/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/*
 * See comments in s_atan.c.
 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
 */

#include <float.h>

#include "invtrig.h"
#include "math.h"
#include "math_private.h"

static const long double
one   = 1.0,
huge   = 1.0e300;

long double
atanl(long double x)
{
        union IEEEl2bits u;
        long double w,s1,s2,z;
        int id;
        int16_t expsign, expt;
        int32_t expman;

        u.e = x;
        expsign = u.xbits.expsign;
        expt = expsign & 0x7fff;
        if(expt >= ATAN_CONST) {        /* if |x| is large, atan(x)~=pi/2 */
            if(expt == BIAS + LDBL_MAX_EXP &&
               ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
                return x+x;             /* NaN */
            if(expsign>0) return  atanhi[3]+atanlo[3];
            else     return -atanhi[3]-atanlo[3];
        }
        /* Extract the exponent and the first few bits of the mantissa. */
        /* XXX There should be a more convenient way to do this. */
        expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
        if (expman < ((BIAS - 2) << 8) + 0xc0) {        /* |x| < 0.4375 */
            if (expt < ATAN_LINEAR) {   /* if |x| is small, atanl(x)~=x */
                if(huge+x>one) return x;        /* raise inexact */
            }
            id = -1;
        } else {
        x = fabsl(x);
        if (expman < (BIAS << 8) + 0x30) {              /* |x| < 1.1875 */
            if (expman < ((BIAS - 1) << 8) + 0x60) {    /* 7/16 <=|x|<11/16 */
                id = 0; x = (2.0*x-one)/(2.0+x);
            } else {                    /* 11/16<=|x|< 19/16 */
                id = 1; x  = (x-one)/(x+one);
            }
        } else {
            if (expman < ((BIAS + 1) << 8) + 0x38) {    /* |x| < 2.4375 */
                id = 2; x  = (x-1.5)/(one+1.5*x);
            } else {                    /* 2.4375 <= |x| < 2^ATAN_CONST */
                id = 3; x  = -1.0/x;
            }
        }}
    /* end of argument reduction */
        z = x*x;
        w = z*z;
    /* break sum aT[i]z**(i+1) into odd and even poly */
        s1 = z*T_even(w);
        s2 = w*T_odd(w);
        if (id<0) return x - x*(s1+s2);
        else {
            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
            return (expsign<0)? -z:z;
        }
}