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
279 lines
10 KiB
C
279 lines
10 KiB
C
/* $NetBSD: n_atan2.c,v 1.6 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[] = "@(#)atan2.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* ATAN2(Y,X)
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* RETURN ARG (X+iY)
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 1/8/85;
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* REVISED BY K.C. NG on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85.
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*
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* Required system supported functions :
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* copysign(x,y)
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* scalb(x,y)
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* logb(x)
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*
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* Method :
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* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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* 2. Reduce x to positive by (if x and y are unexceptional):
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* ARG (x+iy) = arctan(y/x) ... if x > 0,
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* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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* 3. According to the integer k=4t+0.25 truncated , t=y/x, the argument
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* is further reduced to one of the following intervals and the
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* arctangent of y/x is evaluated by the corresponding formula:
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*
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* [0,7/16] atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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* [7/16,11/16] atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) )
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* [11/16.19/16] atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) )
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* [19/16,39/16] atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) )
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* [39/16,INF] atan(y/x) = atan(INF) + atan( -x/y )
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*
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* Special cases:
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* Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
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*
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* ARG( NAN , (anything) ) is NaN;
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* ARG( (anything), NaN ) is NaN;
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* ARG(+(anything but NaN), +-0) is +-0 ;
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* ARG(-(anything but NaN), +-0) is +-PI ;
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* ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2;
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* ARG( +INF,+-(anything but INF and NaN) ) is +-0 ;
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* ARG( -INF,+-(anything but INF and NaN) ) is +-PI;
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* ARG( +INF,+-INF ) is +-PI/4 ;
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* ARG( -INF,+-INF ) is +-3PI/4;
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* ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2;
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*
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* Accuracy:
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* atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded,
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* where
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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 356,000 random argument on [-1,1] * [-1,1] on a
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* VAX, the maximum observed error was 1.41 ulps (units of the last place)
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* compared with (PI/pi)*(the exact ARG(x+iy)).
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*
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* Note:
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* We use machine PI (the true pi rounded) in place of the actual
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* value of pi for all the trig and inverse trig functions. In general,
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* if trig is one of sin, cos, tan, then computed trig(y) returns the
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* exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig
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* returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the
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* trig functions have period PI, and trig(arctrig(x)) returns x for
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* all critical values x.
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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(athfhi, 4.6364760900080611433E-1 ,6338,3fed,da7b,2b0d, -1, .ED63382B0DDA7B)
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vc(athflo, 1.9338828231967579916E-19 ,5005,2164,92c0,9cfe, -62, .E450059CFE92C0)
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vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2)
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vc(at1fhi, 9.8279372324732906796E-1 ,985e,407b,b4d9,940f, 0, .FB985E940FB4D9)
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vc(at1flo,-3.5540295636764633916E-18 ,1edc,a383,eaea,34d6, -57,-.831EDC34D6EAEA)
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vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2)
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vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2)
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vc(a1, 3.3333333333333473730E-1 ,aaaa,3faa,ab75,aaaa, -1, .AAAAAAAAAAAB75)
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vc(a2, -2.0000000000017730678E-1 ,cccc,bf4c,946e,cccd, -2,-.CCCCCCCCCD946E)
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vc(a3, 1.4285714286694640301E-1 ,4924,3f12,4262,9274, -2, .92492492744262)
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vc(a4, -1.1111111135032672795E-1 ,8e38,bee3,6292,ebc6, -3,-.E38E38EBC66292)
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vc(a5, 9.0909091380563043783E-2 ,2e8b,3eba,d70c,b31b, -3, .BA2E8BB31BD70C)
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vc(a6, -7.6922954286089459397E-2 ,89c8,be9d,7f18,27c3, -3,-.9D89C827C37F18)
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vc(a7, 6.6663180891693915586E-2 ,86b4,3e88,9e58,ae37, -3, .8886B4AE379E58)
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vc(a8, -5.8772703698290408927E-2 ,bba5,be70,a942,8481, -4,-.F0BBA58481A942)
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vc(a9, 5.2170707402812969804E-2 ,b0f3,3e55,13ab,a1ab, -4, .D5B0F3A1AB13AB)
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vc(a10, -4.4895863157820361210E-2 ,e4b9,be37,048f,7fd1, -4,-.B7E4B97FD1048F)
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vc(a11, 3.3006147437343875094E-2 ,3174,3e07,2d87,3cf7, -4, .8731743CF72D87)
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vc(a12, -1.4614844866464185439E-2 ,731a,bd6f,76d9,2f34, -6,-.EF731A2F3476D9)
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ic(athfhi, 4.6364760900080609352E-1 , -2, 1.DAC670561BB4F)
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ic(athflo, 4.6249969567426939759E-18 , -58, 1.5543B8F253271)
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ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18)
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ic(at1fhi, 9.8279372324732905408E-1 , -1, 1.F730BD281F69B)
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ic(at1flo,-2.4407677060164810007E-17 , -56, -1.C23DFEFEAE6B5)
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ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18)
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ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18)
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ic(a1, 3.3333333333333942106E-1 , -2, 1.55555555555C3)
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ic(a2, -1.9999999999979536924E-1 , -3, -1.9999999997CCD)
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ic(a3, 1.4285714278004377209E-1 , -3, 1.24924921EC1D7)
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ic(a4, -1.1111110579344973814E-1 , -4, -1.C71C7059AF280)
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ic(a5, 9.0908906105474668324E-2 , -4, 1.745CE5AA35DB2)
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ic(a6, -7.6919217767468239799E-2 , -4, -1.3B0FA54BEC400)
