/* atan2.c - math routines */ /* Copyright 1992-1993 Wind River Systems, Inc. */ /* modification history -------------------- 01f,03jan01,pes Fix compiler warnings 01e,05feb93,jdi doc changes based on kdl review. 01d,02dec92,jdi doc tweaks. 01c,28oct92,jdi documentation cleanup. 01b,20sep92,smb documentation additions 01a,08jul92,smb documentation. */ /* DESCRIPTION * Copyright (c) 1985 Regents of the University of California. * All rights reserved. * * Redistribution and use in source and binary forms are permitted * provided that the above copyright notice and this paragraph are * duplicated in all such forms and that any documentation, * advertising materials, and other materials related to such * distribution and use acknowledge that the software was developed * by the University of California, Berkeley. The name of the * University may not be used to endorse or promote products derived * from this software without specific prior written permission. * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. * * All recipients should regard themselves as participants in an ongoing * research project and hence should feel obligated to report their * experiences (good or bad) with these elementary function codes, using * the sendbug(8) program, to the authors. * SEE ALSO: American National Standard X3.159-1989 NOMANUAL */ #include "vxWorks.h" #include "math.h" #if defined(vax)||defined(tahoe) /* VAX D format */ #ifdef vax #define _0x(A,B) 0x/**/A/**/B #else /* vax */ #define _0x(A,B) 0x/**/B/**/A #endif /* vax */ /*static double */ /*athfhi = 4.6364760900080611433E-1 ,*//*Hex 2^ -1 * .ED63382B0DDA7B */ /*athflo = 1.9338828231967579916E-19 ,*//*Hex 2^-62 * .E450059CFE92C0 */ /*PIo4 = 7.8539816339744830676E-1 ,*//*Hex 2^ 0 * .C90FDAA22168C2 */ /*at1fhi = 9.8279372324732906796E-1 ,*//*Hex 2^ 0 * .FB985E940FB4D9 */ /*at1flo = -3.5540295636764633916E-18 ,*//*Hex 2^-57 * -.831EDC34D6EAEA */ /*PIo2 = 1.5707963267948966135E0 ,*//*Hex 2^ 1 * .C90FDAA22168C2 */ /*PI = 3.1415926535897932270E0 ,*//*Hex 2^ 2 * .C90FDAA22168C2 */ /*a1 = 3.3333333333333473730E-1 ,*//*Hex 2^ -1 * .AAAAAAAAAAAB75 */ /*a2 = -2.0000000000017730678E-1 ,*//*Hex 2^ -2 * -.CCCCCCCCCD946E */ /*a3 = 1.4285714286694640301E-1 ,*//*Hex 2^ -2 * .92492492744262 */ /*a4 = -1.1111111135032672795E-1 ,*//*Hex 2^ -3 * -.E38E38EBC66292 */ /*a5 = 9.0909091380563043783E-2 ,*//*Hex 2^ -3 * .BA2E8BB31BD70C */ /*a6 = -7.6922954286089459397E-2 ,*//*Hex 2^ -3 * -.9D89C827C37F18 */ /*a7 = 6.6663180891693915586E-2 ,*//*Hex 2^ -3 * .8886B4AE379E58 */ /*a8 = -5.8772703698290408927E-2 ,*//*Hex 2^ -4 * -.F0BBA58481A942 */ /*a9 = 5.2170707402812969804E-2 ,*//*Hex 2^ -4 * .D5B0F3A1AB13AB */ /*a10 = -4.4895863157820361210E-2 ,*//*Hex 2^ -4 * -.B7E4B97FD1048F */ /*a11 = 3.3006147437343875094E-2 ,*//*Hex 2^ -4 * .8731743CF72D87 */ /*a12 = -1.4614844866464185439E-2 ;*//*Hex 2^ -6 * -.EF731A2F3476D9 */ static long athfhix[] = { _0x(6338,3fed), _0x(da7b,2b0d)}; #define athfhi (*(double *)athfhix) static long athflox[] = { _0x(5005,2164), _0x(92c0,9cfe)}; #define athflo (*(double *)athflox) static long PIo4x[] = { _0x(0fda,4049), _0x(68c2,a221)}; #define PIo4 (*(double *)PIo4x) static long at1fhix[] = { _0x(985e,407b), _0x(b4d9,940f)}; #define at1fhi (*(double *)at1fhix) static long at1flox[] = { _0x(1edc,a383), _0x(eaea,34d6)}; #define at1flo (*(double *)at1flox) static long