On Thu, 26 May 2005, Paul Koning wrote: > >>>>> "Kevin" == Kevin Handy <[EMAIL PROTECTED]> writes: > > Kevin> But, you are using a number in the range of 2^90, only have 64 > Kevin> bits for storing the floating point representation, and some > Kevin> of that is needed for the exponent. > > Fair enough, so with 64 bit floats you have no right to expect an > accurate answer for sin(2^90). However, you DO have a right to expect > an answer in the range [-1,+1] rather than the 1.2e+27 that Richard > quoted. I see no words in the description of > -funsafe-math-optimizations to lead me to expect such a result.
When I discussed this question with Nick Maclaren a while back after a UK C Panel meeting, his view was that for most applications (a) the output should be close (within 1 or a few ulp) to the sine/cosine of a value close (within 1 or a few ulp) to the floating-point input and (b) sin^2 + cos^2 (of any input value) should equal 1 with high precision, but most applications (using floating-point values as approximations of unrepresentable real numbers) wouldn't care about the answer being close to the sine or cosine of the exact real number represented by the floating-point value when 1ulp is on the order of 2pi or bigger. This does of course disallow 1.2e+27 as a safe answer for sin or cos to give for any input. (And a few applications may care for stronger degrees of accuracy.) -- Joseph S. Myers http://www.srcf.ucam.org/~jsm28/gcc/ [EMAIL PROTECTED] (personal mail) [EMAIL PROTECTED] (CodeSourcery mail) [EMAIL PROTECTED] (Bugzilla assignments and CCs)
