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Diffstat (limited to 'ruby_2_2/lib/cmath.rb')
| -rw-r--r-- | ruby_2_2/lib/cmath.rb | 442 |
1 files changed, 0 insertions, 442 deletions
diff --git a/ruby_2_2/lib/cmath.rb b/ruby_2_2/lib/cmath.rb deleted file mode 100644 index 4753c47545..0000000000 --- a/ruby_2_2/lib/cmath.rb +++ /dev/null @@ -1,442 +0,0 @@ -## -# = 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. -# -# == Usage -# -# To start using this library, simply require cmath library: -# -# require "cmath" -# -# And after call any CMath function. For example: -# -# 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 - - 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(2i) #=> (-0.4161468365471424+0.9092974268256817i) - 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(*args) - begin - z, b = args - unless b.nil? || b.kind_of?(Numeric) - raise TypeError, "Numeric Number required" - end - if z.real? and z >= 0 and (b.nil? or b >= 0) - log!(*args) - else - a = Complex(log!(z.abs), z.arg) - if b - a /= log(b) - end - a - 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 |