stdlib/complex.mli

   1 (***********************************************************************)
   2 (*                                                                     *)
   3 (*                           Objective Caml                            *)
   4 (*                                                                     *)
   5 (*            Xavier Leroy, projet Cristal, INRIA Rocquencourt         *)
   6 (*                                                                     *)
   7 (*  Copyright 2002 Institut National de Recherche en Informatique et   *)
   8 (*  en Automatique.  All rights reserved.  This file is distributed    *)
   9 (*  under the terms of the GNU Library General Public License, with    *)
  10 (*  the special exception on linking described in file ../LICENSE.     *)
  11 (*                                                                     *)
  12 (***********************************************************************)
  13
  14 (* $Id$ *)
  15
  16 (** Complex numbers.
  17
  18     This module provides arithmetic operations on complex numbers.
  19     Complex numbers are represented by their real and imaginary parts
  20     (cartesian representation).  Each part is represented by a
  21     double-precision floating-point number (type [float]).   *)
  22
  23 type t = { re: float; im: float }
  24 (** The type of complex numbers.  [re] is the real part and [im] the
  25     imaginary part. *)
  26
  27 val zero: t
  28 (** The complex number [0]. *)
  29
  30 val one: t
  31 (** The complex number [1]. *)
  32
  33 val i: t
  34 (** The complex number [i]. *)
  35
  36 val neg: t -> t
  37 (** Unary negation. *)
  38
  39 val conj: t -> t
  40 (** Conjugate: given the complex [x + i.y], returns [x - i.y]. *)
  41
  42 val add: t -> t -> t
  43 (** Addition *)
  44
  45 val sub: t -> t -> t
  46 (** Subtraction *)
  47
  48 val mul: t -> t -> t
  49 (** Multiplication *)
  50
  51 val inv: t -> t
  52 (** Multiplicative inverse ([1/z]). *)
  53
  54 val div: t -> t -> t
  55 (** Division *)
  56
  57 val sqrt: t -> t
  58 (** Square root.  The result [x + i.y] is such that [x > 0] or
  59     [x = 0] and [y >= 0].
  60     This function has a discontinuity along the negative real axis. *)
  61
  62 val norm2: t -> float
  63 (** Norm squared: given [x + i.y], returns [x^2 + y^2]. *)
  64
  65 val norm: t -> float
  66 (** Norm: given [x + i.y], returns [sqrt(x^2 + y^2)]. *)
  67
  68 val arg: t -> float
  69 (** Argument.  The argument of a complex number is the angle
  70     in the complex plane between the positive real axis and a line
  71     passing through zero and the number.  This angle ranges from
  72     [-pi] to [pi].  This function has a discontinuity along the
  73     negative real axis. *)
  74
  75 val polar: float -> float -> t
  76 (** [polar norm arg] returns the complex having norm [norm]
  77     and argument [arg]. *)
  78
  79 val exp: t -> t
  80 (** Exponentiation.  [exp z] returns [e] to the [z] power. *)
  81
  82 val log: t -> t
  83 (** Natural logarithm (in base [e]). *)
  84
  85 val pow: t -> t -> t
  86 (** Power function.  [pow z1 z2] returns [z1] to the [z2] power. *)