Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Difference between revisions

=={{header|Haskell}}==

{{works with|GHC|9.0.2}}

<syntaxhighlight lang="haskell">

-- A continued fraction is represented as a lazy list of Int.

-- We borrow real2cf from

-- https://rosettacode.org/wiki/Continued_fraction/Arithmetic/Construct_from_rational_number#Haskell

-- though here some names in it are changed.

import Data.Ratio ((%))

real2cf frac =

let (quotient, remainder) = properFraction frac

in (quotient : (if remainder == 0

then []

else real2cf (1 / remainder)))

apply_hfunc (a1, a, b1, b) cf =

recurs (a1, a, b1, b, cf)

where recurs (a1, a, b1, b, cf) =

if b1 == 0 && b == 0 then

[]

else if b1 /= 0 && b /= 0 then

let q1 = div a1 b1

q = div a b

in

if q1 == q then

q : recurs (b1, b, a1 - (b1 * q), a - (b * q), cf)

else

recurs (take_term (a1, a, b1, b, cf))

else recurs (take_term (a1, a, b1, b, cf))

where take_term (a1, a, b1, b, cf) =

case cf of

[] -> (a1, a1, b1, b1, cf)

(term : cf1) -> (a + (a1 * term), a1,

b + (b1 * term), b1,

cf1)

cf_13_11 = real2cf (13 % 11)

cf_22_7 = real2cf (22 % 7)

cf_sqrt2 = real2cf (sqrt 2)

cfToString cf =

loop 0 0 "[" cf

where loop i sep s lst =

case lst of

[] -> s ++ "]"

(term : tail) ->

if i == 20

then s ++ ",...]"

else

do loop (i + 1) sep1 s1 tail

where sepStr = case sep of

0 -> ""

1 -> ";"

_ -> ","

sep1 = min (sep + 1) 2

termStr = show term

s1 = s ++ sepStr ++ termStr

show_cf expr cf =

do putStr expr;

putStr " => ";

putStrLn (cfToString cf)

main =

do show_cf "13/11" cf_13_11;

show_cf "22/7" cf_22_7;

show_cf "sqrt(2)" cf_sqrt2;

show_cf "13/11 + 1/2" (apply_hfunc (2, 1, 0, 2) cf_13_11);

show_cf "22/7 + 1/2" (apply_hfunc (2, 1, 0, 2) cf_22_7);

show_cf "(22/7)/4" (apply_hfunc (1, 0, 0, 4) cf_22_7);

show_cf "1/sqrt(2)" (apply_hfunc (0, 1, 1, 0) cf_sqrt2);

show_cf "(2 + sqrt(2))/4" (apply_hfunc (1, 2, 0, 4) cf_sqrt2);

show_cf "(1 + 1/sqrt(2))/2" (apply_hfunc (2, 1, 0, 2) -- cf + 1/2

(apply_hfunc (1, 0, 0, 2) -- cf/2

(apply_hfunc (0, 1, 1, 0) -- 1/cf

cf_sqrt2)))

</syntaxhighlight>

{{out}}

<pre>$ ghc univariate_continued_fraction_task.hs && ./univariate_continued_fraction_task

13/11 => [1;5,2]

22/7 => [3;7]

sqrt(2) => [1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]

13/11 + 1/2 => [1;1,2,7]

22/7 + 1/2 => [3;1,1,1,4]

(22/7)/4 => [0;1,3,1,2]

1/sqrt(2) => [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]

(2 + sqrt(2))/4 => [0;1,5,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,...]

(1 + 1/sqrt(2))/2 => [0;1,5,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,...]</pre>