common/C/__cos.c

25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * The contents of this file are subject to the terms of the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Common Development and Distribution License (the "License").
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You may not use this file except in compliance with the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * See the License for the specific language governing permissions
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * and limitations under the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER END
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * __k_cos(double x; double y)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input y is the tail of x.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Algorithm: see __sincos.c
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const double sc[] = {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* ONE  = */  1.0,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* NONE = */ -1.0,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* PP1  = */ -0.166666666666316558867252052378889521480627858683055567,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* PP2  = */   .008333315652997472323564894248466758248475374977974017927,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |                 x             |
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* P1   = */ -1.666666666666629669805215138920301589656e-0001,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* P2   = */  8.333333332390951295683993455280336376663e-0003,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* P3   = */ -1.984126237997976692791551778230098403960e-0004,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* P4   = */  2.753403624854277237649987622848330351110e-0006,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* QQ1  = */ -0.4999999999975492381842911981948418542742729,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* QQ2  = */  0.041666542904352059294545209158357640398771740,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* Q1   = */ -0.5,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* Q2   = */  4.166666666500350703680945520860748617445e-0002,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* Q3   = */ -1.388888596436972210694266290577848696006e-0003,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* Q4   = */  2.478563078858589473679519517892953492192e-0005,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis};
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define ONE sc[0]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define NONE    sc[1]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define PP1 sc[2]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define PP2 sc[3]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define P1  sc[4]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define P2  sc[5]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define P3  sc[6]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define P4  sc[7]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define QQ1 sc[8]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define QQ2 sc[9]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define Q1  sc[10]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define Q2  sc[11]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define Q3  sc[12]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define Q4  sc[13]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const double _TBL_sincos[], _TBL_sincosx[];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisdouble
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis__k_cos(double x, double y) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    double  z, w, s, v, p, q;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int i, j, n, hx, ix;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    hx = ((int *)&x)[HIWORD];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ix = hx & ~0x80000000;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (ix < 0x3e400000)    /* |x| < 2**-27 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if ((int)x == 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                return (ONE);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        z = x * x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (ix < 0x3f800000)    /* |x| < 0.008 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            q = z * (QQ1 + z * QQ2);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (ONE + q);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else {        /* 0.164062500 < |x| < ~pi/4 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        n = ix >> 20;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        j = i - 10;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (hx < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            v = -y - (_TBL_sincosx[j] + x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            v = y - (_TBL_sincosx[j] - x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        s = v * v;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        j <<= 1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        w = _TBL_sincos[j];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        z = _TBL_sincos[j+1];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        p = s * (PP1 + s * PP2);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        q = s * (QQ1 + s * QQ2);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        p = v + v * p;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (z - (w * p - z * q));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}