/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2005 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak __cos = cos /* INDENT OFF */ /* * cos(x) * Accurate Table look-up algorithm by K.C. Ng, May, 1995. * * Algorithm: see sincos.c */ #include "libm.h" static const double sc[] = { /* ONE = */ 1.0, /* NONE = */ -1.0, /* * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008 */ /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567, /* PP2 = */ .008333315652997472323564894248466758248475374977974017927, /* * |(sin(x) - (x+p1*x^3+...+p4*x^9)| * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125 * | x | */ /* P1 = */ -1.666666666666629669805215138920301589656e-0001, /* P2 = */ 8.333333332390951295683993455280336376663e-0003, /* P3 = */ -1.984126237997976692791551778230098403960e-0004, /* P4 = */ 2.753403624854277237649987622848330351110e-0006, /* * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d) */ /* QQ1 = */ -0.4999999999975492381842911981948418542742729, /* QQ2 = */ 0.041666542904352059294545209158357640398771740, /* Q1 = */ -0.5, /* Q2 = */ 4.166666666500350703680945520860748617445e-0002, /* Q3 = */ -1.388888596436972210694266290577848696006e-0003, /* Q4 = */ 2.478563078858589473679519517892953492192e-0005, /* PIO2_H = */ 1.570796326794896557999, /* PIO2_L = */ 6.123233995736765886130e-17, /* PIO2_L0 = */ 6.123233995727922165564e-17, /* PIO2_L1 = */ 8.843720566135701120255e-29, /* PI3O2_H = */ 4.712388980384689673997, /* PI3O2_L = */ 1.836970198721029765839e-16, /* PI3O2_L0 = */ 1.836970198720396133587e-16, /* PI3O2_L1 = */ 6.336322524749201142226e-29, /* PI5O2_H = */ 7.853981633974482789995, /* PI5O2_L = */ 3.061616997868382943065e-16, /* PI5O2_L0 = */ 3.061616997861941598865e-16, /* PI5O2_L1 = */ 6.441344200433640781982e-28, }; /* INDENT ON */ #define ONE sc[0] #define PP1 sc[2] #define PP2 sc[3] #define P1 sc[4] #define P2 sc[5] #define P3 sc[6] #define P4 sc[7] #define QQ1 sc[8] #define QQ2 sc[9] #define Q1 sc[10] #define Q2 sc[11] #define Q3 sc[12] #define Q4 sc[13] #define PIO2_H sc[14] #define PIO2_L sc[15] #define PIO2_L0 sc[16] #define PIO2_L1 sc[17] #define PI3O2_H sc[18] #define PI3O2_L sc[19] #define PI3O2_L0 sc[20] #define PI3O2_L1 sc[21] #define PI5O2_H sc[22] #define PI5O2_L sc[23] #define PI5O2_L0 sc[24] #define PI5O2_L1 sc[25] extern const double _TBL_sincos[], _TBL_sincosx[]; double cos(double x) { double z, y[2], w, s, v, p, q; int i, j, n, hx, ix, lx; hx = ((int *)&x)[HIWORD]; lx = ((int *)&x)[LOWORD]; ix = hx & ~0x80000000; if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */ if (ix < 0x3e400000) { /* |x| < 2**-27 */ if ((int)x == 0) return (ONE); } z = x * x; if (ix < 0x3f800000) /* |x| < 0.008 */ w = z * (QQ1 + z * QQ2); else w = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4)); return (ONE + w); } /* for 0.164062500 < x < M, */ n = ix >> 20; if (n < 0x402) { /* x < 8 */ i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); j = i - 10; x = fabs(x); v = x - _TBL_sincosx[j]; if (((j - 81) ^ (j - 101)) < 0) { /* near pi/2, cos(pi/2-x)=sin(x) */ p = PIO2_H - x; i = ix - 0x3ff921fb; x = p + PIO2_L; if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) { /* very close to pi/2 */ x = p + PIO2_L0; return (x + PIO2_L1); } z = x * x; if (((ix - 0x3ff92000) >> 12) == 0) { /* |pi/2-x|<2**-8 */ w = PIO2_L + (z * x) * (PP1 + z * PP2); } else { w = PIO2_L + (z * x) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)); } return (p + w); } s = v * v; if (((j - 282) ^ (j - 302)) < 0) { /* near 3/2pi, cos(x-3/2pi)=sin(x) */ p = x - PI3O2_H; i = ix - 0x4012D97C; x = p - PI3O2_L; if ((i | ((lx - 0x7f332100) & 0xffffff00)) == 0) { /* very close to 3/2pi */ x = p - PI3O2_L0; return (x - PI3O2_L1); } z = x * x; if (((ix - 0x4012D800) >> 9) == 0) { /* |x-3/2pi|<2**-8 */ w = (z * x) * (PP1 + z * PP2) - PI3O2_L; } else { w = (z * x) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)) - PI3O2_L; } return (p + w); } if (((j - 483) ^ (j - 503)) < 0) { /* near 5pi/2, cos(5pi/2-x)=sin(x) */ p = PI5O2_H - x; i = ix - 0x401F6A7A; x = p + PI5O2_L; if ((i | ((lx - 0x29553800) & 0xffffff00)) == 0) { /* very close to pi/2 */ x = p + PI5O2_L0; return (x + PI5O2_L1); } z = x * x; if (((ix - 0x401F6A7A) >> 7) == 0) { /* |pi/2-x|<2**-8 */ w = PI5O2_L + (z * x) * (PP1 + z * PP2); } else { w = PI5O2_L + (z * x) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)); } return (p + w); } j <<= 1; w = _TBL_sincos[j]; z = _TBL_sincos[j+1]; p = v + (v * s) * (PP1 + s * PP2); q = s * (QQ1 + s * QQ2); return (z - (w * p - z * q)); } if (ix >= 0x7ff00000) /* cos(Inf or NaN) is NaN */ return (x / x); /* argument reduction needed */ n = __rem_pio2(x, y); switch (n & 3) { case 0: return (__k_cos(y[0], y[1])); case 1: return (-__k_sin(y[0], y[1])); case 2: return (-__k_cos(y[0], y[1])); default: return (__k_sin(y[0], y[1])); } }