0001-Update-documentation-for-CMath-library.patch - Ruby master - Ruby Issue Tracking System

Bug #11162 » 0001-Update-documentation-for-CMath-library.patch

davydov_anton (Anton Davydov), 05/19/2015 11:15 PM

 -05-20  Anton Davydov  <antondavydov.o@gmail.com>
     	* lib/cmath.rb: [DOC] update documentation for CMath library
     	[ci skip]
     Mon May 18 15:31:31 2015  Nobuyoshi Nakada  <nobu@ruby-lang.org>
     	* include/ruby/intern.h (rb_f_notimplement): should not respond to

     ##
     # = 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.
+    #
     # == Brief overview of complex numbers
+    #
     # A complex number is a number that can be expressed in the form
     # a + bi, where a and b are real numbers and i is the imaginary unit,
     # that satisfies the equation x**2 = −1, that is, i**2 = −1. In this
     # expression, a is the real part and b is the imaginary part of the
     # complex number.
+    #
     # In ruby, you can create complex object with Complex, ::rect, ::polar
     # or #to_c method.
+    #
     #   Complex(1)             #=> (1+0i)
     #   Complex.polar(2, 3)    #=> (-1.9799849932008908+0.2822400161197344i)
     #   3.to_c                 #=> (3+0i)
+    #
     # == 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.exp(Complex(0,0)) #=> 1.0+0.0i
     #   CMath.log10(-5.to_c)    #=> (0.6989700043360187+1.3643763538418412i)
+    #
     #   CMath.sqrt(-9)  #=> 0+3.0i
     # == References
+    #
     # Kahan, W: Branch cuts for complex elementary functions
     # Solomentsev, E.D. (2001), "Complex number", in Hazewinkel, Michiel,
     # <em>Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
+    #
     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(Complex(0,PI)) #=> -1.0+1.2246467991473532e-16i
       def exp(z)
         begin
           if z.real?
-...
       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(Complex(1,4))     #=> (1.416606672028108+1.3258176636680326i)
       #   CMath.log(Complex(1,4), 10) #=> (0.6152244606891369+0.5757952953408879i)
       def log(z, b=::Math::E)
         begin
           if z.real? && z >= 0 && b >= 0
-...
       ##
       # returns the base 2 logarithm of +z+
+      #
       #   CMath.log2(-1) => (0.0+4.532360141827194i)
       def log2(z)
         begin
           if z.real? and z >= 0
-...
       ##
       # returns the base 10 logarithm of +z+
+      #
       #   CMath.log10(-1) #=> (0.0+1.3643763538418412i)
       def log10(z)
         begin
           if z.real? and z >= 0
-...
       ##
       # 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(Complex(-1,0)) #=> 0.0+1.0i
       def sqrt(z)
         begin
           if z.real?
-...
       ##
       # returns the principal value of the cube root of +z+
+      #
       #   CMath.cbrt(Complex(1,4)) #=> (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(Complex(Math::PI)) #=> (1.2246467991473532e-16-0.0i)
       def sin(z)
         begin
           if z.real?
-...
       ##
       # returns the cosine of +z+, where +z+ is given in radians
+      #
       #   CMath.cos(Complex(Math::PI)) #=> (-1.0-0.0i)
       def cos(z)
         begin
           if z.real?
-...
       ##
       # returns the tangent of +z+, where +z+ is given in radians
+      #
       #   CMath.tan(Complex(Math::PI)) #=> (-1.2246467991473532e-16+0.0i)
       def tan(z)
         begin
           if z.real?
-...
       ##
       # returns the hyperbolic sine of +z+, where +z+ is given in radians
+      #
       #   CMath.sinh(Complex(Math::PI)) #=> (11.548739357257746+0.0i)
       def sinh(z)
         begin
           if z.real?
-...
       ##
       # returns the hyperbolic cosine of +z+, where +z+ is given in radians
+      #
       #   CMath.cosh(Complex(Math::PI)) #=> (11.591953275521519+0.0i)
       def cosh(z)
         begin
           if z.real?
-...
       ##
       # returns the hyperbolic tangent of +z+, where +z+ is given in radians
+      #
       #   CMath.tanh(Complex(Math::PI)) #=> (0.99627207622075+0.0i)
       def tanh(z)
         begin
           if z.real?
-...
       ##
       # returns the arc sine of +z+
+      #
       #   CMath.asin(Complex(Math::PI)) #=> (1.5707963267948966-1.8115262724608532i)
       def asin(z)
         begin
           if z.real? and z >= -1 and z <= 1
-...
       ##
       # returns the arc cosine of +z+
+      #
       #   CMath.acos(Complex(Math::PI)) #=> (0.0+1.8115262724608536i)
       def acos(z)
         begin
           if z.real? and z >= -1 and z <= 1
-...
       ##
       # returns the arc tangent of +z+
+      #
       #   CMath.atan(Complex(Math::PI)) #=> (1.2626272556789118+0.0i)
       def atan(z)
         begin
           if z.real?
-...
       ##
       # returns the arc tangent of +y+ divided by +x+ using the signs of +y+ and
       # +x+ to determine the quadrant
+      #
       #   CMath.atan2(Complex(Math::PI), 0) #=> (1.5707963267948966+0.0i)
       def atan2(y,x)
         begin
           if y.real? and x.real?
-...
       ##
       # returns the inverse hyperbolic sine of +z+
+      #
       #   CMath.asinh(Complex(Math::PI)) #=> (1.8622957433108482+0.0i)
       def asinh(z)
         begin
           if z.real?
-...
       ##
       # returns the inverse hyperbolic cosine of +z+
+      #
       #   CMath.acosh(Complex(Math::PI)) #=> (1.8115262724608532+0.0i)
       def acosh(z)
         begin
           if z.real? and z >= 1
-...
       ##
       # returns the inverse hyperbolic tangent of +z+
+      #
       #   CMath.atanh(Complex(Math::PI)) #=> (0.32976531495669914-1.5707963267948966i)
       def atanh(z)
         begin
           if z.real? and z >= -1 and z <= 1

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Bug #11162 » 0001-Update-documentation-for-CMath-library.patch