# # mathn.rb - # \$Release Version: 0.5 \$ # \$Revision: 1.1.1.1.4.1 \$ # \$Date: 1998/01/16 12:36:05 \$ # by Keiju ISHITSUKA(SHL Japan Inc.) # # -- # # # require "complex.rb" require "rational.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 alias next succ def each loop do yield succ end end end class Fixnum alias / quo end class Bignum alias / quo end class Rational Unify = true def inspect format "%s/%s", numerator.inspect, denominator.inspect end alias power! ** def ** (other) if other.kind_of?(Rational) if self < 0 return Complex.new!(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