Вычислитель математических формул



Плакат: изображена BMW и надпись - наше железо работает хорошо безо всяких Windows...

Вот что я обнаружил несколько дней назад при просмотре зарубежных источников:

FORMULA должна быть стокой, содержащей формулу. Допускаются переменные x, y и z, а также операторы, перечисленные ниже. Пример:


sin(x)*cos(x^y)+exp(cos(x))

Использование:


uses EVALCOMP;
var
calc: EVALVEC; {evalvec - указатель на объект, определяемый evalcomp}
FORMULA: string;
begin
FORMULA := 'x+y+z';
new(calc, init(FORMULA));
(Построение дерева оценки)
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);
(разрушение дерева оценки)
end.

Допустимые операторы:


x <l;> y ; // Логические операторы возвращают 1 в случае истины и 0 если ложь.
x <l;= y
x >= y
x > y
x <l; y
x = y
x + y
x - y
x eor y //( исключающее или )
x or y
x * y
x / y
x and y
x mod y
x div y
x ^ y //( степень )
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 для положительных чисел, 0 для остальных
sgn (x) //; 1 для положительных чисел, -1 для отрицательных и 0 для нуля
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 //; Случайное число в диапазоне [0,1]
rnd (x) //; Случайное число в диапазоне [0,x]
pi
e


