Class: Radix::Float

Inherits:
Numeric
  • Object
show all
Defined in:
lib/radix/float.rb

Overview

TODO:

Make fully immutable. After that we can catch @digits and the library should be a good bit faster.

Advanced float class for Radix conversions and mathematical operations with other bases.

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods inherited from Numeric

#*, #+, #-, #/, #base_decode, #base_encode, #parse_array, #parse_base, #parse_numeric, #parse_string

Constructor Details

#initialize(value, base = 10) ⇒ void (private)

Starts a new instance of the Radix::Float class.

Parameters:

  • value (Radix::Numeric, Numeric, Array, String)

    The value of the new integer in context of base.

  • base (Fixnum, Array<String>) (defaults to: 10)

    The base context in which value is determined. Can be an array of characters to use in place of default.


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# File 'lib/radix/float.rb', line 51

def initialize(value, base=10)
  @base, @code = parse_base(base)
  @value = parse_value(value, @base)
end

Instance Attribute Details

#baseFixnum (readonly)

Base of the number.

Returns:

  • (Fixnum)

    The base level of Float instance.


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# File 'lib/radix/float.rb', line 18

class Float < Numeric

  ##
  # Internal floating point value.
  #
  # @return [Float] Float's decimal value.
  attr :value

  ##
  # Base of the number.
  #
  # @return [Fixnum] The base level of Float instance.
  attr :base

  ##
  # Base encoding table.
  #
  # @return [Array<String>, nil] Substitution chars or nil if default.
  attr :code

  private

  ##
  # Starts a new instance of the Radix::Float class.
  #
  # @param [Radix::Numeric, Numeric, Array, String] value
  #   The value of the new integer in context of base.
  #
  # @param [Fixnum, Array<String>] base
  #   The base context in which value is determined. Can be an array
  #   of characters to use in place of default.
  #
  # @return [void]    
  def initialize(value, base=10)
    @base, @code = parse_base(base)
    @value = parse_value(value, @base)
  end

  ##
  # Takes a Radix::Numeric, String or array and returns the decimal float
  # value for storage in @value.
  #
  # @param [Radix::Numeric, Numeric, String, Array<Numeric, String>] value
  #   The value of the integer in base context.
  #
  # @param [Fixnum, Array<String>] base
  #   The context base of value.
  #
  # @return [Float] Float value of Integer.
  def parse_value(value, base)
    case value
    when Float, Integer # Radix
      parse_numeric(value.to_f, base)
    when ::Array
      parse_array(value, base)
    when ::String
      parse_string(value, base)
    when ::Numeric
      parse_numeric(value.to_f, base)
    end
  end

public

  ##
  # Convert the Radix::Float a Ruby Integer.
  # 
  # @return [Integer] Base(10) value as Integer.
  def to_i
    to_f.to_i
  end

  alias_method :to_int, :to_i

  ##
  # Convert Radix::Float to a Ruby float.
  # 
  # @return [Float] Base(10) value as Float.
  def to_f
    value.to_f
  end

  ##
  # Makes this Radix::Float an array using code if defined. Returns an
  # array using default chars otherwise. 
  #
  # @param [Fixnum] base
  #   Desired base.
  #
  # @return [Array<Fixnum, String>] Current base encoded array.
  def to_a(base=nil)
    if base
      convert(base).digits_encoded
    else
      digits_encoded
    end
  end

  ##
  # Creates an encoded string in passed base, with passed digit divider.
  #
  # @note For base 10 or less does not use a divider unless specified.
  #
  # @param [Fixnum, Array<String>] base
  #   Desired base.
  #
  # @param [String] divider
  #   Desired divider character(s).
  #
  # @return [String] Encoded string with specified divider.
  def to_s(base=nil, divider=nil)
    divider = divider.to_s if divider
    if base
      convert(base).to_s(nil, divider)
    else
      if code
        digits_encoded.join(divider)
      else
        if @base > 10
          digits.join(divider || DIVIDER)
        else
          digits.join(divider)
        end
      end
    end
  end

  ##
  # Creates a string representation of self.
  #
  # @return [String] String rep of self.digits and @base.
  def inspect
    "#{digits.join(' ')} (#{base})"
  end

  ##
  # Returns an array representation of each column's value in decimal chars.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative. 
  def digits
    i, f = base_conversion(value, base)
    if negative?
      ['-'] + i + [DOT] + f
    else
      i + [DOT] + f
    end
  end

  ##
  # Returns digits, or coded version of digits if @code.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative.
  #   Or encoded version if @code is defined.
  def digits_encoded
    base_encode(digits)
  end

  ##
  # Returns true if the number is negative?
  #
  # @return [Boolean] True if float value is < 0.
  def negative?
    value < 0
  end

  ## 
  # Creates a new Radix::Float of same value in different base.
  #
  # @return [Radix::Float] New float of same value in different base.
  def convert(new_base)
    self.class.new(value, new_base)
  end

  ##
  # Power exponentional operation.
  #
  # @param [#to_f] other
  #   The exponent by which to raise Float.
  #
  # @return [Radix::Float] Result of exponential operation.
  def **(other)
    operation(:**, other)
  end

