From nobody Sun Sep 08 07:56:18 2024 X-Original-To: numerics@mlmmj.nyi.freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2610:1c1:1:606c::19:1]) by mlmmj.nyi.freebsd.org (Postfix) with ESMTP id 4X1j2p6ZDkz5WJC4 for ; Sun, 08 Sep 2024 07:56:18 +0000 (UTC) (envelope-from bugzilla-noreply@freebsd.org) Received: from mxrelay.nyi.freebsd.org (mxrelay.nyi.freebsd.org [IPv6:2610:1c1:1:606c::19:3]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (4096 bits) server-digest SHA256 client-signature RSA-PSS (4096 bits) client-digest SHA256) (Client CN "mxrelay.nyi.freebsd.org", Issuer "R11" (verified OK)) by mx1.freebsd.org (Postfix) with ESMTPS id 4X1j2p5V5rz4SHM for ; Sun, 8 Sep 2024 07:56:18 +0000 (UTC) (envelope-from bugzilla-noreply@freebsd.org) ARC-Seal: i=1; s=dkim; d=freebsd.org; t=1725782178; a=rsa-sha256; cv=none; b=evFoRzC70OSw+5r52MXrzrwCORZ4iSIiVwKAd4jtjv2AEPnUszgTkOwKLqQp6lpsKVSFWf InTHvRg49TRqpcNDxPDUqM0U1f/RmNEpcrRoDUnv7IWqFPzkmOThddFo4O4OTwEXCAbyj/ yTcRuQCAccmSTT74EAbXmjodHlRLXEAtTZa+nRVTLCKl3LS1AFoUnXbdMZBy/bNZpmTMJL uNvETivWIOE0wyIkZT7SaA6YQLND8/duY1/vUlvtx0/Ebt0YJ8A8v99mBTxEjji+xqLbv3 WZcEf4e+v4X5AW9vUT52p69x2NOPq/EPVyHMReuOr8I/tmG3uMnOXS2RH/ny7w== ARC-Authentication-Results: i=1; mx1.freebsd.org; none ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=freebsd.org; s=dkim; t=1725782178; h=from:from:reply-to:subject:subject:date:date:message-id:message-id: to:to:cc:mime-version:mime-version:content-type:content-type: content-transfer-encoding:content-transfer-encoding: in-reply-to:in-reply-to:references:references; bh=nHEQ6thRBvBBS/9RrXf5mJlm6Y+7tMN3bgRoptw9bnY=; b=JLB0qu5D5oxE6Y+TnTwOTQkbFL+z2vPPRB6QbKMYXGL075Yrw0ihwNBUY/siar8qINgQFm EQcAltrnuH8DF3pZAIRFGjzcPGGZlnr+AfZKTJ5Q0ln7PlRtKkYHHh9bH40s5tRpc/kc1s hUl7V7faL3WUem29MQ4pRnleYTxMiOdxTZNm+jiq5DmMPDEcQGmULAfWJ3QNd/uZy8KBzF gTg4MsM15wH5kfWGNfPRib7uCbm+sZmtqZaVr28tedBuvirLQniB1jp27QgC0UmN+uxBjq X1bZgaMqVLVbNGBsGfsoSzZzmJKIlXeKkMDHa7TGJC4GNtWDzOrYY0DaoPOTAw== Received: from kenobi.freebsd.org (kenobi.freebsd.org [IPv6:2610:1c1:1:606c::50:1d]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (4096 bits) server-digest SHA256) (Client did not present a certificate) by mxrelay.nyi.freebsd.org (Postfix) with ESMTPS id 4X1j2p56Myz19s4 for ; Sun, 8 Sep 2024 07:56:18 +0000 (UTC) (envelope-from bugzilla-noreply@freebsd.org) Received: from kenobi.freebsd.org ([127.0.1.5]) by kenobi.freebsd.org (8.15.2/8.15.2) with ESMTP id 4887uIxo030123 for ; Sun, 8 Sep 2024 07:56:18 GMT (envelope-from bugzilla-noreply@freebsd.org) Received: (from bugzilla@localhost) by kenobi.freebsd.org (8.15.2/8.15.2/Submit) id 4887uIEF030122 for numerics@FreeBSD.org; Sun, 8 Sep 2024 07:56:18 GMT (envelope-from bugzilla-noreply@freebsd.org) X-Authentication-Warning: kenobi.freebsd.org: bugzilla set sender to bugzilla-noreply@freebsd.org using -f From: bugzilla-noreply@freebsd.org To: numerics@FreeBSD.org Subject: [Bug 281001] Improve accuracy of asinf(x) and acosf(x) Date: Sun, 08 Sep 2024 07:56:18 +0000 X-Bugzilla-Reason: AssignedTo X-Bugzilla-Type: changed X-Bugzilla-Watch-Reason: None X-Bugzilla-Product: Base System X-Bugzilla-Component: bin X-Bugzilla-Version: CURRENT X-Bugzilla-Keywords: X-Bugzilla-Severity: Affects Only Me X-Bugzilla-Who: commit-hook@FreeBSD.org X-Bugzilla-Status: New X-Bugzilla-Resolution: X-Bugzilla-Priority: --- X-Bugzilla-Assigned-To: numerics@FreeBSD.org X-Bugzilla-Flags: X-Bugzilla-Changed-Fields: Message-ID: In-Reply-To: References: Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Bugzilla-URL: https://bugs.freebsd.org/bugzilla/ Auto-Submitted: