From patchwork Fri Mar 9 15:51:26 2018 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Wilco Dijkstra X-Patchwork-Id: 26254 Received: (qmail 20512 invoked by alias); 9 Mar 2018 15:51:33 -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 20501 invoked by uid 89); 9 Mar 2018 15:51:32 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-25.3 required=5.0 tests=AWL, BAYES_00, GIT_PATCH_0, GIT_PATCH_1, GIT_PATCH_2, GIT_PATCH_3, RCVD_IN_DNSWL_NONE, SPF_HELO_PASS, SPF_PASS autolearn=ham version=3.3.2 spammy=UD:And, Assumption, FILES X-HELO: EUR02-VE1-obe.outbound.protection.outlook.com From: Wilco Dijkstra To: "libc-alpha@sourceware.org" CC: nd Subject: [PATCH 5/6] Remove slow paths from sin/cos Date: Fri, 9 Mar 2018 15:51:26 +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; 7:3348+4wRL97hf54xvpVf6YS3R2VEIqYOwCX/U2/50IY7Ax4QouWeq099evvno33aFxjzXN1WBaUK7NLHSZWwXm7P5xR+su2jO8y+07TW9RchcB+rLvenBj41uE3fVXG8vaX21LZtch7zluY8yuVFlXtmcZG+uTtJUij1No5anbQW5w5pCyFAv248jNo1ZJkwLivl9QFSz5ODaEM9cepIwmeRtUOl1zEwEmc8uUSAsxIL1WBSzwRZn1bl6evAPXQJ x-ms-exchange-antispam-srfa-diagnostics: SSOS; x-ms-office365-filtering-ht: Tenant x-ms-office365-filtering-correlation-id: 30dda2b4-6fe8-4357-f364-08d585d59ddc 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)(575784001)(7736002)(305945005)(2906002)(5640700003)(53936002)(106356001)(3660700001)(5250100002)(105586002)(97736004)(33656002)(2501003)(55016002)(5660300001)(4326008)(316002)(53946003)(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: AKcPdJe4SoHWHRwCXsEkchZoajaxp59Vxviu8Sllq6lSvJ0pSGbVOJKgD+Iv1lBx3VknmZDM9XBR2G5xeLd25laVulyFE43JorwUbsBvbeLe8Z1rMo+/I+GwkJlyXMsuAqtXvg0vPYgRXyii/YLuRekI3cYSFGzLjwokno16MMJVCFoztKf4kE+EFhFfcaF6RZFxZZMAJnGO+cExx3gfCskyYTTlBPypIByTiqHK/3eiouBpl0DhgdfRdPuVixVIKtOFTBXsbJhhR+0TCGVfXg4uKwjGOdlWE8Htwat1Zup/ipibDUeb1nmZna9Howrpq3LlSmUa4YOUPG/FtBBK7w== spamdiagnosticoutput: 1:99 spamdiagnosticmetadata: NSPM MIME-Version: 1.0 X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-Network-Message-Id: 30dda2b4-6fe8-4357-f364-08d585d59ddc X-MS-Exchange-CrossTenant-originalarrivaltime: 09 Mar 2018 15:51:26.5355 (UTC) X-MS-Exchange-CrossTenant-fromentityheader: Hosted X-MS-Exchange-CrossTenant-id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-Transport-CrossTenantHeadersStamped: DB6PR0801MB1878 Remove all unused functions. ChangeLog: 2018-03-09 Wilco Dijkstra * sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SLOW): Remove. (do_cos_slow): Likewise. (do_sin_slow): Likewise. (reduce_and_compute): Likewise. (slow): Likewise. (slow1): Likewise. (slow2): Likewise. (sloww): Likewise. (sloww1): Likewise. (sloww2): Likewise. (bslow): Likewise. (bslow1): Likewise. (bslow2): Likewise. (cslow2): Likewise. diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index 5966282db60224528fea2bf55a05dd4120ab12a9..b847a45cb3d3bd9d7c79d63e1577aec48eb0e8b1 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -22,22 +22,11 @@ /* */ /* FUNCTIONS: usin */ /* ucos */ -/* slow */ -/* slow1 */ -/* slow2 */ -/* sloww */ -/* sloww1 */ -/* sloww2 */ -/* bsloww */ -/* bsloww1 */ -/* bsloww2 */ -/* cslow2 */ /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ -/* branred.c sincos32.c dosincos.c mpa.c */ -/* sincos.tbl */ +/* branred.c sincos.tbl */ /* */ -/* An ultimate sin and routine. Given an IEEE double machine number x */ -/* it computes the correctly rounded (to nearest) value of sin(x) or cos(x) */ +/* An ultimate sin and cos routine. Given an IEEE double machine number x */ +/* it computes sin(x) or cos(x) with ~0.55 ULP. */ /* Assumption: Machine arithmetic operations are performed in */ /* round to nearest mode of IEEE 754 standard. */ /* */ @@ -74,29 +63,6 @@ res; \ }) -/* This is again a variation of the Taylor series expansion with the term - x^3/3! expanded into the following for better accuracy: - - bb * x ^ 3 + 3 * aa * x * x1 * x2 + aa * x1 ^ 3 + aa * x2 ^ 3 - - The correction term is dx and bb + aa = -1/3! - */ -#define TAYLOR_SLOW(x0, dx, cor) \ -({ \ - static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ \ - double xx = (x0) * (x0); \ - double x1 = ((x0) + th2_36) - th2_36; \ - double y = aa * x1 * x1 * x1; \ - double r = (x0) + y; \ - double x2 = ((x0) - x1) + (dx); \ - double t = (((POLYNOMIAL2 (xx) + bb) * xx + 3.0 * aa * x1 * x2) \ - * (x0) + aa * x2 * x2 * x2 + (dx)); \ - t = (((x0) - r) + y) + t; \ - double res = r + t; \ - (cor) = (r - res) + t; \ - res; \ -}) - #define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \ ({ \ int4 k = u.i[LOW_HALF] << 2; \ @@ -123,23 +89,7 @@ static const double cs4 = -4.16666666666664434524222570944589E-02, cs6 = 1.38888874007937613028114285595617E-03; -static const double t22 = 0x1.8p22; - -void __dubsin (double x, double dx, double w[]); -void __docos (double x, double dx, double w[]); -double __mpsin (double x, double dx, bool reduce_range); -double __mpcos (double x, double dx, bool reduce_range); -static double slow (double x); -static double slow1 (double x); -static double slow2 (double x); -static double sloww (double x, double dx, double orig, bool shift_quadrant); -static double sloww1 (double x, double dx, double orig, bool shift_quadrant); -static double sloww2 (double x, double dx, double orig, int n); -static double bsloww (double x, double dx, double orig, int n); -static double bsloww1 (double x, double dx, double orig, int n); -static double bsloww2 (double x, double dx, double orig, int n); int __branred (double x, double *a, double *aa); -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 @@ -166,40 +116,6 @@ do_cos (double x, double dx) return cs + cor; } -/* A more precise variant of DO_COS. EPS is the adjustment to the correction - COR. */ -static inline double -__always_inline -do_cos_slow (double x, double dx, double eps, double *corp) -{ - mynumber u; - - if (x <= 0) - dx = -dx; - - u.x = big + fabs (x); - x = fabs (x) - (u.x - big); - - double xx, y, x1, x2, e1, e2, res, cor; - double s, sn, ssn, c, cs, ccs; - xx = x * x; - s = x * xx * (sn3 + xx * sn5); - c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); - SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); - x1 = (x + t22) - t22; - x2 = (x - x1) + dx; - e1 = (sn + t22) - t22; - e2 = (sn - e1) + ssn; - cor = (ccs - cs * c - e1 * x2 - e2 * x) - sn * s; - y = cs - e1 * x1; - cor = cor + ((cs - y) - e1 * x1); - res = y + cor; - cor = (y - res) + cor; - cor = 1.0005 * cor + __copysign (eps, cor); - *corp = cor; - return res; -} - /* 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 @@ -224,70 +140,6 @@ do_sin (double x, double dx) return sn + cor; } -/* A more precise variant of DO_SIN. EPS is the adjustment to the correction - COR. */ -static inline double -__always_inline -do_sin_slow (double x, double dx, double eps, double *corp) -{ - mynumber u; - - if (x <= 0) - dx = -dx; - u.x = big + fabs (x); - x = fabs (x) - (u.x - big); - - double xx, y, x1, x2, c1, c2, res, cor; - double s, sn, ssn, c, cs, ccs; - xx = x * x; - s = x * xx * (sn3 + xx * sn5); - c = xx * (cs2 + xx * (cs4 + xx * cs6)); - SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); - x1 = (x + t22) - t22; - x2 = (x - x1) + dx; - c1 = (cs + t22) - t22; - c2 = (cs - c1) + ccs; - cor = (ssn + s * ccs + cs * s + c2 * x + c1 * x2 - sn * x * dx) - sn * c; - y = sn + c1 * x1; - cor = cor + ((sn - y) + c1 * x1); - res = y + cor; - cor = (y - res) + cor; - cor = 1.0005 * cor + __copysign (eps, cor); - *corp = cor; - return res; -} - -/* Reduce range of X and compute sin of a + da. When SHIFT_QUADRANT is true, - the routine returns the cosine of a + da by rotating the quadrant once and - computing the sine of the result. */ -static inline double -__always_inline -reduce_and_compute (double x, bool shift_quadrant) -{ - double retval = 0, a, da; - unsigned int n = __branred (x, &a, &da); - int4 k = (n + shift_quadrant) % 4; - switch (k) - { - case 2: - a = -a; - da = -da; - /* Fall through. */ - case 0: - if (a * a < 0.01588) - retval = bsloww (a, da, x, n); - else - retval = bsloww1 (a, da, x, n); - break; - - case 1: - case 3: - retval = bsloww2 (a, da, x, n); - break; - } - return retval; -} - static inline int4 __always_inline reduce_sincos (double x, double *a, double *da) @@ -517,299 +369,6 @@ __cos (double x) return retval; } -/************************************************************************/ -/* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */ -/* precision and if still doesn't