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;; Generic interfaces for mathematical functions
;; by Konrad Hinsen
;; last updated May 5, 2009
;; Copyright (c) Konrad Hinsen, 2009. All rights reserved. The use
;; and distribution terms for this software are covered by the Eclipse
;; Public License 1.0 (
;; which can be found in the file epl-v10.html at the root of this
;; distribution. By using this software in any fashion, you are
;; agreeing to be bound by the terms of this license. You must not
;; remove this notice, or any other, from this software.
#^{:author "Konrad Hinsen"
:doc "Generic math function interface
This library defines generic versions of common mathematical
functions such as sqrt or sin as multimethods that can be
defined for any type."}
(:use [clojure.contrib.def :only (defmacro-)])
(:require [clojure.contrib.generic.arithmetic :as ga]
[clojure.contrib.generic.comparison :as gc]))
(defmacro- defmathfn-1
(let [java-symbol (symbol "java.lang.Math" (str name))]
(defmulti ~name
~(str "Return the " name " of x.")
{:arglists '([~'x])}
(defmethod ~name java.lang.Number
(~java-symbol ~'x)))))
(defn- two-types [x y] [(type x) (type y)])
(defmacro- defmathfn-2
(let [java-symbol (symbol "java.lang.Math" (str name))]
(defmulti ~name
~(str "Return the " name " of x and y.")
{:arglists '([~'x ~'y])}
(defmethod ~name [java.lang.Number java.lang.Number]
[~'x ~'y]
(~java-symbol ~'x ~'y)))))
; List of math functions taken from
(defmathfn-1 abs)
(defmathfn-1 acos)
(defmathfn-1 asin)
(defmathfn-1 atan)
(defmathfn-2 atan2)
(defmathfn-1 ceil)
(defmathfn-1 cos)
(defmathfn-1 exp)
(defmathfn-1 floor)
(defmathfn-1 log)
(defmathfn-2 pow)
(defmathfn-1 rint)
(defmathfn-1 round)
(defmathfn-1 sin)
(defmathfn-1 sqrt)
(defmathfn-1 tan)
; Sign
(defmulti sgn
"Return the sign of x (-1, 0, or 1)."
{:arglists '([x])}
(defmethod sgn :default
(cond (gc/zero? x) 0
(gc/> x 0) 1
:else -1))
; Conjugation
(defmulti conjugate
"Return the conjugate of x."
{:arglists '([x])}
(defmethod conjugate :default
[x] x)
; Square
(defmulti sqr
"Return the square of x."
{:arglists '([x])}
(defmethod sqr :default
(ga/* x x))
; Approximate equality for use with floating point types
(defn approx=
"Return true if the absolute value of the difference between x and y
is less than eps."
[x y eps]
(gc/< (abs (ga/- x y)) eps))
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