Stable Cotangent

c++ trigonometry
Meh. picture Meh. · Sep 17, 2010 · Viewed 20.9k times · Source

Is there a more stable implementation for the cotangent function than return 1.0/tan(x);?

Answer

zwol picture zwol · Sep 17, 2010

cot(x) = cos(x)/sin(x) should be more numerically stable close to π/2 than cot(x) = 1/tan(x). You can implement that efficiently using sincos on platforms that have it.

Another possibility is cot(x) = tan(M_PI_2 - x). This should be faster than the above (even if sincos is available), but it may also be less accurate, because M_PI_2 is of course only an approximation of the transcendental number π/2, so the difference M_PI_2 - x will not be accurate to the full width of a double mantissa -- in fact, if you get unlucky, it may have only a few meaningful bits.

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