From: C Erler <erlercw@...>
Date: 2006-01-23T07:47:06+09:00
Subject: BigMath::log speedup patch

Someone else submitted a BigMath::log speedup at
http://www.rcrchive.net/rcr/show/322.  This doesn't appear to be a big
enough change for an RCR, so I'm submitting it as a patch.  To save
you a bit of time, I've combined the suggested log method with the
original (they were separate methods in the RCR) and removed the need
for bigdecimal/util.rb :

In bigdecimal/math.rb :

  def log(x, prec)
    raise ArgumentError, "Zero or negative argument for log" if x <= 0
|| prec <= 0
    return x if x.infinite? || x.nan?
    if x > 10
      sign, fraction, power, exponent =  x.split
      fraction = BigDecimal(".#{fraction}")
      power = BigDecimal(power.to_s)
      log(fraction, prec) + (log(power,  prec) * exponent)
    else
      one = BigDecimal("1")
      two = BigDecimal("2")
      n  = prec + BigDecimal.double_fig
      x  = (x - one).div(x + one,n)
      x2 = x.mult(x,n)
      y  = x
      d  = y
      i  = one
      while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
        m = BigDecimal.double_fig if m < BigDecimal.double_fig
        x = x2.mult(x,n)
        i += two
        d = x.div(i,m)
        y += d
      end
      y * two
    end
  end

I've only tested this by taking the logarithm of 500 to a precision of
200.  This sped it up quite a bit.  If this is good, can someone
please patch it in and attribute it to leonardr on the RCR site
(rather than me) ?  Thanks.