  ##
  # Modulo binary operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Modulo result of division operation.
  def %(other)
    operation(:%, other)
  end

  alias_method :modulo, :%

  ##
  # Returns the absolute value of self in @base.
  #
  # @return [Radix::Float] Absolute of @value.
  def abs
    self.class.new(value.abs, base)
  end

  ##
  # Returns the largest integer greater than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def ceil
    self.class.new(value.ceil, base)
  end

  ##
  # Returns the smallest integer less than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def floor
    self.class.new(value.floor, base)
  end

  ##
  # Returns a new Radix::Float instance of same base, rounded to the nearest 
  # whole integer.
  # 
  # @example Rounding Radix Float
  #   > round_test = Radix::Float.new(123.03, 16)
  #   7 11 . 0 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.03
  #   > round_test.round
  #   7 11 . 0 (16)
  #   > round_test.round.value
  #   123.0
  #   > round_test += 0.5
  #   7 11 . 8 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.53
  #   > round_test.round
  #   7 12 . 0 (16)
  #   > round_test.round.value
  #   124.0
  #
  # @return [Radix::Float] New Instance
  def round
    return self.class.new((value + 0.5).floor, base) if self > 0.0
    return self.class.new((value - 0.5).ceil,  base) if self < 0.0
    return self.class.new(0, base)
  end

  ##
  # Strict equality requires same class as well as value.
  #
  # @param [Object] num
  #   Object to compare.
  #
  # @return [Boolean] True if class and value are equal.
  def eql?(num)
    self.class.equal?(num.class) && self == num
  end

  ##
  # Simple equality requires equal values only.
  #
  # @param [Numeric] other
  #   Any Numeric instance.
  #
  # @return [Boolean] True if values are equal.
   def ==(other)
    case other
    when Float, Integer  # Radix
      value == other.value
    else
      value == other
    end
  end

  ##
  # Comparitive binary operation. Very useful for sorting methods.
  # 
  # @param [#to_f] other
  #   The object to compare value against.
  #
  # @example Comparison testing
  #   > lower = Radix::Float.new(123.00,10)
  #   1 2 3 . 0 (10)
  #   > higher = Radix::Float.new(456.00,16)
  #   1 12 8 . 0 (16)
  #   > lower <=> higher
  #   -1
  #   > lower <=> 123
  #   0
  #   > lower <=> "123"
  #   0
  #   > higher <=> lower
  #   1
  #
  # @return [Fixnum] Returns -1 for less than, 0 for equal or 1 for more than.
  def <=>(other)
    to_f <=> other.to_f
  end

  #
  #def infinite?
  #  digits[0,2] == [0, DOT]
  #end

  #
  #def finite?
  #  !infinite
  #end

  #
  #def nan?
  #  digits[-2,2] == [DOT, 0]
  #end

  ##
  # Create a new Radix::Float from value in Base-10.
  # 
  # @param [Numeric, Array, String] other
  #   The value of the new integer in base-10.
  #
  # @return [Array<Radix::Float>] An array of the new Float object and self.
  def coerce(other)
    [Radix::Float.new(other), self]  
  end

  private

  ##
  # Perform passed arithmetic operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Result of binary operation in @base.
  def operation(op, other)
    a = self.to_f
    b = other.to_f
    x = a.__send__(op, b)
    Radix::Float.new(x, base)

  end

  ##
  # Returns two arrays. The integer part and the fractional part of the Float
  # value in param base.
  #
  # @param [Float] value  Float's decimal value.
  # @param [Fixnum] base  The base level of Float instance.
  # @param [Fixnum] prec  The # of places to extend F-part.
  #
  # @return [Array<(Array[Fixnum], Array[Fixnum])>] 
  def base_conversion(value, base, prec=10)
    #if value < 0
    #  @negative, value = true, value.abs
    #end
    value = value.to_f.abs

    i, f = split_float(value)

    a = []
    while i > 0
      i, r = i.divmod(base)
      a << r
    end

    #c = [] # f-cache 
    p = prec
    b = []
    while !f.zero?
      k = (f * base)
      r, f = split_float(k)
      #c.include?(f) ? break : c << f
      break if p == 0; p -= 1
      b << r
    end

    a << 0 if a.empty?
    b << 0 if b.empty?

    [a.reverse, b]
  end

  ##
  # Convert array of values of a different base to decimal as called by
  # parse_array.
  #
  # @param [Array<Numeric, String>] digits  Representation of Base values.
  # @param [Fixnum, Array<String>] base  The base to convert from.
  #
  # @return [Float] The digits of base converted to decimal.
  def decimal(digits, base)
    i, f = split_digits(digits)
    e = i.size - 1
    v = 0
    (i + f).each do |n|
      v += n * base**e
      e -= 1
    end
    v
  end

  ##
  # Returns the I-Part and F-Part of the passed value as arrays of fixnums.
  # 
  # @param [Array<Numeric, String>] value
  #   The array of decimal values per column of @base.
  #
  # @return [Array<(Array<Fixnum>, Array<Fixnum>)>]
  def split_digits(value)
    if d = value.index(DOT) || value.index('.')
      i, f = value[0...d], value[d+1..-1]
    else
      i, f = value, [0]
    end
    i.map!{ |x| x.to_i }
    f.map!{ |x| x.to_i }
    return i, f
  end

  ##
  # Returns an array of Integer and Float portions of the Radix::Float
  #
  # @param [Radix::Float] float  Float value to split
  #
  # @return [Array<(Integer, Float)>]
  def split_float(float)
    i, f = float.to_s.split('.')
    return i.to_i, ('0.'+f).to_f
  end

end

#codeArray<String>? (readonly)

Base encoding table.

