Note, it occurs to me that while the AVR compiler converts 'double' into being a 32-bit representation (same as 'float'), that ARM chips will provide a 64-bit IEEE format, and for the the OP, this might solve a lot of headaches to switch processors. On October 22nd, the DUE will be available and it should be fairly compatible with the current AVR based Arduino's, but there are various other ARM solutions out there right now that you might need to learn a new IDE for. Or if you don't need hard realtime, the Raspberry Pi is available.
Now, if you are doing lots and lots of floating point arithmetic, you might want to get a chip with hardware floating point (unfortunately the DUE will not have hardware FP).