/*
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 *
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 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
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 * 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
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/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak __atanl = atanl

/*
 * atanl(x)
 * Table look-up algorithm
 * By K.C. Ng, March 9, 1989
 *
 * Algorithm.
 *
 * The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)).
 * We use poly1(x) to approximate atan(x) for x in [0,1/8] with
 * error (relative)
 *      |(atan(x)-poly1(x))/x|<= 2^-115.94      long double
 *      |(atan(x)-poly1(x))/x|<= 2^-58.85       double
 *      |(atan(x)-poly1(x))/x|<= 2^-25.53       float
 * and use poly2(x) to approximate atan(x) for x in [0,1/65] with
 * error (absolute)
 *      |atan(x)-poly2(x)|<= 2^-122.15          long double
 *      |atan(x)-poly2(x)|<= 2^-64.79           double
 *      |atan(x)-poly2(x)|<= 2^-35.36           float
 * Here poly1 and poly2 are odd polynomial with the following form:
 *              x + x^3*(a1+x^2*(a2+...))
 *
 * (0). Purge off Inf and NaN and 0
 * (1). Reduce x to positive by atan(x) = -atan(-x).
 * (2). For x <= 1/8, use
 *      (2.1) if x < 2^(-prec/2-2), atan(x) =  x  with inexact
 *      (2.2) Otherwise
 *              atan(x) = poly1(x)
 * (3). For x >= 8 then
 *      (3.1) if x >= 2^(prec+2),   atan(x) = atan(inf) - pio2lo
 *      (3.2) if x >= 2^(prec/3+2), atan(x) = atan(inf) - 1/x
 *      (3.3) if x >  65,           atan(x) = atan(inf) - poly2(1/x)
 *      (3.4) Otherwise,            atan(x) = atan(inf) - poly1(1/x)
 *
 * (4). Now x is in (0.125, 8)
 *      Find y that match x to 4.5 bit after binary (easy).
 *      If iy is the high word of y, then
 *              single : j = (iy - 0x3e000000) >> 19
 *              double : j = (iy - 0x3fc00000) >> 16
 *              quad   : j = (iy - 0x3ffc0000) >> 12
 *
 *      Let s = (x-y)/(1+x*y). Then
 *      atan(x) = atan(y) + poly1(s)
 *              = _TBL_atanl_hi[j] + (_TBL_atanl_lo[j] + poly2(s) )
 *
 *      Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
 *
 */

#include "libm.h"

extern const long double _TBL_atanl_hi[], _TBL_atanl_lo[];
static const long double
        one     =   1.0L,
        p1      =  -3.333333333333333333333333333331344526118e-0001L,
        p2      =   1.999999999999999999999999989931277668570e-0001L,
        p3      =  -1.428571428571428571428553606221309530901e-0001L,
        p4      =   1.111111111111111111095219842737139747418e-0001L,
        p5      =  -9.090909090909090825503603835248061123323e-0002L,
        p6      =   7.692307692307664052130743214708925258904e-0002L,
        p7      =  -6.666666666660213835187713228363717388266e-0002L,
        p8      =   5.882352940152439399097283359608661949504e-0002L,
        p9      =  -5.263157780447533993046614040509529668487e-0002L,
        p10     =   4.761895816878184933175855990886788439447e-0002L,
        p11     =  -4.347345005832274022681019724553538135922e-0002L,
        p12     =   3.983031914579635037502589204647752042736e-0002L,
        p13     =  -3.348206704469830575196657749413894897554e-0002L,
        q1      =  -3.333333333333333333333333333195273650186e-0001L,
        q2      =   1.999999999999999999999988146114392615808e-0001L,
        q3      =  -1.428571428571428571057630319435467111253e-0001L,
        q4      =   1.111111111111105373263048208994541544098e-0001L,
        q5      =  -9.090909090421834209167373258681021816441e-0002L,
        q6      =   7.692305377813692706850171767150701644539e-0002L,
        q7      =  -6.660896644393861499914731734305717901330e-0002L,
        pio2hi  =   1.570796326794896619231321691639751398740e+0000L,
        pio2lo  =   4.335905065061890512398522013021675984381e-0035L;

