Extended precision logarithmic arithmetic

We present a technique with which arithmetic implemented in the logarithmic number system may be performed at considerably higher precision than normally available at 32 bits, with little additional hardware or execution time. Use of the technique requires that all data lie in a restricted range, and relies on scaling each such value into the maximum range of the number system. We illustrate the procedure using a recursive least squares algorithm. We show that the restriction is easily accommodated, and that the technique can yield very substantial gains in accuracy and numerical stability over 32-bit floating-point.