Class: Float

Inherits:
Object
  • Object
show all
Includes:
Nio::Formattable
Defined in:
lib/nio/fmt.rb,
lib/nio/rtnlzr.rb,
lib/nio/rtnlzr.rb

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Nio::Formattable

append_features, #nio_round, #nio_write

Class Method Details

.nio_read_neutral(neutral) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1303

def self.nio_read_neutral(neutral)
  x = nil
  
  honor_rounding = true
  
  if neutral.special?
    case neutral.special
      when :nan
        x = 0.0/0.0
      when :inf
        x = (neutral.sign=='-' ? -1.0 : +1.0)/0.0
    end
  elsif neutral.rep_pos<neutral.digits.length
    
    x,y = neutral.to_RepDec.getQ
    x = Float(x)/y
    
  else
    nd = neutral.base==10 ? Float::DIG : ((Float::MANT_DIG-1)*Math.log(2)/Math.log(neutral.base)).floor
    k = neutral.dec_pos-neutral.digits.length
    if !honor_rounding && (neutral.digits.length<=nd && k.abs<=15)
      x = neutral.digits.to_i(neutral.base).to_f
      if k<0
        x /= Float(neutral.base**-k)
      else
        x *= Float(neutral.base**k)
      end
      x = -x if neutral.sign=='-'
    elsif !honor_rounding && (k>0 && (k+neutral.digits.length < 2*nd))
      j = k-neutral.digits.length
      x = neutral.digits.to_i(neutral.base).to_f * Float(neutral.base**(j))
      x *= Float(neutral.base**(k-j))
      x = -x if neutral.sign=='-'
    elsif neutral.base.modulo(Float::RADIX)==0
     
     f = neutral.digits.to_i(neutral.base)
     e = neutral.dec_pos-neutral.digits.length

     rounding = case neutral.rounding
     when :even
       :half_even
     when :zero
       :half_down
     when :inf
       :half_up
     when :truncate
       :down
     when :directed_up
       :up
     when :floor
       :floor
     when :ceil
       :ceil
     else
       nil
     end
     
     reader = Flt::Support::Reader.new(:mode=>:fixed)
     sign = neutral.sign == '-' ? -1 : +1
     x = reader.read(Float.context, rounding, sign, f, e, neutral.base)
     exact = reader.exact?
     
    else
     
     f = neutral.digits.to_i(neutral.base)
     e = neutral.dec_pos-neutral.digits.length

     rounding = case neutral.rounding
     when :even
       :half_even
     when :zero
       :half_down
     when :inf
       :half_up
     when :truncate
       :down
     when :directed_up
       :up
     when :floor
       :floor
     when :ceil
       :ceil
     else
       nil
     end
     
     reader = Flt::Support::Reader.new(:mode=>:fixed)
     sign = neutral.sign == '-' ? -1 : +1
     x = reader.read(Float.context, rounding, sign, f, e, neutral.base)
     exact = reader.exact?
     
    end
  end
  
  return x
end

Instance Method Details

#nio_r(tol = Flt.Tolerance(:big_epsilon)) ⇒ Object 



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# File 'lib/nio/rtnlzr.rb', line 107

def nio_r(tol = Flt.Tolerance(:big_epsilon))
  case tol
    when Integer
      Rational(*Nio::Rtnlzr.max_denominator(self,tol,Float))
    else
      Rational(*Nio::Rtnlzr.new(tol).rationalize(self))
  end
end

#nio_write_neutral(fmt) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1399

def nio_write_neutral(fmt)
  neutral = Nio::NeutralNum.new
  x = self
  
  if x.nan?
    neutral.set_special(:nan)
  elsif x.infinite?
    neutral.set_special(:inf, x<0 ? '-' : '+')
  else
    converted = false
    if fmt.get_ndig==:exact && fmt.get_approx==:simplify
      
      if x!=0
        q = x.nio_r(Flt.Tolerance(Float::DIG, :sig_decimals))
        if q!=0
          neutral = q.nio_write_neutral(fmt)
          converted = true if neutral.digits.length<=Float::DIG
        end
      end
      
    elsif fmt.get_approx==:exact
      neutral = x.nio_xr.nio_write_neutral(fmt)
      converted = true
    end
    if !converted
      if fmt.get_base==10 && false
        txt = format "%.*e",Float::DECIMAL_DIG-1,x # note that spec. e output precision+1 significant digits
        
        sign = '+'
        if txt[0,1]=='-'
          sign = '-'
          txt = txt[1...txt.length]
        end
        exp = 0
        x_char = fmt.get_exp_char(fmt.get_base)

        exp_i = txt.index(x_char)
        exp_i = txt.index(x_char.downcase) if exp_i===nil
        if exp_i!=nil
          exp = txt[exp_i+1...txt.length].to_i
          txt = txt[0...exp_i]
        end
        
        dec_pos = txt.index '.'
        if dec_pos==nil
          dec_pos = txt.length
        else
          txt[dec_pos]=''
        end
        dec_pos += exp
        neutral.set sign, txt, dec_pos, nil, fmt.get_base_digits(10), true, fmt.get_round
        
        converted = true
      end
    end
    if !converted
      
      sign = x<0 ? '-' : '+'
      f,e = Math.frexp(x)
      if e < Float::MIN_EXP
        # denormalized number
        f = Math.ldexp(f,e-Float::MIN_EXP+Float::MANT_DIG)
        e = Float::MIN_EXP-Float::MANT_DIG
      else
        # normalized number
        f = Math.ldexp(f,Float::MANT_DIG)
        e -= Float::MANT_DIG
      end
      f = f.to_i
      inexact = true

      rounding = case fmt.get_round
      when :even
        :half_even
      when :zero
        :half_down
      when :inf
        :half_up
      when :truncate
        :down
      when :directed_up
        :up
      when :floor
        :floor
      when :ceil
        :ceil
      else
        nil
      end
      

      # Note: it is assumed that fmt will be used for for input too, otherwise
      # rounding should be Float.context.rounding (input rounding for Float) rather than fmt.get_round (output)
      formatter = Flt::Support::Formatter.new(Float::RADIX,  Float::MIN_EXP-Float::MANT_DIG, fmt.get_base)
      formatter.format(x, f, e, rounding, Float::MANT_DIG, fmt.get_all_digits?)
      inexact = formatter.round_up if formatter.round_up.is_a?(Symbol)
      dec_pos, digits = formatter.digits
      txt = ''
      digits.each{|d| txt << fmt.get_base_digits.digit_char(d)}
      neutral.set sign, txt, dec_pos, nil, fmt.get_base_digits, inexact, fmt.get_round
      
    end
  end
  
  return neutral
end

#nio_xr ⇒ Object

Conversion to Rational preserving the exact value of the number.



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# File 'lib/nio/rtnlzr.rb', line 36

def nio_xr
  return Rational(self.to_i,1) if self.modulo(1)==0
  if !self.finite?
    return Rational(0,0) if self.nan?
    return self<0 ? Rational(-1,0) : Rational(1,0)
  end

  f,e = Math.frexp(self)

  if e < Float::MIN_EXP
     bits = e+Float::MANT_DIG-Float::MIN_EXP
  else
     bits = [Float::MANT_DIG,e].max
     #return Rational(self.to_i,1) if bits<e
  end
    p = Math.ldexp(f,bits)
    e = bits - e
    if e<Float::MAX_EXP
      q = Math.ldexp(1,e)
    else
      q = Float::RADIX**e
    end
  return Rational(p.to_i,q.to_i)
end