[v3,0/7] Improve hypot()

  This patchset uses a different algorithm for hypot()  based on the
'An Improved Algorithm for hypot(a,b)' by Carlos F. Borges [1].  This
method is also used by Julia language.  The motivation for this change
are:

  1. The new algorithm is more precise without minimum performance
     difference.

  2. It allows to consolidate the implementations, since it favor
     floating-point operations over integer ones (as done for powerpc).
     This might be a boost for some architectures as well.

The current hypot() implementation seems already to be bounded to a
maximum of 1 ulp of error, however the new proposed algorithm shows an
slight precision improvement by showing more correctly rounded results.

 With a random 1e9 inputs for different float format I see:

  - An improvement from 3427362 to 18457 results with 1 ulp of
    error for Binary64.
  - An improvement from 233442 to 1274 results with 1 ulp of
    error for Binary96 (x86_64).
  - An improvement from 453045 to 1294 results with 1 ulp of
    error for Binary96 (x86_64).

Also for the maximal known error master shows (in ulps, with
corresponding inputs), determined with [3]:

  binary32  0.500 0x1.3ac98p+67,-0x1.ba5ec2p+77
  binary64  0.987 -0x0.5a934b7eac967p-1022,-0x0.b5265a7e06b82p-1022
  binary96  0.981 0x1.73f339f61eda21dp-16384l,0x2.e45f9f9500877e2p-16384l
  binary128 0.985 -0x2.d8311789103b76133ea1d5bc38c4p-16384,-0x1.6d85492006d7dcc6cc52938684p-16384

With the new implementation:

  binary32  0.500 0x1.3ac98p+67,-0x1.ba5ec2p+77 [same]
  binary64  0.792 0x0.603e52daf0bfdp-1022,-0x0.a622d0a9a433bp-1022
  binary96  0.584 -0x2.97b86706043d619p+7240l,0x1.8256bdd12d2e163ep+7240l
  binary128 0.749 0x2.2d5faf4036d6e68566f01054612p-8192,0x3.5738e8e2505f5d1fc2973716f05p-8192

Along with the newer implementation, the last patch also optimizes the
call with similar work done for other math functions by removing the
POSIX error handling (which is a big performance boost in some cases
and architectures).

I have adapted the dbl-64, ldbl-96, and ldbl-128, the flt-32 is not
required since it calls the dbl-64 one.  I have not adapated ldbl-128ibm
since the format has a lot of caveats and IBM aims to move to ldbl-128.

[1] https://arxiv.org/pdf/1904.09481.pdf
[2] https://github.com/JuliaLang/julia/commit/4a046009a3362ab5e17d369641dbbc9657eb680c
[3] https://gitlab.inria.fr/zimmerma/math_accuracy/-/blob/master/binary64/check_sample2.c

---
Changes from v2:
  - Improved the NaN and infinity checks.
  - Fixed i386 C implementation.

Adhemerval Zanella (7):
  math: Simplify hypotf implementation
  math: Use an improved algorithm for hypot (dbl-64)
  math: Use an improved algorithm for hypotl (ldbl-96)
  math: Use an improved algorithm for hypotl (ldbl-128)
  math: Remove powerpc e_hypot
  i386: Move hypot implementation to C
  math: Remove the error handling wrapper from hypot and hypotf

