From patchwork Fri Nov 29 13:17:38 2024 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Adhemerval Zanella Netto X-Patchwork-Id: 846130 Delivered-To: patch@linaro.org Received: by 2002:adf:f2c4:0:b0:382:43a8:7b94 with SMTP id d4csp859855wrp; Fri, 29 Nov 2024 05:29:40 -0800 (PST) X-Forwarded-Encrypted: i=3; AJvYcCUMXhJKHPLcdOi0yhYLwN2V/1Sqq8hLmnK+L7F7FNdaHKQWLWRvsnUX9ey3zKLJq4zVgdx27g==@linaro.org X-Google-Smtp-Source: AGHT+IFFuYRd/Rdc/AhqiplqmYkjZs6gwI6PEKyzgFde7QLW4GO4+fzCZrTP3uH11rkbyizM8zfk X-Received: by 2002:a05:6902:1586:b0:e38:b85c:31a5 with SMTP id 3f1490d57ef6-e395b891348mr12289063276.16.1732886980209; Fri, 29 Nov 2024 05:29:40 -0800 (PST) ARC-Seal: i=2; a=rsa-sha256; t=1732886980; cv=pass; d=google.com; s=arc-20240605; b=bVontZFgVQsvW9aH7+M4Ifxxl3W++tms9CamIfaiwx+c3Ji+X7uxSz0ynj0HF9f88W p0AJIvdSYtleHljLHStuczwG5Fsk+jRBR9dN38dmQZLdkMMXdBNCIugZSPd/4PHstQsT vPyOmbHUsoMmly53R4x8nFdi8eWMxlw9C+cGAYVDW3A0WIW543BYNJGqoHmanuCRD/w1 QPKGs1J4bX7pVCAQleIww7Ip3bLftMiQZZjc1u27xynxQBm/zxNvgW674psfvCipCeRH vz8B3vOAbq8lAoFfBZ5vOVQz0BCfC5nb4ONNM7G/mHAuxSwX0J8TiWz24mHlcDVSEYog +JVw== ARC-Message-Signature: i=2; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20240605; h=errors-to:list-subscribe:list-help:list-post:list-archive :list-unsubscribe:list-id:precedence:content-transfer-encoding :mime-version:references:in-reply-to:message-id:date:subject:cc:to :from:dkim-signature:dkim-filter:arc-filter:dmarc-filter :delivered-to; bh=aD/U0iBx1knBk62GaPRrG3FNY+ODo4DUmiib4X2UTxE=; fh=sFucH9KQW8Y8eMoQXaNIgycLDa7roysdjTHpHLIprh4=; b=kiWtNsbbtmRFcYeVAqKgJcNWxO0/Qb6vLnEDTRcHzRKWNd1Tp/e8wvnpIMi9Buau6X o5gzQB+s2036P9sKgVYe9i+9kpXjg590uEOiBkuVdydHpIlWWcdTqAfvfGk7Ya24Erjd RlcBewHsSOuhoa18fkck8jduWhKxBtdUbT2qRsXxNT6jXYi2CVuDauLX4l/khKAeil7C 4yUs6wkMVZX6tHidDLALluDTjNDjPvCN7LJO9Jr3+uJ+Xhhg1/N/KjzMB0DDyr3CaC2h zhq7lCbWMND/IyfVDMWeqe42wgswiegAQgMoKAnf8TNMbtwe/a3ilyA7cgUDntChqnY1 JyMw==; dara=google.com ARC-Authentication-Results: i=2; mx.google.com; dkim=pass header.i=@linaro.org header.s=google header.b=LbYzapLh; arc=pass (i=1); spf=pass (google.com: domain of libc-alpha-bounces~patch=linaro.org@sourceware.org designates 2620:52:3:1:0:246e:9693:128c as permitted sender) smtp.mailfrom="libc-alpha-bounces~patch=linaro.org@sourceware.org"; dmarc=pass (p=NONE sp=NONE dis=NONE) header.from=linaro.org Return-Path: Received: from server2.sourceware.org (server2.sourceware.org. [2620:52:3:1:0:246e:9693:128c]) by mx.google.com with ESMTPS id 3f1490d57ef6-e3976c8e252si3174329276.307.2024.11.29.05.29.40 for (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Fri, 29 Nov 2024 05:29:40 -0800 (PST) Received-SPF: pass (google.com: domain of libc-alpha-bounces~patch=linaro.org@sourceware.org designates 2620:52:3:1:0:246e:9693:128c as permitted sender) client-ip=2620:52:3:1:0:246e:9693:128c; Authentication-Results: mx.google.com; dkim=pass header.i=@linaro.org header.s=google header.b=LbYzapLh; arc=pass (i=1); spf=pass (google.com: domain of libc-alpha-bounces~patch=linaro.org@sourceware.org designates 2620:52:3:1:0:246e:9693:128c as permitted sender) smtp.mailfrom="libc-alpha-bounces~patch=linaro.org@sourceware.org"; dmarc=pass (p=NONE sp=NONE dis=NONE) header.from=linaro.