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 }