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Well the Arduino IDE does use the GCC compiler.
Precision limitations are likely to be do to the use of uClibc. You might check there to see how double is implemented.
The Arduino IDE use of UClibc will not change since it is related to the amount of rom on the Galileo.
If you run an SD image based on eglibc, and run your programs directly on that image, 8 byte double precision should work for you. Just don't expect to use the IDE. SSH to the Galileo works like a dream - Mine has been up 24/7 for a month now.
A handy Linux reference that gives GCC options to invoke SSE is:
Message was edited by: Robert Mitchell to add link to GCC operands