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Diffstat (limited to 'ruby_1_9_3/lib/mathn.rb')
| -rw-r--r-- | ruby_1_9_3/lib/mathn.rb | 324 |
1 files changed, 0 insertions, 324 deletions
diff --git a/ruby_1_9_3/lib/mathn.rb b/ruby_1_9_3/lib/mathn.rb deleted file mode 100644 index aae4620c3f..0000000000 --- a/ruby_1_9_3/lib/mathn.rb +++ /dev/null @@ -1,324 +0,0 @@ -#-- -# $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 |