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
449 lines
16 KiB
C
449 lines
16 KiB
C
/* $NetBSD: n_j1.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */
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/*-
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* Copyright (c) 1992, 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[] = "@(#)j1.c 8.2 (Berkeley) 11/30/93";
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#endif
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#endif /* not lint */
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/*
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* 16 December 1992
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* Minor modifications by Peter McIlroy to adapt non-IEEE architecture.
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*/
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/*
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* ====================================================
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* Copyright (C) 1992 by Sun Microsystems, Inc.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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* ******************* WARNING ********************
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* This is an alpha version of SunPro's FDLIBM (Freely
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* Distributable Math Library) for IEEE double precision
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* arithmetic. FDLIBM is a basic math library written
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* in C that runs on machines that conform to IEEE
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* Standard 754/854. This alpha version is distributed
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* for testing purpose. Those who use this software
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* should report any bugs to
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*
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* fdlibm-comments@sunpro.eng.sun.com
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*
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* -- K.C. Ng, Oct 12, 1992
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* ************************************************
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*/
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/* double j1(double x), y1(double x)
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* Bessel function of the first and second kinds of order zero.
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* Method -- j1(x):
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* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
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* 2. Reduce x to |x| since j1(x)=-j1(-x), and
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* for x in (0,2)
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* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
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* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
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* for x in (2,inf)
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* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
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* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
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* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
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* as follows:
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* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
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* = 1/sqrt(2) * (sin(x) - cos(x))
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* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
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* = -1/sqrt(2) * (sin(x) + cos(x))
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* (To avoid cancellation, use
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* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
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* to compute the worse one.)
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*
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* 3 Special cases
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* j1(nan)= nan
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* j1(0) = 0
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* j1(inf) = 0
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*
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* Method -- y1(x):
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* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
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* 2. For x<2.
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* Since
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* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
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* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
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* We use the following function to approximate y1,
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* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
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* where for x in [0,2] (abs err less than 2**-65.89)
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* U(z) = u0 + u1*z + ... + u4*z^4
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* V(z) = 1 + v1*z + ... + v5*z^5
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* Note: For tiny x, 1/x dominate y1 and hence
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* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
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* 3. For x>=2.
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* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
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* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
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* by method mentioned above.
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*/
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#include "mathimpl.h"
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#include <float.h>
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#include <errno.h>
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#if defined(__vax__) || defined(tahoe)
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#define _IEEE 0
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#else
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#define _IEEE 1
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#define infnan(x) (0.0)
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#endif
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static double pone (double), qone (double);
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static const double
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huge = 1e300,
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zero = 0.0,
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one = 1.0,
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invsqrtpi= 5.641895835477562869480794515607725858441e-0001,
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tpi = 0.636619772367581343075535053490057448,
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/* R0/S0 on [0,2] */
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r00 = -6.250000000000000020842322918309200910191e-0002,
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r01 = 1.407056669551897148204830386691427791200e-0003,
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r02 = -1.599556310840356073980727783817809847071e-0005,
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r03 = 4.967279996095844750387702652791615403527e-0008,
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s01 = 1.915375995383634614394860200531091839635e-0002,
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s02 = 1.859467855886309024045655476348872850396e-0004,
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s03 = 1.177184640426236767593432585906758230822e-0006,
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s04 = 5.046362570762170559046714468225101016915e-0009,
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s05 = 1.235422744261379203512624973117299248281e-0011;
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#define two_129 6.80564733841876926e+038 /* 2^129 */
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#define two_m54 5.55111512312578270e-017 /* 2^-54 */
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double
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j1(double x)
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{
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double z, s,c,ss,cc,r,u,v,y;
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y = fabs(x);
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if (!finite(x)) { /* Inf or NaN */
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if (_IEEE && x != x)
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return(x);
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else
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return (copysign(x, zero));
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}
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y = fabs(x);
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if (y >= 2) { /* |x| >= 2.0 */
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s = sin(y);
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c = cos(y);
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ss = -s-c;
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cc = s-c;
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if (y < .5*DBL_MAX) { /* make sure y+y not overflow */