Returns:

  • (Array<String>, nil)

    Substitution chars or nil if default.


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# File 'lib/radix/float.rb', line 18

class Float < Numeric

  ##
  # Internal floating point value.
  #
  # @return [Float] Float's decimal value.
  attr :value

  ##
  # Base of the number.
  #
  # @return [Fixnum] The base level of Float instance.
  attr :base

  ##
  # Base encoding table.
  #
  # @return [Array<String>, nil] Substitution chars or nil if default.
  attr :code

  private

  ##
  # Starts a new instance of the Radix::Float class.
  #
  # @param [Radix::Numeric, Numeric, Array, String] value
  #   The value of the new integer in context of base.
  #
  # @param [Fixnum, Array<String>] base
  #   The base context in which value is determined. Can be an array
  #   of characters to use in place of default.
  #
  # @return [void]    
  def initialize(value, base=10)
    @base, @code = parse_base(base)
    @value = parse_value(value, @base)
  end

  ##
  # Takes a Radix::Numeric, String or array and returns the decimal float
  # value for storage in @value.
  #
  # @param [Radix::Numeric, Numeric, String, Array<Numeric, String>] value
  #   The value of the integer in base context.
  #
  # @param [Fixnum, Array<String>] base
  #   The context base of value.
  #
  # @return [Float] Float value of Integer.
  def parse_value(value, base)
    case value
    when Float, Integer # Radix
      parse_numeric(value.to_f, base)
    when ::Array
      parse_array(value, base)
    when ::String
      parse_string(value, base)
    when ::Numeric
      parse_numeric(value.to_f, base)
    end
  end

public

  ##
  # Convert the Radix::Float a Ruby Integer.
  # 
  # @return [Integer] Base(10) value as Integer.
  def to_i
    to_f.to_i
  end

  alias_method :to_int, :to_i

  ##
  # Convert Radix::Float to a Ruby float.
  # 
  # @return [Float] Base(10) value as Float.
  def to_f
    value.to_f
  end

  ##
  # Makes this Radix::Float an array using code if defined. Returns an
  # array using default chars otherwise. 
  #
  # @param [Fixnum] base
  #   Desired base.
  #
  # @return [Array<Fixnum, String>] Current base encoded array.
  def to_a(base=nil)
    if base
      convert(base).digits_encoded
    else
      digits_encoded
    end
  end

  ##
  # Creates an encoded string in passed base, with passed digit divider.
  #
  # @note For base 10 or less does not use a divider unless specified.
  #
  # @param [Fixnum, Array<String>] base
  #   Desired base.
  #
  # @param [String] divider
  #   Desired divider character(s).
  #
  # @return [String] Encoded string with specified divider.
  def to_s(base=nil, divider=nil)
    divider = divider.to_s if divider
    if base
      convert(base).to_s(nil, divider)
    else
      if code
        digits_encoded.join(divider)
      else
        if @base > 10
          digits.join(divider || DIVIDER)
        else
          digits.join(divider)
        end
      end
    end
  end

  ##
  # Creates a string representation of self.
  #
  # @return [String] String rep of self.digits and @base.
  def inspect
    "#{digits.join(' ')} (#{base})"
  end

  ##
  # Returns an array representation of each column's value in decimal chars.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative. 
  def digits
    i, f = base_conversion(value, base)
    if negative?
      ['-'] + i + [DOT] + f
    else
      i + [DOT] + f
    end
  end

  ##
  # Returns digits, or coded version of digits if @code.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative.
  #   Or encoded version if @code is defined.
  def digits_encoded
    base_encode(digits)
  end

  ##
  # Returns true if the number is negative?
  #
  # @return [Boolean] True if float value is < 0.
  def negative?
    value < 0
  end

  ## 
  # Creates a new Radix::Float of same value in different base.
  #
  # @return [Radix::Float] New float of same value in different base.
  def convert(new_base)
    self.class.new(value, new_base)
  end

  ##
  # Power exponentional operation.
  #
  # @param [#to_f] other
  #   The exponent by which to raise Float.
  #
  # @return [Radix::Float] Result of exponential operation.
  def **(other)
    operation(:**, other)
  end

  ##
  # Modulo binary operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Modulo result of division operation.
  def %(other)
    operation(:%, other)
  end

  alias_method :modulo, :%

  ##
  # Returns the absolute value of self in @base.
  #
  # @return [Radix::Float] Absolute of @value.
  def abs
    self.class.new(value.abs, base)
  end

