diff options
Diffstat (limited to 'ruby_1_8_5/lib/mathn.rb')
| -rw-r--r-- | ruby_1_8_5/lib/mathn.rb | 308 |
1 files changed, 0 insertions, 308 deletions
diff --git a/ruby_1_8_5/lib/mathn.rb b/ruby_1_8_5/lib/mathn.rb deleted file mode 100644 index a5a121c6c6..0000000000 --- a/ruby_1_8_5/lib/mathn.rb +++ /dev/null @@ -1,308 +0,0 @@ -# -# 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 - raise ZeroDivisionError if self == 0 - 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) - other2 = other - 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) ** 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.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 - |