[BACK]Return to s_atan.c CVS log [TXT][DIR] Up to [cvs.NetBSD.org] / src / lib / libm / src

Annotation of src/lib/libm/src/s_atan.c, Revision 1.1.1.1

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: }

CVSweb <webmaster@jp.NetBSD.org>