auto-generated List-Id: Discussions of high quality implementation of libm functions List-Archive: https://lists.freebsd.org/archives/freebsd-numerics List-Help: List-Post: List-Subscribe: List-Unsubscribe: Sender: owner-freebsd-numerics@FreeBSD.org MIME-Version: 1.0 https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=3D281001 --- Comment #6 from commit-hook@FreeBSD.org --- A commit in branch stable/13 references this bug: URL: https://cgit.FreeBSD.org/src/commit/?id=3D75bca9e7553c70d97b36df30ab05bbbba= cb8a499 commit 75bca9e7553c70d97b36df30ab05bbbbacb8a499 Author: Steve Kargl AuthorDate: 2024-08-29 19:44:48 +0000 Commit: Dimitry Andric CommitDate: 2024-09-08 07:37:57 +0000 Improve accuracy of asinf(3) and acosf(3) This uses a better rational approximation to improve the accuracy of both functions. For exhaustive testing of asinf(3) in the interval, the current libm gives: % ./tlibm asin -fPED -x 0x1p-12f -X 1 Interval tested for asinf: [0.000244141,1] ulp <=3D 0.5: 97.916% 98564994 | 97.916% 98564994 0.5 < ulp < 0.6: 2.038% 2051023 | 99.953% 100616017 0.6 < ulp < 0.7: 0.047% 47254 | 100.000% 100663271 0.7 < ulp < 0.8: 0.000% 25 | 100.000% 100663296 Max ulp: 0.729891 at 5.00732839e-01 which isn't too bad given that much of the computation is actually done in double floating point. With the new rational approximation, exhaustive testing yields: % ./tlibm asin -fPED -x 0x1p-12f -X 1 Interval tested for asinf: [0.000244141,1] ulp <=3D 0.5: 99.711% 100372643 | 99.711% 100372643 0.5 < ulp < 0.6: 0.288% 290357 | 100.000% 100663000 0.6 < ulp < 0.7: 0.000% 296 | 100.000% 100663296 Max ulp: 0.636344 at 5.09706438e-01 Similarly, for exhaustive testing of asinf(3) in the interval, the current libm gives: % ./tlibm acos -fPED -x -1 -X -0x1p-12f Interval tested for acosf: [-1,-0.000244141] ulp <=3D 0.5: 97.008% 97651921 | 97.008% 97651921 0.5 < ulp < 0.6: 2.441% 2457242 | 99.450% 100109163 0.6 < ulp < 0.7: 0.472% 475503 | 99.922% 100584666 0.7 < ulp < 0.8: 0.071% 71309 | 99.993% 100655975 0.8 < ulp < 0.9: 0.007% 7319 | 100.000% 100663294 0.9 < ulp < 1.0: 0.000% 2 | 100.000% 100663296 Max ulp: 0.914007 at -5.01484931e-01 % ./tlibm acos -fPED -x 0x1p-12f -X 1 Interval tested for acosf: [0.000244141,1] ulp <=3D 0.5: 97.317% 97962530 | 97.317% 97962530 0.5 < ulp < 0.6: 2.340% 2355182 | 99.657% 100317712 0.6 < ulp < 0.7: 0.314% 316134 | 99.971% 100633846 0.7 < ulp < 0.8: 0.029% 29450 | 100.000% 100663296 Max ulp: 0.796035 at 4.99814630e-01 With the new rational approximation, exhaustive testing yields: % ./tlibm acos -fPED -x -1 -X -0x1p-12f Interval tested for acosf: [-1,-0.000244141] ulp <=3D 0.5: 97.010% 97653245 | 97.010% 97653245 0.5 < ulp < 0.6: 2.442% 2458373 | 99.452% 100111618 0.6 < ulp < 0.7: 0.473% 476012 | 99.925% 100587630 0.7 < ulp < 0.8: 0.068% 68603 | 99.993% 100656233 0.8 < ulp < 0.9: 0.007% 7063 | 100.000% 100663296 Max ulp: 0.896189 at -5.04511118e-01 % ./tlibm acos -fPED -x 0x1p-12f -X 1 Interval tested for acosf: [0.000244141,1] ulp <=3D 0.5: 97.650% 98298175 | 97.650% 98298175 0.5 < ulp < 0.6: 2.028% 2041709 | 99.679% 100339884 0.6 < ulp < 0.7: 0.292% 293555 | 99.970% 100633439 0.7 < ulp < 0.8: 0.030% 29857 | 100.000% 100663296 Max ulp: 0.775875 at 4.91849005e-01 PR: 281001 MFC after: 1 week (cherry picked from commit 41e016289f77deb88b0ef1ec3f7b2ab3515ac7c8) lib/msun/src/e_acosf.c | 20 +++++++++++++------- lib/msun/src/e_asinf.c | 22 ++++++++++++++-------- 2 files changed, 27 insertions(+), 15 deletions(-) --=20 You are receiving this mail because: You are the assignee for the bug.=