From patchwork Mon Nov 1 20:20:52 2021 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Adhemerval Zanella X-Patchwork-Id: 46916 Return-Path: X-Original-To: patchwork@sourceware.org Delivered-To: patchwork@sourceware.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id 64F003857C43 for ; Mon, 1 Nov 2021 20:21:28 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org 64F003857C43 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=sourceware.org; s=default; t=1635798088; bh=toHenmouqIVaaC06guAm/1uDUfUP/VhjXRWuAoehvco=; h=To:Subject:Date:List-Id:List-Unsubscribe:List-Archive:List-Post: List-Help:List-Subscribe:From:Reply-To:Cc:From; b=lOn3lRi2FX0RUZjEN3jzKw07pmSmoXwSmqUy2vDSBbzrkd5uQz7x+ZK4yfNsefJF9 IFBALHFVIzniGbC4wn54hUp1Z47KqDZbYc6vSIZBRxcbYfVbPs6qE2NJ+Iy2q+636Z eLLoRFBaBoWLqvhrQqNI6+Pq4eRBLd/Uif3hzb1E= X-Original-To: libc-alpha@sourceware.org Delivered-To: libc-alpha@sourceware.org Received: from mail-qv1-xf32.google.com (mail-qv1-xf32.google.com [IPv6:2607:f8b0:4864:20::f32]) by sourceware.org (Postfix) with ESMTPS id DD41D3858403 for ; Mon, 1 Nov 2021 20:21:03 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.4.1 sourceware.org DD41D3858403 Received: by mail-qv1-xf32.google.com with SMTP id s9so9349063qvk.12 for ; Mon, 01 Nov 2021 13:21:03 -0700 (PDT) X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:from:to:cc:subject:date:message-id:mime-version :content-transfer-encoding; bh=toHenmouqIVaaC06guAm/1uDUfUP/VhjXRWuAoehvco=; b=FDsZVLCJapMx/hT+Ua0sjvC95PlCIYWcYGr1/hfCC7cxHvs11fxLNLu1xupVA5Oeyc Eu101iPfkxRMoLr1Lq6Oex5KpjXyFhmd9p3fv8dfGnP+8BrZ6eO8xRm0npqzF1PSWj1Y WNsuidCzJOe9HXvlWW4UB6KkTm/imhJHu3uXi7U5h87DCfqIxq3uc/XfdEPeLLunvU2w +du6u1ekAysv5wRAu7AF5eJSI5noxlslAM0Z89No/Wb4sIwZCPtp20iN5IeOWry0HycD mxTTNYAeiqIJTlvBIfzIDDqRIUhpbzVfzP5Ao9yTi2k9egNIeqg0Tdn6+AMR6xJRUUgN +MFg== X-Gm-Message-State: AOAM53201H5OVkZl2uNxSD5p6d1FNhkS0Sj5wu8OGA8lGCLR9nlB7X5f AVOiq/8gUVxox94NhPKLA2QxzJkBZit3xw== X-Google-Smtp-Source: ABdhPJwlyoFIzM3yl+fo4R37nfyB8NWq4ArSSQdyK7vwFQGzmycPwCef1rJRjFhPrspgd6lQmIgMkA== X-Received: by 2002:a0c:edb0:: with SMTP id h16mr20800379qvr.17.1635798063065; Mon, 01 Nov 2021 13:21:03 -0700 (PDT) Received: from birita.. ([2804:431:c7cb:b64f:7c54:165f:8728:a193]) by smtp.gmail.com with ESMTPSA id d11sm10023965qtx.81.2021.11.01.13.21.01 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Mon, 01 Nov 2021 13:21:02 -0700 (PDT) To: libc-alpha@sourceware.org Subject: [PATCH v3 0/7] Improve hypot() Date: Mon, 1 Nov 2021 17:20:52 -0300 Message-Id: <20211101202059.1026032-1-adhemerval.zanella@linaro.org> X-Mailer: git-send-email 2.32.0 MIME-Version: 1.0 X-Spam-Status: No, score=-6.1 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 Reply-To: Adhemerval Zanella Cc: Wilco Dijkstra 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 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