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I did however manage to find the following URL of interest: http://www.active-web.cc/html/research/sine/sin-cos.txt All of the algorithms for precomputing FFT sin/cos tables given on that page appear to be unaffected by -ffast-math.
sin(a + da) = cos(da) * sin(a) + sin(da) * cos(a) = sin(a) + ((cos(da)-1) * sin(a) + sin(da) * cos(a)) = sin(a) + ((-2*sin^2(da/2)) * sin(a) + sin(da) * cos(a))
Then just to double check, I've just built and run "make check" on GNU gmp-4.1.2 as configured by default and then again with CC="gcc -ffast-math". No failures/differences. This is especially relevant to your concerns, as mpn/generic/mul_fft.c contains code to perform bignum multiplications using Karatsuba, 3-way Toom-Cook, and Fermat FFT.
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