  ##
  # Returns the largest integer greater than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def ceil
    self.class.new(value.ceil, base)
  end

  ##
  # Returns the smallest integer less than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def floor
    self.class.new(value.floor, base)
  end

  ##
  # Returns a new Radix::Float instance of same base, rounded to the nearest 
  # whole integer.
  # 
  # @example Rounding Radix Float
  #   > round_test = Radix::Float.new(123.03, 16)
  #   7 11 . 0 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.03
  #   > round_test.round
  #   7 11 . 0 (16)
  #   > round_test.round.value
  #   123.0
  #   > round_test += 0.5
  #   7 11 . 8 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.53
  #   > round_test.round
  #   7 12 . 0 (16)
  #   > round_test.round.value
  #   124.0
  #
  # @return [Radix::Float] New Instance
  def round
    return self.class.new((value + 0.5).floor, base) if self > 0.0
    return self.class.new((value - 0.5).ceil,  base) if self < 0.0
    return self.class.new(0, base)
  end

  ##
  # Strict equality requires same class as well as value.
  #
  # @param [Object] num
  #   Object to compare.
  #
  # @return [Boolean] True if class and value are equal.
  def eql?(num)
    self.class.equal?(num.class) && self == num
  end

  ##
  # Simple equality requires equal values only.
  #
  # @param [Numeric] other
  #   Any Numeric instance.
  #
  # @return [Boolean] True if values are equal.
   def ==(other)
    case other
    when Float, Integer  # Radix
      value == other.value
    else
      value == other
    end
  end

  ##
  # Comparitive binary operation. Very useful for sorting methods.
  # 
  # @param [#to_f] other
  #   The object to compare value against.
  #
  # @example Comparison testing
  #   > lower = Radix::Float.new(123.00,10)
  #   1 2 3 . 0 (10)
  #   > higher = Radix::Float.new(456.00,16)
  #   1 12 8 . 0 (16)
  #   > lower <=> higher
  #   -1
  #   > lower <=> 123
  #   0
  #   > lower <=> "123"
  #   0
  #   > higher <=> lower
  #   1
  #
  # @return [Fixnum] Returns -1 for less than, 0 for equal or 1 for more than.
  def <=>(other)
    to_f <=> other.to_f
  end

  #
  #def infinite?
  #  digits[0,2] == [0, DOT]
  #end

  #
  #def finite?
  #  !infinite
  #end

  #
  #def nan?
  #  digits[-2,2] == [DOT, 0]
  #end

  ##
  # Create a new Radix::Float from value in Base-10.
  # 
  # @param [Numeric, Array, String] other
  #   The value of the new integer in base-10.
  #
  # @return [Array<Radix::Float>] An array of the new Float object and self.
  def coerce(other)
    [Radix::Float.new(other), self]  
  end

  private

  ##
  # Perform passed arithmetic operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Result of binary operation in @base.
  def operation(op, other)
    a = self.to_f
    b = other.to_f
    x = a.__send__(op, b)
    Radix::Float.new(x, base)

  end

  ##
  # Returns two arrays. The integer part and the fractional part of the Float
  # value in param base.
  #
  # @param [Float] value  Float's decimal value.
  # @param [Fixnum] base  The base level of Float instance.
  # @param [Fixnum] prec  The # of places to extend F-part.
  #
  # @return [Array<(Array[Fixnum], Array[Fixnum])>] 
  def base_conversion(value, base, prec=10)
    #if value < 0
    #  @negative, value = true, value.abs
    #end
    value = value.to_f.abs

    i, f = split_float(value)

    a = []
    while i > 0
      i, r = i.divmod(base)
      a << r
    end

    #c = [] # f-cache 
    p = prec
    b = []
    while !f.zero?
      k = (f * base)
      r, f = split_float(k)
      #c.include?(f) ? break : c << f
      break if p == 0; p -= 1
      b << r
    end

    a << 0 if a.empty?
    b << 0 if b.empty?

    [a.reverse, b]
  end

  ##
  # Convert array of values of a different base to decimal as called by
  # parse_array.
  #
  # @param [Array<Numeric, String>] digits  Representation of Base values.
  # @param [Fixnum, Array<String>] base  The base to convert from.
  #
  # @return [Float] The digits of base converted to decimal.
  def decimal(digits, base)
    i, f = split_digits(digits)
    e = i.size - 1
    v = 0
    (i + f).each do |n|
      v += n * base**e
      e -= 1
    end
    v
  end

  ##
  # Returns the I-Part and F-Part of the passed value as arrays of fixnums.
  # 
  # @param [Array<Numeric, String>] value
  #   The array of decimal values per column of @base.
  #
  # @return [Array<(Array<Fixnum>, Array<Fixnum>)>]
  def split_digits(value)
    if d = value.index(DOT) || value.index('.')
      i, f = value[0...d], value[d+1..-1]
    else
      i, f = value, [0]
    end
    i.map!{ |x| x.to_i }
    f.map!{ |x| x.to_i }
    return i, f
  end

  ##
  # Returns an array of Integer and Float portions of the Radix::Float
  #
  # @param [Radix::Float] float  Float value to split
  #
  # @return [Array<(Integer, Float)>]
  def split_float(float)
    i, f = float.to_s.split('.')
    return i.to_i, ('0.'+f).to_f
  end

end

#valueFloat (readonly)

Internal floating point value.

