acos.c raw

   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  }
 102