Commits on Feb 2, 2024

1. Intrinsics: Faster cuberoot scaling functions …

   This patch replaces the intrinsic-based exponent rescaling with explicit
   bit manipulation of the floating point number.
   
   This appears to produce a ~2.5x speedup of the solver, reducing its time
   from embarassingly slow to disappointingly slow.  It is slightly faster
   than the GNU cbrt function, but still about 3x slower than the Intel
   SVML cbrt function.
   
   Timings (s) (16M array, -O3 -mavx -mfma)
   
   | Solver              |  -O2  |  -O3  |
   |---------------------|-------|-------|
   | GNU x**1/3          | 0.225 | 0.198 |
   | GNU cuberoot before | 0.418 | 0.412 |
   | GNU cuberoot after  | 0.208 | 0.187 |
   | Intel x**1/3        | 0.068 | 0.067 |
   | Intel before        | 0.514 | 0.507 |
   | Intel after         | 0.213 | 0.189 |
   
   At least one issue here is that Intel SVML is using fast vectorized
   logic operators whereas the Fortran intrinsics are replaced with slower
   legacy scalar versions.  Not sure there is much we could even do about
   that without complaining to vendors.
   
   Also, I'm sure there's magic in their solvers which we are not
   capturing.  Regardless, I think this is a major improvement.
   
   I do not believe it will change answers, but probably a good idea to
   verify this and get it in before committing any solutions using
   cuberoot().

   

   marshallward authored and Hallberg-NOAA committed Feb 2, 2024
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2. Cuberoot: Refactor (re|de)scale functions …

   Some modifications were made to the cuberoot rescale and descale
   functions:
   
   * The machine parameters were moved from function to module parameters.
     This could dangerously expose them to other functions, but it prevents
     multiple definitions of the same numbers.
   
   * The exponent is now cube-rooted in rescale rather than descale.
   
   * The exponent expressions are broken into more explicit steps, rather
     than combining multiple steps and assumptions into a single
     expression.
   
   * The bias is no longer assumed to be a multiple of three.  This is true
     for double precision but not single precision.
   
   A new test of quasi-random number was also added to the cuberoot test
   suite.  These numbers were able to detect the differences in GNU and
   Intel compiler output.  A potential error in the return value of the
   test was also fixed.
   
   The volatile test of 1 - 0.5*ULP has been added.  The cube root of this
   value rounds to 1, and needs to be handled carefully.
   
   The unit test function `cuberoot(v**3)` was reversed to `cuberoot(v)**`,
   to include testing of this value.  (Cubing would wipe out the anomaly.)

   

   marshallward authored and Hallberg-NOAA committed Feb 2, 2024
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3. Cuberoot: Break **3 into explicit integer cubes …

   In separate testing, we observed that Intel would use the `pow()`
   function to evaluate the cubes of some numbers, causing different
   answers with GNU.
   
   In this patch, I replace the cubic x**3 operations with explicit x*x*x
   multiplication, which appears to avoid this substitution.
   
   Well, for the moment, at least.

   

   marshallward authored and Hallberg-NOAA committed Feb 2, 2024
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