Arithmetic/Rational: Difference between revisions

=={{header|Forth}}==

<lang forth>\ Rationals can use any double cell operations: 2!, 2@, 2dup, 2swap, etc.

\ Uses the stack convention of the built-in "*/" for int * frac -> int

: numerator drop ;

: denominator nip ;

: s>rat 1 ; \ integer to rational (n/1)

: rat>s / ; \ integer

: rat>frac mod ; \ fractional part

: rat>float swap s>f s>f f/ ;

: rat. swap 1 .r [char] / emit . ;

\ normalize: factors out gcd and puts sign into numerator

: gcd ( a b -- gcd ) begin ?dup while tuck mod repeat ;

: rat-normalize ( rat -- rat ) 2dup gcd tuck / >r / r> ;

: rat-abs swap abs swap ;

: rat-negate swap negate swap ;

: 1/rat over 0< if negate swap negate else swap then ;

: rat+ ( a b c d -- ad+bc bd )

rot 2dup * >r

rot * >r * r> +

r> rat-normalize ;

: rat- rat-negate rat+ ;

: rat* ( a b c d -- ac bd )

rot * >r * r> rat-normalize ;

: rat/ swap rat* ;

: rat-equal d= ;

: rat-less ( a b c d -- ad<bc )

-rot * >r * r> < ;

: rat-more 2swap rat-less ;

: rat-inc tuck + swap ;

: rat-dec tuck - swap ;</lang>