RTAI API: base/math/e_acos.c Source File

00001 /* @(#)e_acos.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice 
00009  * is preserved.
00010  * ====================================================
00011  */
00012 
00013 #if defined(LIBM_SCCS) && !defined(lint)
00014 static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
00015 #endif
00016 
00017 /* __ieee754_acos(x)
00018  * Method :                  
00019  *  acos(x)  = pi/2 - asin(x)
00020  *  acos(-x) = pi/2 + asin(x)
00021  * For |x|<=0.5
00022  *  acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
00023  * For x>0.5
00024  *  acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
00025  *      = 2asin(sqrt((1-x)/2))  
00026  *      = 2s + 2s*z*R(z)    ...z=(1-x)/2, s=sqrt(z)
00027  *      = 2f + (2c + 2s*z*R(z))
00028  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
00029  *     for f so that f+c ~ sqrt(z).
00030  * For x<-0.5
00031  *  acos(x) = pi - 2asin(sqrt((1-|x|)/2))
00032  *      = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
00033  *
00034  * Special cases:
00035  *  if x is NaN, return x itself;
00036  *  if |x|>1, return NaN with invalid signal.
00037  *
00038  * Function needed: __ieee754_sqrt
00039  */
00040 
00041 #include "math.h"
00042 #include "mathP.h"
00043 
00044 #ifdef __STDC__
00045 static const double 
00046 #else
00047 static double 
00048 #endif
00049 one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
00050 pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
00051 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
00052 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
00053 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
00054 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
00055 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
00056 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
00057 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
00058 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
00059 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
00060 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
00061 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
00062 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
00063 
00064 #ifdef __STDC__
00065     double __ieee754_acos(double x)
00066 #else
00067     double __ieee754_acos(x)
00068     double x;
00069 #endif
00070 {
00071     double z,p,q,r,w,s,c,df;
00072     int32_t hx,ix;
00073     GET_HIGH_WORD(hx,x);
00074     ix = hx&0x7fffffff;
00075     if(ix>=0x3ff00000) {    /* |x| >= 1 */
00076         u_int32_t lx;
00077         GET_LOW_WORD(lx,x);
00078         if(((ix-0x3ff00000)|lx)==0) {   /* |x|==1 */
00079         if(hx>0) return 0.0;        /* acos(1) = 0  */
00080         else return pi+2.0*pio2_lo; /* acos(-1)= pi */
00081         }
00082         return (x-x)/(x-x);     /* acos(|x|>1) is NaN */
00083     }
00084     if(ix<0x3fe00000) { /* |x| < 0.5 */
00085         if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
00086         z = x*x;
00087         p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
00088         q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
00089         r = p/q;
00090         return pio2_hi - (x - (pio2_lo-x*r));
00091     } else  if (hx<0) {     /* x < -0.5 */
00092         z = (one+x)*0.5;
00093         p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
00094         q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
00095         s = __ieee754_sqrt(z);
00096         r = p/q;
00097         w = r*s-pio2_lo;
00098         return pi - 2.0*(s+w);
00099     } else {            /* x > 0.5 */
00100         z = (one-x)*0.5;
00101         s = __ieee754_sqrt(z);
00102         df = s;
00103         SET_LOW_WORD(df,0);
00104         c  = (z-df*df)/(s+df);
00105         p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
00106         q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
00107         r = p/q;
00108         w = r*s+c;
00109         return 2.0*(df+w);
00110     }
00111 }