From: Adhemerval Zanella <adhemerval.zanella@linaro.org>
To: libc-alpha@sourceware.org,
Paul Zimmermann <Paul.Zimmermann@inria.fr>,
Wilco Dijkstra <Wilco.Dijkstra@arm.com>
Subject: [PATCH v5 00/12] Improve hypot
Date: Tue, 7 Dec 2021 16:03:41 -0300 [thread overview]
Message-ID: <20211207190353.3282666-1-adhemerval.zanella@linaro.org> (raw)
This patchset add a different algorithm along with Wilco [1] performance
improvements. The default implementation is based on the 'An Improved
Algorithm for hypot(a,b)' by Carlos F. Borges [2] with some fixes and
improvements (although the dbl-64 one uses a slight different approach
when fast FMA is avaliable). This method is also used by Julia language
runtime [2].
The motivation for this change are:
1. Use a newer algotihm that favor FP operations over interger ones
(which tends to show better performance specially on newer
processor with multiple FP units). It also allows consolidate
the multiple implementation (for instance, the powerpc one).
2. The new algorithm is more precise without minimum performance
difference.
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
If FMA is uses the binary64 shows a slight worse precision:
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://sourceware.org/pipermail/libc-alpha/2021-November/133523.html
[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 v5:
* Add missing cast on generic hypotf.
* Add missing math_narrow_eval on generic hypot.
* Fixed return value on generic ldbl-96 hypotl.
* Fixed return value on generic ldbl-128 hypotl.
* Add POWER10 performance values.
* Add missing cast on i686 hypotf.
* Rewrite math-use-builtinds-fmax.h and math-use-builtinds-fmin.h
based on Joseph's suggestions.
---
Adhemerval Zanella (9):
math: Simplify hypotf implementation
math: Use an improved algorithm for hypotl (ldbl-96)
math: Use an improved algorithm for hypotl (ldbl-128)
i386: Move hypot implementation to C
math: Remove powerpc e_hypot
math: Add math-use-builtinds-fmax.h
math: Add math-use-builtinds-fmin.h
aarch64: Add math-use-builtins-f{max,min}.h
math: Remove the error handling wrapper from hypot and hypotf
Wilco Dijkstra (3):
math: Use an improved algorithm for hypot (dbl-64)
math: Improve hypot performance with FMA
math: Use fmin/fmax on hypot
math/Versions | 2 +
math/s_fmax_template.c | 5 +
math/s_fmin_template.c | 6 +-
math/w_hypot.c | 8 +
math/w_hypot_compat.c | 13 +-
math/w_hypotf.c | 8 +
math/w_hypotf_compat.c | 6 +-
sysdeps/aarch64/fpu/math-use-builtins-fmax.h | 4 +
sysdeps/aarch64/fpu/math-use-builtins-fmin.h | 4 +
sysdeps/aarch64/fpu/s_fmax.c | 28 --
sysdeps/aarch64/fpu/s_fmaxf.c | 28 --
sysdeps/aarch64/fpu/s_fmin.c | 28 --
sysdeps/aarch64/fpu/s_fminf.c | 28 --
sysdeps/generic/math-type-macros-double.h | 1 +
sysdeps/generic/math-type-macros-float.h | 1 +
sysdeps/generic/math-type-macros-float128.h | 1 +
sysdeps/generic/math-type-macros-ldouble.h | 1 +
sysdeps/generic/math-use-builtins-fmax.h | 4 +
sysdeps/generic/math-use-builtins-fmin.h | 4 +
sysdeps/generic/math-use-builtins.h | 2 +
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 | 270 ++++++++----------
sysdeps/ieee754/dbl-64/w_hypot.c | 1 +
sysdeps/ieee754/flt-32/e_hypotf.c | 79 ++---
sysdeps/ieee754/flt-32/math_config.h | 9 +
sysdeps/ieee754/flt-32/w_hypotf.c | 1 +
sysdeps/ieee754/ldbl-128/e_hypotl.c | 226 +++++++--------
sysdeps/ieee754/ldbl-96/e_hypotl.c | 231 +++++++--------
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 +
65 files changed, 547 insertions(+), 1029 deletions(-)
create mode 100644 math/w_hypot.c
create mode 100644 math/w_hypotf.c
create mode 100644 sysdeps/aarch64/fpu/math-use-builtins-fmax.h
create mode 100644 sysdeps/aarch64/fpu/math-use-builtins-fmin.h
delete mode 100644 sysdeps/aarch64/fpu/s_fmax.c
delete mode 100644 sysdeps/aarch64/fpu/s_fmaxf.c
delete mode 100644 sysdeps/aarch64/fpu/s_fmin.c
delete mode 100644 sysdeps/aarch64/fpu/s_fminf.c
create mode 100644 sysdeps/generic/math-use-builtins-fmax.h
create mode 100644 sysdeps/generic/math-use-builtins-fmin.h
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
--
2.32.0
next reply other threads:[~2021-12-07 19:03 UTC|newest]
Thread overview: 16+ messages / expand[flat|nested] mbox.gz Atom feed top
2021-12-07 19:03 Adhemerval Zanella [this message]
2021-12-07 19:03 ` [PATCH v5 01/12] math: Simplify hypotf implementation Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 02/12] math: Use an improved algorithm for hypot (dbl-64) Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 03/12] math: Improve hypot performance with FMA Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 04/12] math: Use an improved algorithm for hypotl (ldbl-96) Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 05/12] math: Use an improved algorithm for hypotl (ldbl-128) Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 06/12] i386: Move hypot implementation to C Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 07/12] math: Remove powerpc e_hypot Adhemerval Zanella
2021-12-07 19:42 ` Paul A. Clarke
2021-12-07 19:03 ` [PATCH v5 08/12] math: Add math-use-builtinds-fmax.h Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 09/12] math: Add math-use-builtinds-fmin.h Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 10/12] aarch64: Add math-use-builtins-f{max,min}.h Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 11/12] math: Use fmin/fmax on hypot Adhemerval Zanella
2021-12-07 19:03 ` [PATCH v5 12/12] math: Remove the error handling wrapper from hypot and hypotf Adhemerval Zanella
2021-12-08 5:51 ` [PATCH v5 00/12] Improve hypot Paul Zimmermann
2021-12-10 19:31 ` Adhemerval Zanella
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