Returns:

  • (Float)

    Float's decimal value.


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# File 'lib/radix/float.rb', line 18

class Float < Numeric

  ##
  # Internal floating point value.
  #
  # @return [Float] Float's decimal value.
  attr :value

  ##
  # Base of the number.
  #
  # @return [Fixnum] The base level of Float instance.
  attr :base

  ##
  # Base encoding table.
  #
  # @return [Array<String>, nil] Substitution chars or nil if default.
  attr :code

  private

  ##
  # Starts a new instance of the Radix::Float class.
  #
  # @param [Radix::Numeric, Numeric, Array, String] value
  #   The value of the new integer in context of base.
  #
  # @param [Fixnum, Array<String>] base
  #   The base context in which value is determined. Can be an array
  #   of characters to use in place of default.
  #
  # @return [void]    
  def initialize(value, base=10)
    @base, @code = parse_base(base)
    @value = parse_value(value, @base)
  end

  ##
  # Takes a Radix::Numeric, String or array and returns the decimal float
  # value for storage in @value.
  #
  # @param [Radix::Numeric, Numeric, String, Array<Numeric, String>] value
  #   The value of the integer in base context.
  #
  # @param [Fixnum, Array<String>] base
  #   The context base of value.
  #
  # @return [Float] Float value of Integer.
  def parse_value(value, base)
    case value
    when Float, Integer # Radix
      parse_numeric(value.to_f, base)
    when ::Array
      parse_array(value, base)
    when ::String
      parse_string(value, base)
    when ::Numeric
      parse_numeric(value.to_f, base)
    end
  end

public

  ##
  # Convert the Radix::Float a Ruby Integer.
  # 
  # @return [Integer] Base(10) value as Integer.
  def to_i
    to_f.to_i
  end

  alias_method :to_int, :to_i

  ##
  # Convert Radix::Float to a Ruby float.
  # 
  # @return [Float] Base(10) value as Float.
  def to_f
    value.to_f
  end

  ##
  # Makes this Radix::Float an array using code if defined. Returns an
  # array using default chars otherwise. 
  #
  # @param [Fixnum] base
  #   Desired base.
  #
  # @return [Array<Fixnum, String>] Current base encoded array.
  def to_a(base=nil)
    if base
      convert(base).digits_encoded
    else
      digits_encoded
    end
  end

  ##
  # Creates an encoded string in passed base, with passed digit divider.
  #
  # @note For base 10 or less does not use a divider unless specified.
  #
  # @param [Fixnum, Array<String>] base
  #   Desired base.
  #
  # @param [String] divider
  #   Desired divider character(s).
  #
  # @return [String] Encoded string with specified divider.
  def to_s(base=nil, divider=nil)
    divider = divider.to_s if divider
    if base
      convert(base).to_s(nil, divider)
    else
      if code
        digits_encoded.join(divider)
      else
        if @base > 10
          digits.join(divider || DIVIDER)
        else
          digits.join(divider)
        end
      end
    end
  end

  ##
  # Creates a string representation of self.
  #
  # @return [String] String rep of self.digits and @base.
  def inspect
    "#{digits.join(' ')} (#{base})"
  end

  ##
  # Returns an array representation of each column's value in decimal chars.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative. 
  def digits
    i, f = base_conversion(value, base)
    if negative?
      ['-'] + i + [DOT] + f
    else
      i + [DOT] + f
    end
  end

  ##
  # Returns digits, or coded version of digits if @code.
  #
  # @return [Array<String, Fixnum>]
  #   Values per column of @base as array. Prepended with "-" if negative.
  #   Or encoded version if @code is defined.
  def digits_encoded
    base_encode(digits)
  end

  ##
  # Returns true if the number is negative?
  #
  # @return [Boolean] True if float value is < 0.
  def negative?
    value < 0
  end

  ## 
  # Creates a new Radix::Float of same value in different base.
  #
  # @return [Radix::Float] New float of same value in different base.
  def convert(new_base)
    self.class.new(value, new_base)
  end

  ##
  # Power exponentional operation.
  #
  # @param [#to_f] other
  #   The exponent by which to raise Float.
  #
  # @return [Radix::Float] Result of exponential operation.
  def **(other)
    operation(:**, other)
  end

  ##
  # Modulo binary operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Modulo result of division operation.
  def %(other)
    operation(:%, other)
  end

  alias_method :modulo, :%

  ##
  # Returns the absolute value of self in @base.
  #
  # @return [Radix::Float] Absolute of @value.
  def abs
    self.class.new(value.abs, base)
  end

  ##
  # Returns the largest integer greater than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def ceil
    self.class.new(value.ceil, base)
  end

