Bug #4767 » 0001-enhanced-mathn-docs.patch
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##
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# = mathn
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#
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# mathn is a library for changing the way Ruby does math.
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# mathn is a library for changing the way Ruby does math. If you need
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# more precise rounding with multiple division or exponentiation
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# operations, then mathn is the right tool. It makes sense to use this
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# library if you can use it's late rounding. Mathn does not convert
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# Fixnums into Floats as long as you do not convert it yourself.
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# Instead of using Float as intermediate value it use Rational as
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# value representation.
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#
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# Example Fixnum with intermediate Float:
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#
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# 20 / 9 * 3 * 14 / 7 * 3 / 2 #=> 18
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#
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# Example: using mathn Fixnum/Rational:
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#
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# require 'mathn'
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# 20 / 9 * 3 * 14 / 7 * 3 / 2 #=> 20
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#
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# == Usage
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#
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| ... | ... | |
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#
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# 3 / 2
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#
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# will return (3/2) instead of the usual 1.
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# will return +Rational+ (3/2) instead of the usual +Fixnum+ 1.
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#
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# == Copyright
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#
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| ... | ... | |
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Math = CMath
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end
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##
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# Fixnum's division and exponentiation are enhanced to return more
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# precise values in mathematical formulas.
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#
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# 2/3*3 #=> 0
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# require 'mathn'
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# 2/3*3 #=> 2
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#
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class Fixnum
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remove_method :/
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##
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# +/+ defines the Rational division for Fixnum.
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#
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# 1/3 #=> (1/3)
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#
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alias / quo
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alias power! ** unless method_defined? :power!
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| ... | ... | |
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end
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# Bignum's division and exponentiation are enhanced to return more
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# precise values in mathematical formulas.
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class Bignum
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remove_method :/
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##
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# +/+ defines the Rational division for Bignum.
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#
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# (2**72) / ((2**70) * 3) #=> 4/3
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#
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alias / quo
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alias power! ** unless method_defined? :power!
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| ... | ... | |
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end
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##
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# Rational changes that simplfies the usage of Rational opaerations.
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#
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# normal behaviour:
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#
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# Rational.new!(1,3) ** 2 #=> Rational(1, 9)
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# (1 / 3) ** 2 #=> 0
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#
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# mathn behaviour:
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#
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# (1 / 3) ** 2 #=> 1/9
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#
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class Rational
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remove_method :**
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##
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# exponentiate by +other+
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#
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# (1/3) ** 2 #=> 1/9
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#
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def ** (other)
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if other.kind_of?(Rational)
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other2 = other
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| ... | ... | |
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end
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end
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##
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# Changes of the ruby Math module.
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#
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# standard Math module behaviour:
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# Math.sqrt(4/9) #=> 0.0
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# Math.sqrt(4.0/9.0) #=> 0.666666666666667
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# Math.sqrt(- 4/9) #=> Errno::EDOM: Numerical argument out of domain - sqrt
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#
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# using mathn library this is changed to:
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# require 'mathn'
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# Math.sqrt(4/9) #=> 2/3
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# Math.sqrt(4.0/9.0) #=> 0.666666666666667
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# Math.sqrt(- 4/9) #=> Complex(0, 2/3)
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#
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module Math
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remove_method(:sqrt)
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##
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# compute the square root of +a+
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# Compute the square root of +a+. It makes use of Complex and
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# Rational to have no rounding errors if possible.
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#
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# Math.sqrt(4/9) #=> 2/3
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# Math.sqrt(- 4/9) #=> Complex(0, 2/3)
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# Math.sqrt(4.0/9.0) #=> 0.666666666666667
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def sqrt(a)
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if a.kind_of?(Complex)
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abs = sqrt(a.real*a.real + a.imag*a.imag)
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| ... | ... | |
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end
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end
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def rsqrt(a) # :nodoc:
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# Compute square root of a non negative number. This method is
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# internally used by +Math.sqrt+.
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def rsqrt(a)
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if a.kind_of?(Float)
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sqrt!(a)
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elsif a.kind_of?(Rational)
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| ... | ... | |
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module_function :rsqrt
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end
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##
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# Float is changed to know Complex numbers.
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class Float
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alias power! **
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