84d9c625bf
- Fix for possible unset uid/gid in toproto
- Fix for default mtree style
- Update libelf
- Importing libexecinfo
- Resynchronize GCC, mpc, gmp, mpfr
- build.sh: Replace params with show-params.
This has been done as the make target has been renamed in the same
way, while a new target named params has been added. This new
target generates a file containing all the parameters, instead of
printing it on the console.
- Update test48 with new etc/services (Fix by Ben Gras <ben@minix3.org)
get getservbyport() out of the inner loop
Change-Id: Ie6ad5226fa2621ff9f0dee8782ea48f9443d2091
183 lines
5.6 KiB
C
183 lines
5.6 KiB
C
/* $NetBSD: n_asincos.c,v 1.8 2013/11/24 14:41:53 martin 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.
|
|
*/
|
|
|
|
#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 "mathimpl.h"
|
|
|
|
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);
|
|
}
|