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in older generations only high end chips support double precission. that mean 58xx,5970, 69xx. in newest Southern Islands generation all chips will support double precision. only catch is that again only high end chips have "full" speed 1/4 DP rate in compare of SP rate. lower chips have slower DP rates like 1/16 so they are not usefull in some serious DP number crunching.
you can find aditional info in AMD OpenCL programing guide and http://en.wikipedia.org/wiki/Comparison_of_AMD_graphics_processing_units#Southern_Islands_.28HD_7xxx.29_series
The extensions supported are listed in table A.11 of the AMD APP OpenCL Programming Guide.
You can't really understand AMD hardware without that document, so you should always start there.
It's listed here:
Appendix D also has some other per-device specs.