2fe8fb192f
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
170 lines
5.5 KiB
C
170 lines
5.5 KiB
C
/* $NetBSD: n_asincos.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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#if 0
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static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
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#endif
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#endif /* not lint */
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/* ASIN(X)
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* RETURNS ARC SINE OF X
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* DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
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* CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
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*
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* Required system supported functions:
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* copysign(x,y)
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* sqrt(x)
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*
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* Required kernel function:
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* atan2(y,x)
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*
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* Method :
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* asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is
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* computed as follows
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* 1-x*x if x < 0.5,
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* 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN.
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*
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* Accuracy:
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* 1) If atan2() uses machine PI, then
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*
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* asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded;
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* and PI is the exact pi rounded to machine precision (see atan2 for
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* details):
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*
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* in decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* in hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
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*
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* In a test run with more than 200,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 2.06 ulps. (comparing against (PI/pi)*(exact asin(x)));
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*
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* 2) If atan2() uses true pi, then
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*
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* asin(x) returns the exact asin(x) with error below about 2 ulps.
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*
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* In a test run with more than 1,024,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 1.99 ulps.
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*/
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#include "mathimpl.h"
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double
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asin(double x)
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{
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double s,t,one=1.0;
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#if !defined(__vax__)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(__vax__)&&!defined(tahoe) */
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s=copysign(x,one);
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if(s <= 0.5)
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return(atan2(x,sqrt(one-x*x)));
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else
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{ t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); }
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}
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/* ACOS(X)
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* RETURNS ARC COS OF X
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* DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
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* CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
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*
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* Required system supported functions:
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* copysign(x,y)
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* sqrt(x)
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*
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* Required kernel function:
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* atan2(y,x)
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*
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* Method :
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* ________
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* / 1 - x
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* acos(x) = 2*atan2( / -------- , 1 ) .
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* \/ 1 + x
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN.
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*
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* Accuracy:
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* 1) If atan2() uses machine PI, then
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*
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* acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded;
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* and PI is the exact pi rounded to machine precision (see atan2 for
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* details):
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*
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* in decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* in hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
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*
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* In a test run with more than 200,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 2.07 ulps. (comparing against (PI/pi)*(exact acos(x)));
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*
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* 2) If atan2() uses true pi, then
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*
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* acos(x) returns the exact acos(x) with error below about 2 ulps.
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*
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* In a test run with more than 1,024,000 random arguments on a VAX, the
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* maximum observed error in ulps (units in the last place) was
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* 2.15 ulps.
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*/
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double
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acos(double x)
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{
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double t,one=1.0;
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#if !defined(__vax__)&&!defined(tahoe)
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if(x!=x) return(x);
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#endif /* !defined(__vax__)&&!defined(tahoe) */
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if( x != -1.0)
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t=atan2(sqrt((one-x)/(one+x)),one);
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else
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t=atan2(one,0.0); /* t = PI/2 */
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return(t+t);
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}
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