From 1a74fa4b04da04bd2bb33103dd3cf431438df38e Mon Sep 17 00:00:00 2001
From: usa <usa@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Thu, 14 Dec 2017 15:09:35 +0000
Subject: add tag v2_2_9

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/tags/v2_2_9@61257 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 ruby_2_2/lib/mathn.rb | 191 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 191 insertions(+)
 create mode 100644 ruby_2_2/lib/mathn.rb

(limited to 'ruby_2_2/lib/mathn.rb')

diff --git a/ruby_2_2/lib/mathn.rb b/ruby_2_2/lib/mathn.rb
new file mode 100644
index 0000000000..315e5438d7
--- /dev/null
+++ b/ruby_2_2/lib/mathn.rb
@@ -0,0 +1,191 @@
+#--
+# $Release Version: 0.5 $
+# $Revision: 1.1.1.1.4.1 $
+
+##
+# = mathn
+#
+# mathn serves to make mathematical operations more precise in Ruby
+# and to integrate other mathematical standard libraries.
+#
+# Without mathn:
+#
+#   3 / 2 => 1 # Integer
+#
+# With mathn:
+#
+#   3 / 2 => 3/2 # Rational
+#
+# mathn keeps value in exact terms.
+#
+# Without mathn:
+#
+#   20 / 9 * 3 * 14 / 7 * 3 / 2 # => 18
+#
+# With mathn:
+#
+#   20 / 9 * 3 * 14 / 7 * 3 / 2 # => 20
+#
+#
+# When you require 'mathn', the libraries for Prime, CMath, Matrix and Vector
+# are also loaded.
+#
+# == Copyright
+#
+# Author: Keiju ISHITSUKA (SHL Japan Inc.)
+#--
+# class Numeric follows to make this documentation findable in a reasonable
+# location
+
+warn('lib/mathn.rb is deprecated') if $VERBOSE
+
+class Numeric; end
+
+require "cmath.rb"
+require "matrix.rb"
+require "prime.rb"
+
+require "mathn/rational"
+require "mathn/complex"
+
+unless defined?(Math.exp!)
+  Object.instance_eval{remove_const :Math}
+  Math = CMath # :nodoc:
+end
+
+##
+# When mathn is required, Fixnum's division is enhanced to
+# return more precise values from mathematical expressions.
+#
+#   2/3*3  # => 0
+#   require 'mathn'
+#   2/3*3  # => 2
+
+class Fixnum
+  remove_method :/
+
+  ##
+  # +/+ defines the Rational division for Fixnum.
+  #
+  #   1/3  # => (1/3)
+
+  alias / quo
+end
+
+##
+# When mathn is required Bignum's division is enhanced to
+# return more precise values from mathematical expressions.
+#
+#   (2**72) / ((2**70) * 3)  # => 4/3
+
+class Bignum
+  remove_method :/
+
+  ##
+  # +/+ defines the Rational division for Bignum.
+  #
+  #   (2**72) / ((2**70) * 3)  # => 4/3
+
+  alias / quo
+end
+
+##
+# When mathn is required, the Math module changes as follows:
+#
+# Standard Math module behaviour:
+#   Math.sqrt(4/9)     # => 0.0
+#   Math.sqrt(4.0/9.0) # => 0.666666666666667
+#   Math.sqrt(- 4/9)   # => Errno::EDOM: Numerical argument out of domain - sqrt
+#
+# After require 'mathn', this is changed to:
+#
+#   require 'mathn'
+#   Math.sqrt(4/9)      # => 2/3
+#   Math.sqrt(4.0/9.0)  # => 0.666666666666667
+#   Math.sqrt(- 4/9)    # => Complex(0, 2/3)
+
+module Math
+  remove_method(:sqrt)
+
+  ##
+  # Computes the square root of +a+.  It makes use of Complex and
+  # Rational to have no rounding errors if possible.
+  #
+  #   Math.sqrt(4/9)      # => 2/3
+  #   Math.sqrt(- 4/9)    # => Complex(0, 2/3)
+  #   Math.sqrt(4.0/9.0)  # => 0.666666666666667
+
+  def sqrt(a)
+    if a.kind_of?(Complex)
+      abs = sqrt(a.real*a.real + a.imag*a.imag)
+      x = sqrt((a.real + abs)/Rational(2))
+      y = sqrt((-a.real + abs)/Rational(2))
+      if a.imag >= 0
+        Complex(x, y)
+      else
+        Complex(x, -y)
+      end
+    elsif a.respond_to?(:nan?) and a.nan?
+      a
+    elsif a >= 0
+      rsqrt(a)
+    else
+      Complex(0,rsqrt(-a))
+    end
+  end
+
+  ##
+  # Compute square root of a non negative number. This method is
+  # internally used by +Math.sqrt+.
+
+  def rsqrt(a)
+    if a.kind_of?(Float)
+      sqrt!(a)
+    elsif a.kind_of?(Rational)
+      rsqrt(a.numerator)/rsqrt(a.denominator)
+    else
+      src = a
+      max = 2 ** 32
+      byte_a = [src & 0xffffffff]
+      # ruby's bug
+      while (src >= max) and (src >>= 32)
+        byte_a.unshift src & 0xffffffff
+      end
+
+      answer = 0
+      main = 0
+      side = 0
+      for elm in byte_a
+        main = (main << 32) + elm
+        side <<= 16
+        if answer != 0
+          if main * 4  < side * side
+            applo = main.div(side)
+          else
+            applo = ((sqrt!(side * side + 4 * main) - side)/2.0).to_i + 1
+          end
+        else
+          applo = sqrt!(main).to_i + 1
+        end
+
+        while (x = (side + applo) * applo) > main
+          applo -= 1
+        end
+        main -= x
+        answer = (answer << 16) + applo
+        side += applo * 2
+      end
+      if main == 0
+        answer
+      else
+        sqrt!(a)
+      end
+    end
+  end
+
+  class << self
+    remove_method(:sqrt)
+  end
+  module_function :sqrt
+  module_function :rsqrt
+end
-- 
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