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* lib/cmath.rb: [DOC] Add docs [ci skip][Fix GH-909][Bug #11162]

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Patch provided by @davydovanton

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@50793 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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gogotanaka 2015-06-06 20:35:08 +00:00
parent c19d373750
commit 843019f4a0
1 changed files with 56 additions and 13 deletions
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69
lib/cmath.rb
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@ -1,17 +1,30 @@
##
# = Trigonometric and transcendental functions for complex numbers.
#
# CMath is a library that provides trigonometric and transcendental
# functions for complex numbers.
# 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.
#
# == Usage
#
# To start using this library, simply:
# To start using this library, simply require cmath library:
#
# require "cmath"
#
# Square root of a negative number is a complex number.
# And after call any CMath function. For example:
#
# CMath.sqrt(-9) #=> 0+3.0i
# CMath.sqrt(-9) #=> 0+3.0i
# CMath.exp(0 + 0i) #=> 1.0+0.0i
# CMath.log10(-5.to_c) #=> (0.6989700043360187+1.3643763538418412i)
#
#
# For more information you can see Complec class.
module CMath
@ -44,9 +57,7 @@ module CMath
##
# Math::E raised to the +z+ power
#
# exp(Complex(0,0)) #=> 1.0+0.0i
# exp(Complex(0,PI)) #=> -1.0+1.2246467991473532e-16i
# exp(Complex(0,PI/2.0)) #=> 6.123233995736766e-17+1.0i
# CMath.exp(2i) #=> (-0.4161468365471424+0.9092974268256817i)
def exp(z)
begin
if z.real?
@ -62,10 +73,11 @@ module CMath
end
##
# Returns the natural logarithm of Complex. If a second argument is given,
# Returns the natural logarithm of Complex. If a second argument is given,
# it will be the base of logarithm.
#
# log(Complex(0,0)) #=> -Infinity+0.0i
# 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
@ -80,6 +92,8 @@ module CMath
##
# returns the base 2 logarithm of +z+
#
# CMath.log2(-1) => (0.0+4.532360141827194i)
def log2(z)
begin
if z.real? and z >= 0
@ -94,6 +108,8 @@ module CMath
##
# returns the base 10 logarithm of +z+
#
# CMath.log10(-1) #=> (0.0+1.3643763538418412i)
def log10(z)
begin
if z.real? and z >= 0
@ -108,9 +124,8 @@ module CMath
##
# Returns the non-negative square root of Complex.
# sqrt(-1) #=> 0+1.0i
# sqrt(Complex(-1,0)) #=> 0.0+1.0i
# sqrt(Complex(0,8)) #=> 2.0+2.0i
#
# CMath.sqrt(-1 + 0i) #=> 0.0+1.0i
def sqrt(z)
begin
if z.real?
@ -136,12 +151,16 @@ module CMath
##
# 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?
@ -157,6 +176,8 @@ module CMath
##
# 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?
@ -172,6 +193,8 @@ module CMath
##
# 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?
@ -186,6 +209,8 @@ module CMath
##
# 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?
@ -201,6 +226,8 @@ module CMath
##
# 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?
@ -216,6 +243,8 @@ module CMath
##
# 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?
@ -230,6 +259,8 @@ module CMath
##
# 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
@ -244,6 +275,8 @@ module CMath
##
# 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
@ -258,6 +291,8 @@ module CMath
##
# returns the arc tangent of +z+
#
# CMath.atan(1 + 1i) #=> (1.0172219678978514+0.4023594781085251i)
def atan(z)
begin
if z.real?
@ -273,6 +308,8 @@ module CMath
##
# 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?
@ -287,6 +324,8 @@ module CMath
##
# returns the inverse hyperbolic sine of +z+
#
# CMath.asinh(1 + 1i) #=> (1.0612750619050357+0.6662394324925153i)
def asinh(z)
begin
if z.real?
@ -301,6 +340,8 @@ module CMath
##
# 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
@ -315,6 +356,8 @@ module CMath
##
# 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
@ -388,4 +431,4 @@ module CMath
end
module_function :handle_no_method_error
end
end