1) asin[f l]() use Newton’s method to converge on a solution. But Newton’s method converges very slowly (> 500,000 iterations) for values of x close to 1.0; and, in the case of asinl(), sometimes fails to converge (loops forever). The attached patch uses an trig identity for values of x > sqrt(2). The resultant functions converge in no more than 5 iterations, 6 for asinl().
2) The NuttX erf[f l]() functions are based on Chebyshev fitting to a good guess. The problem there’s a bug in the implementation that causes the functions to blow up with x near -3.0. This patch fixes that problem. It should be noted that this method returns the error function erf(x) with fractional error less than 1.2E-07 and that’s fine for the float version erff(), but the same method is used for double and long double version which will yield only slightly better precision. This patch doesn't address the issue of lower precision for erf() and erfl().
3) a faster version of copysignf() for floats is included.
David S. Alessio