blob: 8deb925b26641618ab04122cfa9d4a6f6fa5271a (
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
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
|
;;;; "Transcen.scm", Complex transcendental functions for SCM.
;; 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 Lesser General Public License as
;; published by the Free Software Foundation, either version 3 of the
;; License, 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
;; Lesser General Public License for more details.
;;
;; You should have received a copy of the GNU Lesser General Public
;; License along with this program. If not, see
;; <http://www.gnu.org/licenses/>.
;;; 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)))
(provide 'math-real)
(provide 'srfi-94)
|
