summaryrefslogtreecommitdiffstats
path: root/Transcen.scm
blob: 362420ae435c2b6d511729e6698478978dea6d41 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
;; 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, 675 Mass Ave, Cambridge, MA 02139, USA.
;;
;; As a special exception, the Free Software Foundation gives permission
;; for additional uses of the text contained in its release of GUILE.
;;
;; The exception is that, if you link the GUILE 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 GUILE 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 GUILE.  If you copy
;; code from other Free Software Foundation releases into a copy of
;; GUILE, 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 GUILE, 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 (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 ((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))))