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;; Copyright (C) 1992, 1993, 1995, 1997 Free Software Foundation, Inc.
;;
;; This program is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 2, or (at your option)
;; any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this software; see the file COPYING. If not, write to
;; the Free Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111, USA.
;;
;; As a special exception, the Free Software Foundation gives permission
;; for additional uses of the text contained in its release of SCM.
;;
;; The exception is that, if you link the SCM library with other files
;; to produce an executable, this does not by itself cause the
;; resulting executable to be covered by the GNU General Public License.
;; Your use of that executable is in no way restricted on account of
;; linking the SCM library code into it.
;;
;; This exception does not however invalidate any other reasons why
;; the executable file might be covered by the GNU General Public License.
;;
;; This exception applies only to the code released by the
;; Free Software Foundation under the name SCM. If you copy
;; code from other Free Software Foundation releases into a copy of
;; SCM, as the General Public License permits, the exception does
;; not apply to the code that you add in this way. To avoid misleading
;; anyone as to the status of such modified files, you must delete
;; this exception notice from them.
;;
;; If you write modifications of your own for SCM, it is your choice
;; whether to permit this exception to apply to your modifications.
;; If you do not wish that, delete this exception notice.
;;;; "Transcen.scm", Complex trancendental functions for SCM.
;;; Author: Jerry D. Hedden.
(define compile-allnumbers #t) ;for HOBBIT compiler
(define $pi (* 4 ($atan 1)))
(define pi $pi)
(define (pi* z) (* $pi z))
(define (pi/ z) (/ $pi z))
(define (exp z)
(if (real? z) ($exp z)
(make-polar ($exp (real-part z)) (imag-part z))))
(define (log z)
(if (and (real? z) (>= z 0))
($log z)
(make-rectangular ($log (magnitude z)) (angle z))))
(define (sqrt z)
(if (real? z)
(if (negative? z) (make-rectangular 0 ($sqrt (- z)))
($sqrt z))
(make-polar ($sqrt (magnitude z)) (/ (angle z) 2))))
(define expt
(let ((integer-expt integer-expt))
(lambda (z1 z2)
(cond ((zero? z1) (if (zero? z2) 1 0))
((exact? z2)
(integer-expt z1 z2))
((and (real? z2) (real? z1) (>= z1 0))
($expt z1 z2))
(else
(exp (* z2 (log z1))))))))
(define (sinh z)
(if (real? z) ($sinh z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* ($sinh x) ($cos y))
(* ($cosh x) ($sin y))))))
(define (cosh z)
(if (real? z) ($cosh z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* ($cosh x) ($cos y))
(* ($sinh x) ($sin y))))))
(define (tanh z)
(if (real? z) ($tanh z)
(let* ((x (* 2 (real-part z)))
(y (* 2 (imag-part z)))
(w (+ ($cosh x) ($cos y))))
(make-rectangular (/ ($sinh x) w) (/ ($sin y) w)))))
(define (asinh z)
(if (real? z) ($asinh z)
(log (+ z (sqrt (+ (* z z) 1))))))
(define (acosh z)
(if (and (real? z) (>= z 1))
($acosh z)
(log (+ z (sqrt (- (* z z) 1))))))
(define (atanh z)
(if (and (real? z) (> z -1) (< z 1))
($atanh z)
(/ (log (/ (+ 1 z) (- 1 z))) 2)))
(define (sin z)
(if (real? z) ($sin z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* ($sin x) ($cosh y))
(* ($cos x) ($sinh y))))))
(define (cos z)
(if (real? z) ($cos z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* ($cos x) ($cosh y))
(- (* ($sin x) ($sinh y)))))))
(define (tan z)
(if (real? z) ($tan z)
(let* ((x (* 2 (real-part z)))
(y (* 2 (imag-part z)))
(w (+ ($cos x) ($cosh y))))
(make-rectangular (/ ($sin x) w) (/ ($sinh y) w)))))
(define (asin z)
(if (and (real? z) (>= z -1) (<= z 1))
($asin z)
(* -i (asinh (* +i z)))))
(define (acos z)
(if (and (real? z) (>= z -1) (<= z 1))
($acos z)
(+ (/ (angle -1) 2) (* +i (asinh (* +i z))))))
(define (atan z . y)
(if (null? y)
(if (real? z) ($atan z)
(/ (log (/ (- +i z) (+ +i z))) +2i))
($atan2 z (car y))))
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