JezK
Edit File: mathn.rb
# frozen_string_literal: false #-- # $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