forth (pain)

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jacekpoz 2024-06-23 13:08:18 +02:00
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gnu-smalltalk
zip
julia_19-bin
gforth
];
};
}

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lab5.5/diophantine.fs Normal file
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\ extended gcd algorithm
: extended-gcd ( b a -- y x d )
{: | _b _a :}
over ( b a -- b a b )
0 = if ( b a b -- b a )
swap drop ( b a -- a )
0 swap ( a -- 0 a )
1 swap ( 0 a -- 0 1 a )
else ( b a b -- b a )
dup to _a \ store a for later
swap ( b a -- a b )
dup to _b \ store b for later
swap ( a b -- b a )
over ( b a -- b a b )
mod ( b a b -- b a%b )
swap ( b a%b -- a%b b )
recurse ( a%b b -- y x d )
rot rot ( y x d -- d y x )
over ( d y x -- d y x y )
_a _b / ( d y x y -- d y x y a/b )
* ( d y x y a/b -- d y x [y * [a / b]] = e )
- ( d y x e -- d y [x - e] = f )
swap ( d y f -- d f y )
rot ( d f y -- f y d )
then ;
\ returns -1 if both are equal to 0, 0 otherwise
: check-2-top-0 ( a b -- result )
0 = if 0 = else drop 0 then ;
\ computes the solution of a linear diophantine equation
\ ax + by = c
\ if a solution exists this returns y x -1
\ otherwise 0 0 0
: diophantine ( c b a -- y x result )
{: | _d _c _b _a :}
over over ( c b a -- c b a b a )
check-2-top-0 if ( c b a b a -- c b a )
drop drop drop ( c b a -- )
0 0 0
else ( c b a b a -- c b a )
rot to _c ( c b a -- b a )
over over to _a to _b ( b a -- b a )
extended-gcd ( b a -- y x d ) \ b a extended-gcd
dup to _d ( y x d -- y x d )
_c swap mod ( y x d -- y x c%d )
0 = invert if ( y x c%d -- y x )
drop drop ( y x -- )
0 0 0
else ( y x c%d -- y x )
_c _d / ( y x -- y x [c/d] = e )
dup rot ( y x e -- y e e x )
* ( y e e x -- y e [e*x] = f )
rot rot ( y e f -- f y e )
* ( f y e -- f [y*e] = g )
_b 0 < if -1 * then ( x0 y0 -- x0 -y0 )
swap ( x0 y0 -- y0 x0 )
_a 0 < if -1 * then ( y0 x0 -- y0 -x0 )
-1 ( y0 x0 -- y0 x0 -1 ) \ x = x0; y = y0; result = -1 - true
then
then ;
\ prints and consumes the result of a diophantine equation
\ examples:
\ 0 result = there's no solution
\ -1 result = x = 0 y = 1
: print-diophantine-result ( y x result -- )
invert if ." there's no solution" drop drop else
." x = " . ." ∧ y = " .
then ;
\ prints and consumes the number, adds a space if negative
\ examples:
\ 3: ` 3`
\ -5: `-5`
: print-number ( a -- )
dup 0 < invert if 32 emit else 45 emit -1 * then 48 + emit
;
\ prints and consumes the input of the diophantine equation
\ ax + by = c
: print-diophantine-input ( c b a -- )
print-number ." x + "
print-number ." y = "
print-number
;
\ 3 nested loops in the range [-i, i]
\ diophantine equation results of all those
\ formatted nicely :-)
: diophantine-loop ( i -- )
dup 1 + swap -1 * ( i -- i+1 -i )
cr
over over do
over over do
over over do
i j k print-diophantine-input ." " i j k diophantine print-diophantine-result cr
." ———————————————————————————————————————" cr
loop
loop
loop
drop drop ( i+1 -i -- )
;
\ vim: ft=forth