301 lines
11 KiB
C
301 lines
11 KiB
C
/* atan2.c - math routines */
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/* Copyright 1992-1993 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01f,03jan01,pes Fix compiler warnings
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01e,05feb93,jdi doc changes based on kdl review.
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01d,02dec92,jdi doc tweaks.
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01c,28oct92,jdi documentation cleanup.
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01b,20sep92,smb documentation additions
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01a,08jul92,smb documentation.
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*/
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/*
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DESCRIPTION
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/*static double */
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/*athfhi = 4.6364760900080611433E-1 ,*//*Hex 2^ -1 * .ED63382B0DDA7B */
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/*athflo = 1.9338828231967579916E-19 ,*//*Hex 2^-62 * .E450059CFE92C0 */
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/*PIo4 = 7.8539816339744830676E-1 ,*//*Hex 2^ 0 * .C90FDAA22168C2 */
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/*at1fhi = 9.8279372324732906796E-1 ,*//*Hex 2^ 0 * .FB985E940FB4D9 */
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/*at1flo = -3.5540295636764633916E-18 ,*//*Hex 2^-57 * -.831EDC34D6EAEA */
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/*PIo2 = 1.5707963267948966135E0 ,*//*Hex 2^ 1 * .C90FDAA22168C2 */
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/*PI = 3.1415926535897932270E0 ,*//*Hex 2^ 2 * .C90FDAA22168C2 */
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/*a1 = 3.3333333333333473730E-1 ,*//*Hex 2^ -1 * .AAAAAAAAAAAB75 */
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/*a2 = -2.0000000000017730678E-1 ,*//*Hex 2^ -2 * -.CCCCCCCCCD946E */
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/*a3 = 1.4285714286694640301E-1 ,*//*Hex 2^ -2 * .92492492744262 */
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/*a4 = -1.1111111135032672795E-1 ,*//*Hex 2^ -3 * -.E38E38EBC66292 */
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/*a5 = 9.0909091380563043783E-2 ,*//*Hex 2^ -3 * .BA2E8BB31BD70C */
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/*a6 = -7.6922954286089459397E-2 ,*//*Hex 2^ -3 * -.9D89C827C37F18 */
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/*a7 = 6.6663180891693915586E-2 ,*//*Hex 2^ -3 * .8886B4AE379E58 */
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/*a8 = -5.8772703698290408927E-2 ,*//*Hex 2^ -4 * -.F0BBA58481A942 */
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/*a9 = 5.2170707402812969804E-2 ,*//*Hex 2^ -4 * .D5B0F3A1AB13AB */
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/*a10 = -4.4895863157820361210E-2 ,*//*Hex 2^ -4 * -.B7E4B97FD1048F */
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/*a11 = 3.3006147437343875094E-2 ,*//*Hex 2^ -4 * .8731743CF72D87 */
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/*a12 = -1.4614844866464185439E-2 ;*//*Hex 2^ -6 * -.EF731A2F3476D9 */
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static long athfhix[] = { _0x(6338,3fed), _0x(da7b,2b0d)};
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#define athfhi (*(double *)athfhix)
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static long athflox[] = { _0x(5005,2164), _0x(92c0,9cfe)};
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#define athflo (*(double *)athflox)
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static long PIo4x[] = { _0x(0fda,4049), _0x(68c2,a221)};
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#define PIo4 (*(double *)PIo4x)
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static long at1fhix[] = { _0x(985e,407b), _0x(b4d9,940f)};
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#define at1fhi (*(double *)at1fhix)
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static long at1flox[] = { _0x(1edc,a383), _0x(eaea,34d6)};
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#define at1flo (*(double *)at1flox)
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static long PIo2x[] = { _0x(0fda,40c9), _0x(68c2,a221)};
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#define PIo2 (*(double *)PIo2x)
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static long PIx[] = { _0x(0fda,4149), _0x(68c2,a221)};
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#define PI (*(double *)PIx)
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static long a1x[] = { _0x(aaaa,3faa), _0x(ab75,aaaa)};
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#define a1 (*(double *)a1x)
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static long a2x[] = { _0x(cccc,bf4c), _0x(946e,cccd)};
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#define a2 (*(double *)a2x)
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static long a3x[] = { _0x(4924,3f12), _0x(4262,9274)};
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#define a3 (*(double *)a3x)
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static long a4x[] = { _0x(8e38,bee3), _0x(6292,ebc6)};
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#define a4 (*(double *)a4x)
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static long a5x[] = { _0x(2e8b,3eba), _0x(d70c,b31b)};
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#define a5 (*(double *)a5x)
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static long a6x[] = { _0x(89c8,be9d), _0x(7f18,27c3)};
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#define a6 (*(double *)a6x)
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static long a7x[] = { _0x(86b4,3e88), _0x(9e58,ae37)};
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#define a7 (*(double *)a7x)
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static long a8x[] = { _0x(bba5,be70), _0x(a942,8481)};
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#define a8 (*(double *)a8x)
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static long a9x[] = { _0x(b0f3,3e55), _0x(13ab,a1ab)};
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#define a9 (*(double *)a9x)
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static long a10x[] = { _0x(e4b9,be37), _0x(048f,7fd1)};