 math/Versions                                 |   2 +
 math/w_hypot.c                                |   8 +
 math/w_hypot_compat.c                         |  13 +-
 math/w_hypotf.c                               |   8 +
 math/w_hypotf_compat.c                        |   6 +-
 sysdeps/i386/fpu/e_hypot.S                    |  75 ------
 sysdeps/i386/fpu/e_hypot.c                    |  58 ++++
 sysdeps/i386/fpu/e_hypotf.S                   |  64 -----
 sysdeps/ieee754/dbl-64/e_hypot.c              | 247 ++++++++----------
 sysdeps/ieee754/dbl-64/w_hypot.c              |   1 +
 sysdeps/ieee754/flt-32/e_hypotf.c             |  75 +++---
 sysdeps/ieee754/flt-32/math_config.h          |   9 +
 sysdeps/ieee754/flt-32/w_hypotf.c             |   1 +
 sysdeps/ieee754/ldbl-128/e_hypotl.c           | 224 +++++++---------
 sysdeps/ieee754/ldbl-96/e_hypotl.c            | 229 +++++++---------
 sysdeps/mach/hurd/i386/libm.abilist           |   2 +
 sysdeps/powerpc/fpu/e_hypot.c                 |  87 ------
 sysdeps/powerpc/fpu/e_hypotf.c                |  78 ------
 .../powerpc32/power4/fpu/multiarch/Makefile   |   5 +-
 .../power4/fpu/multiarch/e_hypot-power7.c     |  23 --
 .../power4/fpu/multiarch/e_hypot-ppc32.c      |  23 --
 .../powerpc32/power4/fpu/multiarch/e_hypot.c  |  33 ---
 .../power4/fpu/multiarch/e_hypotf-power7.c    |  23 --
 .../power4/fpu/multiarch/e_hypotf-ppc32.c     |  23 --
 .../powerpc32/power4/fpu/multiarch/e_hypotf.c |  33 ---
 sysdeps/unix/sysv/linux/aarch64/libm.abilist  |   2 +
 sysdeps/unix/sysv/linux/alpha/libm.abilist    |   2 +
 sysdeps/unix/sysv/linux/arm/be/libm.abilist   |   2 +
 sysdeps/unix/sysv/linux/arm/le/libm.abilist   |   2 +
 sysdeps/unix/sysv/linux/hppa/libm.abilist     |   2 +
 sysdeps/unix/sysv/linux/i386/libm.abilist     |   2 +
 .../sysv/linux/m68k/coldfire/libm.abilist     |   2 +
 .../unix/sysv/linux/m68k/m680x0/libm.abilist  |   2 +
 .../sysv/linux/microblaze/be/libm.abilist     |   2 +
 .../sysv/linux/microblaze/le/libm.abilist     |   2 +
 .../unix/sysv/linux/mips/mips32/libm.abilist  |   2 +
 .../unix/sysv/linux/mips/mips64/libm.abilist  |   2 +
 sysdeps/unix/sysv/linux/nios2/libm.abilist    |   2 +
 .../linux/powerpc/powerpc32/fpu/libm.abilist  |   2 +
 .../powerpc/powerpc32/nofpu/libm.abilist      |   2 +
 .../linux/powerpc/powerpc64/be/libm.abilist   |   2 +
 .../linux/powerpc/powerpc64/le/libm.abilist   |   2 +
 .../unix/sysv/linux/s390/s390-32/libm.abilist |   2 +
 .../unix/sysv/linux/s390/s390-64/libm.abilist |   2 +
 sysdeps/unix/sysv/linux/sh/be/libm.abilist    |   2 +
 sysdeps/unix/sysv/linux/sh/le/libm.abilist    |   2 +
 .../sysv/linux/sparc/sparc32/libm.abilist     |   2 +
 .../sysv/linux/sparc/sparc64/libm.abilist     |   2 +
 .../unix/sysv/linux/x86_64/64/libm.abilist    |   2 +
 .../unix/sysv/linux/x86_64/x32/libm.abilist   |   2 +
 50 files changed, 495 insertions(+), 905 deletions(-)
 create mode 100644 math/w_hypot.c
 create mode 100644 math/w_hypotf.c
 delete mode 100644 sysdeps/i386/fpu/e_hypot.S
 create mode 100644 sysdeps/i386/fpu/e_hypot.c
 delete mode 100644 sysdeps/i386/fpu/e_hypotf.S
 create mode 100644 sysdeps/ieee754/dbl-64/w_hypot.c
 create mode 100644 sysdeps/ieee754/flt-32/w_hypotf.c
 delete mode 100644 sysdeps/powerpc/fpu/e_hypot.c
 delete mode 100644 sysdeps/powerpc/fpu/e_hypotf.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot-power7.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot-ppc32.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf-power7.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf-ppc32.c
 delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf.c