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Editing: mathn.rb
#-- # $Release Version: 0.5 $ # $Revision: 1.1.1.1.4.1 $ ## # = mathn # # mathn is a library for changing the way Ruby does math. If you need # more precise rounding with multiple division or exponentiation # operations, then mathn is the right tool. # # Without mathn: # # 3 / 2 => 1 # Integer # # With mathn: # # 3 / 2 => 3/2 # Rational # # mathn features late rounding and lacks truncation of intermediate results: # # 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 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 and exponentiation are 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 alias power! ** unless method_defined? :power! ## # Exponentiate by +other+ def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end ## # When mathn is required Bignum's division and exponentiation are enhanced to # return more precise values from mathematical expressions. class Bignum remove_method :/ ## # +/+ defines the Rational division for Bignum. # # (2**72) / ((2**70) * 3) # => 4/3 alias / quo alias power! ** unless method_defined? :power! ## # Exponentiate by +other+ def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end ## # When mathn is required Rational is changed to simplify the use of Rational # operations. # # Normal behaviour: # # Rational.new!(1,3) ** 2 # => Rational(1, 9) # (1 / 3) ** 2 # => 0 # # require 'mathn' behaviour: # # (1 / 3) ** 2 # => 1/9 class Rational remove_method :** ## # Exponentiate by +other+ # # (1/3) ** 2 # => 1/9 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 ## # 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) # 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 ## # 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 ## # When mathn is required, Float is changed to handle Complex numbers. class Float alias power! ** ## # Exponentiate by +other+ def ** (other) if self < 0 && other.round != other Complex(self, 0.0) ** other else power!(other) end end end
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