# # 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" require "mathn/rational" require "mathn/complex" unless defined?(Math.exp!) Object.instance_eval{remove_const :Math} Math = CMath end class Fixnum remove_method :/ alias / quo alias power! ** unless defined?(0.power!) def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end class Bignum remove_method :/ alias / quo alias power! ** unless defined?(0.power!) def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end class Rational 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.respond_to?(:nan?) and a.nan? a 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 Float alias power! ** def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end