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z = cos(y+y);
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if ((s*c)<zero) cc = z/ss;
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else ss = z/cc;
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}
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/*
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* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
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* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
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*/
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#if !defined(__vax__) && !defined(tahoe)
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if (y > two_129) /* x > 2^129 */
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z = (invsqrtpi*cc)/sqrt(y);
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else
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#endif /* defined(__vax__) || defined(tahoe) */
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{
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u = pone(y); v = qone(y);
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z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
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}
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if (x < 0) return -z;
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else return z;
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}
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if (y < 7.450580596923828125e-009) { /* |x|<2**-27 */
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if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
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}
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z = x*x;
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r = z*(r00+z*(r01+z*(r02+z*r03)));
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s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
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r *= x;
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return (x*0.5+r/s);
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}
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static const double u0[5] = {
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-1.960570906462389484206891092512047539632e-0001,
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5.044387166398112572026169863174882070274e-0002,
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-1.912568958757635383926261729464141209569e-0003,
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2.352526005616105109577368905595045204577e-0005,
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-9.190991580398788465315411784276789663849e-0008,
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};
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static const double v0[5] = {
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1.991673182366499064031901734535479833387e-0002,
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2.025525810251351806268483867032781294682e-0004,
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1.356088010975162198085369545564475416398e-0006,
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6.227414523646214811803898435084697863445e-0009,
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1.665592462079920695971450872592458916421e-0011,
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};
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double
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y1(double x)
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{
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double z, s, c, ss, cc, u, v;
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/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
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if (!finite(x)) {
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if (!_IEEE) return (infnan(EDOM));
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else if (x < 0)
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return(zero/zero);
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else if (x > 0)
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return (0);
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else
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return(x);
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}
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if (x <= 0) {
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if (_IEEE && x == 0) return -one/zero;
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else if(x == 0) return(infnan(-ERANGE));
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else if(_IEEE) return (zero/zero);
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else return(infnan(EDOM));
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}
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if (x >= 2) { /* |x| >= 2.0 */
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s = sin(x);
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c = cos(x);
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ss = -s-c;
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cc = s-c;
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if (x < .5 * DBL_MAX) { /* make sure x+x not overflow */
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z = cos(x+x);
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if ((s*c)>zero) cc = z/ss;
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else ss = z/cc;
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}
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/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
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* where x0 = x-3pi/4
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* Better formula:
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* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
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* = 1/sqrt(2) * (sin(x) - cos(x))
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* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
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* = -1/sqrt(2) * (cos(x) + sin(x))
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* To avoid cancellation, use
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* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
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* to compute the worse one.
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*/
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if (_IEEE && x>two_129) {
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z = (invsqrtpi*ss)/sqrt(x);
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} else {
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u = pone(x); v = qone(x);
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z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
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}
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return z;
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}
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if (x <= two_m54) { /* x < 2**-54 */
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return (-tpi/x);
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}
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z = x*x;
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u = u0[0]+z*(u0[1]+z*(u0[2]+z*(u0[3]+z*u0[4])));
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v = one+z*(v0[0]+z*(v0[1]+z*(v0[2]+z*(v0[3]+z*v0[4]))));
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return (x*(u/v) + tpi*(j1(x)*log(x)-one/x));
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}
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/* For x >= 8, the asymptotic expansions of pone is
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* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
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* We approximate pone by
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* pone(x) = 1 + (R/S)
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* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
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* S = 1 + ps0*s^2 + ... + ps4*s^10
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* and
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* | pone(x)-1-R/S | <= 2 ** ( -60.06)
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*/
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static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
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0.0,
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1.171874999999886486643746274751925399540e-0001,
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1.323948065930735690925827997575471527252e+0001,
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4.120518543073785433325860184116512799375e+0002,
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3.874745389139605254931106878336700275601e+0003,
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7.914479540318917214253998253147871806507e+0003,
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};
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static const double ps8[5] = {
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1.142073703756784104235066368252692471887e+0002,
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3.650930834208534511135396060708677099382e+0003,
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3.695620602690334708579444954937638371808e+0004,
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9.760279359349508334916300080109196824151e+0004,
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3.080427206278887984185421142572315054499e+0004,
