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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 Complex.generic?(z)
exp!(z)
else
Complex(exp!(z.real) * cos!(z.image),
exp!(z.real) * sin!(z.image))
end
end
def log(*args)
z, b = args
if Complex.generic?(z) 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 Complex.generic?(z)
log10!(z)
else
log(z) / log!(10)
end
end
def sqrt(z)
if Complex.generic?(z)
if z >= 0
sqrt!(z)
else
Complex(0,sqrt!(-z))
end
else
if z.image < 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 Complex.generic?(z)
sin!(z)
else
Complex(sin!(z.real) * cosh!(z.image),
cos!(z.real) * sinh!(z.image))
end
end
def cos(z)
if Complex.generic?(z)
cos!(z)
else
Complex(cos!(z.real) * cosh!(z.image),
-sin!(z.real) * sinh!(z.image))
end
end
def tan(z)
if Complex.generic?(z)
tan!(z)
else
sin(z)/cos(z)
end
end
def sinh(z)
if Complex.generic?(z)
sinh!(z)
else
Complex(sinh!(z.real) * cos!(z.image),
cosh!(z.real) * sin!(z.image))
end
end
def cosh(z)
if Complex.generic?(z)
cosh!(z)
else
Complex(cosh!(z.real) * cos!(z.image),
sinh!(z.real) * sin!(z.image))
end
end
def tanh(z)
if Complex.generic?(z)
tanh!(z)
else
sinh(z) / cosh(z)
end
end
def asin(z)
if Complex.generic?(z) and z >= -1 and z <= 1
asin!(z)
else
-1.0.im * log(1.0.im * z + sqrt(1.0 - z * z))
end
end
def acos(z)
if Complex.generic?(z) and z >= -1 and z <= 1
acos!(z)
else
-1.0.im * log(z + 1.0.im * sqrt(1.0 - z * z))
end
end
def atan(z)
if Complex.generic?(z)
atan!(z)
else
1.0.im * log((1.0.im + z) / (1.0.im - z)) / 2.0
end
end
def atan2(y,x)
if Complex.generic?(y) and Complex.generic?(x)
atan2!(y,x)
else
-1.0.im * log((x + 1.0.im * y) / sqrt(x * x + y * y))
end
end
def acosh(z)
if Complex.generic?(z) and z >= 1
acosh!(z)
else
log(z + sqrt(z * z - 1.0))
end
end
def asinh(z)
if Complex.generic?(z)
asinh!(z)
else
log(z + sqrt(1.0 + z * z))
end
end
def atanh(z)
if Complex.generic?(z) 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
end
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