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([2804:431:c7ca:2654:4c60:ad20:95b6:1d6c]) by smtp.gmail.com with ESMTPSA id k11sm4230490vsh.3.2021.10.25.04.57.59 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Mon, 25 Oct 2021 04:58:00 -0700 (PDT) To: libc-alpha@sourceware.org Subject: [PATCH v2 0/9] Improve hypot() Date: Mon, 25 Oct 2021 08:57:47 -0300 Message-Id: <20211025115756.11767-1-adhemerval.zanella@linaro.org> X-Mailer: git-send-email 2.32.0 MIME-Version: 1.0 X-Spam-Status: No, score=-5.5 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, RCVD_IN_DNSWL_NONE, SPF_HELO_NONE, SPF_PASS, TXREP autolearn=ham autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Adhemerval Zanella via Libc-alpha From: Adhemerval Zanella Netto Reply-To: Adhemerval Zanella Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org Sender: "Libc-alpha" 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 v1: - Improved benchmarks to have the exponents of the two arguments close together. - Fixed typos. - Fixed i386 C implementation. --- Adhemerval Zanella (9): benchtests: Make hypot input random benchtests: Add hypotf 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 benchtests/Makefile | 2 +- benchtests/hypot-inputs | 1015 ++++++++++++++++- benchtests/hypotf-inputs | 1007 ++++++++++++++++ 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 | 56 + 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 | 72 +- sysdeps/ieee754/flt-32/w_hypotf.c | 1 + sysdeps/ieee754/ldbl-128/e_hypotl.c | 222 ++-- sysdeps/ieee754/ldbl-96/e_hypotl.c | 227 ++-- 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 + 52 files changed, 2487 insertions(+), 919 deletions(-) create mode 100644 benchtests/hypotf-inputs 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