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
118 lines
3.8 KiB
C
118 lines
3.8 KiB
C
/* $NetBSD: n_cbrt.c,v 1.5 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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static char sccsid[] = "@(#)cbrt.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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#include <sys/cdefs.h>
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/* kahan's cube root (53 bits IEEE double precision)
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* for IEEE machines only
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* coded in C by K.C. Ng, 4/30/85
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*
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* Accuracy:
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* better than 0.667 ulps according to an error analysis. Maximum
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* error observed was 0.666 ulps in an 1,000,000 random arguments test.
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*
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* Warning: this code is semi machine dependent; the ordering of words in
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* a floating point number must be known in advance. I assume that the
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* long interger at the address of a floating point number will be the
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* leading 32 bits of that floating point number (i.e., sign, exponent,
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* and the 20 most significant bits).
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* On a National machine, it has different ordering; therefore, this code
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* must be compiled with flag -DNATIONAL.
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*/
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#if !defined(__vax__)&&!defined(tahoe)
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static const unsigned long
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B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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static const double
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C= 19./35.,
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D= -864./1225.,
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E= 99./70.,
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F= 45./28.,
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G= 5./14.;
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double
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cbrt(double x)
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{
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double r,s,t=0.0,w;
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unsigned long *px = (unsigned long *) &x,
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*pt = (unsigned long *) &t,
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mexp,sign;
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#ifdef national /* ordering of words in a floating points number */
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const int n0=1,n1=0;
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#else /* national */
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const int n0=0,n1=1;
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#endif /* national */
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mexp=px[n0]&0x7ff00000;
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if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */
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if(x==0.0) return(x); /* cbrt(0) is itself */
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sign=px[n0]&0x80000000; /* sign= sign(x) */
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px[n0] ^= sign; /* x=|x| */
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/* rough cbrt to 5 bits */
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if(mexp==0) /* subnormal number */
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{pt[n0]=0x43500000; /* set t= 2**54 */
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t*=x; pt[n0]=pt[n0]/3+B2;
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}
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else
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pt[n0]=px[n0]/3+B1;
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/* new cbrt to 23 bits, may be implemented in single precision */
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r=t*t/x;
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s=C+r*t;
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t*=G+F/(s+E+D/s);
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/* chopped to 20 bits and make it larger than cbrt(x) */
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pt[n1]=0; pt[n0]+=0x00000001;
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/* one step newton iteration to 53 bits with error less than 0.667 ulps */
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s=t*t; /* t*t is exact */
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r=x/s;
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w=t+t;
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r=(r-t)/(w+r); /* r-t is exact */
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t=t+t*r;
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/* retore the sign bit */
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pt[n0] |= sign;
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return(t);
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}
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#endif
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