src/math/atanf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   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 "libm.h"
  18
  19 static const float atanhi[] = {
  20   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
  21   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
  22   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
  23   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
  24 };
  25
  26 static const float atanlo[] = {
  27   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
  28   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
  29   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
  30   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
  31 };
  32
  33 static const float aT[] = {
  34   3.3333328366e-01,
  35  -1.9999158382e-01,
  36   1.4253635705e-01,
  37  -1.0648017377e-01,
  38   6.1687607318e-02,
  39 };
  40
  41 float atanf(float x)
  42 {
  43         float_t w,s1,s2,z;
  44         uint32_t ix,sign;
  45         int id;
  46
  47         GET_FLOAT_WORD(ix, x);
  48         sign = ix>>31;
  49         ix &= 0x7fffffff;
  50         if (ix >= 0x4c800000) {  /* if |x| >= 2**26 */
  51                 if (isnan(x))
  52                         return x;
  53                 z = atanhi[3] + 0x1p-120f;
  54                 return sign ? -z : z;
  55         }
  56         if (ix < 0x3ee00000) {   /* |x| < 0.4375 */
  57                 if (ix < 0x39800000) {  /* |x| < 2**-12 */
  58                         if (ix < 0x00800000)
  59                                 /* raise underflow for subnormal x */
  60                                 FORCE_EVAL(x*x);
  61                         return x;
  62                 }
  63                 id = -1;
  64         } else {
  65                 x = fabsf(x);
  66                 if (ix < 0x3f980000) {  /* |x| < 1.1875 */
  67                         if (ix < 0x3f300000) {  /*  7/16 <= |x| < 11/16 */
  68                                 id = 0;
  69                                 x = (2.0f*x - 1.0f)/(2.0f + x);
  70                         } else {                /* 11/16 <= |x| < 19/16 */
  71                                 id = 1;
  72                                 x = (x - 1.0f)/(x + 1.0f);
  73                         }
  74                 } else {
  75                         if (ix < 0x401c0000) {  /* |x| < 2.4375 */
  76                                 id = 2;
  77                                 x = (x - 1.5f)/(1.0f + 1.5f*x);
  78                         } else {                /* 2.4375 <= |x| < 2**26 */
  79                                 id = 3;
  80                                 x = -1.0f/x;
  81                         }
  82                 }
  83         }
  84         /* end of argument reduction */
  85         z = x*x;
  86         w = z*z;
  87         /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  88         s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
  89         s2 = w*(aT[1]+w*aT[3]);
  90         if (id < 0)
  91                 return x - x*(s1+s2);
  92         z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  93         return sign ? -z : z;
  94 }