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

     1  /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunSoft, 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  /* acos(x)
    13   * Method :
    14   *      acos(x)  = pi/2 - asin(x)
    15   *      acos(-x) = pi/2 + asin(x)
    16   * For |x|<=0.5
    17   *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
    18   * For x>0.5
    19   *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
    20   *              = 2asin(sqrt((1-x)/2))
    21   *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
    22   *              = 2f + (2c + 2s*z*R(z))
    23   *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
    24   *     for f so that f+c ~ sqrt(z).
    25   * For x<-0.5
    26   *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
    27   *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
    28   *
    29   * Special cases:
    30   *      if x is NaN, return x itself;
    31   *      if |x|>1, return NaN with invalid signal.
    32   *
    33   * Function needed: sqrt
    34   */
    35  
    36  #include "libm.h"
    37  
    38  static const double
    39  pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
    40  pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
    41  pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
    42  pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
    43  pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
    44  pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
    45  pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
    46  pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
    47  qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
    48  qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
    49  qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
    50  qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
    51  
    52  static double R(double z)
    53  {
    54  	double_t p, q;
    55  	p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
    56  	q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
    57  	return p/q;
    58  }
    59  
    60  double acos(double x)
    61  {
    62  	double z,w,s,c,df;
    63  	uint32_t hx,ix;
    64  
    65  	GET_HIGH_WORD(hx, x);
    66  	ix = hx & 0x7fffffff;
    67  	/* |x| >= 1 or nan */
    68  	if (ix >= 0x3ff00000) {
    69  		uint32_t lx;
    70  
    71  		GET_LOW_WORD(lx,x);
    72  		if ((ix-0x3ff00000 | lx) == 0) {
    73  			/* acos(1)=0, acos(-1)=pi */
    74  			if (hx >> 31)
    75  				return 2*pio2_hi + 0x1p-120f;
    76  			return 0;
    77  		}
    78  		return 0/(x-x);
    79  	}
    80  	/* |x| < 0.5 */
    81  	if (ix < 0x3fe00000) {
    82  		if (ix <= 0x3c600000)  /* |x| < 2**-57 */
    83  			return pio2_hi + 0x1p-120f;
    84  		return pio2_hi - (x - (pio2_lo-x*R(x*x)));
    85  	}
    86  	/* x < -0.5 */
    87  	if (hx >> 31) {
    88  		z = (1.0+x)*0.5;
    89  		s = sqrt(z);
    90  		w = R(z)*s-pio2_lo;
    91  		return 2*(pio2_hi - (s+w));
    92  	}
    93  	/* x > 0.5 */
    94  	z = (1.0-x)*0.5;
    95  	s = sqrt(z);
    96  	df = s;
    97  	SET_LOW_WORD(df,0);
    98  	c = (z-df*df)/(s+df);
    99  	w = R(z)*s+c;
   100  	return 2*(df+w);
   101  }