Line data    Source code

       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             :  */
      12             : 
      13             : //#include <sys/cdefs.h>
      14             : //__FBSDID("$FreeBSD$");
      15             : 
      16             : /* atan(x)
      17             :  * Method
      18             :  *   1. Reduce x to positive by atan(x) = -atan(-x).
      19             :  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
      20             :  *      is further reduced to one of the following intervals and the
      21             :  *      arctangent of t is evaluated by the corresponding formula:
      22             :  *
      23             :  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
      24             :  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
      25             :  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
      26             :  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
      27             :  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
      28             :  *
      29             :  * Constants:
      30             :  * The hexadecimal values are the intended ones for the following
      31             :  * constants. The decimal values may be used, provided that the
      32             :  * compiler will convert from decimal to binary accurately enough
      33             :  * to produce the hexadecimal values shown.
      34             :  */
      35             : 
      36             : #include <float.h>
      37             : 
      38             : #include "math_private.h"
      39             : 
      40             : static const double atanhi[] = {
      41             :   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
      42             :   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
      43             :   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
      44             :   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
      45             : };
      46             : 
      47             : static const double atanlo[] = {
      48             :   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
      49             :   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
      50             :   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
      51             :   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
      52             : };
      53             : 
      54             : static const double aT[] = {
      55             :   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
      56             :  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
      57             :   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
      58             :  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
      59             :   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
      60             :  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
      61             :   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
      62             :  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
      63             :   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
      64             :  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
      65             :   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
      66             : };
      67             : 
      68             :         static const double
      69             : one   = 1.0,
      70             : huge   = 1.0e300;
      71             : 
      72             : double
      73           0 : atan(double x)
      74             : {
      75             :         double w,s1,s2,z;
      76             :         int32_t ix,hx,id;
      77             : 
      78           0 :         GET_HIGH_WORD(hx,x);
      79           0 :         ix = hx&0x7fffffff;
      80           0 :         if(ix>=0x44100000) { /* if |x| >= 2^66 */
      81             :             u_int32_t low;
      82           0 :             GET_LOW_WORD(low,x);
      83           0 :             if(ix>0x7ff00000||
      84           0 :                 (ix==0x7ff00000&&(low!=0)))
      85           0 :                 return x+x;             /* NaN */
      86           0 :             if(hx>0) return  atanhi[3]+*(volatile double *)&atanlo[3];
      87           0 :             else     return -atanhi[3]-*(volatile double *)&atanlo[3];
      88           0 :         } if (ix < 0x3fdc0000) {     /* |x| < 0.4375 */
      89           0 :             if (ix < 0x3e400000) {   /* |x| < 2^-27 */
      90           0 :                 if(huge+x>one) return x;     /* raise inexact */
      91             :             }
      92           0 :             id = -1;
      93             :         } else {
      94           0 :         x = fabs(x);
      95           0 :         if (ix < 0x3ff30000) {               /* |x| < 1.1875 */
      96           0 :             if (ix < 0x3fe60000) {   /* 7/16 <=|x|<11/16 */
      97           0 :                 id = 0; x = (2.0*x-one)/(2.0+x);
      98             :             } else {                    /* 11/16<=|x|< 19/16 */
      99           0 :                 id = 1; x  = (x-one)/(x+one);
     100             :             }
     101             :         } else {
     102           0 :             if (ix < 0x40038000) {   /* |x| < 2.4375 */
     103           0 :                 id = 2; x  = (x-1.5)/(one+1.5*x);
     104             :             } else {                    /* 2.4375 <= |x| < 2^66 */
     105           0 :                 id = 3; x  = -1.0/x;
     106             :             }
     107             :         }}
     108             :     /* end of argument reduction */
     109           0 :         z = x*x;
     110           0 :         w = z*z;
     111             :     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
     112           0 :         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
     113           0 :         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
     114           0 :         if (id<0) return x - x*(s1+s2);
     115             :         else {
     116           0 :             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
     117           0 :             return (hx<0)? -z:z;
     118             :         }
     119             : }