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  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) */
  130.