# Board index » delphi » Math formula routine

## Math formula routine

LancePKing <lancepk...@aol.com> wrote in

##### Quote
> Do you know where I could get a *proven* routine to read a mathematical
> equation from a string and return the value?  I will write one - but I'm
> sure someone has already solved this long ago.

Here is a routine (written by a Frank Fetthauer) that I found in a group
some days ago:

FORMULA has to be a string containing the formular. Variables x y and z are
allowed, as well as the operatins below. Example:
sin(x)*cos(x^y)+exp(cos(x))

Useage:

uses EVALCOMP;

var calc:    EVALVEC ; (evalvec is a pointer to an object befined by
evalcomp)
FORMULA: string;

begin

FORMULA:='x+y+z';

new (calc,init(FORMULA)); (Building the evaluation tree)

writeln ( calc^.eval1d(7) )     ; (x=7 y=0 z=0; result:  7)
writeln ( calc^.eval2d(7,8) )   ; (x=7 y=8 z=0; result: 15)
writeln ( calc^.eval3d(7,8,9) ) ; (x=7 y=8 z=9; result: 24)

dispose(calc,done); (destroing the evaluation tree)

end.

Allowed operations:

x <> y ; Logical operations return 1 if true and 0 if false.
x <= y
x >= y
x > y
x < y
x = y
x + y
x - y
x eor y ( exclusive or )
x or y
x * y
x / y
x and y
x mod y
x div y
x ^ y ( power )
x shl y
x shr y
not (x)
sinc (x)
sinh (x)
cosh (x)
tanh (x)
coth (x)
sin (x)
cos (x)
tan (x)
cot (x)
sqrt (x)
sqr (x)
arcsinh (x)
arccosh (x)
arctanh (x)
arccoth (x)
arcsin (x)
arccos (x)
arctan (x)
arccot (x)
heavy (x) ; 1 for positive numbers, 0 else
sgn (x) ; 1 for positive, -1 for negative, 0 for 0
frac (x)
exp (x)
abs (x)
trunc (x)
ln (x)
odd (x)
pred (x)
succ (x)
round (x)
int (x)
fac (x) ; x*(x-1)*(x-2)*...*3*2*1
rnd ; Random number in [0,1]
rnd (x) ; Random number in [0,x]
pi
e

--------------------------------------------------------------------

Und nun der QUELLCODE:

unit evalcomp;

interface

type fun= function(x,y:real):real;
evalvec= ^evalobj;
evalobj= object
f1,f2:evalvec;
f1x,f2y:real;
f3:fun;
function eval:real;
function eval1d(x:real):real;
function eval2d(x,y:real):real;
function eval3d(x,y,z:real):real;
constructor init(st:string);
destructor done;
end;
var  evalx,evaly,evalz:real;

implementation

var analysetmp:fun;

function search (text,code:string; var pos:integer):boolean;
var i,count:integer;
flag:boolean;
newtext:string;
begin
if length(text)<length(code) then begin search:=false; exit; end;
flag:=false;
pos:=length(text)-length(code)+1;
repeat
if code=copy(text,pos,length(code))
then flag:=true
else dec(pos);
if flag
then
begin
count:=0;
for i:= pos+1 to length(text) do
begin
if copy(text,i,1) = '(' then inc(count);
if copy(text,i,1) = ')' then dec(count);
end;
if count<>0
then
begin
dec(pos);
flag:=false;
end;
end;
until (flag=true) or (pos=0);
search:=flag;
end;

function myid(x,y:real):real;
begin
myid:=x;
end;

function myunequal(x,y:real):real;
begin
if x<>y then
myunequal:=1
else
myunequal:=0;
end;

function mylessequal(x,y:real):real;
begin
if x<=y then
mylessequal:=1
else
mylessequal:=0;
end;

function mygreaterequal(x,y:real):real;
begin
if x>=y then
mygreaterequal:=1
else
mygreaterequal:=0;
end;