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) < l;
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 < l;
> 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;
function myadd(x, y: real): real;
begin
myadd := x + y;
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(' Немогу вычислить 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(' Немогу вычислить факториал ');
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
analysetmp := myadd;
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);
st3 := copy(term, pos + 1, length(term) - pos);
exit;
end;
if search(term, 'and', pos) then
begin
analysetmp := myand;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 3, length(term) - pos - 2);
exit;
end;
if search(term, 'mod', pos) then
begin
analysetmp := mymod;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 3, length(term) - pos - 2);
exit;
end;
if search(term, 'div', pos) then
begin
analysetmp := mydiv;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 3, length(term) - pos - 2);
exit;
end;
if search(term, '^', pos) then
begin
analysetmp := mypower;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 1, length(term) - pos);
exit;
end;
if search(term, 'shl', pos) then
begin
analysetmp := myshl;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 3, length(term) - pos - 2);
exit;
end;
if search(term, 'shr', pos) then
begin
analysetmp := myshr;
st2 := copy(term, 1, pos - 1);
st3 := copy(term, pos + 3, length(term) - pos - 2);
exit;
end;
if copy(term, 1, 1) = '(' then
begin
term := copy(term, 2, length(term) - 2);
goto start;
end;
if copy(term, 1, 3) = 'not' then
begin
analysetmp := mynot;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'sinc' then
begin
analysetmp := mysinc;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'sinh' then
begin
analysetmp := mysinh;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'cosh' then
begin
analysetmp := mycosh;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'tanh' then
begin
analysetmp := mytanh;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'coth' then
begin
analysetmp := mycoth;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'sin' then
begin
analysetmp := mysin;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'cos' then
begin
analysetmp := mycos;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'tan' then
begin
analysetmp := mytan;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'cot' then
begin
analysetmp := mycot;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'sqrt' then
begin
analysetmp := mysqrt;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'sqr' then
begin
analysetmp := mysqr;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 7) = 'arcsinh' then
begin
analysetmp := myarcsinh;
st2 := copy(term, 8, length(term) - 7);
st3 := '';
exit;
end;
if copy(term, 1, 7) = 'arccosh' then
begin
analysetmp := myarccosh;
st2 := copy(term, 8, length(term) - 7);
st3 := '';
exit;
end;
if copy(term, 1, 7) = 'arctanh' then
begin
analysetmp := myarctanh;
st2 := copy(term, 8, length(term) - 7);
st3 := '';
exit;
end;
if copy(term, 1, 7) = 'arccoth' then
begin
analysetmp := myarccoth;
st2 := copy(term, 8, length(term) - 7);
st3 := '';
exit;
end;
if copy(term, 1, 6) = 'arcsin' then
begin
analysetmp := myarcsin;
st2 := copy(term, 7, length(term) - 6);
st3 := '';
exit;
end;
if copy(term, 1, 6) = 'arccos' then
begin
analysetmp := myarccos;
st2 := copy(term, 7, length(term) - 6);
st3 := '';
exit;
end;
if copy(term, 1, 6) = 'arctan' then
begin
analysetmp := myarctan;
st2 := copy(term, 7, length(term) - 6);
st3 := '';
exit;
end;
if copy(term, 1, 6) = 'arccot' then
begin
analysetmp := myarccot;
st2 := copy(term, 7, length(term) - 6);
st3 := '';
exit;
end;
if copy(term, 1, 5) = 'heavy' then
begin
analysetmp := myheavy;
st2 := copy(term, 6, length(term) - 5);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'sgn' then
begin
analysetmp := mysgn;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'frac' then
begin
analysetmp := myfrac;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'exp' then
begin
analysetmp := myexp;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'abs' then
begin
analysetmp := myabs;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 5) = 'trunc' then
begin
analysetmp := mytrunc;
st2 := copy(term, 6, length(term) - 5);
st3 := '';
exit;
end;
if copy(term, 1, 2) = 'ln' then
begin
analysetmp := myln;
st2 := copy(term, 3, length(term) - 2);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'odd' then
begin
analysetmp := myodd;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'pred' then
begin
analysetmp := mypred;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 4) = 'succ' then
begin
analysetmp := mysucc;
st2 := copy(term, 5, length(term) - 4);
st3 := '';
exit;
end;
if copy(term, 1, 5) = 'round' then
begin
analysetmp := myround;
st2 := copy(term, 6, length(term) - 5);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'int' then
begin
analysetmp := myint;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'fac' then
begin
analysetmp := myfac;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if term = 'rnd' then
begin
analysetmp := myrnd;
st2 := '';
st3 := '';
exit;
end;
if copy(term, 1, 3) = 'rnd' then
begin
analysetmp := myrandom;
st2 := copy(term, 4, length(term) - 3);
st3 := '';
exit;
end;
if term = 'x' then
begin
analysetmp := myevalx;
st2 := '';
st3 := '';
exit;
end;
if term = 'y' then
begin
analysetmp := myevaly;
st2 := '';
st3 := '';
exit;
end;
if term = 'z' then
begin
analysetmp := myevalz;
st2 := '';
st3 := '';
exit;
end;
if (term = 'pi') then
begin
analysetmp := myid;
str(pi, st2);
st3 := '';
exit;
end;
if term = 'e' then
begin
analysetmp := myid;
str(exp(1), st2);
sst3 := '';
exit;
end;
writeln(' ВНИМАНИЕ : НЕДЕКОДИРУЕМАЯ ФОРМУЛА ');
analysetmp := myid;
st2 := '';
st3 := '';
end;
function evalobj.eval: real;
var
tmpx, tmpy: real;
begin
if f1 = nil then
tmpx := f1x
else
tmpx := f1^.eval;
if f2 = nil then
tmpy := f2y
else
tmpy := f2^.eval;
eval := f3(tmpx, tmpy);
end;
function evalobj.eval1d(x: real): real;
begin
evalx := x;
evaly := 0;
evalz := 0;
eval1d := eval;
end;
function evalobj.eval2d(x, y: real): real;
begin
evalx := x;
evaly := y;
evalz := 0;
eval2d := eval;
end;
function evalobj.eval3d(x, y, z: real): real;
begin
evalx := x;
evaly := y;
evalz := z;
eval3d := eval;
end;
constructor evalobj.init(st: string);
var
st2, st3: string;
error: integer;
begin
f1 := nil;
f2 := nil;
analyse(st, st2, st3);
f3 := analysetmp;
val(st2, f1x, error);
if st2 = '' then
begin
f1x := 0;
error := 0;
end;
if error <> 0 then
new(f1, init(st2));
val(st3, f2y, error);
if st3 = '' then
begin
f2y := 0;
error := 0;
end;
if error <> 0 then
new(f2, init(st3));
end;
destructor evalobj.done;
begin
if f1 <> nil then
dispose(f1, done);
if f2 <> nil then
dispose(f2, done);
end;
end.


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