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ic(a7, 6.6614695906082474486E-2 , -4, 1.10DA924597FFF)
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ic(a8, -5.8358371008508623523E-2 , -5, -1.DE125FDDBD793)
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ic(a9, 4.9850617156082015213E-2 , -5, 1.9860524BDD807)
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ic(a10, -3.6700606902093604877E-2 , -5, -1.2CA6C04C6937A)
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ic(a11, 1.6438029044759730479E-2 , -6, 1.0D52174A1BB54)
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#ifdef vccast
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#define athfhi vccast(athfhi)
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#define athflo vccast(athflo)
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#define PIo4 vccast(PIo4)
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#define at1fhi vccast(at1fhi)
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#define at1flo vccast(at1flo)
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#define PIo2 vccast(PIo2)
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#define PI vccast(PI)
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#define a1 vccast(a1)
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#define a2 vccast(a2)
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#define a3 vccast(a3)
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#define a4 vccast(a4)
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#define a5 vccast(a5)
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#define a6 vccast(a6)
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#define a7 vccast(a7)
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#define a8 vccast(a8)
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#define a9 vccast(a9)
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#define a10 vccast(a10)
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#define a11 vccast(a11)
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#define a12 vccast(a12)
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#endif
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double
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atan2(double y, double x)
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{
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static const double zero=0, one=1, small=1.0E-9, big=1.0E18;
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double t,z,signy,signx,hi,lo;
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int k,m;
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#if !defined(__vax__)&&!defined(tahoe)
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/* if x or y is NAN */
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if(x!=x) return(x); if(y!=y) return(y);
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#endif /* !defined(__vax__)&&!defined(tahoe) */
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/* copy down the sign of y and x */
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signy = copysign(one,y) ;
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signx = copysign(one,x) ;
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/* if x is 1.0, goto begin */
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if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;}
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/* when y = 0 */
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if(y==zero) return((signx==one)?y:copysign(PI,signy));
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/* when x = 0 */
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if(x==zero) return(copysign(PIo2,signy));
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/* when x is INF */
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if(!finite(x))
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if(!finite(y))
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return(copysign((signx==one)?PIo4:3*PIo4,signy));
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else
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return(copysign((signx==one)?zero:PI,signy));
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/* when y is INF */
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if(!finite(y)) return(copysign(PIo2,signy));
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/* compute y/x */
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x=copysign(x,one);
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y=copysign(y,one);
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if((m=(k=logb(y))-logb(x)) > 60) t=big+big;
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else if(m < -80 ) t=y/x;
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else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); }
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/* begin argument reduction */
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begin:
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if (t < 2.4375) {
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/* truncate 4(t+1/16) to integer for branching */
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k = 4 * (t+0.0625);
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switch (k) {
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/* t is in [0,7/16] */
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case 0:
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case 1:
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if (t < small)
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{ big + small ; /* raise inexact flag */
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return (copysign((signx>zero)?t:PI-t,signy)); }
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hi = zero; lo = zero; break;
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/* t is in [7/16,11/16] */
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case 2:
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hi = athfhi; lo = athflo;
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z = x+x;
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t = ( (y+y) - x ) / ( z + y ); break;
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/* t is in [11/16,19/16] */
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case 3:
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case 4:
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hi = PIo4; lo = zero;
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t = ( y - x ) / ( x + y ); break;
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/* t is in [19/16,39/16] */
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default:
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hi = at1fhi; lo = at1flo;
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z = y-x; y=y+y+y; t = x+x;
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t = ( (z+z)-x ) / ( t + y ); break;
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}
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}
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/* end of if (t < 2.4375) */
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else
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{
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hi = PIo2; lo = zero;
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/* t is in [2.4375, big] */
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if (t <= big) t = - x / y;
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/* t is in [big, INF] */
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else
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{ big+small; /* raise inexact flag */
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t = zero; }
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}
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/* end of argument reduction */
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/* compute atan(t) for t in [-.4375, .4375] */
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z = t*t;
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#if defined(__vax__)||defined(tahoe)
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z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
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z*(a9+z*(a10+z*(a11+z*a12))))))))))));
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#else /* defined(__vax__)||defined(tahoe) */
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z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
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z*(a9+z*(a10+z*a11)))))))))));
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#endif /* defined(__vax__)||defined(tahoe) */
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z = lo - z; z += t; z += hi;
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return(copysign((signx>zero)?z:PI-z,signy));
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}
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