github.com/afumu/libc@v0.0.6/musl/src/math/atan.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunPro, a Sun Microsystems, Inc. business.
     7   * Permission to use, copy, modify, and distribute this
     8   * software is freely granted, provided that this notice
     9   * is preserved.
    10   * ====================================================
    11   */
    12  /* atan(x)
    13   * Method
    14   *   1. Reduce x to positive by atan(x) = -atan(-x).
    15   *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
    16   *      is further reduced to one of the following intervals and the
    17   *      arctangent of t is evaluated by the corresponding formula:
    18   *
    19   *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
    20   *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
    21   *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
    22   *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
    23   *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
    24   *
    25   * Constants:
    26   * The hexadecimal values are the intended ones for the following
    27   * constants. The decimal values may be used, provided that the
    28   * compiler will convert from decimal to binary accurately enough
    29   * to produce the hexadecimal values shown.
    30   */
    31  
    32  
    33  #include "libm.h"
    34  
    35  static const double atanhi[] = {
    36    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    37    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    38    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    39    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
    40  };
    41  
    42  static const double atanlo[] = {
    43    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    44    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    45    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    46    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
    47  };
    48  
    49  static const double aT[] = {
    50    3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
    51   -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
    52    1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
    53   -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
    54    9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
    55   -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
    56    6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
    57   -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
    58    4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
    59   -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
    60    1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
    61  };
    62  
    63  double atan(double x)
    64  {
    65  	double_t w,s1,s2,z;
    66  	uint32_t ix,sign;
    67  	int id;
    68  
    69  	GET_HIGH_WORD(ix, x);
    70  	sign = ix >> 31;
    71  	ix &= 0x7fffffff;
    72  	if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
    73  		if (isnan(x))
    74  			return x;
    75  		z = atanhi[3] + 0x1p-120f;
    76  		return sign ? -z : z;
    77  	}
    78  	if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
    79  		if (ix < 0x3e400000) {  /* |x| < 2^-27 */
    80  			if (ix < 0x00100000)
    81  				/* raise underflow for subnormal x */
    82  				FORCE_EVAL((float)x);
    83  			return x;
    84  		}
    85  		id = -1;
    86  	} else {
    87  		x = fabs(x);
    88  		if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
    89  			if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */
    90  				id = 0;
    91  				x = (2.0*x-1.0)/(2.0+x);
    92  			} else {                /* 11/16 <= |x| < 19/16 */
    93  				id = 1;
    94  				x = (x-1.0)/(x+1.0);
    95  			}
    96  		} else {
    97  			if (ix < 0x40038000) {  /* |x| < 2.4375 */
    98  				id = 2;
    99  				x = (x-1.5)/(1.0+1.5*x);
   100  			} else {                /* 2.4375 <= |x| < 2^66 */
   101  				id = 3;
   102  				x = -1.0/x;
   103  			}
   104  		}
   105  	}
   106  	/* end of argument reduction */
   107  	z = x*x;
   108  	w = z*z;
   109  	/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
   110  	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
   111  	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
   112  	if (id < 0)
   113  		return x - x*(s1+s2);
   114  	z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
   115  	return sign ? -z : z;
   116  }