bigdecimal_to_f.rb

x = x0 = BigDecimal('1100000000000000087944964434022145632029003198634030825446485394267219165647576318369821312487531766087629873357328440099001976504255934373246955159552')
def to_f(x0)
  6.times do |shift|
    prec = 27 << shift
    exp = 0
    x = x0r = x0.mult(1, prec)
    [59, 16, 4, 1].each do |bit|
      while bit == 1 ? x >= 2**53 : x.exponent - 1 >= (53 + bit)*0.30104
        x = x.div(2**bit, prec)
        exp += bit
      end
    end
    [59, 16, 4, 1].each do |bit|
      while bit == 1 ? x < 2**52 : x.exponent < (53 - bit)*0.30102
        x = x.mult(2**bit, prec)
        exp -= bit
      end
    end
    d = BigDecimal(1)._decimal_shift(-prec + 20)
    if x.frac < 0.5 - d
      return [x.to_i, exp, prec]
    elsif x.frac > 0.5 + d
      return [x.to_i + 1, exp, prec]
    elsif shift == 5
      xi = x.to_i
      return [xi + (x0 < x0r ? 0 : x0 > x0r ? 1 : xi % 2), exp, prec, x0 <=> x0r]
    end
  end
end

xu = x + 1
xl = x - 1
xu2 = x + BigDecimal('1e-1000')
xl2 = x - BigDecimal('1e-1000')

[xu, xl, xu2, xl2, x].each do
  ans = to_f(it)
  p [ans, Math.ldexp(ans[0], ans[1]), eval(it.to_s)]
end