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(**************************************************************************)
(* *)
(* OCaml *)
(* *)
(* 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 Lesser General Public License version 2.1, with the *)
(* special exception on linking described in the file LICENSE. *)
(* *)
(**************************************************************************)
(** Complex numbers.
This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type [float]). *)
type t = { re: float; im: float }
(** The type of complex numbers. [re] is the real part and [im] the
imaginary part. *)
val zero: t
(** The complex number [0]. *)
val one: t
(** The complex number [1]. *)
val i: t
(** The complex number [i]. *)
val neg: t -> t
(** Unary negation. *)
val conj: t -> t
(** Conjugate: given the complex [x + i.y], returns [x - i.y]. *)
val add: t -> t -> t
(** Addition *)
val sub: t -> t -> t
(** Subtraction *)
val mul: t -> t -> t
(** Multiplication *)
val inv: t -> t
(** Multiplicative inverse ([1/z]). *)
val div: t -> t -> t
(** Division *)
val sqrt: t -> t
(** Square root. The result [x + i.y] is such that [x > 0] or
[x = 0] and [y >= 0].
This function has a discontinuity along the negative real axis. *)
val norm2: t -> float
(** Norm squared: given [x + i.y], returns [x^2 + y^2]. *)
val norm: t -> float
(** Norm: given [x + i.y], returns [sqrt(x^2 + y^2)]. *)
val arg: t -> float
(** Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from
[-pi] to [pi]. This function has a discontinuity along the
negative real axis. *)
val polar: float -> float -> t
(** [polar norm arg] returns the complex having norm [norm]
and argument [arg]. *)
val exp: t -> t
(** Exponentiation. [exp z] returns [e] to the [z] power. *)
val log: t -> t
(** Natural logarithm (in base [e]). *)
val pow: t -> t -> t
(** Power function. [pow z1 z2] returns [z1] to the [z2] power. *)
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