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id BE07A3858C42 for ; Fri, 29 Nov 2024 13:29:39 +0000 (GMT) X-Original-To: libc-alpha@sourceware.org Delivered-To: libc-alpha@sourceware.org Received: from mail-pl1-x634.google.com (mail-pl1-x634.google.com [IPv6:2607:f8b0:4864:20::634]) by sourceware.org (Postfix) with ESMTPS id ED7953858D37 for ; Fri, 29 Nov 2024 13:21:18 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.4.2 sourceware.org ED7953858D37 Authentication-Results: sourceware.org; dmarc=pass (p=none dis=none) header.from=linaro.org Authentication-Results: sourceware.org; spf=pass smtp.mailfrom=linaro.org ARC-Filter: OpenARC Filter v1.0.0 sourceware.org ED7953858D37 Authentication-Results: server2.sourceware.org; arc=none smtp.remote-ip=2607:f8b0:4864:20::634 ARC-Seal: i=1; a=rsa-sha256; d=sourceware.org; s=key; t=1732886479; cv=none; b=VfjdnOViXpmDgR52+Ho+s2SqPdEhpt36oyggT6oSHHTlp6IFTVnOjmENjrKQrtcWsC6I0tziGbrpYA6y8vqi6o62MCh3llhu1rd3Sk5S/ejGJZ/ZdyGvFvXn6+WWPu+D9HwKxiUB5go1t9GPJl2aGOAAGomPuoUn5QBNKHQSYu4= ARC-Message-Signature: i=1; a=rsa-sha256; d=sourceware.org; s=key; t=1732886479; c=relaxed/simple; bh=kK3PcU4q5k1HiBFfxYXx/vrKAc7OSepp9dVK6249WaY=; h=DKIM-Signature:From:To:Subject:Date:Message-ID:MIME-Version; b=SPScBGqzVP4V9PRsLGRCJo036jAoWG4kjcGu/yGcXu0VwNKHj2hJ9cA9/INio0ypXXOK9Qnt8dO+siB8ry3UWlHLHSpP4un6fNRBLiD4HKfjdF320AElBlUEPN1BgQpJMJ/juhD9yWomrNs6C+LJMZ6ksUOlr+0LCRLSQO17x4I= ARC-Authentication-Results: i=1; server2.sourceware.org DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org ED7953858D37 Authentication-Results: sourceware.org; dkim=pass (2048-bit key, unprotected) header.d=linaro.org header.i=@linaro.org header.a=rsa-sha256 header.s=google header.b=LbYzapLh Received: by mail-pl1-x634.google.com with SMTP id d9443c01a7336-215348d1977so9965485ad.3 for ; Fri, 29 Nov 2024 05:21:18 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=linaro.org; s=google; t=1732886477; x=1733491277; darn=sourceware.org; h=content-transfer-encoding:mime-version:references:in-reply-to :message-id:date:subject:cc:to:from:from:to:cc:subject:date :message-id:reply-to; bh=aD/U0iBx1knBk62GaPRrG3FNY+ODo4DUmiib4X2UTxE=; b=LbYzapLhnVW5+nwShJRw4bjldTeVhzeGveHe6PoL39K+bvPZ0h4hwQi0/hXqPnYTEa T5bIjaiTkz0NlbrgMJp/W4hB3WbA3bDtlpKZMfQiNRoxPOo1MiAPONrlD/gkwh5y8kcn jCJQRBgMKc82FVuF7wC8gEDI7pIanLQI62JgTviMET7bEBdStV103rlZKvpYkMwqXZcG BOqGK6Ne2Ru/eJ+yvY/LCqAt1KiJeREt/NdOV06i6iH+5QUquAMEPK6NbUYHUyBt8E/I 72vX2FfcDNWO0r9XI6cRXiRVMh/7fM/Dj/E0VWkaIpu5YQ56bnuDkBVb5FT5yyrzPW2Z Wxow== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20230601; t=1732886477; x=1733491277; h=content-transfer-encoding:mime-version:references:in-reply-to :message-id:date:subject:cc:to:from:x-gm-message-state:from:to:cc :subject:date:message-id:reply-to; bh=aD/U0iBx1knBk62GaPRrG3FNY+ODo4DUmiib4X2UTxE=; b=F2mT30ymulTuFYcC0+XKSphzAJYxqiSSFdPMWhI6dZbfDeFnMIawnMaaOJfJCP98H7 1hZ9y3EZtKV+Hp5rySkNiRWrRFW+aOIpf9S7H7cRY0WpXzIChXYklhmTR1unW4+N25Gc 6Sc0D1nX+YjiOWEPCnekYaK7MZxoC1nfUyVDLYEjt9bKN8YHkJ9L17EVDAlacxLeAn3S cwRUdrspjILBx9xJGcA0tI/MGGY4D0wr8JCQxpXLdnuaDJ5JlLxr7HVDeuSuQQK2/HTs fJbMwO8Gk3p2a7c7sAiyqaPuRC6rLJS8TStt/c/bNyaeBf00xXyUPA8iTgvgTO5S8s+Y 9DBQ== X-Gm-Message-State: AOJu0Yxdqr5mNPZY7Y3fYSYUCRE4DhNHOuJ7e1PQYZzgnKLv8aAkSjI9 ABNRFtDOlPZXyA+Nemqlk56y4WBeqAQ/KbdsyB2+WDWab5wUuEOtUIc3o9HsPovOs4GL7ElCf4/ QDT8p0A== X-Gm-Gg: ASbGncv4TGPHN/UyhesZ0b5rBzhDFKsSETWa9QB4iVbDNNV9uVASqO1DwfDbawRpMzG xwI+YU6Q/anAoDc0QpmD1makWZg334WGIqXn2ks9iqawaJsskm1AxEC6VNpH9Qq8nkpo12iSi6v Wo9384sMFojnYoJrXwSIaWVTEMKNHmVDHALUw0rc7vjYaeLsitKgnqLo6dqRYWGg4TaIFaBo5jr RR8KCXX22CX0W2VvYhOOxuxolzhVcRin4/6Bs8uWD4dcbE9PL5kO/XT6WCn/Xc= X-Received: by 2002:a17:902:ecce:b0:20b:51b0:4b22 with SMTP id d9443c01a7336-21501e6c3e6mr129510325ad.47.1732886477179; Fri, 29 Nov 2024 05:21:17 -0800 (PST) Received: from mandiga.. ([2804:1b3:a7c1:68c8:3143:6603:ad16:715e]) by smtp.gmail.com with ESMTPSA id d9443c01a7336-2153d5f66d5sm14472255ad.201.2024.11.29.05.21.15 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Fri, 29 Nov 2024 05:21:16 -0800 (PST) From: Adhemerval Zanella To: libc-alpha@sourceware.org Cc: DJ Delorie , Alexei Sibidanov , Paul Zimmermann Subject: [PATCH 14/23] math: Use acosf from CORE-MATH Date: Fri, 29 Nov 2024 10:17:38 -0300 Message-ID: <20241129132032.476978-15-adhemerval.zanella@linaro.org> X-Mailer: git-send-email 2.43.0 In-Reply-To: <20241129132032.476978-1-adhemerval.zanella@linaro.org> References: <20241129132032.476978-1-adhemerval.zanella@linaro.org> MIME-Version: 1.0 X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces~patch=linaro.org@sourceware.org The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic acosf. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): Latency master patched improvement x86_64 52.5098 36.6312 30.24% x86_64v2 53.0217 37.3091 29.63% x86_64v3 42.8501 32.3977 24.39% i686 207.3960 109.4000 47.25% aarch64 21.3694 13.7871 35.48% power10 14.5542 7.2891 49.92% reciprocal-throughput master patched improvement x86_64 14.1487 15.9508 -12.74% x86_64v2 14.3293 16.1899 -12.98% x86_64v3 13.6563 12.6161 7.62% i686 158.4060 45.7354 71.13% aarch64 12.5515 9.19233 26.76% power10 5.7868 3.3487 42.13% Signed-off-by: Alexei Sibidanov Signed-off-by: Paul Zimmermann Signed-off-by: Adhemerval Zanella --- SHARED-FILES | 4 + sysdeps/aarch64/libm-test-ulps | 4 - sysdeps/alpha/fpu/libm-test-ulps | 4 - sysdeps/arc/fpu/libm-test-ulps | 4 - sysdeps/arc/nofpu/libm-test-ulps | 1 - sysdeps/arm/libm-test-ulps | 4 - sysdeps/csky/fpu/libm-test-ulps | 4 - sysdeps/csky/nofpu/libm-test-ulps | 4 - sysdeps/hppa/fpu/libm-test-ulps | 4 - sysdeps/i386/fpu/e_acosf.S | 23 ---- sysdeps/ieee754/flt-32/e_acosf.c | 191 +++++++++++++++++--------- sysdeps/loongarch/lp64/libm-test-ulps | 4 - sysdeps/microblaze/libm-test-ulps | 1 - sysdeps/mips/mips32/libm-test-ulps | 4 - sysdeps/mips/mips64/libm-test-ulps | 4 - sysdeps/or1k/fpu/libm-test-ulps | 4 - sysdeps/or1k/nofpu/libm-test-ulps | 4 - sysdeps/powerpc/fpu/libm-test-ulps | 4 - sysdeps/powerpc/nofpu/libm-test-ulps | 4 - sysdeps/riscv/nofpu/libm-test-ulps | 4 - sysdeps/riscv/rvd/libm-test-ulps | 4 - sysdeps/s390/fpu/libm-test-ulps | 4 - sysdeps/sh/libm-test-ulps | 2 - sysdeps/sparc/fpu/libm-test-ulps | 4 - sysdeps/x86_64/fpu/libm-test-ulps | 4 - 25 files changed, 128 insertions(+), 170 deletions(-) delete mode 100644 sysdeps/i386/fpu/e_acosf.S diff --git a/SHARED-FILES b/SHARED-FILES index 9f4de81b66..3d32f0f3b6 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -294,3 +294,7 @@ sysdeps/ieee754/flt-32/s_tanf.c: functions to handle errno, overflow, and underflow. It was changed to use an internal wrapper for 128 bit unsigned integer operations for ABIs that do not support the type natively. +sysdeps/ieee754/flt-32/e_acosf.c: + (src/binary32/acos/acosf.c in CORE-MATH) + - The code was adapted to use glibc code style and internal + functions to handle errno, overflow, and underflow. diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 89b166b71b..a593a4f8cb 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -3,7 +3,6 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_advsimd": @@ -12,7 +11,6 @@ float: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_sve": @@ -21,12 +19,10 @@ float: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps index 0f7628b75b..aac2e31951 100644 --- a/sysdeps/alpha/fpu/libm-test-ulps +++ b/sysdeps/alpha/fpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index 4d4b22db47..b80f97b5ed 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 3 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index 4faf784aad..de1fdd9b1e 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -3,7 +3,6 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index c80122de79..a2e6549e65 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps index d67cfe1785..3e7b07e81a 100644 --- a/sysdeps/csky/fpu/libm-test-ulps +++ b/sysdeps/csky/fpu/libm-test-ulps @@ -2,19 +2,15 @@ # Maximal error of functions: Function: "acos": -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps index 6cdf9fd034..58bd5eaa15 100644 --- a/sysdeps/csky/nofpu/libm-test-ulps +++ b/sysdeps/csky/nofpu/libm-test-ulps @@ -2,19 +2,15 @@ # Maximal error of functions: Function: "acos": -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index 9ed2204d38..ecef024df5 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/i386/fpu/e_acosf.S b/sysdeps/i386/fpu/e_acosf.S deleted file mode 100644 index 435dcd9f67..0000000000 --- a/sysdeps/i386/fpu/e_acosf.S +++ /dev/null @@ -1,23 +0,0 @@ -/* - * Public domain. - */ - -#include -#include - -RCSID("$NetBSD: $") - -/* acos = atan (sqrt(1 - x^2) / x) */ -ENTRY(__ieee754_acosf) - flds 4(%esp) /* x */ - fld %st - fmul %st(0) /* x^2 */ - fld1 - fsubp /* 1 - x^2 */ - fsqrt /* sqrt (1 - x^2) */ - fabs - fxch %st(1) - fpatan - ret -END (__ieee754_acosf) -libm_alias_finite (__ieee754_acosf, __acosf) diff --git a/sysdeps/ieee754/flt-32/e_acosf.c b/sysdeps/ieee754/flt-32/e_acosf.c index e3b3bbc928..9adc02a241 100644 --- a/sysdeps/ieee754/flt-32/e_acosf.c +++ b/sysdeps/ieee754/flt-32/e_acosf.c @@ -1,78 +1,135 @@ -/* e_acosf.c -- float version of e_acos.c. - */ +/* Correctly-rounded arc-cosine function for binary32 value. -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ +Copyright (c) 2023-2024 Alexei Sibidanov. +The original version of this file was copied from the CORE-MATH +project (file src/binary32/acos/acosf.c, revision d680516). + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +*/ + +#include #include #include #include +#include "math_config.h" -static const float -one = 1.0000000000e+00, /* 0x3F800000 */ -pi = 3.1415925026e+00, /* 0x40490fda */ -pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ -pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ -pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ -pS1 = -3.2556581497e-01, /* 0xbea6b090 */ -pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ -pS3 = -4.0055535734e-02, /* 0xbd241146 */ -pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ -pS5 = 3.4793309169e-05, /* 0x3811ef08 */ -qS1 = -2.4033949375e+00, /* 0xc019d139 */ -qS2 = 2.0209457874e+00, /* 0x4001572d */ -qS3 = -6.8828397989e-01, /* 0xbf303361 */ -qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ +static __attribute__ ((noinline)) float +as_special (float x) +{ + const float pih = 0x1.921fb6p+1; + const float pil = -0x1p-24f; + uint32_t t = asuint (x); + if (t == (0x7fu << 23)) + return 0.0f; /* x=1 */ + if (t == (0x17fu << 23)) + return pih + pil; /* x=-1 */ + uint32_t ax = t << 1; + if (ax > (0xffu << 24)) + return x + x; /* nan */ + return __math_invalidf (0.0); +} + +static inline double +poly12 (double z, const double *c) +{ + double z2 = z * z, z4 = z2 * z2; + double c0 = c[0] + z * c[1]; + double c2 = c[2] + z * c[3]; + double c4 = c[4] + z * c[5]; + double c6 = c[6] + z * c[7]; + double c8 = c[8] + z * c[9]; + double c10 = c[10] + z * c[11]; + c0 += c2 * z2; + c4 += c6 * z2; + c8 += z2 * c10; + c0 += z4 * (c4 + z4 * c8); + return c0; +} float -__ieee754_acosf(float x) +__ieee754_acosf (float x) { - float z,p,q,r,w,s,c,df; - int32_t hx,ix; - GET_FLOAT_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix==0x3f800000) { /* |x|==1 */ - if(hx>0) return 0.0; /* acos(1) = 0 */ - else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ - } else if(ix>0x3f800000) { /* |x| >= 1 */ - return (x-x)/(x-x); /* acos(|x|>1) is NaN */ - } - if(ix<0x3f000000) { /* |x| < 0.5 */ - if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<=2**-26*/ - z = x*x; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - r = p/q; - return pio2_hi - (x - (pio2_lo-x*r)); - } else if (hx<0) { /* x < -0.5 */ - z = (one+x)*(float)0.5; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - s = sqrtf(z); - r = p/q; - w = r*s-pio2_lo; - return pi - (float)2.0*(s+w); - } else { /* x > 0.5 */ - int32_t idf; - z = (one-x)*(float)0.5; - s = sqrtf(z); - df = s; - GET_FLOAT_WORD(idf,df); - SET_FLOAT_WORD(df,idf&0xfffff000); - c = (z-df*df)/(s+df); - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - r = p/q; - w = r*s+c; - return (float)2.0*(df+w); - } + const double pi2 = 0x1.921fb54442d18p+0; + static const double o[] = { 0, 0x1.921fb54442d18p+1 }; + double xs = x; + double r; + uint32_t t = asuint (x); + uint32_t ax = t << 1; + if (__glibc_unlikely (ax>=0x7f<<24)) + return as_special (x); + if (__glibc_likely (ax < 0x7ec2a1dcu)) /* |x| < 0x1.c2a1dcp-1 */ + { + static const double b[] = + { + 0x1.fffffffd9ccb8p-1, 0x1.5555c94838007p-3, 0x1.32ded4b7c20fap-4, + 0x1.8566df703309ep-5, -0x1.980c959bec9a3p-6, 0x1.56fbb04998344p-1, + -0x1.403d8e4c49f52p+2, 0x1.b06c3e9f311eap+4, -0x1.9ea97c4e2c21fp+6, + 0x1.200b8261cc61bp+8, -0x1.2274c2799a5c7p+9, 0x1.a558a59cc19d3p+9, + -0x1.aca4b6a529ffp+9, 0x1.228744703f813p+9, -0x1.d7dbb0b322228p+7, + 0x1.5c2018c0c0105p+5 + }; + /* Avoid spurious underflow exception. */ + if (__glibc_unlikely (ax <= 0x40000000u)) /* |x| < 2^-63 */ + return (float) pi2; + double z = xs, z2 = z * z, z4 = z2 * z2, z8 = z4 * z4, z16 = z8 * z8; + r = z * ((((b[0] + z2 * b[1]) + z4 * (b[2] + z2 * b[3])) + + z8 * ((b[4] + z2 * b[5]) + z4 * (b[6] + z2 * b[7]))) + + z16 * (((b[8] + z2 * b[9]) + z4 * (b[10] + z2 * b[11])) + + z8 + * ((b[12] + z2 * b[13])+ z4 * (b[14] + z2 * b[15])))); + float ub = 0x1.921fb54574191p+0 - r; + float lb = 0x1.921fb543118ap+0 - r; + if (ub == lb) + return ub; + } + /* accurate path */ + if (ax < (0x7eu << 24)) + { + static const double c[] = + { + 0x1.555555555529cp-3, 0x1.333333337e0ddp-4, 0x1.6db6db3b4465ep-5, + 0x1.f1c72e13ac306p-6, 0x1.6e89cebe06bc4p-6, 0x1.1c6dcf5289094p-6, + 0x1.c6dbbcc7c6315p-7, 0x1.8f8dc2615e996p-7, 0x1.a5833b7bf15e8p-8, + 0x1.43f44ace1665cp-6, -0x1.0fb17df881c73p-6, 0x1.07520c026b2d6p-5 + }; + if (t == 0x328885a3u) + return 0x1.921fb6p+0f + 0x1p-25; + if (t == 0x39826222u) + return 0x1.920f6ap+0f + 0x1p-25; + double x2 = xs * xs; + r = (pi2 - xs) - (xs * x2) * poly12 (x2, c); + } + else + { + static const double c[] = + { + 0x1.6a09e667f3bcbp+0, 0x1.e2b7dddff2db9p-4, 0x1.b27247ab42dbcp-6, + 0x1.02995cc4e0744p-7, 0x1.5ffb0276ec8eap-9, 0x1.033885a928decp-10, + 0x1.911f2be23f8c7p-12, 0x1.4c3c55d2437fdp-13, 0x1.af477e1d7b461p-15, + 0x1.abd6bdff67dcbp-15, -0x1.1717e86d0fa28p-16, 0x1.6ff526de46023p-16 + }; + double bx = fabs (xs); + double z = 1.0 - bx; + double s = copysign (sqrt (z), xs); + r = o[t >> 31] + s * poly12 (z, c); + } + return r; } libm_alias_finite (__ieee754_acosf, __acosf) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index 03fa6a410a..67bf2d2f9f 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps