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Diffstat (limited to 'ruby_2_2/lib/mathn.rb')
| -rw-r--r-- | ruby_2_2/lib/mathn.rb | 191 |
1 files changed, 191 insertions, 0 deletions
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 |