Re: cos (100000000.0)

Given the points about floating point numbers that other Monks have mentioned, there's a few points I'd like to raise:

Why are you taking the cosine of 100 million radians? I cannot think of any valid reason for doing that.
Why do you care that the answer has an error of 1 part in 1,000,000,000,000?
Why do you assume that it's perl that has the wrong answer?

Finally, my 64-bit perl running on AMD gives:

$ perl -le 'printf "%.55f\n", cos(100_000_000.0)'
-0.3633850893556905270465051671635592356324195861816406250
[download]

Thus proving that Perl >> Java >> C++, AMD >> Intel and that Thursday is the new pink :-)

Comment on Re: cos (100000000.0) Download Code

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Re^2: cos (100000000.0) by bart (Canon) on Sep 02, 2009 at 07:59 UTC
Why are you taking the cosine of 100 million radians? I cannot think of any valid reason for doing that. Amen to that. To the OP: trigonometric functions are about the most unreliable calculations that you can do on a computer. I think it is just not reasonable to expect very precise results, for such a huge parameter value. Actually, the difference in results between the different implementations is a lot smaller, than I had anticipated. Floating point in Perl has about 15 significant digits. For a function like `cos`, the digits before the decimal point don't really matter, as you may just as well use the parameter value modulo 2*PI, and (ideally) expect the same outcome. That means that for this parameter, with 8 digits wasted, you have about 6-7 significant digits left. That is how close you may expect the result of the calculation of `cos` to be. I am guessing you just made that parameter up, as a silly test.	[reply] [d/l] [select]

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Re^2: cos (100000000.0)
by bart (Canon) on Sep 02, 2009 at 07:59 UTC

Why are you taking the cosine of 100 million radians? I cannot think of any valid reason for doing that.

Amen to that.

To the OP: trigonometric functions are about the most unreliable calculations that you can do on a computer. I think it is just not reasonable to expect very precise results, for such a huge parameter value. Actually, the difference in results between the different implementations is a lot smaller, than I had anticipated.

Floating point in Perl has about 15 significant digits. For a function like cos, the digits before the decimal point don't really matter, as you may just as well use the parameter value modulo 2*PI, and (ideally) expect the same outcome. That means that for this parameter, with 8 digits wasted, you have about 6-7 significant digits left. That is how close you may expect the result of the calculation of cos to be.

I am guessing you just made that parameter up, as a silly test.

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