function mygreater(x,y:real):real;
begin
if x>y then
mygreater:=1
else
mygreater:=0;
end;

function myless(x,y:real):real;
begin
if x<y then
myless:=1
else
myless:=0;
end;

function myequal(x,y:real):real;
begin
if x=y then
myequal:=1
else
myequal:=0;
end;

begin
end;

function mysub(x,y:real):real;
begin
mysub:=x-y;
end;

function myeor(x,y:real):real;
begin
myeor:=trunc(x) xor trunc(y);
end;

function myor(x,y:real):real;
begin
myor:=trunc(x) or trunc(y);
end;

function mymult(x,y:real):real;
begin
mymult:=x*y;
end;

function mydivid(x,y:real):real;
begin
mydivid:=x/y;
end;

function myand(x,y:real):real;
begin
myand:=trunc(x) and trunc(y);
end;

function mymod(x,y:real):real;
begin
mymod:=trunc(x) mod trunc(y);
end;

function mydiv(x,y:real):real;
begin
mydiv:=trunc(x) div trunc(y);
end;

function mypower(x,y:real):real;
begin
if x=0 then
mypower:=0
else
if x>0 then
mypower:=exp(y*ln(x))
else
if trunc(y)<>y  then
begin
writeln (' Fehler in x^y ');
halt;
end
else
if odd(trunc(y))=true then
mypower:=-exp(y*ln(-x))
else
mypower:=exp(y*ln(-x))
end;

function myshl(x,y:real):real;
begin
myshl:=trunc(x) shl trunc(y);
end;

function myshr(x,y:real):real;
begin
myshr:=trunc(x) shr trunc(y);
end;

function mynot(x,y:real):real;
begin
mynot:=not trunc(x);
end;

function mysinc(x,y:real):real;
begin
if x=0 then
mysinc:=1
else
mysinc:=sin(x)/x
end;

function mysinh(x,y:real):real;
begin
mysinh:=0.5*(exp(x)-exp(-x))
end;

function mycosh(x,y:real):real;
begin
mycosh:=0.5*(exp(x)+exp(-x))
end;

function mytanh(x,y:real):real;
begin
mytanh:=mysinh(x,0)/mycosh(x,0)
end;

function mycoth(x,y:real):real;
begin
mycoth:=mycosh(x,0)/mysinh(x,0)
end;

function mysin(x,y:real):real;
begin
mysin:=sin(x)
end;

function mycos(x,y:real):real;
begin
mycos:=cos(x)
end;

function mytan(x,y:real):real;
begin
mytan:=sin(x)/cos(x)
end;

function mycot(x,y:real):real;
begin
mycot:=cos(x)/sin(x)
end;

function mysqrt(x,y:real):real;
begin
mysqrt:=sqrt(x)
end;

function mysqr(x,y:real):real;
begin
mysqr:=sqr(x)
end;

function myarcsinh(x,y:real):real;
begin
myarcsinh:=ln(x+sqrt(sqr(x)+1))
end;

function mysgn(x,y:real):real;
begin
if x=0 then
mysgn:=0
else
mysgn:=x/abs(x)
end;

function myarccosh(x,y:real):real;
begin
myarccosh:=ln(x+mysgn(x,0)*sqrt(sqr(x)-1))
end;

function myarctanh(x,y:real):real;
begin
myarctanh:=ln((1+x)/(1-x))/2
end;

function myarccoth(x,y:real):real;
begin
myarccoth:=ln((1-x)/(1+x))/2
end;

function myarcsin(x,y:real):real;
begin
if x=1 then
myarcsin:=pi/2
else
myarcsin:=arctan(x/sqrt(1-sqr(x)))
end;

function myarccos(x,y:real):real;
begin
myarccos:=pi/2-myarcsin(x,0)
end;

function myarctan(x,y:real):real;
begin
myarctan:=arctan(x);
end;

