nsz Git - musl/blob - 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 static const float
  42 one = 1.0,
  43 huge = 1.0e30;
  44
  45 float atanf(float x)
  46 {
  47         float w,s1,s2,z;
  48         int32_t ix,hx,id;
  49
  50         GET_FLOAT_WORD(hx, x);
  51         ix = hx & 0x7fffffff;
  52         if (ix >= 0x4c800000) {  /* if |x| >= 2**26 */
  53                 if (ix > 0x7f800000)  /* NaN */
  54                         return x+x;
  55                 if (hx > 0)
  56                         return  atanhi[3] + *(volatile float *)&atanlo[3];
  57                 else
  58                         return -atanhi[3] - *(volatile float *)&atanlo[3];
  59         }
  60         if (ix < 0x3ee00000) {   /* |x| < 0.4375 */
  61                 if (ix < 0x39800000) {  /* |x| < 2**-12 */
  62                         /* raise inexact */
  63                         if(huge+x>one)
  64                                 return x;
  65                 }
  66                 id = -1;
  67         } else {
  68                 x = fabsf(x);
  69                 if (ix < 0x3f980000) {  /* |x| < 1.1875 */
  70                         if (ix < 0x3f300000) {  /*  7/16 <= |x| < 11/16 */
  71                                 id = 0;
  72                                 x = (2.0f*x - one)/(2.0f + x);
  73                         } else {                /* 11/16 <= |x| < 19/16 */
  74                                 id = 1;
  75                                 x = (x - one)/(x + one);
  76                         }
  77                 } else {
  78                         if (ix < 0x401c0000) {  /* |x| < 2.4375 */
  79                                 id = 2;
  80                                 x = (x - 1.5f)/(one + 1.5f*x);
  81                         } else {                /* 2.4375 <= |x| < 2**26 */
  82                                 id = 3;
  83                                 x = -1.0f/x;
  84                         }
  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]));
  92         s2 = w*(aT[1]+w*aT[3]);
  93         if (id < 0)
  94                 return x - x*(s1+s2);
  95         z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  96         return hx < 0 ? -z : z;
  97 }