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# 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