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authorJari Vetoniemi <jari.vetoniemi@indooratlas.com>2020-03-16 18:49:26 +0900
committerJari Vetoniemi <jari.vetoniemi@indooratlas.com>2020-03-30 00:39:06 +0900
commitfcbf63e62c627deae76c1b8cb8c0876c536ed811 (patch)
tree64cb17de3f41a2b6fef2368028fbd00349946994 /jni/ruby/lib/cmath.rb
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+##
+# = 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.
+#
+# == Usage
+#
+# To start using this library, simply require cmath library:
+#
+# require "cmath"
+#
+# And after call any CMath function. For example:
+#
+# CMath.sqrt(-9) #=> 0+3.0i
+# CMath.exp(0 + 0i) #=> 1.0+0.0i
+# CMath.log10(-5.to_c) #=> (0.6989700043360187+1.3643763538418412i)
+#
+#
+# For more information you can see Complec class.
+
+module CMath
+
+ include Math
+
+ alias exp! exp
+ alias log! log
+ alias log2! log2
+ alias log10! log10
+ alias sqrt! sqrt
+ alias cbrt! cbrt
+
+ alias sin! sin
+ alias cos! cos
+ alias tan! tan
+
+ alias sinh! sinh
+ alias cosh! cosh
+ alias tanh! tanh
+
+ alias asin! asin
+ alias acos! acos
+ alias atan! atan
+ alias atan2! atan2
+
+ alias asinh! asinh
+ alias acosh! acosh
+ alias atanh! atanh
+
+ ##
+ # Math::E raised to the +z+ power
+ #
+ # CMath.exp(2i) #=> (-0.4161468365471424+0.9092974268256817i)
+ def exp(z)
+ begin
+ if z.real?
+ exp!(z)
+ else
+ ere = exp!(z.real)
+ Complex(ere * cos!(z.imag),
+ ere * 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(*args)
+ begin
+ z, b = args
+ unless b.nil? || b.kind_of?(Numeric)
+ raise TypeError, "Numeric Number required"
+ end
+ if z.real? and z >= 0 and (b.nil? or b >= 0)
+ log!(*args)
+ else
+ a = Complex(log!(z.abs), z.arg)
+ if b
+ a /= log(b)
+ end
+ a
+ 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
+ log2!(z)
+ else
+ log(z) / 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
+ log10!(z)
+ else
+ log(z) / 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, sqrt!(-z))
+ else
+ 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(sqrt!((r + x) / 2.0), 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?
+ sin!(z)
+ else
+ Complex(sin!(z.real) * cosh!(z.imag),
+ cos!(z.real) * 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?
+ cos!(z)
+ else
+ Complex(cos!(z.real) * cosh!(z.imag),
+ -sin!(z.real) * 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?
+ 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?
+ sinh!(z)
+ else
+ Complex(sinh!(z.real) * cos!(z.imag),
+ cosh!(z.real) * 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?
+ cosh!(z)
+ else
+ Complex(cosh!(z.real) * cos!(z.imag),
+ sinh!(z.real) * 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?
+ 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
+ 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
+ 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?
+ 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?
+ 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?
+ 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
+ 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
+ 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