Figure 1 A Number in Factorial-Base Expressed as an Array

      |<-- integer part ->|  |<- fraction part ->|
 +----+----+----+    +----+----+----+----+    +----+----+
 |    | 1! | 2! | .. | i! |    | 1! | 2! | .. | f! |    |
 +----+----+----+    +----+----+----+----+    +----+----+
    0   1     2         i    G   G+1  G+2       G+f  G2
 [0]   The sign.
 [1]   An integer portion of i factorial-base digits.
  |    The value of [n] ranges from 0 to n, The value
 [i]   of the integer portion is ?*1! + ?*2! + ... + ?*i!
 [G]   A guard to detect integer overflow.
 [G+1] Records carrys & borrows during normalization.
 [G+2] A fractional portion of f-1 factorial-base digits.
  |    The value of [n] ranges from 0 to n-1. The value
 [G+f] of the fraction is ?/2! + ?/3! + ... + ?/f!
 [G2]  A guard to detect fractional underflow.