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};
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static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
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1.319905195562435287967533851581013807103e-0011,
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1.171874931906140985709584817065144884218e-0001,
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6.802751278684328781830052995333841452280e+0000,
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1.083081829901891089952869437126160568246e+0002,
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5.176361395331997166796512844100442096318e+0002,
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5.287152013633375676874794230748055786553e+0002,
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};
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static const double ps5[5] = {
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5.928059872211313557747989128353699746120e+0001,
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9.914014187336144114070148769222018425781e+0002,
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5.353266952914879348427003712029704477451e+0003,
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7.844690317495512717451367787640014588422e+0003,
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1.504046888103610723953792002716816255382e+0003,
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};
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static const double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
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3.025039161373736032825049903408701962756e-0009,
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1.171868655672535980750284752227495879921e-0001,
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3.932977500333156527232725812363183251138e+0000,
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3.511940355916369600741054592597098912682e+0001,
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9.105501107507812029367749771053045219094e+0001,
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4.855906851973649494139275085628195457113e+0001,
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};
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static const double ps3[5] = {
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3.479130950012515114598605916318694946754e+0001,
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3.367624587478257581844639171605788622549e+0002,
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1.046871399757751279180649307467612538415e+0003,
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8.908113463982564638443204408234739237639e+0002,
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1.037879324396392739952487012284401031859e+0002,
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};
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static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
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1.077108301068737449490056513753865482831e-0007,
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1.171762194626833490512746348050035171545e-0001,
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2.368514966676087902251125130227221462134e+0000,
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1.224261091482612280835153832574115951447e+0001,
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1.769397112716877301904532320376586509782e+0001,
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5.073523125888185399030700509321145995160e+0000,
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};
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static const double ps2[5] = {
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2.143648593638214170243114358933327983793e+0001,
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1.252902271684027493309211410842525120355e+0002,
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2.322764690571628159027850677565128301361e+0002,
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1.176793732871470939654351793502076106651e+0002,
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8.364638933716182492500902115164881195742e+0000,
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};
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static double
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pone(double x)
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{
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const double *p,*q;
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double z,r,s;
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if (x >= 8.0) {p = pr8; q= ps8;}
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else if (x >= 4.54545211791992188) {p = pr5; q= ps5;}
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else if (x >= 2.85714149475097656) {p = pr3; q= ps3;}
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else /* if (x >= 2.0) */ {p = pr2; q= ps2;}
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z = one/(x*x);
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r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
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s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
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return (one + r/s);
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}
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/* For x >= 8, the asymptotic expansions of qone is
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* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
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* We approximate pone by
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* qone(x) = s*(0.375 + (R/S))
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* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
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* S = 1 + qs1*s^2 + ... + qs6*s^12
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* and
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* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
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*/
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static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
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0.0,
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-1.025390624999927207385863635575804210817e-0001,
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-1.627175345445899724355852152103771510209e+0001,
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-7.596017225139501519843072766973047217159e+0002,
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-1.184980667024295901645301570813228628541e+0004,
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-4.843851242857503225866761992518949647041e+0004,
|
|
};
|
|
static const double qs8[6] = {
|
|
1.613953697007229231029079421446916397904e+0002,
|
|
7.825385999233484705298782500926834217525e+0003,
|
|
1.338753362872495800748094112937868089032e+0005,
|
|
7.196577236832409151461363171617204036929e+0005,
|
|
6.666012326177764020898162762642290294625e+0005,
|
|
-2.944902643038346618211973470809456636830e+0005,
|
|
};
|
|
|
|
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
|
-2.089799311417640889742251585097264715678e-0011,
|
|
-1.025390502413754195402736294609692303708e-0001,
|
|
-8.056448281239359746193011295417408828404e+0000,
|
|
-1.836696074748883785606784430098756513222e+0002,
|
|
-1.373193760655081612991329358017247355921e+0003,
|
|
-2.612444404532156676659706427295870995743e+0003,
|
|
};
|
|
static const double qs5[6] = {
|
|
8.127655013843357670881559763225310973118e+0001,
|
|
1.991798734604859732508048816860471197220e+0003,
|
|
1.746848519249089131627491835267411777366e+0004,
|
|
4.985142709103522808438758919150738000353e+0004,
|
|
2.794807516389181249227113445299675335543e+0004,
|
|
-4.719183547951285076111596613593553911065e+0003,
|
|
};
|
|
|
|
static const double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
|
-5.078312264617665927595954813341838734288e-0009,
|
|
-1.025378298208370901410560259001035577681e-0001,
|
|
-4.610115811394734131557983832055607679242e+0000,
|
|
-5.784722165627836421815348508816936196402e+0001,
|
|
-2.282445407376317023842545937526967035712e+0002,
|
|
-2.192101284789093123936441805496580237676e+0002,
|
|
};
|
|
static const double qs3[6] = {
|
|
4.766515503237295155392317984171640809318e+0001,
|
|
6.738651126766996691330687210949984203167e+0002,
|
|
3.380152866795263466426219644231687474174e+0003,
|
|
5.547729097207227642358288160210745890345e+0003,
|
|
1.903119193388108072238947732674639066045e+0003,
|
|
-1.352011914443073322978097159157678748982e+0002,
|
|
};
|
|
|
|
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
|
-1.783817275109588656126772316921194887979e-0007,
|
|
-1.025170426079855506812435356168903694433e-0001,
|
|
-2.752205682781874520495702498875020485552e+0000,
|
|
-1.966361626437037351076756351268110418862e+0001,
|
|
-4.232531333728305108194363846333841480336e+0001,
|
|
-2.137192117037040574661406572497288723430e+0001,
|
|
};
|
|
static const double qs2[6] = {
|
|
2.953336290605238495019307530224241335502e+0001,
|
|
2.529815499821905343698811319455305266409e+0002,
|
|
7.575028348686454070022561120722815892346e+0002,
|
|
7.393932053204672479746835719678434981599e+0002,
|
|
1.559490033366661142496448853793707126179e+0002,
|
|
-4.959498988226281813825263003231704397158e+0000,
|
|
};
|
|
|
|
static double
|
|
qone(double x)
|
|
{
|
|
const double *p,*q;
|
|
double s,r,z;
|
|
if (x >= 8.0) {p = qr8; q= qs8;}
|
|
else if (x >= 4.54545211791992188) {p = qr5; q= qs5;}
|
|
else if (x >= 2.85714149475097656) {p = qr3; q= qs3;}
|
|
else /* if (x >= 2.0) */ {p = qr2; q= qs2;}
|
|
z = one/(x*x);
|
|
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
|
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
|
return (.375 + r/s)/x;
|
|
}
|