  ##
  # Returns the smallest integer less than or equal to self as a
  # Radix::Float.
  #
  # @return [Radix::Float] 
  def floor
    self.class.new(value.floor, base)
  end

  ##
  # Returns a new Radix::Float instance of same base, rounded to the nearest 
  # whole integer.
  # 
  # @example Rounding Radix Float
  #   > round_test = Radix::Float.new(123.03, 16)
  #   7 11 . 0 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.03
  #   > round_test.round
  #   7 11 . 0 (16)
  #   > round_test.round.value
  #   123.0
  #   > round_test += 0.5
  #   7 11 . 8 7 10 14 1 4 7 10 14 1 (16)
  #   > round_test.value
  #   123.53
  #   > round_test.round
  #   7 12 . 0 (16)
  #   > round_test.round.value
  #   124.0
  #
  # @return [Radix::Float] New Instance
  def round
    return self.class.new((value + 0.5).floor, base) if self > 0.0
    return self.class.new((value - 0.5).ceil,  base) if self < 0.0
    return self.class.new(0, base)
  end

  ##
  # Strict equality requires same class as well as value.
  #
  # @param [Object] num
  #   Object to compare.
  #
  # @return [Boolean] True if class and value are equal.
  def eql?(num)
    self.class.equal?(num.class) && self == num
  end

  ##
  # Simple equality requires equal values only.
  #
  # @param [Numeric] other
  #   Any Numeric instance.
  #
  # @return [Boolean] True if values are equal.
   def ==(other)
    case other
    when Float, Integer  # Radix
      value == other.value
    else
      value == other
    end
  end

  ##
  # Comparitive binary operation. Very useful for sorting methods.
  # 
  # @param [#to_f] other
  #   The object to compare value against.
  #
  # @example Comparison testing
  #   > lower = Radix::Float.new(123.00,10)
  #   1 2 3 . 0 (10)
  #   > higher = Radix::Float.new(456.00,16)
  #   1 12 8 . 0 (16)
  #   > lower <=> higher
  #   -1
  #   > lower <=> 123
  #   0
  #   > lower <=> "123"
  #   0
  #   > higher <=> lower
  #   1
  #
  # @return [Fixnum] Returns -1 for less than, 0 for equal or 1 for more than.
  def <=>(other)
    to_f <=> other.to_f
  end

  #
  #def infinite?
  #  digits[0,2] == [0, DOT]
  #end

  #
  #def finite?
  #  !infinite
  #end

  #
  #def nan?
  #  digits[-2,2] == [DOT, 0]
  #end

  ##
  # Create a new Radix::Float from value in Base-10.
  # 
  # @param [Numeric, Array, String] other
  #   The value of the new integer in base-10.
  #
  # @return [Array<Radix::Float>] An array of the new Float object and self.
  def coerce(other)
    [Radix::Float.new(other), self]  
  end

  private

  ##
  # Perform passed arithmetic operation.
  #
  # @param [#to_f] other
  #
  # @return [Radix::Float] Result of binary operation in @base.
  def operation(op, other)
    a = self.to_f
    b = other.to_f
    x = a.__send__(op, b)
    Radix::Float.new(x, base)

  end

  ##
  # Returns two arrays. The integer part and the fractional part of the Float
  # value in param base.
  #
  # @param [Float] value  Float's decimal value.
  # @param [Fixnum] base  The base level of Float instance.
  # @param [Fixnum] prec  The # of places to extend F-part.
  #
  # @return [Array<(Array[Fixnum], Array[Fixnum])>] 
  def base_conversion(value, base, prec=10)
    #if value < 0
    #  @negative, value = true, value.abs
    #end
    value = value.to_f.abs

    i, f = split_float(value)

    a = []
    while i > 0
      i, r = i.divmod(base)
      a << r
    end

    #c = [] # f-cache 
    p = prec
    b = []
    while !f.zero?
      k = (f * base)
      r, f = split_float(k)
      #c.include?(f) ? break : c << f
      break if p == 0; p -= 1
      b << r
    end

    a << 0 if a.empty?
    b << 0 if b.empty?

    [a.reverse, b]
  end

  ##
  # Convert array of values of a different base to decimal as called by
  # parse_array.
  #
  # @param [Array<Numeric, String>] digits  Representation of Base values.
  # @param [Fixnum, Array<String>] base  The base to convert from.
  #
  # @return [Float] The digits of base converted to decimal.
  def decimal(digits, base)
    i, f = split_digits(digits)
    e = i.size - 1
    v = 0
    (i + f).each do |n|
      v += n * base**e
      e -= 1
    end
    v
  end

  ##
  # Returns the I-Part and F-Part of the passed value as arrays of fixnums.
  # 
  # @param [Array<Numeric, String>] value
  #   The array of decimal values per column of @base.
  #
  # @return [Array<(Array<Fixnum>, Array<Fixnum>)>]
  def split_digits(value)
    if d = value.index(DOT) || value.index('.')
      i, f = value[0...d], value[d+1..-1]
    else
      i, f = value, [0]
    end
    i.map!{ |x| x.to_i }
    f.map!{ |x| x.to_i }
    return i, f
  end

  ##
  # Returns an array of Integer and Float portions of the Radix::Float
  #
  # @param [Radix::Float] float  Float value to split
  #
  # @return [Array<(Integer, Float)>]
  def split_float(float)
    i, f = float.to_s.split('.')
    return i.to_i, ('0.'+f).to_f
  end

end

Instance Method Details

#%(other) ⇒ Radix::Float Also known as: modulo

Modulo binary operation.