PIo2x[] = { _0x(0fda,40c9), _0x(68c2,a221)}; #define PIo2 (*(double *)PIo2x) static long PIx[] = { _0x(0fda,4149), _0x(68c2,a221)}; #define PI (*(double *)PIx) static long a1x[] = { _0x(aaaa,3faa), _0x(ab75,aaaa)}; #define a1 (*(double *)a1x) static long a2x[] = { _0x(cccc,bf4c), _0x(946e,cccd)}; #define a2 (*(double *)a2x) static long a3x[] = { _0x(4924,3f12), _0x(4262,9274)}; #define a3 (*(double *)a3x) static long a4x[] = { _0x(8e38,bee3), _0x(6292,ebc6)}; #define a4 (*(double *)a4x) static long a5x[] = { _0x(2e8b,3eba), _0x(d70c,b31b)}; #define a5 (*(double *)a5x) static long a6x[] = { _0x(89c8,be9d), _0x(7f18,27c3)}; #define a6 (*(double *)a6x) static long a7x[] = { _0x(86b4,3e88), _0x(9e58,ae37)}; #define a7 (*(double *)a7x) static long a8x[] = { _0x(bba5,be70), _0x(a942,8481)}; #define a8 (*(double *)a8x) static long a9x[] = { _0x(b0f3,3e55), _0x(13ab,a1ab)}; #define a9 (*(double *)a9x) static long a10x[] = { _0x(e4b9,be37), _0x(048f,7fd1)}; #define a10 (*(double *)a10x) static long a11x[] = { _0x(3174,3e07), _0x(2d87,3cf7)}; #define a11 (*(double *)a11x) static long a12x[] = { _0x(731a,bd6f), _0x(76d9,2f34)}; #define a12 (*(double *)a12x) #else /* defined(vax)||defined(tahoe) */ static double athfhi = 4.6364760900080609352E-1 , /*Hex 2^ -2 * 1.DAC670561BB4F */ athflo = 4.6249969567426939759E-18 , /*Hex 2^-58 * 1.5543B8F253271 */ PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */ at1fhi = 9.8279372324732905408E-1 , /*Hex 2^ -1 * 1.F730BD281F69B */ at1flo = -2.4407677060164810007E-17 , /*Hex 2^-56 * -1.C23DFEFEAE6B5 */ PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */ PI = 3.1415926535897931160E0 , /*Hex 2^ 1 * 1.921FB54442D18 */ a1 = 3.3333333333333942106E-1 , /*Hex 2^ -2 * 1.55555555555C3 */ a2 = -1.9999999999979536924E-1 , /*Hex 2^ -3 * -1.9999999997CCD */ a3 = 1.4285714278004377209E-1 , /*Hex 2^ -3 * 1.24924921EC1D7 */ a4 = -1.1111110579344973814E-1 , /*Hex 2^ -4 * -1.C71C7059AF280 */ a5 = 9.0908906105474668324E-2 , /*Hex 2^ -4 * 1.745CE5AA35DB2 */ a6 = -7.6919217767468239799E-2 , /*Hex 2^ -4 * -1.3B0FA54BEC400 */ a7 = 6.6614695906082474486E-2 , /*Hex 2^ -4 * 1.10DA924597FFF */ a8 = -5.8358371008508623523E-2 , /*Hex 2^ -5 * -1.DE125FDDBD793 */ a9 = 4.9850617156082015213E-2 , /*Hex 2^ -5 * 1.9860524BDD807 */ a10 = -3.6700606902093604877E-2 , /*Hex 2^ -5 * -1.2CA6C04C6937A */ a11 = 1.6438029044759730479E-2 ; /*Hex 2^ -6 * 1.0D52174A1BB54 */ #endif /* defined(vax)||defined(tahoe) */ /******************************************************************************* * * atan2 - compute the arc tangent of y/x (ANSI) * * This routine returns the principal value of the arc tangent of / in * double precision (IEEE double, 53 bits). * This routine uses the signs of both arguments to determine the quadrant of the * return value. A domain error may occur if both arguments are zero. * * INTERNAL: * (1) Reduce to positive by: * * atan2(y,x)=-atan2(-y,x) * * (2) Reduce to positive by (if and are unexceptional): * * ARG (x+iy) = arctan(y/x) ... if x > 0 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0 * * (3) According to the integer k=4t+0.25 truncated , t=y/x, the argument * is further reduced to one of the following intervals and the * arc tangent of y/x is evaluated by the corresponding formula: * * [0,7/16] atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) * [7/16,11/16] atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) ) * [11/16.19/16] atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) ) * [19/16,39/16] atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) ) * [39/16,INF] atan(y/x) = atan(INF) + atan( -x/y ) * * INCLUDE FILES: math.h * * RETURNS: * The double-precision arc tangent of /, in the range [-pi,pi] radians. * * Special cases: * Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y). * * .TS * tab(|); * l0 c0 l. * ARG(NAN, (anything)) | is | NaN * ARG((anything), NaN) | is | NaN * ARG(+(anything but NaN), +-0) | is | +-0 * ARG(-(anything but NaN), +-0) | is | +-PI * ARG(0, +-(anything but 0 and NaN)) | is | +-PI/2 * ARG(+INF, +-(anything but INF and NaN)) | is | +-0 * ARG(-INF, +-(anything but INF and NaN)) | is | +-PI * ARG(+INF, +-INF) | is | +-PI/4 * ARG(-INF, +-INF) | is | +-3PI/4 * ARG((anything but 0, NaN, and INF),+-INF) | is | +-PI/2 * .TE * * SEE ALSO: mathALib * * INTERNAL: * Coded in C by K.C. Ng, 1/8/85; * Revised by K.C. Ng on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85. */ double atan2 ( double y, /* numerator */ double x /* denominator */ ) { static double zero=0, one=1, small=1.0E-9, big=1.0E18; double copysign(),logb(),scalb(),t,z,signy,signx,hi,lo; int finite(), k,m; #if !defined(vax)&&!defined(tahoe) /* if x or y is NAN */ if(x!=x) return(x); if(y!=y) return(y); #endif /* !defined(vax)&&!defined(tahoe) */ /* copy down the sign of y and x */ signy = copysign(one,y) ; signx = copysign(one,x) ; /* if x is 1.0, goto begin */ if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;} /* when y = 0 */ if(y==zero) return((signx==one)?y:copysign(PI,signy)); /* when x = 0 */ if(x==zero) return(copysign(PIo2,signy)); /* when x is INF */ if(!finite(x)) if(!finite(y)) return(copysign((signx==one)?PIo4:3*PIo4,signy)); else return(copysign((signx==one)?zero:PI,signy)); /* when y is INF */ if(!finite(y)) return(copysign(PIo2,signy)); /* compute y/x */ x=copysign(x,one); y=copysign(y,one); if((m=(k=logb(y))-logb(x)) > 60) t=big+big; else if(m < -80 ) t=y/x; else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); } /* begin argument reduction */ begin: if (t < 2.4375) { /* truncate 4(t+1/16) to integer for branching */ k = 4 * (t+0.0625); switch (k) { /* t is in [0,7/16] */ case 0: case 1: if (t < small) { big + small ; /* raise inexact flag */ return (copysign((signx>zero)?t:PI-t,signy)); } hi = zero; lo = zero; break; /* t is in [7/16,11/16] */ case 2: hi = athfhi; lo = athflo; z = x+x; t = ( (y+y) - x ) / ( z + y ); break; /* t is in [11/16,19/16] */ case 3: case 4: hi = PIo4; lo = zero; t = ( y - x ) / ( x + y ); break; /* t is in [19/16,39/16] */ default: hi = at1fhi; lo = at1flo; z = y-x; y=y+y+y; t = x+x; t = ( (z+z)-x ) / ( t + y ); break; } } /* end of if (t < 2.4375) */ else { hi = PIo2; lo = zero; /* t is in [2.4375, big] */ if (t <= big) t = - x / y; /* t is in [big, INF] */ else { big+small; /* raise inexact flag */ t = zero; } } /* end of argument reduction */ /* compute atan(t) for t in [-.4375, .4375] */ z = t*t; #if defined(vax)||defined(tahoe) z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ z*(a9+z*(a10+z*(a11+z*a12)))))))))))); #else /* defined(vax)||defined(tahoe) */ z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ z*(a9+z*(a10+z*a11))))))))))); #endif /* defined(vax)||defined(tahoe) */ z = lo - z; z += t; z += hi; return(copysign((signx>zero)?z:PI-z,signy)); }