index c96652a022..c93ebfa21b 100644 --- a/sysdeps/microblaze/libm-test-ulps +++ b/sysdeps/microblaze/libm-test-ulps @@ -2,7 +2,6 @@ # Maximal error of functions: Function: "acos": -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps index 17034d44ba..d23762642b 100644 --- a/sysdeps/mips/mips32/libm-test-ulps +++ b/sysdeps/mips/mips32/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index a757f69a9a..aece335d6b 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index 115a73ef26..862ab6b559 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index e130fd8a1d..3c364480f4 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -3,19 +3,15 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 Function: "acos_downward": double: 1 -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acos_upward": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index adaa10fb56..135853f213 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -3,25 +3,21 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 float128: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 float128: 1 ldouble: 3 Function: "acos_towardzero": double: 1 -float: 1 float128: 1 ldouble: 3 Function: "acos_upward": double: 1 -float: 1 float128: 1 ldouble: 2 diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps index 2c44e39c2c..44cf9983dc 100644 --- a/sysdeps/powerpc/nofpu/libm-test-ulps +++ b/sysdeps/powerpc/nofpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 3 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 3 Function: "acos_upward": double: 1 -float: 1 ldouble: 2 Function: "acosh": diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index 84b9e15f43..8d3b048e84 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index b9446e5a7c..a1d85be3b6 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index 62d3f145fc..7a3d526d69 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps index a6d271eb3f..d1e5b05531 100644 --- a/sysdeps/sh/libm-test-ulps +++ b/sysdeps/sh/libm-test-ulps @@ -2,11 +2,9 @@ # Maximal error of functions: Function: "acos": -float: 1 Function: "acos_towardzero": double: 1 -float: 1 Function: "acosh": double: 2 diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index 9276ff9726..6a70b6f5ea 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 ldouble: 1 Function: "acos_downward": double: 1 -float: 1 ldouble: 1 Function: "acos_towardzero": double: 1 -float: 1 ldouble: 1 Function: "acos_upward": double: 1 -float: 1 ldouble: 1 Function: "acosh": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index f4360598a9..ff532cea1e 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -3,25 +3,21 @@ # Maximal error of functions: Function: "acos": double: 1 -float: 1 float128: 1 ldouble: 2 Function: "acos_downward": double: 1 -float: 1 float128: 1 ldouble: 2 Function: "acos_towardzero": double: 1 -float: 1 float128: 1 ldouble: 2 Function: "acos_upward": double: 1 -float: 1 float128: 1 ldouble: 2