  Data files often consist of numbers having only a few significant decimal
digits, whose information content would allow storage in only 32 bits. However,
we may require that arithmetic operations involving these numbers be done with
64-bit floating-point precision, which precludes simply representing the data
as 32-bit floating-point values. Decimal floating point gives a compact and
exact representation, but requires conversion with a slow division operation
before it can be used. Here, I show that interesting subsets of 64-bit
floating-point values can be compactly and exactly represented by the 32 bits
consisting of the sign, exponent, and high-order part of the mantissa, with the
lower-order 32 bits of the mantissa filled in by table lookup, indexed by bits
from the part of the mantissa retained, and possibly from the exponent. For
example, decimal data with 4 or fewer digits to the left of the decimal point
and 2 or fewer digits to the right of the decimal point can be represented in
this way using the lower-order 5 bits of the retained part of the mantissa as
the index. Data consisting of 6 decimal digits with the decimal point in any of
the 7 positions before or after one of the digits can also be represented this
way, and decoded using 19 bits from the mantissa and exponent as the index.
Encoding with such a scheme is a simple copy of half the 64-bit value, followed
if necessary by verification that the value can be represented, by checking
that it decodes correctly. Decoding requires only extraction of index bits and
a table lookup. Lookup in a small table will usually reference cache; even with
larger tables, decoding is still faster than conversion from decimal floating
point with a division operation. I discuss how such schemes perform on recent
computer systems, and how they might be used to automatically compress large
arrays in interpretive languages such as R.

Computation;Mathematical Software;Numerical Analysis