Parameters:

Returns:


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# File 'lib/radix/float.rb', line 210

def %(other)
  operation(:%, other)
end

#**(other) ⇒ Radix::Float

Power exponentional operation.

Parameters:

  • other (#to_f)

    The exponent by which to raise Float.

Returns:


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# File 'lib/radix/float.rb', line 200

def **(other)
  operation(:**, other)
end

#<=>(other) ⇒ Fixnum

Comparitive binary operation. Very useful for sorting methods.

Examples:

Comparison testing

> lower = Radix::Float.new(123.00,10)
1 2 3 . 0 (10)
> higher = Radix::Float.new(456.00,16)
1 12 8 . 0 (16)
> lower <=> higher
-1
> lower <=> 123
0
> lower <=> "123"
0
> higher <=> lower
1

Parameters:

  • other (#to_f)

    The object to compare value against.

Returns:

  • (Fixnum)

    Returns -1 for less than, 0 for equal or 1 for more than.


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# File 'lib/radix/float.rb', line 319

def <=>(other)
  to_f <=> other.to_f
end

#==(other) ⇒ Boolean

Simple equality requires equal values only.

Parameters:

  • other (Numeric)

    Any Numeric instance.

Returns:

  • (Boolean)

    True if values are equal.


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# File 'lib/radix/float.rb', line 289

def ==(other)
  case other
  when Float, Integer  # Radix
    value == other.value
  else
    value == other
  end
end

#absRadix::Float

Returns the absolute value of self in @base.

Returns:


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# File 'lib/radix/float.rb', line 220

def abs
  self.class.new(value.abs, base)
end

#base_conversion(value, base, prec = 10) ⇒ Array<(Array[Fixnum], Array[Fixnum])> (private)

Returns two arrays. The integer part and the fractional part of the Float value in param base.

Parameters:

  • value (Float)

    Float's decimal value.

  • base (Fixnum)

    The base level of Float instance.

  • prec (Fixnum) (defaults to: 10)

    The # of places to extend F-part.

Returns:


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# File 'lib/radix/float.rb', line 374

def base_conversion(value, base, prec=10)
  #if value < 0
  #  @negative, value = true, value.abs
  #end
  value = value.to_f.abs

  i, f = split_float(value)

  a = []
  while i > 0
    i, r = i.divmod(base)
    a << r
  end

  #c = [] # f-cache 
  p = prec
  b = []
  while !f.zero?
    k = (f * base)
    r, f = split_float(k)
    #c.include?(f) ? break : c << f
    break if p == 0; p -= 1
    b << r
  end

  a << 0 if a.empty?
  b << 0 if b.empty?

  [a.reverse, b]
end

#ceilRadix::Float

Returns the largest integer greater than or equal to self as a Radix::Float.

Returns:


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# File 'lib/radix/float.rb', line 229

def ceil
  self.class.new(value.ceil, base)
end

#coerce(other) ⇒ Array<Radix::Float>

Create a new Radix::Float from value in Base-10.

Parameters:

Returns:


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# File 'lib/radix/float.rb', line 345

def coerce(other)
  [Radix::Float.new(other), self]  
end

#convert(new_base) ⇒ Radix::Float

Creates a new Radix::Float of same value in different base.

Returns:

  • (Radix::Float)

    New float of same value in different base.


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# File 'lib/radix/float.rb', line 189

def convert(new_base)
  self.class.new(value, new_base)
end

#decimal(digits, base) ⇒ Float (private)

Convert array of values of a different base to decimal as called by parse_array.

Parameters:

Returns:

  • (Float)

    The digits of base converted to decimal.


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# File 'lib/radix/float.rb', line 413

def decimal(digits, base)
  i, f = split_digits(digits)
  e = i.size - 1
  v = 0
  (i + f).each do |n|
    v += n * base**e
    e -= 1
  end
  v
end

#digitsArray<String, Fixnum>

Returns an array representation of each column's value in decimal chars.

Returns:

  • (Array<String, Fixnum>)

    Values per column of @base as array. Prepended with “-” if negative.


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# File 'lib/radix/float.rb', line 158

def digits
  i, f = base_conversion(value, base)
  if negative?
    ['-'] + i + [DOT] + f
  else
    i + [DOT] + f
  end
end

#digits_encodedArray<String, Fixnum>

Returns digits, or coded version of digits if @code.

Returns:

  • (Array<String, Fixnum>)

    Values per column of @base as array. Prepended with “-” if negative. Or encoded version if @code is defined.


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# File 'lib/radix/float.rb', line 173

def digits_encoded
  base_encode(digits)
end

#eql?(num) ⇒ Boolean

Strict equality requires same class as well as value.

