compiler/mlib/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 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_atanf.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float atanhi[] = {
  24   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
  25   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
  26   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
  27   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
  28 };
  29
  30 static const float atanlo[] = {
  31   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
  32   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
  33   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
  34   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
  35 };
  36
  37 static const float aT[] = {
  38   3.3333334327e-01, /* 0x3eaaaaaa */
  39  -2.0000000298e-01, /* 0xbe4ccccd */
  40   1.4285714924e-01, /* 0x3e124925 */
  41  -1.1111110449e-01, /* 0xbde38e38 */
  42   9.0908870101e-02, /* 0x3dba2e6e */
  43  -7.6918758452e-02, /* 0xbd9d8795 */
  44   6.6610731184e-02, /* 0x3d886b35 */
  45  -5.8335702866e-02, /* 0xbd6ef16b */
  46   4.9768779427e-02, /* 0x3d4bda59 */
  47  -3.6531571299e-02, /* 0xbd15a221 */
  48   1.6285819933e-02, /* 0x3c8569d7 */
  49 };
  50
  51         static const float
  52 one   = 1.0,
  53 huge   = 1.0e30;
  54
  55 float
  56 atanf(float x)
  57 {
  58         float w,s1,s2,z;
  59         int32_t ix,hx,id;
  60
  61         GET_FLOAT_WORD(hx,x);
  62         ix = hx&0x7fffffff;
  63         if(ix>=0x50800000) {    /* if |x| >= 2^34 */
  64             if(ix>0x7f800000)
  65                 return x+x;             /* NaN */
  66             if(hx>0) return  atanhi[3]+atanlo[3];
  67             else     return -atanhi[3]-atanlo[3];
  68         } if (ix < 0x3ee00000) {        /* |x| < 0.4375 */
  69             if (ix < 0x31000000) {      /* |x| < 2^-29 */
  70                 if(huge+x>one) return x;        /* raise inexact */
  71             }
  72             id = -1;
  73         } else {
  74         x = fabsf(x);
  75         if (ix < 0x3f980000) {          /* |x| < 1.1875 */
  76             if (ix < 0x3f300000) {      /* 7/16 <=|x|<11/16 */
  77                 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
  78             } else {                    /* 11/16<=|x|< 19/16 */
  79                 id = 1; x  = (x-one)/(x+one);
  80             }
  81         } else {
  82             if (ix < 0x401c0000) {      /* |x| < 2.4375 */
  83                 id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
  84             } else {                    /* 2.4375 <= |x| < 2^66 */
  85                 id = 3; x  = -(float)1.0/x;
  86             }
  87         }}
  88     /* end of argument reduction */
  89         z = x*x;
  90         w = z*z;
  91     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  92         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  93         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  94         if (id<0) return x - x*(s1+s2);
  95         else {
  96             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  97             return (hx<0)? -z:z;
  98         }
  99 }