#define i0      0
#define i1      3

long double
atanl(long double x) {
        long double y, z, r, p, s;
        int *px = (int *) &x, *py = (int *) &y;
        int ix, iy, sign, j;

        ix = px[i0];
        sign = ix & 0x80000000;
        ix ^= sign;

        /* for |x| < 1/8 */
        if (ix < 0x3ffc0000) {
                if (ix < 0x3feb0000) {  /* when |x| < 2**(-prec/6-2) */
                        if (ix < 0x3fc50000) {  /* if |x| < 2**(-prec/2-2) */
                                s = one;
                                *(3 - i0 + (int *) &s) = -1;    /* s = 1-ulp */
                                *(1 + (int *) &s) = -1;
                                *(2 + (int *) &s) = -1;
                                *(i0 + (int *) &s) -= 1;
                                if ((int) (s * x) < 1)
                                        return (x);     /* raise inexact */
                        }
                        z = x * x;
                        if (ix < 0x3fe20000) {  /* if |x| < 2**(-prec/4-1) */
                                return (x + (x * z) * p1);
                        } else {        /* if |x| < 2**(-prec/6-2) */
                                return (x + (x * z) * (p1 + z * p2));
                        }
                }
                z = x * x;
                return (x + (x * z) * (p1 + z * (p2 + z * (p3 + z * (p4 +
                        z * (p5 + z * (p6 + z * (p7 + z * (p8 + z * (p9 +
                        z * (p10 + z * (p11 + z * (p12 + z * p13)))))))))))));
        }

        /* for |x| >= 8.0 */
        if (ix >= 0x40020000) {
                px[i0] = ix;
                if (ix < 0x40050400) {  /* x <  65 */
                        r = one / x;
                        z = r * r;
                        /*
                         * poly1
                         */
                        y = r * (one + z * (p1 + z * (p2 + z * (p3 +
                                z * (p4 + z * (p5 + z * (p6 + z * (p7 +
                                z * (p8 + z * (p9 + z * (p10 + z * (p11 +
                                z * (p12 + z * p13)))))))))))));
                        y -= pio2lo;
                } else if (ix < 0x40260000) {   /* x <  2**(prec/3+2) */
                        r = one / x;
                        z = r * r;
                        /*
                         * poly2
                         */
                        y = r * (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
                                z * (q5 + z * (q6 + z * q7)))))));
                        y -= pio2lo;
                } else if (ix < 0x40720000) {   /* x <  2**(prec+2) */
                        y = one / x - pio2lo;
                } else if (ix < 0x7fff0000) {   /* x <  inf */
                        y = -pio2lo;
                } else {                /* x is inf or NaN */
                        if (((ix - 0x7fff0000) | px[1] | px[2] | px[i1]) != 0)
                                return (x - x);
                        y = -pio2lo;
                }

                if (sign == 0)
                        return (pio2hi - y);
                else
                        return (y - pio2hi);
        }

        /* now x is between 1/8 and 8 */
        px[i0] = ix;
        iy = (ix + 0x00000800) & 0x7ffff000;
        py[i0] = iy;
        py[1] = py[2] = py[i1] = 0;
        j = (iy - 0x3ffc0000) >> 12;

        if (sign == 0)
                s = (x - y) / (one + x * y);
        else
                s = (y - x) / (one + x * y);
        z = s * s;
        if (ix == iy)
                p = s * (one + z * (q1 + z * (q2 + z * (q3 + z * q4))));
        else
                p = s * (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
                        z * (q5 + z * (q6 + z * q7)))))));
        if (sign == 0) {
                r = p + _TBL_atanl_lo[j];
                return (r + _TBL_atanl_hi[j]);
        } else {
                r = p - _TBL_atanl_lo[j];
                return (r - _TBL_atanl_hi[j]);
        }
}