toolchain/gcc/newlib/libm/math/sf_atan.c

   1 /* sf_atan.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
  17 #include "fdlibm.h"
  18
  19 #ifdef __STDC__
  20 static const float atanhi[] = {
  21 #else
  22 static float atanhi[] = {
  23 #endif
  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 #ifdef __STDC__
  31 static const float atanlo[] = {
  32 #else
  33 static float atanlo[] = {
  34 #endif
  35   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
  36   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
  37   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
  38   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
  39 };
  40
  41 #ifdef __STDC__
  42 static const float aT[] = {
  43 #else
  44 static float aT[] = {
  45 #endif
  46   3.3333334327e-01, /* 0x3eaaaaaa */
  47  -2.0000000298e-01, /* 0xbe4ccccd */
  48   1.4285714924e-01, /* 0x3e124925 */
  49  -1.1111110449e-01, /* 0xbde38e38 */
  50   9.0908870101e-02, /* 0x3dba2e6e */
  51  -7.6918758452e-02, /* 0xbd9d8795 */
  52   6.6610731184e-02, /* 0x3d886b35 */
  53  -5.8335702866e-02, /* 0xbd6ef16b */
  54   4.9768779427e-02, /* 0x3d4bda59 */
  55  -3.6531571299e-02, /* 0xbd15a221 */
  56   1.6285819933e-02, /* 0x3c8569d7 */
  57 };
  58
  59 #ifdef __STDC__
  60         static const float
  61 #else
  62         static float
  63 #endif
  64 one   = 1.0,
  65 huge   = 1.0e30;
  66
  67 #ifdef __STDC__
  68         float atanf(float x)
  69 #else
  70         float atanf(x)
  71         float x;
  72 #endif
  73 {
  74         float w,s1,s2,z;
  75         __int32_t ix,hx,id;
  76
  77         GET_FLOAT_WORD(hx,x);
  78         ix = hx&0x7fffffff;
  79         if(ix>=0x50800000) {    /* if |x| >= 2^34 */
  80             if(FLT_UWORD_IS_NAN(ix))
  81                 return x+x;             /* NaN */
  82             if(hx>0) return  atanhi[3]+atanlo[3];
  83             else     return -atanhi[3]-atanlo[3];
  84         } if (ix < 0x3ee00000) {        /* |x| < 0.4375 */
  85             if (ix < 0x31000000) {      /* |x| < 2^-29 */
  86                 if(huge+x>one) return x;        /* raise inexact */
  87             }
  88             id = -1;
  89         } else {
  90         x = fabsf(x);
  91         if (ix < 0x3f980000) {          /* |x| < 1.1875 */
  92             if (ix < 0x3f300000) {      /* 7/16 <=|x|<11/16 */
  93                 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
  94             } else {                    /* 11/16<=|x|< 19/16 */
  95                 id = 1; x  = (x-one)/(x+one);
  96             }
  97         } else {
  98             if (ix < 0x401c0000) {      /* |x| < 2.4375 */
  99                 id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
 100             } else {                    /* 2.4375 <= |x| < 2^66 */
 101                 id = 3; x  = -(float)1.0/x;
 102             }
 103         }}
 104     /* end of argument reduction */
 105         z = x*x;
 106         w = z*z;
 107     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
 108         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
 109         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
 110         if (id<0) return x - x*(s1+s2);
 111         else {
 112             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
 113             return (hx<0)? -z:z;
 114         }
 115 }
 116
 117 #ifdef _DOUBLE_IS_32BITS
 118
 119 #ifdef __STDC__
 120         double atan(double x)
 121 #else
 122         double atan(x)
 123         double x;
 124 #endif
 125 {
 126         return (double) atanf((float) x);
 127 }
 128
 129 #endif /* defined(_DOUBLE_IS_32BITS) */