From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.4.2 (2018-09-13) on dcvr.yhbt.net X-Spam-Level: X-Spam-Status: No, score=-3.7 required=3.0 tests=AWL,BAYES_00, HEADER_FROM_DIFFERENT_DOMAINS,MAILING_LIST_MULTI,SPF_HELO_PASS, SPF_PASS shortcircuit=no autolearn=ham autolearn_force=no version=3.4.2 Received: from sourceware.org (server2.sourceware.org [IPv6:2620:52:3:1:0:246e:9693:128c]) (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) (No client certificate requested) by dcvr.yhbt.net (Postfix) with ESMTPS id 46E5C1F5AE for ; Tue, 28 Jul 2020 08:23:12 +0000 (UTC) Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id A09FC3861896; Tue, 28 Jul 2020 08:23:09 +0000 (GMT) Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83]) by sourceware.org (Postfix) with ESMTPS id 2CDBC3858D35 for ; Tue, 28 Jul 2020 08:23:07 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.3.2 sourceware.org 2CDBC3858D35 Authentication-Results: sourceware.org; dmarc=none (p=none dis=none) header.from=inria.fr Authentication-Results: sourceware.org; spf=pass smtp.mailfrom=Paul.Zimmermann@inria.fr X-IronPort-AV: E=Sophos;i="5.75,405,1589234400"; d="scan'208";a="461590328" Received: from tomate.loria.fr (HELO tomate) ([152.81.10.51]) by mail2-relais-roc.national.inria.fr with ESMTP/TLS/DHE-RSA-AES256-GCM-SHA384; 28 Jul 2020 10:23:05 +0200 Date: Tue, 28 Jul 2020 10:23:05 +0200 Message-Id: From: Paul Zimmermann To: Joseph Myers In-reply-to: (message from Joseph Myers on Mon, 27 Jul 2020 21:35:29 +0000) Subject: Re: fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny References: 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: , Cc: libc-alpha@sourceware.org Errors-To: libc-alpha-bounces@sourceware.org Sender: "Libc-alpha" > In new code we generally prefer to use hex float constants in such cases > where a specific floating-point value is wanted. thank you Joseph. Here is a new version. The maximal error for x >= 2^127 is now 4 ulps (attained for x=1.740713465e+38). Total: errors=4220511 (0.10%) errors2=393216 maxerr=4 ulp(s) Paul >From 6b731f36b1a5badf4704645d0dda40957cedd0db Mon Sep 17 00:00:00 2001 From: Paul Zimmermann Date: Mon, 27 Jul 2020 19:01:18 +0200 Subject: [PATCH 1/2] fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny --- sysdeps/ieee754/flt-32/e_j0f.c | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c index c89b9f2688..f85d8a59e0 100644 --- a/sysdeps/ieee754/flt-32/e_j0f.c +++ b/sysdeps/ieee754/flt-32/e_j0f.c @@ -56,6 +56,22 @@ __ieee754_j0f(float x) if ((s*c)From 44124c42fe519c7dcac829160181ba0bb6c8751c Mon Sep 17 00:00:00 2001 From: Paul Zimmermann Date: Tue, 28 Jul 2020 10:05:38 +0200 Subject: [PATCH 2/2] use hex float constants as advised by Joseph Myers --- sysdeps/ieee754/flt-32/e_j0f.c | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c index f85d8a59e0..883a1a4d13 100644 --- a/sysdeps/ieee754/flt-32/e_j0f.c +++ b/sysdeps/ieee754/flt-32/e_j0f.c @@ -61,15 +61,15 @@ __ieee754_j0f(float x) is very near from 0, and use the identity sin(x-x0) = sin(x)*cos(x0)-cos(x)*sin(x0) to get sin(x) + cos(x) with extra accuracy */ - float x0 = 3.153646966e+38f; + float x0 = 0xe.d4108p+124f; float y = x - x0; /* exact */ /* sin(y) = sin(x)*cos(x0)-cos(x)*sin(x0) */ z = __sinf (y); - float eps = 8.17583368e-8f; + float eps = 0x1.5f263ep-24f; /* cos(x0) ~ -sin(x0) + eps */ z += eps * __cosf (x); /* now z ~ (sin(x)-cos(x))*cos(x0) */ - float cosx0 = -0.707106740f; + float cosx0 = -0xb.504f3p-4f; cc = z / cosx0; } /* -- 2.27.0