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e48bf65db3
"* lib/cmath.rb: methods which has suffix '!' are now deprecated." It breaks rubyspec: http://rubyci.s3.amazonaws.com/ubuntu1510/ruby-trunk/log/20151106T153002Z.fail.html.gz git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@52471 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
427 lines
9 KiB
Ruby
427 lines
9 KiB
Ruby
##
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# = Trigonometric and transcendental functions for complex numbers.
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#
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# CMath is a library that provides trigonometric and transcendental
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# functions for complex numbers. The functions in this module accept
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# integers, floating-point numbers or complex numbers as arguments.
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#
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# Note that the selection of functions is similar, but not identical,
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# to that in module math. The reason for having two modules is that
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# some users aren't interested in complex numbers, and perhaps don't
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# even know what they are. They would rather have Math.sqrt(-1) raise
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# an exception than return a complex number.
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#
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# For more information you can see Complex class.
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#
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# == Usage
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#
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# To start using this library, simply require cmath library:
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#
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# require "cmath"
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module CMath
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include Math
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alias exp! exp
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alias log! log
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alias log2! log2
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alias log10! log10
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alias sqrt! sqrt
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alias cbrt! cbrt
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alias sin! sin
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alias cos! cos
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alias tan! tan
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alias sinh! sinh
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alias cosh! cosh
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alias tanh! tanh
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alias asin! asin
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alias acos! acos
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alias atan! atan
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alias atan2! atan2
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alias asinh! asinh
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alias acosh! acosh
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alias atanh! atanh
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##
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# Math::E raised to the +z+ power
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#
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# CMath.exp(1.i * Math::PI) #=> (-1.0+1.2246467991473532e-16i)
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def exp(z)
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begin
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if z.real?
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exp!(z)
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else
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ere = exp!(z.real)
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Complex(ere * cos!(z.imag),
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ere * sin!(z.imag))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the natural logarithm of Complex. If a second argument is given,
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# it will be the base of logarithm.
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#
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# CMath.log(1 + 4i) #=> (1.416606672028108+1.3258176636680326i)
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# CMath.log(1 + 4i, 10) #=> (0.6152244606891369+0.5757952953408879i)
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def log(z, b=::Math::E)
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begin
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if z.real? && z >= 0 && b >= 0
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log!(z, b)
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else
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Complex(log!(z.abs), z.arg) / log(b)
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the base 2 logarithm of +z+
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#
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# CMath.log2(-1) => (0.0+4.532360141827194i)
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def log2(z)
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begin
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if z.real? and z >= 0
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log2!(z)
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else
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log(z) / log!(2)
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the base 10 logarithm of +z+
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#
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# CMath.log10(-1) #=> (0.0+1.3643763538418412i)
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def log10(z)
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begin
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if z.real? and z >= 0
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log10!(z)
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else
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log(z) / log!(10)
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the non-negative square root of Complex.
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#
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# CMath.sqrt(-1 + 0i) #=> 0.0+1.0i
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def sqrt(z)
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begin
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if z.real?
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if z < 0
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Complex(0, sqrt!(-z))
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else
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sqrt!(z)
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end
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else
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if z.imag < 0 ||
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(z.imag == 0 && z.imag.to_s[0] == '-')
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sqrt(z.conjugate).conjugate
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else
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r = z.abs
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x = z.real
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Complex(sqrt!((r + x) / 2.0), sqrt!((r - x) / 2.0))
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end
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the principal value of the cube root of +z+
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#
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# CMath.cbrt(1 + 4i) #=> (1.449461632813119+0.6858152562177092i)
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def cbrt(z)
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z ** (1.0/3)
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end
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##
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# Returns the sine of +z+, where +z+ is given in radians
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#
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# CMath.sin(1 + 1i) #=> (1.2984575814159773+0.6349639147847361i)
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def sin(z)
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begin
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if z.real?
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sin!(z)
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else
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Complex(sin!(z.real) * cosh!(z.imag),
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cos!(z.real) * sinh!(z.imag))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the cosine of +z+, where +z+ is given in radians
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#
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# CMath.cos(1 + 1i) #=> (0.8337300251311491-0.9888977057628651i)
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def cos(z)
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begin
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if z.real?
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cos!(z)
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else
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Complex(cos!(z.real) * cosh!(z.imag),
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-sin!(z.real) * sinh!(z.imag))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the tangent of +z+, where +z+ is given in radians
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#
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# CMath.tan(1 + 1i) #=> (0.27175258531951174+1.0839233273386943i)
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def tan(z)
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begin
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if z.real?
