CVS log for src/tests/lib/libm/t_cbrt.c

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Keyword substitution: kv
Default branch: MAIN

fix the cbrtl/powl test

Sync with HEAD

Sync with HEAD, resolve a couple of conflicts

cbrtl_powl is xfail only if long double has more bits than double.

Fix up libm tests.

- Fix up last few digits of a lot of known-answer tests.

  Confirmed with GNU mpfr to 200 bits of precision and cross-checked
  with whatever libm Ubuntu ships with.

- Test relative error, not absolute error.

- Set bounds in terms of *_EPSILON, not magic numbers.

  *_EPSILON is twice the largest relative error of a correctly
  rounded operation, and equal to the largest relative error of an
  operation with up to 1ulp error.

  Most of the operations we're testing are not correctly rounded, but
  they ought to be no more than 1ulp away.  For the few cases where
  that's not a priori clear (like comparing cbrt and pow(x, 1/3)),
  use twice *_EPSILON to allow some leeway.

- Write the success condition positively as error <= eps.

  This comes out false if the result is a NaN, meaning failure.  In
  contrast, if we write error > eps for the _failure_ condition, then
  if the result is a NaN, it will also come out false, but meaning
  success, which is not what we want.

- Fix the trigonometric test cases near bad spots.

  sin(pi - d) for nonzero d is not zero; it is d + O(d^3).  pi is not
  a floating-point number, so these results should be approximately
  the nonzero error of our approximation to pi.  Likewise with
  cos(pi/2 - d) and tan(pi + d).

  (Yes, I know the sin _function_ is ill-conditioned near pi so you
  shouldn't pass approximate inputs near there, but that's separate
  from whether a sin _implementation_ gives an answer that is wrong
  by quintillions of ulps.)

  Since on x86 (i386 and amd64 alike) we currently use x87 hardware
  trigonometric instructions, which are bad, these are marked xfail
  on x86 for now until we switch to software implementations (coming
  soon to a repository near you).

- Use %.8g, %.17g, %.35g to print float, double, long double in failures.

  This should be enough to identify the problematic outputs and/or
  reproduce the computation, even if long double is binary128 with
  115 bits of precision.

If there are any new libm test failures after this, tell me what
architecture you're on and send me the atf output and I'll try to
figure it out.

Rebase to HEAD as of a few days ago.

sync with head.

for a reference, the tree before this commit was tagged
as yamt-pagecache-tag8.

this commit was splitted into small chunks to avoid
a limitation of cvs.  ("Protocol error: too many arguments")

Remove all cargo-cult #ifndef __vax__ from the tests, that just paper
over bugs in the vax libm.

Add cbrtl(3) and sqrtl(3), from FreeBSD.

Basic checks for the root functions.