On Feb 5, 2012, at 11:08, James Courtier-Dutton wrote: > But, r should be > 5.26300791462049950360708478127784... or > -1.020177392559086973318201985281... > according to wolfram alpha and most arbitrary maths libs I tried. > > I need to do a bit more digging, but this might point to a bug in the > cpu instruction FPREM1
No, this is all as expected. The instructions are documented to use a 66-bit approximation of Pi (really 64 bits, but the next two happen to be 0). Ada requires a relative error less than 2 eps for arguments in the range - 2.0**32 .. 2.0**32, for a binary floating point type with 64 bits of mantissa. So, he GCC Ada run time library uses a 150-bit or so approximation to ensure accurate argument reduction over the required range. Even with an approximation of Pi that is not precise enough to guarantee a small relative error of the result, there is still value in consistent argument reduction. For example, a point (Sin (X), Cos (X)) should always be close to the unit circle, regardless of the magnitude of X. -Geert
