atan

# File ext/bigdecimal/lib/bigdecimal/math.rb, line 145
  def atan(x, prec)
    raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
    return BigDecimal("NaN") if x.nan?
    pi = PI(prec)
    x = -x if neg = x < 0
    return pi.div(neg ? -2 : 2, prec) if x.infinite?
    return pi / (neg ? -4 : 4) if x.round(prec) == 1
    x = BigDecimal("1").div(x, prec) if inv = x > 1
    x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5
    n    = prec + BigDecimal.double_fig
    y = x
    d = y
    t = x
    r = BigDecimal("3")
    x2 = x.mult(x,n)
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      t = -t.mult(x2,n)
      d = t.div(r,m)
      y += d
      r += 2
    end
    y *= 2 if dbl
    y = pi / 2 - y if inv
    y = -y if neg
    y
  end