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Annotation of src/lib/libm/src/s_atan.c, Revision 1.9

1.1       jtc         1: /* @(#)s_atan.c 5.1 93/09/24 */
                      2: /*
                      3:  * ====================================================
                      4:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
                      5:  *
                      6:  * Developed at SunPro, a Sun Microsystems, Inc. business.
                      7:  * Permission to use, copy, modify, and distribute this
                      8:  * software is freely granted, provided that this notice
                      9:  * is preserved.
                     10:  * ====================================================
                     11:  */
1.3       jtc        12:
1.9     ! lukem      13: #include <sys/cdefs.h>
1.7       jtc        14: #if defined(LIBM_SCCS) && !defined(lint)
1.9     ! lukem      15: __RCSID("$NetBSD$");
1.3       jtc        16: #endif
1.1       jtc        17:
                     18: /* atan(x)
                     19:  * Method
                     20:  *   1. Reduce x to positive by atan(x) = -atan(-x).
                     21:  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
                     22:  *      is further reduced to one of the following intervals and the
                     23:  *      arctangent of t is evaluated by the corresponding formula:
                     24:  *
                     25:  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
                     26:  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
                     27:  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
                     28:  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
                     29:  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
                     30:  *
                     31:  * Constants:
                     32:  * The hexadecimal values are the intended ones for the following
                     33:  * constants. The decimal values may be used, provided that the
                     34:  * compiler will convert from decimal to binary accurately enough
                     35:  * to produce the hexadecimal values shown.
                     36:  */
                     37:
1.5       jtc        38: #include "math.h"
                     39: #include "math_private.h"
1.1       jtc        40:
                     41: #ifdef __STDC__
                     42: static const double atanhi[] = {
                     43: #else
                     44: static double atanhi[] = {
                     45: #endif
                     46:   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
                     47:   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
                     48:   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
                     49:   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
                     50: };
                     51:
                     52: #ifdef __STDC__
                     53: static const double atanlo[] = {
                     54: #else
                     55: static double atanlo[] = {
                     56: #endif
                     57:   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
                     58:   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
                     59:   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
                     60:   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
                     61: };
                     62:
                     63: #ifdef __STDC__
                     64: static const double aT[] = {
                     65: #else
                     66: static double aT[] = {
                     67: #endif
                     68:   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
                     69:  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
                     70:   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
                     71:  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
                     72:   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
                     73:  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
                     74:   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
                     75:  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
                     76:   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
                     77:  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
                     78:   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
                     79: };
                     80:
                     81: #ifdef __STDC__
                     82:        static const double
                     83: #else
                     84:        static double
                     85: #endif
                     86: one   = 1.0,
                     87: huge   = 1.0e300;
                     88:
                     89: #ifdef __STDC__
                     90:        double atan(double x)
                     91: #else
                     92:        double atan(x)
                     93:        double x;
                     94: #endif
                     95: {
                     96:        double w,s1,s2,z;
1.6       jtc        97:        int32_t ix,hx,id;
1.1       jtc        98:
1.5       jtc        99:        GET_HIGH_WORD(hx,x);
1.1       jtc       100:        ix = hx&0x7fffffff;
                    101:        if(ix>=0x44100000) {    /* if |x| >= 2^66 */
1.6       jtc       102:            u_int32_t low;
1.5       jtc       103:            GET_LOW_WORD(low,x);
1.1       jtc       104:            if(ix>0x7ff00000||
1.5       jtc       105:                (ix==0x7ff00000&&(low!=0)))
1.1       jtc       106:                return x+x;             /* NaN */
                    107:            if(hx>0) return  atanhi[3]+atanlo[3];
                    108:            else     return -atanhi[3]-atanlo[3];
                    109:        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
                    110:            if (ix < 0x3e200000) {      /* |x| < 2^-29 */
                    111:                if(huge+x>one) return x;        /* raise inexact */
                    112:            }
                    113:            id = -1;
                    114:        } else {
                    115:        x = fabs(x);
                    116:        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
                    117:            if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
                    118:                id = 0; x = (2.0*x-one)/(2.0+x);
                    119:            } else {                    /* 11/16<=|x|< 19/16 */
                    120:                id = 1; x  = (x-one)/(x+one);
                    121:            }
                    122:        } else {
                    123:            if (ix < 0x40038000) {      /* |x| < 2.4375 */
                    124:                id = 2; x  = (x-1.5)/(one+1.5*x);
                    125:            } else {                    /* 2.4375 <= |x| < 2^66 */
                    126:                id = 3; x  = -1.0/x;
                    127:            }
                    128:        }}
                    129:     /* end of argument reduction */
                    130:        z = x*x;
                    131:        w = z*z;
                    132:     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
                    133:        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
                    134:        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
                    135:        if (id<0) return x - x*(s1+s2);
                    136:        else {
                    137:            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
                    138:            return (hx<0)? -z:z;
                    139:        }
                    140: }

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