Parameters:

  • num (Object)

    Object to compare.

Returns:

  • (Boolean)

    True if class and value are equal.


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# File 'lib/radix/float.rb', line 278

def eql?(num)
  self.class.equal?(num.class) && self == num
end

#floorRadix::Float

Returns the smallest integer less than or equal to self as a Radix::Float.

Returns:


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# File 'lib/radix/float.rb', line 238

def floor
  self.class.new(value.floor, base)
end

#inspectString

Creates a string representation of self.

Returns:

  • (String)

    String rep of self.digits and @base.


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# File 'lib/radix/float.rb', line 149

def inspect
  "#{digits.join(' ')} (#{base})"
end

#negative?Boolean

Returns true if the number is negative?

Returns:

  • (Boolean)

    True if float value is < 0.


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# File 'lib/radix/float.rb', line 181

def negative?
  value < 0
end

#operation(op, other) ⇒ Radix::Float (private)

Perform passed arithmetic operation.

Parameters:

Returns:


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# File 'lib/radix/float.rb', line 357

def operation(op, other)
  a = self.to_f
  b = other.to_f
  x = a.__send__(op, b)
  Radix::Float.new(x, base)

end

#parse_value(value, base) ⇒ Float (private)

Takes a Radix::Numeric, String or array and returns the decimal float value for storage in @value.

Parameters:

Returns:

  • (Float)

    Float value of Integer.


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# File 'lib/radix/float.rb', line 67

def parse_value(value, base)
  case value
  when Float, Integer # Radix
    parse_numeric(value.to_f, base)
  when ::Array
    parse_array(value, base)
  when ::String
    parse_string(value, base)
  when ::Numeric
    parse_numeric(value.to_f, base)
  end
end

#roundRadix::Float

Returns a new Radix::Float instance of same base, rounded to the nearest whole integer.

Examples:

Rounding Radix Float

> round_test = Radix::Float.new(123.03, 16)
7 11 . 0 7 10 14 1 4 7 10 14 1 (16)
> round_test.value
123.03
> round_test.round
7 11 . 0 (16)
> round_test.round.value
123.0
> round_test += 0.5
7 11 . 8 7 10 14 1 4 7 10 14 1 (16)
> round_test.value
123.53
> round_test.round
7 12 . 0 (16)
> round_test.round.value
124.0

Returns:


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# File 'lib/radix/float.rb', line 265

def round
  return self.class.new((value + 0.5).floor, base) if self > 0.0
  return self.class.new((value - 0.5).ceil,  base) if self < 0.0
  return self.class.new(0, base)
end

#split_digits(value) ⇒ Array<(Array<Fixnum>, Array<Fixnum>)> (private)

Returns the I-Part and F-Part of the passed value as arrays of fixnums.

Parameters:

Returns:


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# File 'lib/radix/float.rb', line 431

def split_digits(value)
  if d = value.index(DOT) || value.index('.')
    i, f = value[0...d], value[d+1..-1]
  else
    i, f = value, [0]
  end
  i.map!{ |x| x.to_i }
  f.map!{ |x| x.to_i }
  return i, f
end

#split_float(float) ⇒ Array<(Integer, Float)> (private)

Returns an array of Integer and Float portions of the Radix::Float

Parameters:

Returns:


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# File 'lib/radix/float.rb', line 448

def split_float(float)
  i, f = float.to_s.split('.')
  return i.to_i, ('0.'+f).to_f
end

#to_a(base = nil) ⇒ Array<Fixnum, String>

Makes this Radix::Float an array using code if defined. Returns an array using default chars otherwise.

Parameters:

  • base (Fixnum) (defaults to: nil)

    Desired base.

Returns:

  • (Array<Fixnum, String>)

    Current base encoded array.


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# File 'lib/radix/float.rb', line 108

def to_a(base=nil)
  if base
    convert(base).digits_encoded
  else
    digits_encoded
  end
end

#to_fFloat

Convert Radix::Float to a Ruby float.

Returns:

  • (Float)

    Base(10) value as Float.


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# File 'lib/radix/float.rb', line 96

def to_f
  value.to_f
end

#to_iInteger Also known as: to_int

Convert the Radix::Float a Ruby Integer.

Returns:

  • (Integer)

    Base(10) value as Integer.


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# File 'lib/radix/float.rb', line 86

def to_i
  to_f.to_i
end

#to_s(base = nil, divider = nil) ⇒ String

Note:

For base 10 or less does not use a divider unless specified.

Creates an encoded string in passed base, with passed digit divider.

Parameters:

  • base (Fixnum, Array<String>) (defaults to: nil)

    Desired base.

  • divider (String) (defaults to: nil)

    Desired divider character(s).

Returns:

  • (String)

    Encoded string with specified divider.


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# File 'lib/radix/float.rb', line 128

def to_s(base=nil, divider=nil)
  divider = divider.to_s if divider
  if base
    convert(base).to_s(nil, divider)
  else
    if code
      digits_encoded.join(divider)
    else
      if @base > 10
        digits.join(divider || DIVIDER)
      else
        digits.join(divider)
      end
    end
  end
end