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tan!(z)
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else
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sin(z) / cos(z)
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the hyperbolic sine of +z+, where +z+ is given in radians
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#
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# CMath.sinh(1 + 1i) #=> (0.6349639147847361+1.2984575814159773i)
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def sinh(z)
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begin
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if z.real?
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sinh!(z)
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else
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Complex(sinh!(z.real) * cos!(z.imag),
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cosh!(z.real) * sin!(z.imag))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the hyperbolic cosine of +z+, where +z+ is given in radians
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#
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# CMath.cosh(1 + 1i) #=> (0.8337300251311491+0.9888977057628651i)
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def cosh(z)
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begin
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if z.real?
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cosh!(z)
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else
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Complex(cosh!(z.real) * cos!(z.imag),
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sinh!(z.real) * sin!(z.imag))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the hyperbolic tangent of +z+, where +z+ is given in radians
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#
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# CMath.tanh(1 + 1i) #=> (1.0839233273386943+0.27175258531951174i)
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def tanh(z)
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begin
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if z.real?
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tanh!(z)
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else
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sinh(z) / cosh(z)
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the arc sine of +z+
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#
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# CMath.asin(1 + 1i) #=> (0.6662394324925153+1.0612750619050355i)
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def asin(z)
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begin
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if z.real? and z >= -1 and z <= 1
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asin!(z)
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else
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(-1.0).i * log(1.0.i * z + sqrt(1.0 - z * z))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the arc cosine of +z+
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#
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# CMath.acos(1 + 1i) #=> (0.9045568943023813-1.0612750619050357i)
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def acos(z)
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begin
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if z.real? and z >= -1 and z <= 1
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acos!(z)
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else
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(-1.0).i * log(z + 1.0.i * sqrt(1.0 - z * z))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# Returns the arc tangent of +z+
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#
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# CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)
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def atan(z)
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begin
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if z.real?
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atan!(z)
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else
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1.0.i * log((1.0.i + z) / (1.0.i - z)) / 2.0
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# returns the arc tangent of +y+ divided by +x+ using the signs of +y+ and
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# +x+ to determine the quadrant
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#
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# CMath.atan2(1 + 1i, 0) #=> (1.5707963267948966+0.0i)
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def atan2(y,x)
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begin
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if y.real? and x.real?
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atan2!(y,x)
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else
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(-1.0).i * log((x + 1.0.i * y) / sqrt(x * x + y * y))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# returns the inverse hyperbolic sine of +z+
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#
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# CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)
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def asinh(z)
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begin
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if z.real?
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asinh!(z)
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else
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log(z + sqrt(1.0 + z * z))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# returns the inverse hyperbolic cosine of +z+
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#
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# CMath.acosh(1 + 1i) #=> (1.0612750619050357+0.9045568943023813i)
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def acosh(z)
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begin
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if z.real? and z >= 1
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acosh!(z)
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else
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log(z + sqrt(z * z - 1.0))
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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##
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# returns the inverse hyperbolic tangent of +z+
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#
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# CMath.atanh(1 + 1i) #=> (0.4023594781085251+1.0172219678978514i)
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def atanh(z)
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begin
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if z.real? and z >= -1 and z <= 1
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atanh!(z)
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else
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log((1.0 + z) / (1.0 - z)) / 2.0
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end
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rescue NoMethodError
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handle_no_method_error
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end
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end
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module_function :exp!
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module_function :exp
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module_function :log!
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module_function :log
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module_function :log2!
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module_function :log2
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module_function :log10!
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module_function :log10
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module_function :sqrt!
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module_function :sqrt
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module_function :cbrt!
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module_function :cbrt
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module_function :sin!
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module_function :sin
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module_function :cos!
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module_function :cos
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module_function :tan!
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module_function :tan
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module_function :sinh!
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module_function :sinh
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module_function :cosh!
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module_function :cosh
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module_function :tanh!
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module_function :tanh
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module_function :asin!
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module_function :asin
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module_function :acos!
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module_function :acos
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module_function :atan!
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module_function :atan
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module_function :atan2!
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module_function :atan2
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module_function :asinh!
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module_function :asinh
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module_function :acosh!
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module_function :acosh
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module_function :atanh!
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module_function :atanh
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module_function :frexp
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module_function :ldexp
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module_function :hypot
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module_function :erf
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module_function :erfc
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module_function :gamma
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module_function :lgamma
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private
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def handle_no_method_error # :nodoc:
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if $!.name == :real?
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raise TypeError, "Numeric Number required"
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else
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raise
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end
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end
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module_function :handle_no_method_error
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end
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