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Newton's method on integers, converging when y >= x:
let isqrt n =
if n < 2 then n
else
let x = ref n in
let y = ref ((!x + 1) / 2) in
while !y < !x do
x := !y;
y := (!x + n / !x) / 2
done;
!x
Test cases:
isqrt 144 = 12 (perfect square)
isqrt 200 = 14 (floor of sqrt(200) ~= 14.14)
isqrt 1000000 = 1000
isqrt 2 = 1
sum = 1027
Companion to newton_sqrt.ml (iter 124, float Newton). Tests integer
division semantics from iter 94 and a while-until-convergence loop.
88 baseline programs total.
15 lines
229 B
OCaml
15 lines
229 B
OCaml
let isqrt n =
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if n < 2 then n
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else
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let x = ref n in
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let y = ref ((!x + 1) / 2) in
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while !y < !x do
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x := !y;
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y := (!x + n / !x) / 2
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done;
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!x
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;;
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isqrt 144 + isqrt 200 + isqrt 1000000 + isqrt 2
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