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#define a10 (*(double *)a10x)
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static long a11x[] = { _0x(3174,3e07), _0x(2d87,3cf7)};
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#define a11 (*(double *)a11x)
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static long a12x[] = { _0x(731a,bd6f), _0x(76d9,2f34)};
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#define a12 (*(double *)a12x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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athfhi = 4.6364760900080609352E-1 , /*Hex 2^ -2 * 1.DAC670561BB4F */
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athflo = 4.6249969567426939759E-18 , /*Hex 2^-58 * 1.5543B8F253271 */
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PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */
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at1fhi = 9.8279372324732905408E-1 , /*Hex 2^ -1 * 1.F730BD281F69B */
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at1flo = -2.4407677060164810007E-17 , /*Hex 2^-56 * -1.C23DFEFEAE6B5 */
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PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */
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PI = 3.1415926535897931160E0 , /*Hex 2^ 1 * 1.921FB54442D18 */
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a1 = 3.3333333333333942106E-1 , /*Hex 2^ -2 * 1.55555555555C3 */
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a2 = -1.9999999999979536924E-1 , /*Hex 2^ -3 * -1.9999999997CCD */
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a3 = 1.4285714278004377209E-1 , /*Hex 2^ -3 * 1.24924921EC1D7 */
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a4 = -1.1111110579344973814E-1 , /*Hex 2^ -4 * -1.C71C7059AF280 */
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a5 = 9.0908906105474668324E-2 , /*Hex 2^ -4 * 1.745CE5AA35DB2 */
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a6 = -7.6919217767468239799E-2 , /*Hex 2^ -4 * -1.3B0FA54BEC400 */
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a7 = 6.6614695906082474486E-2 , /*Hex 2^ -4 * 1.10DA924597FFF */
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a8 = -5.8358371008508623523E-2 , /*Hex 2^ -5 * -1.DE125FDDBD793 */
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a9 = 4.9850617156082015213E-2 , /*Hex 2^ -5 * 1.9860524BDD807 */
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a10 = -3.6700606902093604877E-2 , /*Hex 2^ -5 * -1.2CA6C04C6937A */
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a11 = 1.6438029044759730479E-2 ; /*Hex 2^ -6 * 1.0D52174A1BB54 */
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#endif /* defined(vax)||defined(tahoe) */
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/*******************************************************************************
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*
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* atan2 - compute the arc tangent of y/x (ANSI)
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*
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* This routine returns the principal value of the arc tangent of <y>/<x> in
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* double precision (IEEE double, 53 bits).
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* This routine uses the signs of both arguments to determine the quadrant of the
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* return value. A domain error may occur if both arguments are zero.
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*
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* INTERNAL:
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* (1) Reduce <y> to positive by:
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*
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* atan2(y,x)=-atan2(-y,x)
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*
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* (2) Reduce <x> to positive by (if <x> and <y> are unexceptional):
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*
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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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*
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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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* arc tangent 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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* INCLUDE FILES: math.h
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*
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* RETURNS:
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* The double-precision arc tangent of <y>/<x>, in the range [-pi,pi] radians.
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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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* .TS
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* tab(|);
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* l0 c0 l.
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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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* .TE
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*
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* SEE ALSO: mathALib
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*
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* INTERNAL:
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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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double atan2
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double y, /* numerator */
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double x /* denominator */
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)
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{
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static double zero=0, one=1, small=1.0E-9, big=1.0E18;
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double copysign(),logb(),scalb(),t,z,signy,signx,hi,lo;
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int finite(), 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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