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