ruby--ruby/lib/mathn.rb

#
#   mathn.rb - 
#   	$Release Version: 0.5 $
#   	$Revision: 1.1.1.1.4.1 $
#   	by Keiju ISHITSUKA(SHL Japan Inc.)
#
# --
#
#   
#

require "cmath.rb"
require "matrix.rb"
require "prime.rb"

unless defined?(Math.exp!)
  Object.instance_eval{remove_const :Math}
  Math = CMath
end

class Object

  def canon
    if Rational === self
      if denominator == 1
	return numerator
      end
    elsif Complex === self
      if Integer === imag && imag == 0
	return real
      end
    end
    self
  end

  private :canon

end

class Numeric

  class << self

    def def_canon(*ids)
      for id in ids
	module_eval <<-"end;"
	  alias_method :__#{id.object_id}__, :#{id.to_s}
	  private :__#{id.object_id}__
	  def #{id.to_s}(*args, &block)
	    __#{id.object_id}__(*args, &block).__send__(:canon)
	  end
	end;
      end
    end

  end

end

class Fixnum
  remove_method :/
  alias / quo

  alias power! **

  def ** (other)
    if self < 0 && other.round != other
      Complex(self, 0.0) ** other
    else
      power!(other)
    end
  end

  def_canon *(instance_methods - Object.methods - [:canon])

end

class Bignum
  remove_method :/
  alias / quo

  alias power! **

  def ** (other)
    if self < 0 && other.round != other
      Complex(self, 0.0) ** other
    else
      power!(other)
    end
  end

  def_canon *(instance_methods - Object.methods - [:canon])

end

alias RationalOrig Rational
private :RationalOrig
def Rational(*args) RationalOrig(*args).__send__(:canon) end

class Rational
  Unify = true

  class << self
    alias convert_orig convert
    private :convert_orig
    def convert(*args) convert_orig(*args).__send__(:canon) end
  end

  def_canon *(instance_methods - Object.methods - [:canon])

  alias power! **

  def ** (other)
    if other.kind_of?(Rational)
      other2 = other
      if self < 0
	return Complex(self, 0.0) ** other
      elsif other == 0
	return Rational(1,1)
      elsif self == 0
	return Rational(0,1)
      elsif self == 1
	return Rational(1,1)
      end
      
      npd = numerator.prime_division
      dpd = denominator.prime_division
      if other < 0
	other = -other
	npd, dpd = dpd, npd
      end
      
      for elm in npd
	elm[1] = elm[1] * other
	if !elm[1].kind_of?(Integer) and elm[1].denominator != 1
         return Float(self) ** other2
	end
	elm[1] = elm[1].to_i
      end
      
      for elm in dpd
	elm[1] = elm[1] * other
	if !elm[1].kind_of?(Integer) and elm[1].denominator != 1
         return Float(self) ** other2
	end
	elm[1] = elm[1].to_i
      end
      
      num = Integer.from_prime_division(npd)
      den = Integer.from_prime_division(dpd)
      
      Rational(num,den)
      
    elsif other.kind_of?(Integer)
      if other > 0
	num = numerator ** other
	den = denominator ** other
      elsif other < 0
	num = denominator ** -other
	den = numerator ** -other
      elsif other == 0
	num = 1
	den = 1
      end
      Rational(num, den)
    elsif other.kind_of?(Float)
      Float(self) ** other
    else
      x , y = other.coerce(self)
      x ** y
    end
  end
end

module Math
  remove_method(:sqrt)
  def sqrt(a)
    if a.kind_of?(Complex)
      abs = sqrt(a.real*a.real + a.imag*a.imag)
#      if not abs.kind_of?(Rational)
#	return a**Rational(1,2)
#      end
      x = sqrt((a.real + abs)/Rational(2))
      y = sqrt((-a.real + abs)/Rational(2))
#      if !(x.kind_of?(Rational) and y.kind_of?(Rational))
#	return a**Rational(1,2)
#      end
      if a.imag >= 0 
	Complex(x, y)
      else
	Complex(x, -y)
      end
    elsif a >= 0
      rsqrt(a)
    else
      Complex(0,rsqrt(-a))
    end
  end
  
  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

  module_function :sqrt
  module_function :rsqrt
end

alias ComplexOrig Complex
private :ComplexOrig
def Complex(*args) ComplexOrig(*args).__send__(:canon) end

class Complex
  Unify = true

  class << self
    alias convert_orig convert
    private :convert_orig
    def convert(*args) convert_orig(*args).__send__(:canon) end
  end

  def_canon *(instance_methods - Object.methods - [:canon])

end

class NilClass

  def to_r() 0 end
  def to_c() 0 end

end

class Integer

  def to_r() self end
  def to_c() self end

end

class Float

  def_canon *(instance_methods - Object.methods - [:canon])

  alias power! **

  def ** (other)
    if self < 0 && other.round != other
      Complex(self, 0.0) ** other
    else
      power!(other)
    end
  end

end