Geohash encode/decode floating point problems [LUCENE-1815]

i'm finding the Geohash support in the spatial package to be rather unreliable.
Here is the outcome of a test that encodes/decodes the same lat/lon and geohash a few times.
the format:
action geohash=(latitude, longitude)

the result:
encode u173zq37x014=(52.3738007,4.8909347)
decode u173zq37x014=(52.373799999999996,4.890934)
encode u173zq37rpbw=(52.373799999999996,4.890934)
decode u173zq37rpbw=(52.373799999999996,4.8909329999999995)
encode u173zq37qzzy=(52.373799999999996,4.8909329999999995)

if I now change to the google code implementation:

encode u173zq37x014=(52.3738007,4.8909347)
decode u173zq37x014=(52.37380061298609,4.890934377908707)
encode u173zq37x014=(52.37380061298609,4.890934377908707)
decode u173zq37x014=(52.37380061298609,4.890934377908707)
encode u173zq37x014=(52.37380061298609,4.890934377908707)

Note the differences between the geohashes in both situations and the lat/lon's!
Now things get worse if you work on low-precision geohashes:

decode u173=(52.0,4.0)
encode u14zg429yy84=(52.0,4.0)
decode u14zg429yy84=(52.0,3.999999)
encode u14zg429ywx6=(52.0,3.999999)

and google:

decode u173=(52.20703125,4.5703125)
encode u17300000000=(52.20703125,4.5703125)
decode u17300000000=(52.20703125,4.5703125)
encode u17300000000=(52.20703125,4.5703125)

We are using geohashes extensively and will now use the google code version unfortunately.

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Migrated from [LUCENE-1815](https://issues.apache.org/jira/browse/LUCENE-1815) by Wouter Heijke (@wheijke), updated Nov 30 2013

Start in Lucene's spatial package and inspect the current geohash encode/decode implementation against the Google code version described in the issue. Reproduce the supplied high- and low-precision examples, then verify that repeated encode/decode operations remain stable and that the resulting coordinates and geohashes match the intended behavior.

Written by the indexing model from the issue text.