Home | History | Annotate | Line # | Download | only in src
e_acos.c revision 1.5 
      1 /* @(#)e_acos.c 5.1 93/09/24 */
      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 
     13 #ifndef lint
     14 static char rcsid[] = "$Id: e_acos.c,v 1.5 1994/08/10 20:30:28 jtc Exp $";
     15 #endif
     16 
     17 /* __ieee754_acos(x)
     18  * Method :
     19  *	acos(x)  = pi/2 - asin(x)
     20  *	acos(-x) = pi/2 + asin(x)
     21  * For |x|<=0.5
     22  *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
     23  * For x>0.5
     24  * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
     25  *		= 2asin(sqrt((1-x)/2))
     26  *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
     27  *		= 2f + (2c + 2s*z*R(z))
     28  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
     29  *     for f so that f+c ~ sqrt(z).
     30  * For x<-0.5
     31  *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
     32  *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
     33  *
     34  * Special cases:
     35  *	if x is NaN, return x itself;
     36  *	if |x|>1, return NaN with invalid signal.
     37  *
     38  * Function needed: sqrt
     39  */
     40 
     41 #include "math.h"
     42 #include "math_private.h"
     43 
     44 #ifdef __STDC__
     45 static const double
     46 #else
     47 static double
     48 #endif
     49 one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
     50 pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
     51 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
     52 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
     53 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
     54 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
     55 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
     56 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
     57 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
     58 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
     59 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
     60 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
     61 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
     62 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
     63 
     64 #ifdef __STDC__
     65 	double __ieee754_acos(double x)
     66 #else
     67 	double __ieee754_acos(x)
     68 	double x;
     69 #endif
     70 {
     71 	double z,p,q,r,w,s,c,df;
     72 	int hx,ix;
     73 	GET_HIGH_WORD(hx,x);
     74 	ix = hx&0x7fffffff;
     75 	if(ix>=0x3ff00000) {	/* |x| >= 1 */
     76 	    unsigned int lx;
     77 	    GET_LOW_WORD(lx,x);
     78 	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */
     79 		if(hx>0) return 0.0;		/* acos(1) = 0  */
     80 		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
     81 	    }
     82 	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
     83 	}
     84 	if(ix<0x3fe00000) {	/* |x| < 0.5 */
     85 	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
     86 	    z = x*x;
     87 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
     88 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
     89 	    r = p/q;
     90 	    return pio2_hi - (x - (pio2_lo-x*r));
     91 	} else  if (hx<0) {		/* x < -0.5 */
     92 	    z = (one+x)*0.5;
     93 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
     94 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
     95 	    s = sqrt(z);
     96 	    r = p/q;
     97 	    w = r*s-pio2_lo;
     98 	    return pi - 2.0*(s+w);
     99 	} else {			/* x > 0.5 */
    100 	    z = (one-x)*0.5;
    101 	    s = sqrt(z);
    102 	    df = s;
    103 	    SET_LOW_WORD(df,0);
    104 	    c  = (z-df*df)/(s+df);
    105 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
    106 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
    107 	    r = p/q;
    108 	    w = r*s+c;
    109 	    return 2.0*(df+w);
    110 	}
    111 }
    112