Initial revision

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@2 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

lib/mathn.rb

@@ -0,0 +1,308 @@
+#
+#   mathn.rb - 
+#   	$Release Version: 0.5 $
+#   	$Revision: 1.1 $
+#   	$Date: 1997/07/03 04:43:47 $
+#   	by Keiju ISHITSUKA(SHL Japan Inc.)
+#
+# --
+#
+#   
+#
+
+require "rational.rb"
+require "complex.rb"
+require "matrix.rb"
+
+class Integer
+
+  def gcd2(int)
+    a = self.abs
+    b = int.abs
+    a, b = b, a if a < b
+    
+    pd_a = a.prime_division
+    pd_b = b.prime_division
+    
+    gcd = 1
+    for pair in pd_a
+      as = pd_b.assoc(pair[0])
+      if as
+	gcd *= as[0] ** [as[1], pair[1]].min
+      end
+    end
+    return gcd
+  end
+  
+  def Integer.from_prime_division(pd)
+    value = 1
+    for prime, index in pd
+      value *= prime**index
+    end
+    value
+  end
+  
+  def prime_division
+    ps = Prime.new
+    value = self
+    pv = []
+    for prime in ps
+      count = 0
+      while (value1, mod = value.divmod(prime)
+	     mod) == 0
+	value = value1
+	count += 1
+      end
+      if count != 0
+	pv.push [prime, count]
+      end
+      break if prime * prime  >= value
+    end
+    if value > 1
+      pv.push [value, 1]
+    end
+    return pv
+  end
+end
+  
+class Prime
+  include Enumerable
+
+  def initialize
+    @seed = 1
+    @primes = []
+    @counts = []
+  end
+  
+  def succ
+    i = -1
+    size = @primes.size
+    while i < size
+      if i == -1
+	@seed += 1
+	i += 1
+      else
+	while @seed > @counts[i]
+	  @counts[i] += @primes[i]
+	end
+	if @seed != @counts[i]
+	  i += 1
+	else
+	  i = -1
+	end
+      end
+    end
+    @primes.push @seed
+    @counts.push @seed + @seed
+    return @seed
+  end
+
+  def each
+    loop do
+      yield succ
+    end
+  end
+end
+
+class Fixnum
+  alias divmod! divmod
+  alias / rdiv
+  def divmod(other)
+    a = self.div(other)
+    b = self % other
+    return a,b
+  end
+end
+
+class Bignum
+  alias divmod! divmod
+  alias / rdiv
+end
+
+class Rational
+  Unify = TRUE
+  
+  alias power! **
+
+  def ** (other)
+    if other.kind_of?(Rational)
+      if self < 0
+	return Complex(self, 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) ** other
+	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) ** other
+	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.new!(num, den)
+    elsif other.kind_of?(Float)
+      Float(self) ** other
+    else
+      x , y = other.coerce(self)
+      x ** y
+    end
+  end
+
+  def power2(other)
+    if other.kind_of?(Rational)
+      if self < 0
+	return Complex(self, 0) ** other
+      elsif other == 0
+	return Rational(1,1)
+      elsif self == 0
+	return Rational(0,1)
+      elsif self == 1
+	return Rational(1,1)
+      end
+      
+      dem = nil
+      x = self.denominator.to_f.to_i
+      neard = self.denominator.to_f ** (1.0/other.denominator.to_f)
+      loop do
+	if (neard**other.denominator == self.denominator)
+	  dem = neaed
+	  break
+	end
+      end
+      nearn = self.numerator.to_f ** (1.0/other.denominator.to_f)
+      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.new!(num, den)
+    elsif other.kind_of?(Float)
+      Float(self) ** other
+    else
+      x , y = other.coerce(self)
+      x ** y
+    end
+  end
+end
+
+module Math
+  def sqrt(a)
+    if a.kind_of?(Complex)
+      abs = sqrt(a.real*a.real + a.image*a.image)
+#      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.image >= 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
+
+class Complex
+  Unify = TRUE
+end
+