From patchwork Fri Mar 9 15:50:18 2018 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Wilco Dijkstra X-Patchwork-Id: 26253 Received: (qmail 18648 invoked by alias); 9 Mar 2018 15:50:23 -0000 Mailing-List: contact libc-alpha-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Unsubscribe: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: libc-alpha-owner@sourceware.org Delivered-To: mailing list libc-alpha@sourceware.org Received: (qmail 18633 invoked by uid 89); 9 Mar 2018 15:50:23 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-24.5 required=5.0 tests=AWL, BAYES_00, GIT_PATCH_0, GIT_PATCH_1, GIT_PATCH_2, GIT_PATCH_3, KAM_ASCII_DIVIDERS, RCVD_IN_DNSWL_NONE, SPF_HELO_PASS, SPF_PASS autolearn=ham version=3.3.2 spammy=sine X-HELO: EUR03-DB5-obe.outbound.protection.outlook.com From: Wilco Dijkstra To: "libc-alpha@sourceware.org" CC: nd Subject: [PATCH 4/6] Remove slow paths from sin/cos Date: Fri, 9 Mar 2018 15:50:18 +0000 Message-ID: authentication-results: spf=none (sender IP is ) smtp.mailfrom=Wilco.Dijkstra@arm.com; x-ms-publictraffictype: Email x-microsoft-exchange-diagnostics: 1; DB6PR0801MB1878; 6:0S5i2/nTCyUoWZjgb1qQQ+QAIhmlh7U4AHO1Cy5XkW5EnkDtTO0dvQ2yWC0E9P2NkYxxCQ9x+CaI3UfP2bHylm8Wk5cMsxiBzsklIIbOL+rJp+Ycke4p2P1/rSaryXd/WZQSMrLZI/Svl3NAMZjtNMcFdYVMz6pZeyHeXcEUPs0gpdDH8PcXAi/WjgreS5S4imESHntEh8fFDnb1q1v39w7yDerVraUBsC2J+lSQTKKKvlk465DN3kOwgrUuWoy4qts+oy7RIClGa1JpwmGsLCNd58gYvmr4fkqU495WSQO5nGFxzVHrE+KtSRuwSg8AtmTN6Bp3y6e/Y5OzqwlmxpzoI6jmC8R0tC+D3ddOCyqDlnm2rZaTWt8Nxw852QOo; 5:7+JNn1pZyGTiirTz/3ns9CfeYyaU2Y06T+RYn7D0udmBseUEzcB08Vir34E10X8VxZETIUvFzJNoiL9PZJ2XV+8xeEJylH8YRt4XpD9XTf+WLTTtTxjhraYp3sh6RtTVCckp7Fb6I26KKbWBljEv5/AXbjQBF7LTYxcJpt6zuSo=; 24:O2KyGmptnqAuYvvxa+E4kBKiIxqok+S77BCE8E1hsBtCY6STSmLmUrNWfaG2MO/x/qV86u5naL3htRAxtiu2gIGcK/zJ9ZQZhggjctUE3So=; 7:KTL1nFGIAAolTmpzsA3//QxnkAaOA/s3KZo04srzYSWErq32ZRhDOqnNVVC1FB0LmNeZShq3c8WQOloOozlVNZYv4Pbwf4WL0QmpxiPcOSyBztvQfutEdy8ltDg6vG3ipHL+5L+2qDiRdzBqIsPELUPloLQOWkw0B/9y7b8jPU1j0wS1O2Lv0XpcE5nD9dacKU9sE6sjwSunRbJ360bNqEPPNq9PiLE0tB4FsCHZRw0lljLQ2lNUaMhrfG/z/wdK x-ms-exchange-antispam-srfa-diagnostics: SSOS; x-ms-office365-filtering-ht: Tenant x-ms-office365-filtering-correlation-id: 6438cf11-077b-4f42-6975-08d585d5752c x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(7020095)(4652020)(48565401081)(5600026)(4604075)(3008032)(2017052603328)(7153060)(7193020); SRVR:DB6PR0801MB1878; x-ms-traffictypediagnostic: DB6PR0801MB1878: nodisclaimer: True x-microsoft-antispam-prvs: x-exchange-antispam-report-test: UriScan:(180628864354917); x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(8211001083)(6040522)(2401047)(8121501046)(5005006)(3002001)(10201501046)(93006095)(93001095)(3231220)(944501244)(52105095)(6055026)(6041310)(20161123558120)(201703131423095)(201702281528075)(20161123555045)(201703061421075)(201703061406153)(20161123564045)(20161123562045)(20161123560045)(6072148)(201708071742011); SRVR:DB6PR0801MB1878; BCL:0; PCL:0; RULEID:; SRVR:DB6PR0801MB1878; x-forefront-prvs: 0606BBEB39 x-forefront-antispam-report: SFV:NSPM; SFS:(10009020)(366004)(39860400002)(39380400002)(396003)(376002)(346002)(54534003)(377424004)(189003)(199004)(102836004)(74316002)(6436002)(3846002)(66066001)(72206003)(8676002)(8936002)(6116002)(81166006)(81156014)(3280700002)(2900100001)(68736007)(25786009)(14454004)(6506007)(6916009)(99286004)(2351001)(7696005)(86362001)(478600001)(7736002)(305945005)(2906002)(5640700003)(53936002)(106356001)(3660700001)(5250100002)(105586002)(97736004)(33656002)(2501003)(55016002)(5660300001)(4326008)(316002)(9686003)(26005); DIR:OUT; SFP:1101; SCL:1; SRVR:DB6PR0801MB1878; H:DB6PR0801MB2053.eurprd08.prod.outlook.com; FPR:; SPF:None; PTR:InfoNoRecords; MX:1; A:1; LANG:en; received-spf: None (protection.outlook.com: arm.com does not designate permitted