Module: Flt::Support::AuxiliarFunctions

Included in:
Num
Defined in:
lib/flt/support.rb

Constant Summary

NBITS_BLOCK =
32
NBITS_LIMIT =
Math.ldexp(1,Float::MANT_DIG).to_i
NDIGITS_BLOCK =
50
NDIGITS_LIMIT =
Float::MAX.to_i

Class Method Summary collapse

Class Method Details

._nbits(x) ⇒ Object

Number of bits in binary representation of the positive integer n, or 0 if n == 0.

Raises:

  • (TypeError)


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# File 'lib/flt/support.rb', line 75

def _nbits(x)
  raise  TypeError, "The argument to _nbits should be nonnegative." if x < 0
  if x.is_a?(Fixnum)
    return 0 if x==0
    x.to_s(2).length
  elsif x <= NBITS_LIMIT
    Math.frexp(x).last
  else
    n = 0
    while x!=0
      y = x
      x >>= NBITS_BLOCK
      n += NBITS_BLOCK
    end
    n += y.to_s(2).length - NBITS_BLOCK if y!=0
    n
  end
end

._ndigits(x, b) ⇒ Object

Number of base b digits in an integer

Raises:

  • (TypeError)


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# File 'lib/flt/support.rb', line 97

def _ndigits(x, b)
  raise  TypeError, "The argument to _ndigits should be nonnegative." if x < 0
  return 0 unless x.is_a?(Integer)
  return _nbits(x) if b==2
  if x.is_a?(Fixnum)
    return 0 if x==0
    x.to_s(b).length
  elsif x <= NDIGITS_LIMIT
    (Math.log(x)/Math.log(b)).floor + 1
  else
    n = 0
    block = b**NDIGITS_BLOCK
    while x!=0
      y = x
      x /= block
      n += NDIGITS_BLOCK
    end
    n += y.to_s(b).length - NDIGITS_BLOCK if y!=0
    n
  end
end

.detect_float_roundingObject



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# File 'lib/flt/support.rb', line 121

def detect_float_rounding
  x = x = Math::ldexp(1, Float::MANT_DIG+1) # 10000...00*Float::RADIX**2 == Float::RADIX**(Float::MANT_DIG+1)
  y = x + Math::ldexp(1, 2)                 # 00000...01*Float::RADIX**2 == Float::RADIX**2
  h = Float::RADIX/2
  b = h*Float::RADIX
  z = Float::RADIX**2 - 1
  if x + 1 == y
    if (y + 1 == y) && Float::RADIX==10
      :up05
    elsif -x - 1 == -y
      :up
    else
      :ceiling
    end
  else # x + 1 == x
    if x + z == x
      if -x - z == -x
        :down
      else
        :floor
      end
    else # x + z == y
      # round to nearest
      if x + b == x
        if y + b == y
          :half_down
        else
          :half_even
        end
      else # x + b == y
        :half_up
      end
    end
  end
end