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

     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  }