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Annotation of src/lib/libm/src/s_atan.c, Revision 1.1

1.1     ! jtc         1:
        !             2: /* @(#)s_atan.c 5.1 93/09/24 */
        !             3: /*
        !             4:  * ====================================================
        !             5:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
        !             6:  *
        !             7:  * Developed at SunPro, a Sun Microsystems, Inc. business.
        !             8:  * Permission to use, copy, modify, and distribute this
        !             9:  * software is freely granted, provided that this notice
        !            10:  * is preserved.
        !            11:  * ====================================================
        !            12:  *
        !            13:  */
        !            14:
        !            15: /* atan(x)
        !            16:  * Method
        !            17:  *   1. Reduce x to positive by atan(x) = -atan(-x).
        !            18:  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
        !            19:  *      is further reduced to one of the following intervals and the
        !            20:  *      arctangent of t is evaluated by the corresponding formula:
        !            21:  *
        !            22:  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
        !            23:  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
        !            24:  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
        !            25:  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
        !            26:  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
        !            27:  *
        !            28:  * Constants:
        !            29:  * The hexadecimal values are the intended ones for the following
        !            30:  * constants. The decimal values may be used, provided that the
        !            31:  * compiler will convert from decimal to binary accurately enough
        !            32:  * to produce the hexadecimal values shown.
        !            33:  */
        !            34:
        !            35: #include "fdlibm.h"
        !            36:
        !            37: #ifdef __STDC__
        !            38: static const double atanhi[] = {
        !            39: #else
        !            40: static double atanhi[] = {
        !            41: #endif
        !            42:   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
        !            43:   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
        !            44:   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
        !            45:   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
        !            46: };
        !            47:
        !            48: #ifdef __STDC__
        !            49: static const double atanlo[] = {
        !            50: #else
        !            51: static double atanlo[] = {
        !            52: #endif
        !            53:   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
        !            54:   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
        !            55:   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
        !            56:   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
        !            57: };
        !            58:
        !            59: #ifdef __STDC__
        !            60: static const double aT[] = {
        !            61: #else
        !            62: static double aT[] = {
        !            63: #endif
        !            64:   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
        !            65:  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
        !            66:   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
        !            67:  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
        !            68:   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
        !            69:  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
        !            70:   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
        !            71:  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
        !            72:   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
        !            73:  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
        !            74:   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
        !            75: };
        !            76:
        !            77: #ifdef __STDC__
        !            78:        static const double
        !            79: #else
        !            80:        static double
        !            81: #endif
        !            82: one   = 1.0,
        !            83: huge   = 1.0e300;
        !            84:
        !            85: #ifdef __STDC__
        !            86:        double atan(double x)
        !            87: #else
        !            88:        double atan(x)
        !            89:        double x;
        !            90: #endif
        !            91: {
        !            92:        double w,s1,s2,z;
        !            93:        int n0,ix,hx,id;
        !            94:
        !            95:        n0 = ((*(int*)&one)>>29)^1;
        !            96:        hx = *(n0+(int*)&x);
        !            97:        ix = hx&0x7fffffff;
        !            98:        if(ix>=0x44100000) {    /* if |x| >= 2^66 */
        !            99:            if(ix>0x7ff00000||
        !           100:                (ix==0x7ff00000&&(*(1-n0+(int*)&x)!=0)))
        !           101:                return x+x;             /* NaN */
        !           102:            if(hx>0) return  atanhi[3]+atanlo[3];
        !           103:            else     return -atanhi[3]-atanlo[3];
        !           104:        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
        !           105:            if (ix < 0x3e200000) {      /* |x| < 2^-29 */
        !           106:                if(huge+x>one) return x;        /* raise inexact */
        !           107:            }
        !           108:            id = -1;
        !           109:        } else {
        !           110:        x = fabs(x);
        !           111:        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
        !           112:            if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
        !           113:                id = 0; x = (2.0*x-one)/(2.0+x);
        !           114:            } else {                    /* 11/16<=|x|< 19/16 */
        !           115:                id = 1; x  = (x-one)/(x+one);
        !           116:            }
        !           117:        } else {
        !           118:            if (ix < 0x40038000) {      /* |x| < 2.4375 */
        !           119:                id = 2; x  = (x-1.5)/(one+1.5*x);
        !           120:            } else {                    /* 2.4375 <= |x| < 2^66 */
        !           121:                id = 3; x  = -1.0/x;
        !           122:            }
        !           123:        }}
        !           124:     /* end of argument reduction */
        !           125:        z = x*x;
        !           126:        w = z*z;
        !           127:     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
        !           128:        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
        !           129:        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
        !           130:        if (id<0) return x - x*(s1+s2);
        !           131:        else {
        !           132:            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
        !           133:            return (hx<0)? -z:z;
        !           134:        }
        !           135: }

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