;?add 2010 modified by Tuncay to make it stdlib conform.
;?add Outcommented lines from autoexecution section.
;?add Added the prefix Eval_ to all functions now.
;?add Eval1() becomes Eval_1() and Fib() becomes Eval_Fib().
;?add Originally by Laszlo at http://www.autohotkey.com/forum/viewtopic.php?t=17058
; 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 $6g)
;?out-begin
/*
#SingleInstance Force
#NoEnv
SetBatchLines -1
Process Priority,,High
xe := 2.718281828459045, xpi := 3.141592653589793 ; referenced as "e", "pi"
xinch := 2.54, xfoot := 30.48, xmile := 1.609344 ; [cm], [cm], [Km]
xounce := 0.02841, xpint := 0.5682, xgallon := 4.54609 ; liters
xoz := 28.35, xlb := 453.59237 ; gramms
*/
;?out-end
/* -test cases
MsgBox % Eval("1e1") ; 10
MsgBox % Eval("0x1E") ; 30
MsgBox % Eval("ToBin(35)") ; 100011
MsgBox % Eval("$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]
*/
;?out-begin
/*
^#-:: ; 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
*/
;?out-end
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 . Eval_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 := Eval_1(A_LoopField) ; work on pre-processed sub expressions
; return result of last sub-expression (numeric)
If FORM = b ; convert output to binary
y := W ? Eval_ToBinW(Round(y),W) : Eval_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
}
Eval_1(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% := Eval_1(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 . Eval_@(y2) . y3 ; replace (x) with value of x
Else Break
}
Return Eval_@(x)
}
Eval_@(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 Eval_@(y1) ? Eval_@(y3) : ""
IfEqual y2,:, Return ((y := Eval_@(y1)) = "" ? Eval_@(y3) : y)
StringGetPos i, x, ||, R ; execute rightmost || operator
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) || Eval_@(SubStr(x,3+i))
StringGetPos i, x, &&, R ; execute rightmost && operator
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) && Eval_@(SubStr(x,3+i))
; execute rightmost =, <> operator
RegExMatch(x, "(.*)(?<![\<\>])(\<\>|=)(.*)", y)
IfEqual y2,=, Return Eval_@(y1) = Eval_@(y3)
IfEqual y2,<>, Return Eval_@(y1) <> Eval_@(y3)
; execute rightmost <,>,<=,>= operator
RegExMatch(x, "(.*)(?<![\<\>])(\<=?|\>=?)(?![\<\>])(.*)", y)
IfEqual y2,<, Return Eval_@(y1) < Eval_@(y3)
IfEqual y2,>, Return Eval_@(y1) > Eval_@(y3)
IfEqual y2,<=, Return Eval_@(y1) <= Eval_@(y3)
IfEqual y2,>=, Return Eval_@(y1) >= Eval_@(y3)
; execute rightmost user operator (low precedence)
RegExMatch(x, "i)(.*)«(.*?)»(.*)", y)
If IsFunc(y2)
Return %y2%(Eval_@(y1),Eval_@(y3)) ; predefined relational ops
StringGetPos i, x, |, R ; execute rightmost | operator
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) | Eval_@(SubStr(x,2+i))
StringGetPos i, x, ^, R ; execute rightmost ^ operator
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) ^ Eval_@(SubStr(x,2+i))
StringGetPos i, x, &, R ; execute rightmost & operator
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) & Eval_@(SubStr(x,2+i))
; execute rightmost <<, >> operator
RegExMatch(x, "(.*)(\<\<|\>\>)(.*)", y)
IfEqual y2,<<, Return Eval_@(y1) << Eval_@(y3)
IfEqual y2,>>, Return Eval_@(y1) >> Eval_@(y3)
; execute rightmost +- (not unary) operator
RegExMatch(x, "(.*[^!\~±¬\@\*/\\])(±|¬)(.*)", y) ; lower precedence ops already handled
IfEqual y2,±, Return Eval_@(y1) + Eval_@(y3)
IfEqual y2,¬, Return Eval_@(y1) - Eval_@(y3)
; execute rightmost */% operator
RegExMatch(x, "(.*)(\*|/|\\)(.*)", y)
IfEqual y2,*, Return Eval_@(y1) * Eval_@(y3)
IfEqual y2,/, Return Eval_@(y1) / Eval_@(y3)
IfEqual y2,\, Return Mod(Eval_@(y1),Eval_@(y3))
; execute rightmost power
StringGetPos i, x, @, R
IfGreaterOrEqual i,0, Return Eval_@(SubStr(x,1,i)) ** Eval_@(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 Eval_@(y1 . !y4) ; unary !
IfEqual y2,±,Return Eval_@(y1 . y4) ; unary +
IfEqual y2,¬,Return Eval_@(y1 . -y4) ; unary - (they behave like functions)
IfEqual y2,~,Return Eval_@(y1 . ~y4) ; unary ~
If IsFunc(y3)
Return Eval_@(y1 . %y3%(y4)) ; built-in and predefined functions(y4)
Return Eval_@(y1 . Eval_1(RegExReplace(f%y3%__F, f%y3%__X, y4))) ; LAST: user defined functions
}
Eval_ToBin(n) { ; Binary representation of n. 1st bit is SIGN: -8 -> 1000, -1 -> 1, 0 -> 0, 8 -> 01000
Return n=0||n=-1 ? -n : Eval_ToBin(n>>1) . n&1
}
Eval_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
}
Eval_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))
}
Eval_Sgn(x) {
Return (x>0)-(x<0)
}
Eval_MIN(a,b) {
Return a<b ? a : b
}
Eval_MAX(a,b) {
Return a<b ? b : a
}
Eval_GCD(a,b) { ; Euclidean GCD
Return b=0 ? Abs(a) : Eval_GCD(b, mod(a,b))
}
Eval_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)
}
Eval_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
}
Eval_fac(n) { ; n!
Return n<2 ? 1 : n*Eval_fac(n-1)
}