IfEqual y2,*, Return [email protected](y1) * [email protected](y3) IfEqual y2,/, Return [email protected](y1) / [email protected](y3) IfEqual y2,\, Return Mod([email protected](y1),[email protected](y3)) ; execute rightmost power StringGetPos i, x, @, R IfGreaterOrEqual i,0, Return [email protected](SubStr(x,1,i)) ** [email protected](SubStr(x,2+i)) ; execute rightmost function, unary operator If !RegExMatch(x,"(.*)(!|±|¬|~|'(.*)')(.*)", y) Return x ; no more function (y1 <> "" only at multiple unaries: --+-) IfEqual y2,!,Return [email protected](y1 . !y4) ; unary ! IfEqual y2,±,Return [email protected](y1 . y4) ; unary + IfEqual y2,¬,Return [email protected](y1 . -y4) ; unary - (they behave like functions) IfEqual y2,~,Return [email protected](y1 . ~y4) ; unary ~ If IsFunc(y3) Return [email protected](y1 . %y3%(y4)) ; built-in and predefined functions(y4) Return [email protected](y1 . Eval1(RegExReplace(f%y3%__F, f%y3%__X, y4))) ; LAST: user defined functions } ToBin(n) { ; Binary representation of n. 1st bit is SIGN: -8 -> 1000, -1 -> 1, 0 -> 0, 8 -> 01000 Return n=0||n=-1 ? -n : ToBin(n>>1) . n&1 } ToBinW(n,W=8) { ; LS W-bits of Binary representation of n Loop %W% ; Recursive (slower): Return W=1 ? n&1 : ToBinW(n>>1,W-1) . n&1 b := n&1 . b, n >>= 1 Return b } FromBin(bits) { ; Number converted from the binary "bits" string, 1st bit is SIGN n = 0 Loop Parse, bits n += n + A_LoopField Return n - (SubStr(bits,1,1)<<StrLen(bits)) } Sgn(x) { Return (x>0)-(x<0) } MIN(a,b) { Return a<b ? a : b } MAX(a,b) { Return a<b ? b : a } GCD(a,b) { ; Euclidean GCD Return b=0 ? Abs(a) : GCD(b, mod(a,b)) } Choose(n,k) { ; Binomial coefficient p := 1, i := 0, k := k < n-k ? k : n-k Loop %k% ; Recursive (slower): Return k = 0 ? 1 : Choose(n-1,k-1)*n//k p *= (n-i)/(k-i), i+=1 ; FOR INTEGERS: p *= n-i, p //= ++i Return Round(p) } Fib(n) { ; n-th Fibonacci number (n < 0 OK, iterative to avoid globals) a := 0, b := 1 Loop % abs(n)-1 c := b, b += a, a := c Return n=0 ? 0 : n>0 || n&1 ? b : -b } fac(n) { ; n! Return n<2 ? 1 : n*fac(n-1) }Edit 20070228: Removed restrictions on user variable names, documented forbidden consecutive operators

Edit 20070301: Version 0.3 handles unary operators after others, like 2*-3.

Edit 20070302: Version 0.4 - minor speedup and fixed ATan, ASin, ACos.

Edit 20070302: Version 0.5 - further speedup, unary "!" and the ternary "? :" implemented, internal function renaming.

Edit 20070304: Version 0.6 - restores original number formats, to help using Monster in other scripts; removed work around fixed AHK bugs

Edit 20070309: Version 0.7 - scientific constants (1.2e+5), minor simplifications, negative Fibonacci, • -> '

Edit 20070309: Version 0.8 - $b{W}: Width of binary output is supported; Rounded results at binary and hex output

Edit 20070314: Version 1.0 - User defined functions; removed [..] around operators

Edit 20070425: Version 1.1 - Full 64-bit internal precision, scientific output format with $6E, $9g type directives

Edit 20080524: Bugfix. Order of converting hex to decimal and adding missing decimal point to scientific numbers is swapped (Thanks Rajat)

Edit 20100511: gallon is now US, not imperial (thanks flyingDman)

Edit 20100818: Version 1.2 - use dynamic function calls to shorten code, make adding predefined functions easier