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Filename : cdesc-Numeric.ri
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U:RDoc::NormalClass[iI"Numeric:ET@I"Object;To:RDoc::Markup::Document:@parts[o;;[(o:RDoc::Markup::Paragraph;[I"UNumeric is the class from which all higher-level numeric classes should inherit.;To:RDoc::Markup::BlankLine�o;	;[I"`Numeric allows instantiation of heap-allocated objects. Other core numeric classes such as ;TI"`Integer are implemented as immediates, which means that each Integer is a single immutable ;TI",object which is always passed by value.;T@o:RDoc::Markup::Verbatim;[I"a = 1
;TI"+1.object_id == a.object_id   #=> true
;T:@format0o;	;[I"\There can only ever be one instance of the integer +1+, for example. Ruby ensures this ;TI"]by preventing instantiation. If duplication is attempted, the same instance is returned.;T@o;;[I"bInteger.new(1)                   #=> NoMethodError: undefined method `new' for Integer:Class
;TI",1.dup                            #=> 1
;TI"/1.object_id == 1.dup.object_id   #=> true
;T;0o;	;[I"QFor this reason, Numeric should be used when defining other numeric classes.;T@o;	;[I"\Classes which inherit from Numeric must implement +coerce+, which returns a two-member ;TI"XArray containing an object that has been coerced into an instance of the new class ;TI"and +self+ (see #coerce).;T@o;	;[	I"[Inheriting classes should also implement arithmetic operator methods (<code>+</code>, ;TI"_<code>-</code>, <code>*</code> and <code>/</code>) and the <code><=></code> operator (see ;TI"UComparable). These methods may rely on +coerce+ to ensure interoperability with ;TI"(instances of other numeric classes.;T@o;;[.I"class Tally < Numeric
;TI"  def initialize(string)
;TI"    @string = string
;TI"  end
;TI"
;TI"  def to_s
;TI"    @string
;TI"  end
;TI"
;TI"  def to_i
;TI"    @string.size
;TI"  end
;TI"
;TI"  def coerce(other)
;TI"2    [self.class.new('|' * other.to_i), self]
;TI"  end
;TI"
;TI"  def <=>(other)
;TI"    to_i <=> other.to_i
;TI"  end
;TI"
;TI"  def +(other)
;TI"3    self.class.new('|' * (to_i + other.to_i))
;TI"  end
;TI"
;TI"  def -(other)
;TI"3    self.class.new('|' * (to_i - other.to_i))
;TI"  end
;TI"
;TI"  def *(other)
;TI"3    self.class.new('|' * (to_i * other.to_i))
;TI"  end
;TI"
;TI"  def /(other)
;TI"3    self.class.new('|' * (to_i / other.to_i))
;TI"  end
;TI"	end
;TI"
;TI"tally = Tally.new('||')
;TI"*puts tally * 2            #=> "||||"
;TI"(puts tally > 1            #=> true
;T;0S:RDoc::Markup::Heading:
leveli:	textI"What's Here;T@o;	;[I".First, what's elsewhere. \Class \Numeric:;T@o:RDoc::Markup::List:
@type:BULLET:@items[o:RDoc::Markup::ListItem:@label0;[o;	;[I"PInherits from {class Object}[Object.html#class-Object-label-What-27s+Here].;To;;0;[o;	;[I"YIncludes {module Comparable}[Comparable.html#module-Comparable-label-What-27s+Here].;T@o;	;[I"/Here, class \Numeric provides methods for:;T@o;;;;[	o;;0;[o;	;[I".{Querying}[#class-Numeric-label-Querying];To;;0;[o;	;[I"0{Comparing}[#class-Numeric-label-Comparing];To;;0;[o;	;[I"2{Converting}[#class-Numeric-label-Converting];To;;0;[o;	;[I"({Other}[#class-Numeric-label-Other];T@S;
;i;I"
Querying;T@o;;;;[
o;;0;[o;;:	NOTE;[o;;[I"
#finite?;T;[o;	;[I"<Returns true unless +self+ is infinite or not a number.;To;;0;[o;;;;[o;;[I"#infinite?;T;[o;	;[I":Returns -1, +nil+ or +1, depending on whether +self+ ;TI"9is <tt>-Infinity<tt>, finite, or <tt>+Infinity</tt>.;To;;0;[o;;;;[o;;[I"#integer?;T;[o;	;[I"*Returns whether +self+ is an integer.;To;;0;[o;;;;[o;;[I"#negative?;T;[o;	;[I"(Returns whether +self+ is negative.;To;;0;[o;;;;[o;;[I"#nonzero?;T;[o;	;[I"(Returns whether +self+ is not zero.;To;;0;[o;;;;[o;;[I"#positive?;T;[o;	;[I"(Returns whether +self+ is positive.;To;;0;[o;;;;[o;;[I"#real?;T;[o;	;[I",Returns whether +self+ is a real value.;To;;0;[o;;;;[o;;[I"#zero?;T;[o;	;[I"$Returns whether +self+ is zero.;T@S;
