summaryrefslogtreecommitdiff
path: root/lib/cmath.rb
blob: 7dbd65e7995443a2ad8634d29284d23e1ed31c01 (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
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
# frozen_string_literal: true
##
# = Trigonometric and transcendental functions for complex numbers.
#
# CMath is a library that provides trigonometric and transcendental
# functions for complex numbers. The functions in this module accept
# integers, floating-point numbers or complex numbers as arguments.
#
# Note that the selection of functions is similar, but not identical,
# to that in module math. The reason for having two modules is that
# some users aren't interested in complex numbers, and perhaps don't
# even know what they are. They would rather have Math.sqrt(-1) raise
# an exception than return a complex number.
#
# For more information you can see Complex class.
#
# == Usage
#
# To start using this library, simply require cmath library:
#
#   require "cmath"

module CMath

  include Math

  # Backup of Math is needed because mathn.rb replaces Math with CMath.
  RealMath = Math # :nodoc:
  private_constant :RealMath

  %w[
    exp
    log
    log2
    log10
    sqrt
    cbrt
    sin
    cos
    tan
    sinh
    cosh
    tanh
    asin
    acos
    atan
    atan2
    asinh
    acosh
    atanh
  ].each do |meth|
    define_method(meth + '!') do |*args, &block|
      warn("CMath##{meth}! is deprecated; use CMath##{meth} or Math##{meth}", uplevel: 1) if $VERBOSE
      RealMath.send(meth, *args, &block)
    end
  end

  ##
  # Math::E raised to the +z+ power
  #
  #   CMath.exp(1.i * Math::PI) #=> (-1.0+1.2246467991473532e-16i)
  def exp(z)
    begin
      if z.real?
        RealMath.exp(z)
      else
        ere = RealMath.exp(z.real)
        Complex(ere * RealMath.cos(z.imag),
                ere * RealMath.sin(z.imag))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the natural logarithm of Complex. If a second argument is given,
  # it will be the base of logarithm.
  #
  #   CMath.log(1 + 4i)     #=> (1.416606672028108+1.3258176636680326i)
  #   CMath.log(1 + 4i, 10) #=> (0.6152244606891369+0.5757952953408879i)
  def log(z, b=::Math::E)
    begin
      if z.real? && z >= 0 && b >= 0
        RealMath.log(z, b)
      else
        Complex(RealMath.log(z.abs), z.arg) / log(b)
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the base 2 logarithm of +z+
  #
  #   CMath.log2(-1) => (0.0+4.532360141827194i)
  def log2(z)
    begin
      if z.real? and z >= 0
        RealMath.log2(z)
      else
        log(z) / RealMath.log(2)
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the base 10 logarithm of +z+
  #
  #   CMath.log10(-1) #=> (0.0+1.3643763538418412i)
  def log10(z)
    begin
      if z.real? and z >= 0
        RealMath.log10(z)
      else
        log(z) / RealMath.log(10)
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the non-negative square root of Complex.
  #
  #   CMath.sqrt(-1 + 0i) #=> 0.0+1.0i
  def sqrt(z)
    begin
      if z.real?
        if z < 0
          Complex(0, RealMath.sqrt(-z))
        else
          RealMath.sqrt(z)
        end
      else
        if z.imag < 0 ||
            (z.imag == 0 && z.imag.to_s[0] == '-')
          sqrt(z.conjugate).conjugate
        else
          r = z.abs
          x = z.real
          Complex(RealMath.sqrt((r + x) / 2.0), RealMath.sqrt((r - x) / 2.0))
        end
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the principal value of the cube root of +z+
  #
  #   CMath.cbrt(1 + 4i) #=> (1.449461632813119+0.6858152562177092i)
  def cbrt(z)
    z ** (1.0/3)
  end

