mirror of
https://github.com/ruby/ruby.git
synced 2022-11-09 12:17:21 -05:00
6ddfcd93fc
custom, single quote is seen as the same as apostrophe in computer typography. [skip ci] git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@51120 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
427 lines
9 KiB
Ruby
427 lines
9 KiB
Ruby
##
|
|
# = 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
|
|
|
|
alias exp! exp
|
|
alias log! log
|
|
alias log2! log2
|
|
alias log10! log10
|
|
alias sqrt! sqrt
|
|
alias cbrt! cbrt
|
|
|
|
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
|
|
|
|
##
|
|
# 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?
|
|
exp!(z)
|
|
else
|
|
ere = exp!(z.real)
|
|
Complex(ere * cos!(z.imag),
|
|
ere * 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
|
|
log!(z, b)
|
|
else
|
|
Complex(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
|
|
log2!(z)
|
|
else
|
|
log(z) / 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
|
|
log10!(z)
|
|
else
|
|
log(z) / 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, sqrt!(-z))
|
|
else
|
|
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(sqrt!((r + x) / 2.0), 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?
|
|
sin!(z)
|
|
else
|
|
Complex(sin!(z.real) * cosh!(z.imag),
|
|
cos!(z.real) * 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?
|
|
cos!(z)
|
|
else
|
|
Complex(cos!(z.real) * cosh!(z.imag),
|
|
-sin!(z.real) * 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?
|
|
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?
|
|
sinh!(z)
|
|
else
|
|
Complex(sinh!(z.real) * cos!(z.imag),
|
|
cosh!(z.real) * 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?
|
|
cosh!(z)
|
|
else
|
|
Complex(cosh!(z.real) * cos!(z.imag),
|
|
sinh!(z.real) * 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?
|
|
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
|
|
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
|
|
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?
|
|
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?
|
|
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?
|
|
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
|
|
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
|
|
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
|