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Diffstat (limited to 'ocaml-binary-annot/stdlib/complex.ml')
| -rw-r--r-- | ocaml-binary-annot/stdlib/complex.ml | 87 |
1 files changed, 87 insertions, 0 deletions
diff --git a/ocaml-binary-annot/stdlib/complex.ml b/ocaml-binary-annot/stdlib/complex.ml new file mode 100644 index 0000000000..3c28a58b79 --- /dev/null +++ b/ocaml-binary-annot/stdlib/complex.ml @@ -0,0 +1,87 @@ +(***********************************************************************) +(* *) +(* Objective Caml *) +(* *) +(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *) +(* *) +(* Copyright 2002 Institut National de Recherche en Informatique et *) +(* en Automatique. All rights reserved. This file is distributed *) +(* under the terms of the GNU Library General Public License, with *) +(* the special exception on linking described in file ../LICENSE. *) +(* *) +(***********************************************************************) + +(* $Id$ *) + +(* Complex numbers *) + +type t = { re: float; im: float } + +let zero = { re = 0.0; im = 0.0 } +let one = { re = 1.0; im = 0.0 } +let i = { re = 0.0; im = 1.0 } + +let add x y = { re = x.re +. y.re; im = x.im +. y.im } + +let sub x y = { re = x.re -. y.re; im = x.im -. y.im } + +let neg x = { re = -. x.re; im = -. x.im } + +let conj x = { re = x.re; im = -. x.im } + +let mul x y = { re = x.re *. y.re -. x.im *. y.im; + im = x.re *. y.im +. x.im *. y.re } + +let div x y = + if abs_float y.re >= abs_float y.im then + let r = y.im /. y.re in + let d = y.re +. r *. y.im in + { re = (x.re +. r *. x.im) /. d; + im = (x.im -. r *. x.re) /. d } + else + let r = y.re /. y.im in + let d = y.im +. r *. y.re in + { re = (r *. x.re +. x.im) /. d; + im = (r *. x.im -. x.re) /. d } + +let inv x = div one x + +let norm2 x = x.re *. x.re +. x.im *. x.im + +let norm x = + (* Watch out for overflow in computing re^2 + im^2 *) + let r = abs_float x.re and i = abs_float x.im in + if r = 0.0 then i + else if i = 0.0 then r + else if r >= i then + let q = i /. r in r *. sqrt(1.0 +. q *. q) + else + let q = r /. i in i *. sqrt(1.0 +. q *. q) + +let arg x = atan2 x.im x.re + +let polar n a = { re = cos a *. n; im = sin a *. n } + +let sqrt x = + if x.re = 0.0 && x.im = 0.0 then { re = 0.0; im = 0.0 } + else begin + let r = abs_float x.re and i = abs_float x.im in + let w = + if r >= i then begin + let q = i /. r in + sqrt(r) *. sqrt(0.5 *. (1.0 +. sqrt(1.0 +. q *. q))) + end else begin + let q = r /. i in + sqrt(i) *. sqrt(0.5 *. (q +. sqrt(1.0 +. q *. q))) + end in + if x.re >= 0.0 + then { re = w; im = 0.5 *. x.im /. w } + else { re = 0.5 *. i /. w; im = if x.im >= 0.0 then w else -. w } + end + +let exp x = + let e = exp x.re in { re = e *. cos x.im; im = e *. sin x.im } + +let log x = { re = log (norm x); im = atan2 x.im x.re } + +let pow x y = exp (mul y (log x)) |
