RCR 322: Use log identities to improve BigMath::log performance

From the identity log(x*y) == log(x) + log(y) it follows that log(x*10^y) == log(x) + log(10^y). It also follows that log(10^y) == log(10) * y. Therefore, log(x*10^y) == log(x) + (log(10) * y).

This means the log of an arbitrarily large scientific-notation number can be calculated by taking the log of the fraction and the log of the power, both of which are very small by BigDecimal standards. Since BigDecimal addition and multiplication don't lose precision, the result is as precise as taking the log of the number without decomposing it.

A simple reimplementation of BigDecimal#log will use the existing implementation for small numbers, and decompose large numbers into their component parts.

 require 'bigdecimal'
 require 'bigdecimal/math'
 require 'bigdecimal/util'
 module BigMath
   alias :_log :log
   def log(x, prec)
     raise ArgumentError, "Zero or  negative argument for log" if x <= 0 ||  prec <= 0
     return _log(x, prec) if x <= 10
     return x if x.infinite? || x.nan?
     sign, fraction, power, exponent =  x.split
     fraction = BigDecimal(".#{fraction}")
     power = power.to_s.to_d
     _log(fraction, prec) + (_log(power,  prec) * exponent)
   end
 end