function myarccot(x,y:real):real;
begin
myarccot:=pi/2-arctan(x)
end;

function myheavy(x,y:real):real;
begin
myheavy:=mygreater(x,0)
end;

function myfrac(x,y:real):real;
begin
myfrac:=frac(x)
end;

function myexp(x,y:real):real;
begin
myexp:=exp(x)
end;

function myabs(x,y:real):real;
begin
myabs:=abs(x)
end;

function mytrunc(x,y:real):real;
begin
mytrunc:=trunc(x)
end;

function myln(x,y:real):real;
begin
myln:=ln(x)
end;

function myodd(x,y:real):real;
begin
if odd(trunc(x)) then
myodd:=1
else
myodd:=0;
end;

function mypred(x,y:real):real;
begin
mypred:=pred(trunc(x));
end;

function mysucc(x,y:real):real;
begin
mysucc:=succ(trunc(x));
end;

function myround(x,y:real):real;
begin
myround:=round(x);
end;

function myint(x,y:real):real;
begin
myint:=int(x);
end;

function myfac(x,y:real):real;
var n : integer;
r : real;
begin
if x<0 then begin writeln(' Fehler in Fakult?t '); halt; end;
if x = 0 then myfac := 1
else
begin
r := 1;
for n := 1 to trunc ( x ) do
r := r * n;
myfac:= r;
end;
end;

function myrnd(x,y:real):real;
begin
myrnd:=random;
end;

function myrandom(x,y:real):real;
begin
myrandom:=random(trunc(x));
end;

function myevalx(x,y:real):real;
begin
myevalx:=evalx;
end;

function myevaly(x,y:real):real;
begin
myevaly:=evaly;
end;

function myevalz(x,y:real):real;
begin
myevalz:=evalz;
end;

procedure analyse (st:string; var st2,st3:string);
label start;
var pos:integer;
value:real;
newterm,term:string;
begin
term:=st;
start:
if term='' then begin analysetmp:=myid; st2:='0'; st3:=''; exit; end;
newterm:='';
for pos:= 1 to length(term) do
if copy(term,pos,1)<>' ' then newterm:=newterm+copy(term,pos,1);
term:=newterm;
if term='' then begin analysetmp:=myid; st2:='0'; st3:=''; exit; end;
val(term,value,pos);
if pos=0 then begin
analysetmp:=myid;
st2:=term;
st3:='';
exit;
end;
if search(term,'<>',pos) then begin
analysetmp:=myunequal;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+2,length(term)-pos-1);
exit;
end;
if search(term,'<=',pos) then begin
analysetmp:=mylessequal;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+2,length(term)-pos-1);
exit;
end;
if search(term,'>=',pos) then begin
analysetmp:=mygreaterequal;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+2,length(term)-pos-1);
exit;
end;
if search(term,'>',pos) then begin
analysetmp:=mygreater;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'<',pos) then begin
analysetmp:=myless;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'=',pos) then begin
analysetmp:=myequal;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'+',pos) then begin
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'-',pos) then begin
analysetmp:=mysub;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'eor',pos) then begin
analysetmp:=myeor;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+3,length(term)-pos-2);
exit;
end;
if search(term,'or',pos) then begin
analysetmp:=myor;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+2,length(term)-pos-1);
exit;
end;
if search(term,'*',pos) then begin
analysetmp:=mymult;
st2:=copy(term,1,pos-1);
st3:=copy(term,pos+1,length(term)-pos);
exit;
end;
if search(term,'/',pos) then begin
analysetmp:=mydivid;
st2:=copy(term,1,pos-1);
...

## Re:Math formula routine

##### Quote
lancepk...@aol.com (LancePKing) wrote:
>Do you know where I could get a *proven* routine to read a mathematical
>equation from a string and return the value?  I will write one - but I'm
>sure someone has already solved this long ago.

There are a couple formula-evaluation components available on the
Delphi Super Page.  IIRC, one of them claims to be 40% faster than
compiled code...