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Linux x86_64; rv:68.0) Gecko/20100101 Thunderbird/68.10.0 MIME-Version: 1.0 In-Reply-To: Content-Type: text/plain; charset=utf-8 Content-Language: en-US Content-Transfer-Encoding: 7bit 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: , From: Adhemerval Zanella via Libc-alpha Reply-To: Adhemerval Zanella Errors-To: libc-alpha-bounces@sourceware.org Sender: "Libc-alpha" On 28/07/2020 07:50, Paul Zimmermann wrote: > Dear Andreas, > > yes thanks. Sorry my english is not perfect. > > Paul Could you send v2 patch with all the fixes indicated by Joseph and Andreas (this change from a change format is confusing)? Also please fix the indentation issue and the open brackets on next line. I also think this fix should also add an entry on math/auto-libm-test-out-y0 that exercises this code path and with a check if the ULPs file require some adjustments as well. > > From 6b731f36b1a5badf4704645d0dda40957cedd0db Mon Sep 17 00:00:00 2001 > From: Paul Zimmermann > Date: Mon, 27 Jul 2020 19:01:18 +0200 > Subject: [PATCH 1/3] 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) else ss = z/cc; > } > + else { > + /* we subtract (exactly) a value x0 such that cos(x0)+sin(x0) > + 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 y = x - x0; /* exact */ > + /* sin(y) = sin(x)*cos(x0)-cos(x)*sin(x0) */ > + z = __sinf (y); > + float eps = 8.17583368e-8f; > + /* cos(x0) ~ -sin(x0) + eps */ > + z += eps * __cosf (x); > + /* now z ~ (sin(x)-cos(x))*cos(x0) */ > + float cosx0 = -0.707106740f; > + cc = z / cosx0; > + } > /* > * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) > * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) >