;i;I"Comparing;T@o;;;;[o;;0;[o;;;;[o;;[I"{<=>}[#method-i-3C-3D-3E];T;[o;	;[I"
Returns:;To;;;;[	o;;0;[o;	;[I"0-1 if  +self+ is less than the given value.;To;;0;[o;	;[I"-0 if +self+ is equal to the given value.;To;;0;[o;	;[I"11 if +self+ is greater than the given value.;To;;0;[o;	;[I"<+nil+ if +self+ and the given value are not comparable.;To;;0;[o;;;;[o;;[I"
#eql?;T;[o;	;[I"MReturns whether +self+ and the given value have the same value and type.;T@S;
;i;I"Converting;T@o;;;;[o;;0;[o;;;;[o;;[I"#% (aliased as #modulo);T;[o;	;[I"@Returns the remainder of +self+ divided by the given value.;To;;0;[o;;;;[o;;[I"#-@;T;[o;	;[I"*Returns the value of +self+, negated.;To;;0;[o;;;;[o;;[I"!#abs (aliased as #magnitude);T;[o;	;[I"*Returns the absolute value of +self+.;To;;0;[o;;;;[o;;[I"
#abs2;T;[o;	;[I""Returns the square of +self+.;To;;0;[o;;;;[o;;[I"(#angle (aliased as #arg and #phase);T;[o;	;[I"&Returns 0 if +self+ is positive, ;TI"Math::PI otherwise.;To;;0;[o;;;;[o;;[I"
#ceil;T;[o;	;[I"BReturns the smallest number greater than or equal to +self+, ;TI"to a given precision.;To;;0;[o;;;;[o;;[I"#coerce;T;[o;	;[I":Returns array <tt>[coerced_self, coerced_other]</tt> ;TI"for the given other value.;To;;0;[o;;;;[o;;[I""#conj (aliased as #conjugate);T;[o;	;[I"-Returns the complex conjugate of +self+.;To;;0;[o;;;;[o;;[I"#denominator;T;[o;	;[I"/Returns the denominator (always positive) ;TI".of the Rational representation of +self+.;To;;0;[o;;;;[o;;[I"	#div;T;[o;	;[I"<Returns the value of +self+ divided by the given value ;TI"!and converted to an integer.;To;;0;[o;;;;[o;;[I"#divmod;T;[o;	;[I":Returns array <tt>[quotient, modulus]</tt> resulting ;TI",from dividing +self+ the given divisor.;To;;0;[o;;;;[o;;[I"
#fdiv;T;[o;	;[I"FReturns the Float result of dividing +self+ by the given divisor.;To;;0;[o;;;;[o;;[I"#floor;T;[o;	;[I">Returns the largest number less than or equal to +self+, ;TI"to a given precision.;To;;0;[o;;;;[o;;[I"#i;T;[o;	;[I";Returns the Complex object <tt>Complex(0, self)</tt>. ;TI"the given value.;To;;0;[o;;;;[o;;[I""#imaginary (aliased as #imag);T;[o;	;[I".Returns the imaginary part of the +self+.;To;;0;[o;;;;[o;;[I"#numerator;T;[o;	;[I"EReturns the numerator of the Rational representation of +self+; ;TI"!has the same sign as +self+.;To;;0;[o;;;;[o;;[I"#polar;T;[o;	;[I"5Returns the array <tt>[self.abs, self.arg]</tt>.;To;;0;[o;;;;[o;;[I"	#quo;T;[o;	;[I"<Returns the value of +self+ divided by the given value.;To;;0;[o;;;;[o;;[I"
#real;T;[o;	;[I"%Returns the real part of +self+.;To;;0;[o;;;;[o;;[I"$#rect (aliased as #rectangular);T;[o;	;[I"*Returns the array <tt>[self, 0]</tt>.;To;;0;[o;;;;[o;;[I"#remainder;T;[o;	;[I"GReturns <tt>self-arg*(self/arg).truncate</tt> for the given +arg+.;To;;0;[o;;;;[o;;[I"#round;T;[o;	;[I">Returns the value of +self+ rounded to the nearest value ;TI"for the given a precision.;To;;0;[o;;;;[o;;[I"
#to_c;T;[o;	;[I"2Returns the Complex representation of +self+.;To;;0;[o;;;;[o;;[I"#to_int;T;[o;	;[I"KReturns the Integer representation of +self+, truncating if necessary.;To;;0;[o;;;;[o;;[I"#truncate;T;[o;	;[I"AReturns +self+ truncated (toward zero) to a given precision.;T@S;
;i;I"
Other;T@o;;;;[o;;0;[o;;;;[o;;[I"#clone;T;[o;	;[I"-Returns +self+; does not allow freezing.;To;;0;[o;;;;[o;;[I"#dup (aliased as #+@);T;[o;	;[I"Returns +self+.;To;;0;[o;;;;[o;;[I"
#step;T;[o;	;[I"DInvokes the given block with the sequence of specified numbers.;T:
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