/* $NetBSD: n_asincos.c,v 1.11 2024/06/09 13:35:38 riastradh Exp $ */ /* * Copyright (c) 1985, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include <sys/cdefs.h> __RCSID("$NetBSD: n_asincos.c,v 1.11 2024/06/09 13:35:38 riastradh Exp $"); #ifndef lint #if 0 static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; #endif #endif /* not lint */ /* ASIN(X) * RETURNS ARC SINE OF X * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. * * Required system supported functions: * copysign(x,y) * sqrt(x) * * Required kernel function: * atan2(y,x) * * Method : * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is * computed as follows * 1-x*x if x < 0.5, * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5. * * Special cases: * if x is NaN, return x itself; * if |x|>1, return NaN. * * Accuracy: * 1) If atan2() uses machine PI, then * * asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded; * and PI is the exact pi rounded to machine precision (see atan2 for * details): * * in decimal: * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , * 56 bits PI = 3.141592653589793 227020265 ..... , * * in hexadecimal: * pi = 3.243F6A8885A308D313198A2E.... * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps * * In a test run with more than 200,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 2.06 ulps. (comparing against (PI/pi)*(exact asin(x))); * * 2) If atan2() uses true pi, then * * asin(x) returns the exact asin(x) with error below about 2 ulps. * * In a test run with more than 1,024,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 1.99 ulps. */ #include "namespace.h" #include "mathimpl.h" __weak_alias(acos, _acos) __weak_alias(acosf, _asinf) __weak_alias(asin, _asin) __weak_alias(asinf, _asinf) double asin(double x) { double s,t,one=1.0; #if !defined(__vax__)&&!defined(tahoe) if(x!=x) return(x); /* x is NaN */ #endif /* !defined(__vax__)&&!defined(tahoe) */ s=copysign(x,one); if(s <= 0.5) return(atan2(x,sqrt(one-x*x))); else { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); } } float asinf(float x) { return (float)asin(x); } /* ACOS(X) * RETURNS ARC COS OF X * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. * * Required system supported functions: * copysign(x,y) * sqrt(x) * * Required kernel function: * atan2(y,x) * * Method : * ________ * / 1 - x * acos(x) = 2*atan2( / -------- , 1 ) . * \/ 1 + x * * Special cases: * if x is NaN, return x itself; * if |x|>1, return NaN. * * Accuracy: * 1) If atan2() uses machine PI, then * * acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded; * and PI is the exact pi rounded to machine precision (see atan2 for * details): * * in decimal: * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , * 56 bits PI = 3.141592653589793 227020265 ..... , * * in hexadecimal: * pi = 3.243F6A8885A308D313198A2E.... * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps * * In a test run with more than 200,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 2.07 ulps. (comparing against (PI/pi)*(exact acos(x))); * * 2) If atan2() uses true pi, then * * acos(x) returns the exact acos(x) with error below about 2 ulps. * * In a test run with more than 1,024,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 2.15 ulps. */ double acos(double x) { double t,one=1.0; #if !defined(__vax__)&&!defined(tahoe) if(x!=x) return(x); #endif /* !defined(__vax__)&&!defined(tahoe) */ if( x != -1.0) t=atan2(sqrt((one-x)/(one+x)),one); else t=atan2(one,0.0); /* t = PI/2 */ return(t+t); } float acosf(float x) { return (float)acos(x); }
