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
136 lines
5 KiB
C
136 lines
5 KiB
C
/* $NetBSD: n_exp__E.c,v 1.7 2008/04/29 15:10:02 uwe 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[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
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#endif
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#endif /* not lint */
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/* exp__E(x,c)
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* ASSUMPTION: c << x SO THAT fl(x+c)=x.
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* (c is the correction term for x)
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* exp__E RETURNS
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*
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* / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
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* exp__E(x,c) = |
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* \ 0 , |x| < 1E-19.
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*
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* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
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* KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
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* CODED IN C BY K.C. NG, 1/31/85;
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* REVISED BY K.C. NG on 3/16/85, 4/16/85.
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*
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* Required system supported function:
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* copysign(x,y)
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*
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* Method:
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* 1. Rational approximation. Let r=x+c.
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* Based on
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* 2 * sinh(r/2)
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* exp(r) - 1 = ---------------------- ,
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* cosh(r/2) - sinh(r/2)
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* exp__E(r) is computed using
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* x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
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* --- + (c + x*[---------------------------------- + c ])
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* 2 1 - W
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* where P := p1*x^2 + p2*x^4,
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* Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
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* W := x/2-(Q-x*P),
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*
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* (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
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* nomials P and Q may be regarded as the approximations to sinh
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* and cosh :
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* sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
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*
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* The coefficients were obtained by a special Remez algorithm.
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*
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* Approximation error:
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*
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* | exp(x) - 1 | 2**(-57), (IEEE double)
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* | ------------ - (exp__E(x,0)+x)/x | <=
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* | x | 2**(-69). (VAX D)
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#define _LIBM_STATIC
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#include "mathimpl.h"
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vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A)
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vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173)
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vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45)
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vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7)
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vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395)
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ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF)
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ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4)
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ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597)
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ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8)
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#ifdef vccast
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#define p1 vccast(p1)
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#define p2 vccast(p2)
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#define q1 vccast(q1)
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#define q2 vccast(q2)
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#define q3 vccast(q3)
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#endif
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double
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__exp__E(double x, double c)
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{
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static const double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
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double z,p,q,xp,xh,w;
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if(copysign(x,one)>small) {
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z = x*x ;
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p = z*( p1 +z* p2 );
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#if defined(__vax__)||defined(tahoe)
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q = z*( q1 +z*( q2 +z* q3 ));
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#else /* defined(__vax__)||defined(tahoe) */
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q = z*( q1 +z* q2 );
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#endif /* defined(__vax__)||defined(tahoe) */
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xp= x*p ;
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xh= x*half ;
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w = xh-(q-xp) ;
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p = p+p;
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c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
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return(z*half+c);
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}
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/* end of |x| > small */
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else {
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if(x!=zero) w=one+small; /* raise the inexact flag ??? -ragge */
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return(copysign(zero,x));
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}
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}
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