88 lines
2.9 KiB
OCaml
88 lines
2.9 KiB
OCaml
(**************************************************************************)
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(* *)
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(* OCaml *)
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(* *)
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(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
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(* *)
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(* Copyright 2002 Institut National de Recherche en Informatique et *)
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(* en Automatique. *)
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(* *)
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(* All rights reserved. This file is distributed under the terms of *)
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(* the GNU Lesser General Public License version 2.1, with the *)
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(* special exception on linking described in the file LICENSE. *)
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(* *)
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(**************************************************************************)
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(* Complex numbers *)
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type t = { re: float; im: float }
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let zero = { re = 0.0; im = 0.0 }
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let one = { re = 1.0; im = 0.0 }
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let i = { re = 0.0; im = 1.0 }
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let add x y = { re = x.re +. y.re; im = x.im +. y.im }
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let sub x y = { re = x.re -. y.re; im = x.im -. y.im }
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let neg x = { re = -. x.re; im = -. x.im }
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let conj x = { re = x.re; im = -. x.im }
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let mul x y = { re = x.re *. y.re -. x.im *. y.im;
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im = x.re *. y.im +. x.im *. y.re }
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let div x y =
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if abs_float y.re >= abs_float y.im then
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let r = y.im /. y.re in
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let d = y.re +. r *. y.im in
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{ re = (x.re +. r *. x.im) /. d;
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im = (x.im -. r *. x.re) /. d }
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else
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let r = y.re /. y.im in
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let d = y.im +. r *. y.re in
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{ re = (r *. x.re +. x.im) /. d;
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im = (r *. x.im -. x.re) /. d }
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let inv x = div one x
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let norm2 x = x.re *. x.re +. x.im *. x.im
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let norm x =
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(* Watch out for overflow in computing re^2 + im^2 *)
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let r = abs_float x.re and i = abs_float x.im in
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if r = 0.0 then i
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else if i = 0.0 then r
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else if r >= i then
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let q = i /. r in r *. sqrt(1.0 +. q *. q)
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else
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let q = r /. i in i *. sqrt(1.0 +. q *. q)
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let arg x = atan2 x.im x.re
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let polar n a = { re = cos a *. n; im = sin a *. n }
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let sqrt x =
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if x.re = 0.0 && x.im = 0.0 then { re = 0.0; im = 0.0 }
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else begin
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let r = abs_float x.re and i = abs_float x.im in
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let w =
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if r >= i then begin
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let q = i /. r in
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sqrt(r) *. sqrt(0.5 *. (1.0 +. sqrt(1.0 +. q *. q)))
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end else begin
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let q = r /. i in
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sqrt(i) *. sqrt(0.5 *. (q +. sqrt(1.0 +. q *. q)))
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end in
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if x.re >= 0.0
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then { re = w; im = 0.5 *. x.im /. w }
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else { re = 0.5 *. i /. w; im = if x.im >= 0.0 then w else -. w }
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end
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let exp x =
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let e = exp x.re in { re = e *. cos x.im; im = e *. sin x.im }
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let log x = { re = log (norm x); im = atan2 x.im x.re }
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let pow x y = exp (mul y (log x))
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