accurate enough by mpsin or dubsin */ -/************************************************************************/ - -static inline double -__always_inline -slow (double x) -{ - double res, cor, w[2]; - res = TAYLOR_SLOW (x, 0, cor); - if (res == res + 1.0007 * cor) - return res; - - __dubsin (fabs (x), 0, w); - if (w[0] == w[0] + 1.000000001 * w[1]) - return __copysign (w[0], x); - - return __copysign (__mpsin (fabs (x), 0, false), x); -} - -/*******************************************************************************/ -/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */ -/* and if result still doesn't accurate enough by mpsin or dubsin */ -/*******************************************************************************/ - -static inline double -__always_inline -slow1 (double x) -{ - double w[2], cor, res; - - res = do_sin_slow (x, 0, 0, &cor); - if (res == res + cor) - return res; - - __dubsin (fabs (x), 0, w); - if (w[0] == w[0] + 1.000000005 * w[1]) - return w[0]; - - return __mpsin (fabs (x), 0, false); -} - -/**************************************************************************/ -/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */ -/* and if result still doesn't accurate enough by mpsin or dubsin */ -/**************************************************************************/ -static inline double -__always_inline -slow2 (double x) -{ - double w[2], y, y1, y2, cor, res; - - double t = hp0 - fabs (x); - res = do_cos_slow (t, hp1, 0, &cor); - if (res == res + cor) - return res; - - y = fabs (x) - hp0; - y1 = y - hp1; - y2 = (y - y1) - hp1; - __docos (y1, y2, w); - if (w[0] == w[0] + 1.000000005 * w[1]) - return w[0]; - - return __mpsin (fabs (x), 0, false); -} - -/* Compute sin(x + dx) where X is small enough to use Taylor series around zero - and (x + dx) in the first or third quarter of the unit circle. ORIG is the - original value of X for computing error of the result. If the result is not - accurate enough, the routine calls mpsin or dubsin. SHIFT_QUADRANT rotates - the unit circle by 1 to compute the cosine instead of sine. */ -static inline double -__always_inline -sloww (double x, double dx, double orig, bool shift_quadrant) -{ - double y, t, res, cor, w[2], a, da, xn; - mynumber v; - int4 n; - res = TAYLOR_SLOW (x, dx, cor); - - double eps = fabs (orig) * 3.1e-30; - - cor = 1.0005 * cor + __copysign (eps, cor); - - if (res == res + cor) - return res; - - a = fabs (x); - da = (x > 0) ? dx : -dx; - __dubsin (a, da, w); - eps = fabs (orig) * 1.1e-30; - cor = 1.000000001 * w[1] + __copysign (eps, w[1]); - - if (w[0] == w[0] + cor) - return __copysign (w[0], x); - - t = (orig * hpinv + toint); - xn = t - toint; - v.x = t; - y = (orig - xn * mp1) - xn * mp2; - n = (v.i[LOW_HALF] + shift_quadrant) & 3; - da = xn * pp3; - t = y - da; - da = (y - t) - da; - y = xn * pp4; - a = t - y; - da = ((t - a) - y) + da; - - if (n & 2) - { - a = -a; - da = -da; - } - x = fabs (a); - dx = (a > 0) ? da : -da; - __dubsin (x, dx, w); - eps = fabs (orig) * 1.1e-40; - cor = 1.000000001 * w[1] + __copysign (eps, w[1]); - - if (w[0] == w[0] + cor) - return __copysign (w[0], a); - - return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); -} - -/* Compute sin(x + dx) where X is in the first or third quarter of the unit - circle. ORIG is the original value of X for computing error of the result. - If the result is not accurate enough, the routine calls mpsin or dubsin. - SHIFT_QUADRANT rotates the unit circle by 1 to compute the cosine instead of - sine. */ -static inline double -__always_inline -sloww1 (double x, double dx, double orig, bool shift_quadrant) -{ - double w[2], cor, res; - - res = do_sin_slow (x, dx, 3.1e-30 * fabs (orig), &cor); - - if (res == res + cor) - return __copysign (res, x); - - dx = (x > 0 ? dx : -dx); - __dubsin (fabs (x), dx, w); - - double eps = 1.1e-30 * fabs (orig); - cor = 1.000000005 * w[1] + __copysign (eps, w[1]); - - if (w[0] == w[0] + cor) - return __copysign (w[0], x); - - return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); -} - -/***************************************************************************/ -/* Routine compute sin(x+dx) (Double-Length number) where x in second or */ -/* fourth