sender hosts) x-microsoft-antispam-message-info: rsbav708y+fNJ8IZu1+74C7oehprL8asE53hOF8NlN3jYXDgv4+LoBoQRSZTkrresiHwNB9pMZWgYudZUan9qk3qdJ136f21LCQgVqDBVIXunqYOwZ3oZuSzlJijB1Ddmf/l2rEPl+2kGD5NS5Qz/6qkS/yhl9fRbEEwkZPvrUkWqE8qK8KcqvJzOSy16Y2xEKxh1LsEPmKH+AMXCzihKVQpQ/nFZGqXGZPJeW3QcvNUpuKEZHOjwBtur1o3rUqfeuj0Fxe6DKd1WxMjklKoTi/6ADxv1IHUWs/+iWSL5l14qL7j2BztVQ+yUkFslnHyyfOolUm5TvG8dzyaPYZjQg== spamdiagnosticoutput: 1:99 spamdiagnosticmetadata: NSPM MIME-Version: 1.0 X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-Network-Message-Id: 6438cf11-077b-4f42-6975-08d585d5752c X-MS-Exchange-CrossTenant-originalarrivaltime: 09 Mar 2018 15:50:18.2385 (UTC) X-MS-Exchange-CrossTenant-fromentityheader: Hosted X-MS-Exchange-CrossTenant-id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-Transport-CrossTenantHeadersStamped: DB6PR0801MB1878 For huge inputs use the improved do_sincos function as well. Now no cases use the correction factor returned by do_sin, do_cos and TAYLOR_SIN, so remove it. ChangeLog: 2018-03-09 Wilco Dijkstra * sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SIN): Remove cor parameter. (do_cos): Remove corp parameter and calculations. (do_sin): Likewise. (do_sincos): Remove cor variable. (__sin): Use do_sincos for huge inputs. (__cos): Likewise. * sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Likewise. diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index 3b748821f6e5f817dc234ec7f96d951910299e21..5966282db60224528fea2bf55a05dd4120ab12a9 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -67,11 +67,10 @@ The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so on. The result is returned to LHS and correction in COR. */ -#define TAYLOR_SIN(xx, a, da, cor) \ +#define TAYLOR_SIN(xx, a, da) \ ({ \ double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \ double res = (a) + t; \ - (cor) = ((a) - res) + t; \ res; \ }) @@ -145,10 +144,10 @@ static double cslow2 (double x); /* Given a number partitioned into X and DX, this function computes the cosine of the number by combining the sin and cos of X (as computed by a variation of the Taylor series) with the values looked up from the sin/cos table to - get the result in RES and a correction value in COR. */ + get the result. */ static inline double __always_inline -do_cos (double x, double dx, double *corp) +do_cos (double x, double dx) { mynumber u; @@ -158,16 +157,13 @@ do_cos (double x, double dx, double *corp) u.x = big + fabs (x); x = fabs (x) - (u.x - big) + dx; - double xx, s, sn, ssn, c, cs, ccs, res, cor; + double xx, s, sn, ssn, c, cs, ccs, cor; xx = x * x; s = x + x * xx * (sn3 + xx * sn5); c = xx * (cs2 + xx * (cs4 + xx * cs6)); SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); cor = (ccs - s * ssn - cs * c) - sn * s; - res = cs + cor; - cor = (cs - res) + cor; - *corp = cor; - return res; + return cs + cor; } /* A more precise variant of DO_COS. EPS is the adjustment to the correction @@ -207,10 +203,10 @@ do_cos_slow (double x, double dx, double eps, double *corp) /* Given a number partitioned into X and DX, this function computes the sine of the number by combining the sin and cos of X (as computed by a variation of the Taylor series) with the values looked up from the sin/cos table to get - the result in RES and a correction value in COR. */ + the result. */ static inline double __always_inline -do_sin (double x, double dx, double *corp) +do_sin (double x, double dx) { mynumber u; @@ -219,16 +215,13 @@ do_sin (double x, double dx, double *corp) u.x = big + fabs (x); x = fabs (x) - (u.x - big); - double xx, s, sn, ssn, c, cs, ccs, cor, res; + double xx, s, sn, ssn, c, cs, ccs, cor; xx = x * x; s = x + (dx + x * xx * (sn3 + xx * sn5)); c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); cor = (ssn + s * ccs - sn * c) + cs * s; - res = sn + cor; - cor = (sn - res) + cor; - *corp = cor; - return res; + return sn + cor; } /* A more precise variant of DO_SIN. EPS is the adjustment to the correction @@ -340,19 +333,19 @@ static double __always_inline do_sincos (double a, double da, int4 n) { - double retval, cor; + double retval; if (n & 1) /* Max ULP is 0.513. */ - retval = do_cos (a, da, &cor); + retval = do_cos (a, da); else { double xx = a * a; /* Max ULP is 0.501 if xx < 0.01588, otherwise ULP is 0.518. */ if (xx < 0.01588) - retval = TAYLOR_SIN (xx, a, da, cor); + retval = TAYLOR_SIN (xx, a, da); else - retval = __copysign (do_sin (a, da, &cor), a); + retval = __copysign (do_sin (a, da), a); } return (n & 2) ? -retval : retval; @@ -371,7 +364,7 @@ SECTION #endif __sin (double x) { - double xx, t, a, da, cor; + double xx, t, a, da; mynumber u; int4 k, m, n; double retval = 0; @@ -401,7 +394,7 @@ __sin (double x) else if (k < 0x3feb6000) { /* Max ULP is 0.548. */ - retval = __copysign (do_sin (x, 0, &cor), x); + retval = __copysign (do_sin (x, 0), x); } /* else if (k < 0x3feb6000) */ /*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ @@ -409,7 +402,7 @@ __sin (double x) { t = hp0 - fabs (x); /* Max ULP is 0.51. */ - retval = __copysign (do_cos (t, hp1, &cor), x); + retval = __copysign (do_cos (t, hp1), x); } /* else if (k < 0x400368fd) */ #ifndef IN_SINCOS @@ -422,8 +415,10 @@ __sin (double x) /* --------------------105414350 <|x| <2^1024------------------------------*/ else if (k < 0x7ff00000) - retval = reduce_and_compute (x, false); - + { + n = __branred (x, &a, &da); + retval = do_sincos (a, da, n); + } /*--------------------- |x| > 2^1024 ----------------------------------*/ else { @@ -455,7 +450,7 @@ SECTION #endif __cos (double x) { - double y, xx, cor, a, da; + double y, xx, a, da; mynumber u; int4 k, m, n; @@ -476,7 +471,7 @@ __cos (double x) else if (k < 0x3feb6000) { /* 2^-27 < |x| < 0.855469 */ /* Max ULP is 0.51. */ - retval = do_cos (x, 0, &cor); + retval = do_cos (x, 0); } /* else if (k < 0x3feb6000) */ else if (k < 0x400368fd) @@ -488,9 +483,9 @@ __cos (double x) /* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise. Range reduction uses 106 bits here which is sufficient. */ if (xx < 0.01588) - retval = TAYLOR_SIN (xx, a, da, cor); + retval = TAYLOR_SIN (xx, a, da); else - retval = __copysign (do_sin (a, da, &cor), a); + retval = __copysign (do_sin (a, da), a); } /* else if (k < 0x400368fd) */ @@ -503,7 +498,10 @@ __cos (double x) /* 105414350 <|x| <2^1024 */ else if (k < 0x7ff00000) - retval = reduce_and_compute (x, true); + { + n = __branred (x, &a, &da); + retval = do_sincos (a, da, n + 1); + } else { diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c index 4f032d2e42593ccde22169b374728386dd8fca8e..4335ecbba3c9894e61c087ac970b392fa73abfab 100644 --- a/sysdeps/ieee754/dbl-64/s_sincos.c +++ b/sysdeps/ieee754/dbl-64/s_sincos.c @@ -28,37 +28,6 @@ #define IN_SINCOS 1 #include "s_sin.c" -/* Consolidated version of reduce_and_compute in s_sin.c that does range - reduction only once and computes sin and cos together. */ -static inline void -__always_inline -reduce_and_compute_sincos (double x, double *sinx, double *cosx) -{ - double a, da; - unsigned int n = __branred (x, &a, &da); - - n = n & 3; - - if (n == 1 || n == 2) - { - a = -a; - da = -da; - } - - if (n & 1) - { - double *temp = cosx; - cosx = sinx; - sinx = temp; - } - - if (a * a < 0.01588) - *sinx = bsloww (a, da, x, n); - else - *sinx = bsloww1 (a, da, x, n); - *cosx = bsloww2 (a, da, x, n); -} - void __sincos (double x, double *sinx, double *cosx) { @@ -88,8 +57,11 @@ __sincos (double x, double *sinx, double *cosx) } if (k < 0x7ff00000) { - reduce_and_compute_sincos (x, sinx, cosx); - return; + double a, da; + int4 n = __branred (x, &a, &da); + + *sinx = do_sincos (a, da, n);