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;; Copyright (C) 1992, 1993, 1995, 1997, 2005, 2006 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.
;;;; 2005-05 SRFI-70 extensions.
;;; Author: Aubrey Jaffer
(define compile-allnumbers #t) ;for HOBBIT compiler
;;;; Legacy real function names
(cond
((defined? $exp)
(define real-sqrt $sqrt)
(define real-exp $exp)
(define real-expt $expt)
(define real-ln $log)
(define real-log10 $log10)
(define real-sin $sin)
(define real-cos $cos)
(define real-tan $tan)
(define real-asin $asin)
(define real-acos $acos)
(define real-atan $atan)
(define real-sinh $sinh)
(define real-cosh $cosh)
(define real-tanh $tanh)
(define real-asinh $asinh)
(define real-acosh $acosh)
(define real-atanh $atanh))
(else
(define $sqrt real-sqrt)
(define $exp real-exp)
(define $expt real-expt)
(define $log real-ln)
(define $log10 real-log10)
(define $sin real-sin)
(define $cos real-cos)
(define $tan real-tan)
(define $asin real-asin)
(define $acos real-acos)
(define $atan real-atan)
(define $sinh real-sinh)
(define $cosh real-cosh)
(define $tanh real-tanh)
(define $asinh real-asinh)
(define $acosh real-acosh)
(define $atanh real-atanh)))
(define $pi (* 4 (real-atan 1)))
(define pi $pi)
(define (pi* z) (* $pi z))
(define (pi/ z) (/ $pi z))
;;;; Complex functions
(define (exp z)
(if (real? z) (real-exp z)
(make-polar (real-exp (real-part z)) (imag-part z))))
(define (ln z)
(if (and (real? z) (>= z 0))
(real-ln z)
(make-rectangular (real-ln (magnitude z)) (angle z))))
(define log ln)
(define (sqrt z)
(if (real? z)
(if (negative? z) (make-rectangular 0 (real-sqrt (- z)))
(real-sqrt z))
(make-polar (real-sqrt (magnitude z)) (/ (angle z) 2))))
(define (sinh z)
(if (real? z) (real-sinh z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* (real-sinh x) (real-cos y))
(* (real-cosh x) (real-sin y))))))
(define (cosh z)
(if (real? z) (real-cosh z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* (real-cosh x) (real-cos y))
(* (real-sinh x) (real-sin y))))))
(define (tanh z)
(if (real? z) (real-tanh z)
(let* ((x (* 2 (real-part z)))
(y (* 2 (imag-part z)))
(w (+ (real-cosh x) (real-cos y))))
(make-rectangular (/ (real-sinh x) w) (/ (real-sin y) w)))))
(define (asinh z)
(if (real? z) (real-asinh z)
(log (+ z (sqrt (+ (* z z) 1))))))
(define (acosh z)
(if (and (real? z) (>= z 1))
(real-acosh z)
(log (+ z (sqrt (- (* z z) 1))))))
(define (atanh z)
(if (and (real? z) (> z -1) (< z 1))
(real-atanh z)
(/ (log (/ (+ 1 z) (- 1 z))) 2)))
(define (sin z)
(if (real? z) (real-sin z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* (real-sin x) (real-cosh y))
(* (real-cos x) (real-sinh y))))))
(define (cos z)
(if (real? z) (real-cos z)
(let ((x (real-part z)) (y (imag-part z)))
(make-rectangular (* (real-cos x) (real-cosh y))
(- (* (real-sin x) (real-sinh y)))))))
(define (tan z)
(if (real? z) (real-tan z)
(let* ((x (* 2 (real-part z)))
(y (* 2 (imag-part z)))
(w (+ (real-cos x) (real-cosh y))))
(make-rectangular (/ (real-sin x) w) (/ (real-sinh y) w)))))
(define (asin z)
(if (and (real? z) (>= z -1) (<= z 1))
(real-asin z)
(* -i (asinh (* +i z)))))
(define (acos z)
(if (and (real? z) (>= z -1) (<= z 1))
(real-acos z)
(+ (/ (angle -1) 2) (* +i (asinh (* +i z))))))
(define (atan z . y)
(if (null? y)
(if (real? z)
(real-atan z)
(/ (log (/ (- +i z) (+ +i z))) +2i))
($atan2 z (car y))))
;;;; SRFI-70
(define (expt z1 z2)
(cond ((and (exact? z2) (not (and (zero? z1) (negative? z2))))
(integer-expt z1 z2))
((zero? z2) (+ 1 (* z1 z2)))
((and (real? z2) (real? z1) (positive? z1))
(real-expt z1 z2))
(else
(exp (* (if (zero? z1) (real-part z2) z2) (log z1))))))
(define (quo x1 x2)
(if (and (exact? x1) (exact? x2))
(quotient x1 x2)
(truncate (/ x1 x2))))
(define (rem x1 x2)
(if (and (exact? x1) (exact? x2))
(remainder x1 x2)
(- x1 (* x2 (quo x1 x2)))))
(define (mod x1 x2)
(if (and (exact? x1) (exact? x2))
(modulo x1 x2)
(- x1 (* x2 (floor (/ x1 x2))))))
(define (exact-round x) (inexact->exact (round x)))
(define (exact-floor x) (inexact->exact (floor x)))
(define (exact-ceiling x) (inexact->exact (ceiling x)))
(define (exact-truncate x) (inexact->exact (truncate x)))
(define (infinite? z) (and (= z (* 2 z)) (not (zero? z))))
(define (finite? z) (not (infinite? z)))
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