  ##
  # Returns the sine of +z+, where +z+ is given in radians
  #
  #   CMath.sin(1 + 1i) #=> (1.2984575814159773+0.6349639147847361i)
  def sin(z)
    begin
      if z.real?
        RealMath.sin(z)
      else
        Complex(RealMath.sin(z.real) * RealMath.cosh(z.imag),
                RealMath.cos(z.real) * RealMath.sinh(z.imag))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the cosine of +z+, where +z+ is given in radians
  #
  #   CMath.cos(1 + 1i) #=> (0.8337300251311491-0.9888977057628651i)
  def cos(z)
    begin
      if z.real?
        RealMath.cos(z)
      else
        Complex(RealMath.cos(z.real) * RealMath.cosh(z.imag),
                -RealMath.sin(z.real) * RealMath.sinh(z.imag))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the tangent of +z+, where +z+ is given in radians
  #
  #   CMath.tan(1 + 1i) #=> (0.27175258531951174+1.0839233273386943i)
  def tan(z)
    begin
      if z.real?
        RealMath.tan(z)
      else
        sin(z) / cos(z)
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the hyperbolic sine of +z+, where +z+ is given in radians
  #
  #   CMath.sinh(1 + 1i) #=> (0.6349639147847361+1.2984575814159773i)
  def sinh(z)
    begin
      if z.real?
        RealMath.sinh(z)
      else
        Complex(RealMath.sinh(z.real) * RealMath.cos(z.imag),
                RealMath.cosh(z.real) * RealMath.sin(z.imag))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the hyperbolic cosine of +z+, where +z+ is given in radians
  #
  #   CMath.cosh(1 + 1i) #=> (0.8337300251311491+0.9888977057628651i)
  def cosh(z)
    begin
      if z.real?
        RealMath.cosh(z)
      else
        Complex(RealMath.cosh(z.real) * RealMath.cos(z.imag),
                RealMath.sinh(z.real) * RealMath.sin(z.imag))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the hyperbolic tangent of +z+, where +z+ is given in radians
  #
  #   CMath.tanh(1 + 1i) #=> (1.0839233273386943+0.27175258531951174i)
  def tanh(z)
    begin
      if z.real?
        RealMath.tanh(z)
      else
        sinh(z) / cosh(z)
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the arc sine of +z+
  #
  #   CMath.asin(1 + 1i) #=> (0.6662394324925153+1.0612750619050355i)
  def asin(z)
    begin
      if z.real? and z >= -1 and z <= 1
        RealMath.asin(z)
      else
        (-1.0).i * log(1.0.i * z + sqrt(1.0 - z * z))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the arc cosine of +z+
  #
  #   CMath.acos(1 + 1i) #=> (0.9045568943023813-1.0612750619050357i)
  def acos(z)
    begin
      if z.real? and z >= -1 and z <= 1
        RealMath.acos(z)
      else
        (-1.0).i * log(z + 1.0.i * sqrt(1.0 - z * z))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # Returns the arc tangent of +z+
  #
  #   CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)
  def atan(z)
    begin
      if z.real?
        RealMath.atan(z)
      else
        1.0.i * log((1.0.i + z) / (1.0.i - z)) / 2.0
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # returns the arc tangent of +y+ divided by +x+ using the signs of +y+ and
  # +x+ to determine the quadrant
  #
  #   CMath.atan2(1 + 1i, 0) #=> (1.5707963267948966+0.0i)
  def atan2(y,x)
    begin
      if y.real? and x.real?
        RealMath.atan2(y,x)
      else
        (-1.0).i * log((x + 1.0.i * y) / sqrt(x * x + y * y))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # returns the inverse hyperbolic sine of +z+
  #
  #   CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)
  def asinh(z)
    begin
      if z.real?
        RealMath.asinh(z)
      else
        log(z + sqrt(1.0 + z * z))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # returns the inverse hyperbolic cosine of +z+
  #
  #   CMath.acosh(1 + 1i) #=> (1.0612750619050357+0.9045568943023813i)
  def acosh(z)
    begin
      if z.real? and z >= 1
        RealMath.acosh(z)
      else
        log(z + sqrt(z * z - 1.0))
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  ##
  # returns the inverse hyperbolic tangent of +z+
  #
  #   CMath.atanh(1 + 1i) #=> (0.4023594781085251+1.0172219678978514i)
  def atanh(z)
    begin
      if z.real? and z >= -1 and z <= 1
        RealMath.atanh(z)
      else
        log((1.0 + z) / (1.0 - z)) / 2.0
      end
    rescue NoMethodError
      handle_no_method_error
    end
  end

  module_function :exp!
  module_function :exp
  module_function :log!
  module_function :log
  module_function :log2!
  module_function :log2
  module_function :log10!
  module_function :log10
  module_function :sqrt!
  module_function :sqrt
  module_function :cbrt!
  module_function :cbrt

  module_function :sin!
  module_function :sin
  module_function :cos!
  module_function :cos
  module_function :tan!
  module_function :tan

  module_function :sinh!
  module_function :sinh
  module_function :cosh!
  module_function :cosh
  module_function :tanh!
  module_function :tanh

  module_function :asin!
  module_function :asin
  module_function :acos!
  module_function :acos
  module_function :atan!
  module_function :atan
  module_function :atan2!
  module_function :atan2

  module_function :asinh!
  module_function :asinh
  module_function :acosh!
  module_function :acosh
  module_function :atanh!
  module_function :atanh

  module_function :frexp
  module_function :ldexp
  module_function :hypot
  module_function :erf
  module_function :erfc
  module_function :gamma
  module_function :lgamma

  private
  def handle_no_method_error # :nodoc:
    if $!.name == :real?
      raise TypeError, "Numeric Number required"
    else
      raise
    end
  end
  module_function :handle_no_method_error

end