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Diffstat (limited to 'lib/cmath.rb')
| -rw-r--r-- | lib/cmath.rb | 435 |
1 files changed, 435 insertions, 0 deletions
diff --git a/lib/cmath.rb b/lib/cmath.rb new file mode 100644 index 0000000000..7dbd65e799 --- /dev/null +++ b/lib/cmath.rb @@ -0,0 +1,435 @@ +# 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 |