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  * $NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/s_atanf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static const float atanhi[] = {
  23   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
  24   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
  25   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
  26   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
  27 };
  28
  29 static const float atanlo[] = {
  30   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
  31   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
  32   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
  33   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
  34 };
  35
  36 static const float aT[] = {
  37   3.3333334327e-01, /* 0x3eaaaaaa */
  38  -2.0000000298e-01, /* 0xbe4ccccd */
  39   1.4285714924e-01, /* 0x3e124925 */
  40  -1.1111110449e-01, /* 0xbde38e38 */
  41   9.0908870101e-02, /* 0x3dba2e6e */
  42  -7.6918758452e-02, /* 0xbd9d8795 */
  43   6.6610731184e-02, /* 0x3d886b35 */
  44  -5.8335702866e-02, /* 0xbd6ef16b */
  45   4.9768779427e-02, /* 0x3d4bda59 */
  46  -3.6531571299e-02, /* 0xbd15a221 */
  47   1.6285819933e-02, /* 0x3c8569d7 */
  48 };
  49
  50 static const float
  51 one   = 1.0,
  52 huge   = 1.0e30;
  53
  54 float
  55 atanf(float x)
  56 {
  57         float w,s1,s2,z;
  58         int32_t ix,hx,id;
  59
  60         GET_FLOAT_WORD(hx,x);
  61         ix = hx&0x7fffffff;
  62         if(ix>=0x50800000) {    /* if |x| >= 2^34 */
  63             if(ix>0x7f800000)
  64                 return x+x;             /* NaN */
  65             if(hx>0) return  atanhi[3]+atanlo[3];
  66             else     return -atanhi[3]-atanlo[3];
  67         } if (ix < 0x3ee00000) {        /* |x| < 0.4375 */
  68             if (ix < 0x31000000) {      /* |x| < 2^-29 */
  69                 if(huge+x>one) return x;        /* raise inexact */
  70             }
  71             id = -1;
  72         } else {
  73         x = fabsf(x);
  74         if (ix < 0x3f980000) {          /* |x| < 1.1875 */
  75             if (ix < 0x3f300000) {      /* 7/16 <=|x|<11/16 */
  76                 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
  77             } else {                    /* 11/16<=|x|< 19/16 */
  78                 id = 1; x  = (x-one)/(x+one);
  79             }
  80         } else {
  81             if (ix < 0x401c0000) {      /* |x| < 2.4375 */
  82                 id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
  83             } else {                    /* 2.4375 <= |x| < 2^66 */
  84                 id = 3; x  = -(float)1.0/x;
  85             }
  86         }}
  87     /* end of argument reduction */
  88         z = x*x;
  89         w = z*z;
  90     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  91         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  92         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  93         if (id<0) return x - x*(s1+s2);
  94         else {
  95             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  96             return (hx<0)? -z:z;
  97         }
  98 }