module CMath include Math alias exp! exp alias log! log alias log10! log10 alias sqrt! sqrt 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 def exp(z) if z.real? exp!(z) else Complex(exp!(z.real) * cos!(z.imag), exp!(z.real) * sin!(z.imag)) end end def log(*args) z, b = args if z.real? and z >= 0 and (b.nil? or b >= 0) log!(*args) else r, theta = z.polar a = Complex(log!(r.abs), theta) if b a /= log(b) end a end end def log10(z) if z.real? log10!(z) else log(z) / log!(10) end end def sqrt(z) if z.real? if z < 0 Complex(0, sqrt!(-z)) else sqrt!(z) end else if z.imag < 0 sqrt(z.conjugate).conjugate else r = z.abs x = z.real Complex(sqrt!((r + x) / 2), sqrt!((r - x) / 2)) end end end def sin(z) if z.real? sin!(z) else Complex(sin!(z.real) * cosh!(z.imag), cos!(z.real) * sinh!(z.imag)) end end def cos(z) if z.real? cos!(z) else Complex(cos!(z.real) * cosh!(z.imag), -sin!(z.real) * sinh!(z.imag)) end end def tan(z) if z.real? tan!(z) else sin(z)/cos(z) end end def sinh(z) if z.real? sinh!(z) else Complex(sinh!(z.real) * cos!(z.imag), cosh!(z.real) * sin!(z.imag)) end end def cosh(z) if z.real? cosh!(z) else Complex(cosh!(z.real) * cos!(z.imag), sinh!(z.real) * sin!(z.imag)) end end def tanh(z) if z.real? tanh!(z) else sinh(z) / cosh(z) end end def asin(z) if z.real? and z >= -1 and z <= 1 asin!(z) else Complex(0, -1.0) * log(Complex(0, 1.0) * z + sqrt(1.0 - z * z)) end end def acos(z) if z.real? and z >= -1 and z <= 1 acos!(z) else Complex(0, -1.0) * log(z + Complex(0, 1.0) * sqrt(1.0 - z * z)) end end def atan(z) if z.real? atan!(z) else Complex(0, 1.0) * log((Complex(0, 1.0) + z) / (Complex(0, 1.0) - z)) / 2.0 end end def atan2(y,x) if y.real? and x.real? atan2!(y,x) else Complex(0, -1.0) * log((x + Complex(0, 1.0) * y) / sqrt(x * x + y * y)) end end def acosh(z) if z.real? and z >= 1 acosh!(z) else log(z + sqrt(z * z - 1.0)) end end def asinh(z) if z.real? asinh!(z) else log(z + sqrt(1.0 + z * z)) end end def atanh(z) if z.real? and z >= -1 and z <= 1 atanh!(z) else log((1.0 + z) / (1.0 - z)) / 2.0 end end module_function :exp! module_function :exp module_function :log! module_function :log module_function :log10! module_function :log10 module_function :sqrt! module_function :sqrt 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 :log2 module_function :cbrt module_function :frexp module_function :ldexp module_function :hypot module_function :erf module_function :erfc module_function :gamma module_function :lgamma end