lib/libm/src/s_atanf.c

   1 /* s_atanf.c -- float version of s_atan.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float atanhi[] = {
  25   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
  26   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
  27   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
  28   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
  29 };
  30
  31 static const float atanlo[] = {
  32   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
  33   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
  34   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
  35   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
  36 };
  37
  38 static const float aT[] = {
  39   3.3333334327e-01, /* 0x3eaaaaaa */
  40  -2.0000000298e-01, /* 0xbe4ccccd */
  41   1.4285714924e-01, /* 0x3e124925 */
  42  -1.1111110449e-01, /* 0xbde38e38 */
  43   9.0908870101e-02, /* 0x3dba2e6e */
  44  -7.6918758452e-02, /* 0xbd9d8795 */
  45   6.6610731184e-02, /* 0x3d886b35 */
  46  -5.8335702866e-02, /* 0xbd6ef16b */
  47   4.9768779427e-02, /* 0x3d4bda59 */
  48  -3.6531571299e-02, /* 0xbd15a221 */
  49   1.6285819933e-02, /* 0x3c8569d7 */
  50 };
  51
  52 static const float
  53 one   = 1.0,
  54 huge   = 1.0e30;
  55
  56 float
  57 atanf(float x)
  58 {
  59         float w,s1,s2,z;
  60         int32_t ix,hx,id;
  61
  62         GET_FLOAT_WORD(hx,x);
  63         ix = hx&0x7fffffff;
  64         if(ix>=0x50800000) {    /* if |x| >= 2^34 */
  65             if(ix>0x7f800000)
  66                 return x+x;             /* NaN */
  67             if(hx>0) return  atanhi[3]+atanlo[3];
  68             else     return -atanhi[3]-atanlo[3];
  69         } if (ix < 0x3ee00000) {        /* |x| < 0.4375 */
  70             if (ix < 0x31000000) {      /* |x| < 2^-29 */
  71                 if(huge+x>one) return x;        /* raise inexact */
  72             }
  73             id = -1;
  74         } else {
  75         x = fabsf(x);
  76         if (ix < 0x3f980000) {          /* |x| < 1.1875 */
  77             if (ix < 0x3f300000) {      /* 7/16 <=|x|<11/16 */
  78                 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
  79             } else {                    /* 11/16<=|x|< 19/16 */
  80                 id = 1; x  = (x-one)/(x+one);
  81             }
  82         } else {
  83             if (ix < 0x401c0000) {      /* |x| < 2.4375 */
  84                 id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
  85             } else {                    /* 2.4375 <= |x| < 2^66 */
  86                 id = 3; x  = -(float)1.0/x;
  87             }
  88         }}
  89     /* end of argument reduction */
  90         z = x*x;
  91         w = z*z;
  92     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  93         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  94         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  95         if (id<0) return x - x*(s1+s2);
  96         else {
  97             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  98             return (hx<0)? -z:z;
  99         }
 100 }