# Re: nth_root of num?

From: Claude Marche (Claude.Marche@lri.fr)
Date: Thu Nov 26 1998 - 17:23:49 MET

From: Claude Marche <Claude.Marche@lri.fr>
Date: Thu, 26 Nov 1998 17:23:49 +0100 (MET)
To: N Hur <mapnh@maths.bath.ac.uk>
Subject: Re: nth_root of num?

>>>>> "Namhyun Hur" == N Hur <mapnh@maths.bath.ac.uk> writes:

Namhyun Hur> Hi,

Namhyun Hur> I am wondering if anyone has a function "nth_root"
Namhyun Hur> for big_int in camllight. As far as I know only
Namhyun Hur> "sqrt_big_int" is provided in the num library. Could
Namhyun Hur> anyone send me the code if it is possible?

Namhyun Hur> Regards,

Namhyun Hur> Namhyun Hur.

I have written one, here is the code. It works with a personal version
of power, where the second argument is an int, not a num.

There is one function that rounds the result to the floor, one to the
ceiling. Of course, it is working only on big_ints, not ratios.

Hope this helps, (Any comments welcome)

```--
| Claude Marchť           | mailto:Claude.Marche@lri.fr |
| LRI - B‚t. 490          | http://www.lri.fr/~marche/  |
| Universitť de Paris-Sud | phoneto: +33 1 69 15 64 85  |
| F-91405 ORSAY Cedex     | faxto: +33 1 69 15 65 86    |
open Num;;
let num_one = Int 1;;
let rec power_num x = function
0 -> num_one
| 1 -> x
| n ->
let y = square_num (power_num x (n/2))
in
if (n mod 2)=0
then y
else mult_num y x
;;
let root_floor n x =
if le_num x num_one
then x
else
let predn = pred n
in
let numpredn = Int predn
and numn = Int n
in
let rec approx y =
let ypnm1 = (power_num y predn)
in
let new_y =
quo_num
(add_num (mult_num numpredn (mult_num y ypnm1)) x)
(mult_num numn ypnm1)
in
if ge_num new_y y
then y
else approx new_y
in
approx x
;;
let root_ceil n x =
succ_num (root_floor n (pred_num x))
;;
```

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