Module: Nio::BurgerDybvig

Defined in:
lib/nio/fmt.rb

Overview

:nodoc: all

Class Method Summary collapse

Class Method Details

.exptt(_B, k) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1425

def exptt(_B, k)
  if _B==10 && k>=0 && k<326 
    $exptt_table[k]
  else
    _B**k
  end
end

.fixup(r, s, m_p, m_m, k, _B, low_ok, high_ok) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1363

def fixup(r,s,m_p,m_m,k,_B,low_ok,high_ok)
  if (high_ok ? (r+m_p >= s) : (r+m_p > s)) # too low?
    [r,s*_B,m_p,m_m,k+1]
  else
    [r,s,m_p,m_m,k]
  end
end

.float_to_digits(v, f, e, round_mode, min_e, p, b, _B) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1314

def float_to_digits(v,f,e,round_mode,min_e,p,b,_B)
 
 case round_mode
   when :even
     roundl = roundh = f.even?
   when :inf
     roundl = true
     roundh = false
   when :zero
     roundl = false
     roundh = true
   else
     # here we don't assume any rounding in the floating point numbers
     # the result is valid for any rounding but may produce more digits
     # than stricly necessary for specifica rounding modes.
     roundl = false
     roundh = false
 end
  
    if e >= 0
      if f != exptt(b,p-1)
        be = exptt(b,e)
        r,s,m_p,m_m,k = scale(f*be*2,2,be,be,0,_B,roundl ,roundh,v)
      else
        be = exptt(b,e)
        be1 = be*b
        r,s,m_p,m_m,k = scale(f*be1*2,b*2,be1,be,0,_B,roundl ,roundh,v)
      end
    else
      if e==min_e or f != exptt(b,p-1)
        r,s,m_p,m_m,k = scale(f*2,exptt(b,-e)*2,1,1,0,_B,roundl ,roundh,v)
      else
        r,s,m_p,m_m,k = scale(f*b*2,exptt(b,1-e)*2,b,1,0,_B,roundl ,roundh,v)
      end
    end
    [k]+generate(r,s,m_p,m_m,_B,roundl ,roundh)
end

.float_to_digits_max(v, f, e, round_mode, min_e, p, b, _B) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1443

def float_to_digits_max(v,f,e,round_mode,min_e,p,b,_B)
 
 case round_mode
   when :even
     roundl = roundh = f.even?
   when :inf
     roundl = true
     roundh = false
   when :zero
     roundl = false
     roundh = true
   else
     # here we don't assume any rounding in the floating point numbers
     # the result is valid for any rounding but may produce more digits
     # than stricly necessary for specifica rounding modes.
     roundl = false
     roundh = false
 end
  
    if e >= 0
      if f != exptt(b,p-1)
        be = exptt(b,e)
        r,s,m_p,m_m,k = scale(f*be*2,2,be,be,0,_B,roundl ,roundh,v)
      else
        be = exptt(b,e)
        be1 = be*b
        r,s,m_p,m_m,k = scale(f*be1*2,b*2,be1,be,0,_B,roundl ,roundh,v)
      end
    else
      if e==min_e or f != exptt(b,p-1)
        r,s,m_p,m_m,k = scale(f*2,exptt(b,-e)*2,1,1,0,_B,roundl ,roundh,v)
      else
        r,s,m_p,m_m,k = scale(f*b*2,exptt(b,1-e)*2,b,1,0,_B,roundl ,roundh,v)
      end
    end
    [k]+generate_max(r,s,m_p,m_m,_B,roundl ,roundh)
end

.generate(r, s, m_p, m_m, _B, low_ok, high_ok) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1388

def generate(r,s,m_p,m_m,_B,low_ok ,high_ok)
  list = []
  loop do
    d,r = (r*_B).divmod(s)
    m_p *= _B
    m_m *= _B
    tc1 = low_ok ? (r<=m_m) : (r<m_m)
    tc2 = high_ok ? (r+m_p >= s) : (r+m_p > s)

     if not tc1
      if not tc2
        list << d
      else
        list << d+1
        break
      end
    else
      if not tc2
        list << d
        break
      else
        if r*2 < s
          list << d
          break
        else
          list << d+1
          break
        end
      end
    end
    
  end
  list
end

.generate_max(r, s, m_p, m_m, _B, low_ok, high_ok) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1481

def generate_max(r,s,m_p,m_m,_B,low_ok ,high_ok)
  list = [false]
  loop do
    d,r = (r*_B).divmod(s)
    m_p *= _B
    m_m *= _B
    
    list << d
        
    tc1 = low_ok ? (r<=m_m) : (r<m_m)
    tc2 = high_ok ? (r+m_p >= s) : (r+m_p > s)
        
    if tc1 && tc2
      list[0] = true if r*2 >= s
      break
    end    
  end
  list
end

.logB(_B, x) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1435

def logB(_B, x)
  if _B>=2 && _B<37
    Math.log(x)*$logB_table[_B]
  else
    Math.log(x)/Math.log(_B)
  end
end

.scale(r, s, m_p, m_m, k, _B, low_ok, high_ok, v) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1352

def scale(r,s,m_p,m_m,k,_B,low_ok ,high_ok,v)
  return scale2(r,s,m_p,m_m,k,_B,low_ok ,high_ok) if v==0
  est = (logB(_B,v)-1E-10).ceil.to_i
  if est>=0 
    fixup(r,s*exptt(_B,est),m_p,m_m,est,_B,low_ok,high_ok)
  else
    sc = exptt(_B,-est)
    fixup(r*sc,s,m_p*sc,m_m*sc,est,_B,low_ok,high_ok)
  end
end

.scale2(r, s, m_p, m_m, k, _B, low_ok, high_ok) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 1371

def scale2(r,s,m_p,m_m,k,_B,low_ok ,high_ok)
  loop do
    if (high_ok ? (r+m_p >= s) : (r+m_p > s)) # k is too low
      s *= _B
      k += 1
    elsif (high_ok ? ((r+m_p)*_B<s) : ((r+m_p)*_B<=s)) # k is too high
      r *= _B
      m_p *= _B
      m_m *= _B
      k -= 1
    else
      break
    end
  end
  [r,s,m_p,m_m,k]
end