Is there a more stable implementation for the cotangent function than return 1.0/tan(x);?
Is there a more stable implementation for the cotangent function than return 1.0/tan(x);?
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Is there a more stable implementation for the cotangent function than return 1.0/tan(x);?
cot(x) = cos(x)/sin(x)should be more numerically stable close to π/2 thancot(x) = 1/tan(x). You can implement that efficiently usingsincoson platforms that have it.Another possibility is
cot(x) = tan(M_PI_2 - x). This should be faster than the above (even ifsincosis available), but it may also be less accurate, becauseM_PI_2is of course only an approximation of the transcendental number π/2, so the differenceM_PI_2 - xwill not be accurate to the full width of adoublemantissa — in fact, if you get unlucky, it may have only a few meaningful bits.