diff options
Diffstat (limited to 'usr/src/lib/libm/common/C/cos.c')
| -rw-r--r-- | usr/src/lib/libm/common/C/cos.c | 223 |
1 files changed, 223 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/C/cos.c b/usr/src/lib/libm/common/C/cos.c new file mode 100644 index 0000000000..1558872b70 --- /dev/null +++ b/usr/src/lib/libm/common/C/cos.c @@ -0,0 +1,223 @@ +/* + * 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])); + } +} |