Fourth Draft "Unsafe fp optimizations" project description.
Stephen L Moshier
moshier@mediaone.net
Sun Aug 12 08:37:00 GMT 2001
> | The loss of accuracy is due to subtractive cancellation, an error source
> | that your document does not mention.
>
> Actually on x86, sin(x) just returns x for "large" values of x.
x at about 2^62 is the coprocessor's total loss of precision
threshold, where the error approaches 100% and the 8087 sets a
hardware flag. The error increases gradually to that point, however.
The threshold, where the range reduction error due to cancellation
begins, is about x = 2^18 for double precision and x = 2^47 for single
precision.
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