quarter of unit circle.Routine receive also the original value */ -/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ -/* accurate enough routine calls mpsin1 or dubsin */ -/***************************************************************************/ - -static inline double -__always_inline -sloww2 (double x, double dx, double orig, int n) -{ - double w[2], cor, res; - - res = do_cos_slow (x, dx, 3.1e-30 * fabs (orig), &cor); - - if (res == res + cor) - return (n & 2) ? -res : res; - - dx = x > 0 ? dx : -dx; - __docos (fabs (x), dx, w); - - double eps = 1.1e-30 * fabs (orig); - cor = 1.000000005 * w[1] + __copysign (eps, w[1]); - - if (w[0] == w[0] + cor) - return (n & 2) ? -w[0] : w[0]; - - return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); -} - -/***************************************************************************/ -/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ -/* is small enough to use Taylor series around zero and (x+dx) */ -/* in first or third quarter of unit circle.Routine receive also */ -/* (right argument) the original value of x for computing error of */ -/* result.And if result not accurate enough routine calls other routines */ -/***************************************************************************/ - -static inline double -__always_inline -bsloww (double x, double dx, double orig, int n) -{ - double res, cor, w[2], a, da; - - res = TAYLOR_SLOW (x, dx, cor); - cor = 1.0005 * cor + __copysign (1.1e-24, cor); - if (res == res + cor) - return res; - - a = fabs (x); - da = (x > 0) ? dx : -dx; - __dubsin (a, da, w); - cor = 1.000000001 * w[1] + __copysign (1.1e-24, w[1]); - - if (w[0] == w[0] + cor) - return __copysign (w[0], x); - - return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); -} - -/***************************************************************************/ -/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ -/* in first or third quarter of unit circle.Routine receive also */ -/* (right argument) the original value of x for computing error of result.*/ -/* And if result not accurate enough routine calls other routines */ -/***************************************************************************/ - -static inline double -__always_inline -bsloww1 (double x, double dx, double orig, int n) -{ - double w[2], cor, res; - - res = do_sin_slow (x, dx, 1.1e-24, &cor); - if (res == res + cor) - return (x > 0) ? res : -res; - - dx = (x > 0) ? dx : -dx; - __dubsin (fabs (x), dx, w); - - cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); - - if (w[0] == w[0] + cor) - return __copysign (w[0], x); - - return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); -} - -/***************************************************************************/ -/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ -/* in second or fourth quarter of unit circle.Routine receive also the */ -/* original value and quarter(n= 1or 3)of x for computing error of result. */ -/* And if result not accurate enough routine calls other routines */ -/***************************************************************************/ - -static inline double -__always_inline -bsloww2 (double x, double dx, double orig, int n) -{ - double w[2], cor, res; - - res = do_cos_slow (x, dx, 1.1e-24, &cor); - if (res == res + cor) - return (n & 2) ? -res : res; - - dx = (x > 0) ? dx : -dx; - __docos (fabs (x), dx, w); - - cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); - - if (w[0] == w[0] + cor) - return (n & 2) ? -w[0] : w[0]; - - return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); -} - -/************************************************************************/ -/* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */ -/* precision and if still doesn't accurate enough by mpcos or docos */ -/************************************************************************/ - -static inline double -__always_inline -cslow2 (double x) -{ - double w[2], cor, res; - - res = do_cos_slow (x, 0, 0, &cor); - if (res == res + cor) - return res; - - __docos (fabs (x), 0, w); - if (w[0] == w[0] + 1.000000005 * w[1]) - return w[0]; - - return __mpcos (x, 0, false); -} - #ifndef __cos libm_alias_double (__cos, cos) #endif