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Diffstat (limited to 'sysdeps/generic/atan2.c')
| -rw-r--r-- | sysdeps/generic/atan2.c | 281 |
1 files changed, 281 insertions, 0 deletions
diff --git a/sysdeps/generic/atan2.c b/sysdeps/generic/atan2.c new file mode 100644 index 0000000000..958a154726 --- /dev/null +++ b/sysdeps/generic/atan2.c @@ -0,0 +1,281 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)atan2.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* ATAN2(Y,X) + * RETURN ARG (X+iY) + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * 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. + * + * Required system supported functions : + * copysign(x,y) + * scalb(x,y) + * logb(x) + * + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y 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 + * arctangent 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 ) + * + * Special cases: + * Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y). + * + * 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; + * + * Accuracy: + * atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded, + * where + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with 356,000 random argument on [-1,1] * [-1,1] on a + * VAX, the maximum observed error was 1.41 ulps (units of the last place) + * compared with (PI/pi)*(the exact ARG(x+iy)). + * + * Note: + * We use machine PI (the true pi rounded) in place of the actual + * value of pi for all the trig and inverse trig functions. In general, + * if trig is one of sin, cos, tan, then computed trig(y) returns the + * exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig + * returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the + * trig functions have period PI, and trig(arctrig(x)) returns x for + * all critical values x. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "mathimpl.h" + +vc(athfhi, 4.6364760900080611433E-1 ,6338,3fed,da7b,2b0d, -1, .ED63382B0DDA7B) +vc(athflo, 1.9338828231967579916E-19 ,5005,2164,92c0,9cfe, -62, .E450059CFE92C0) +vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2) +vc(at1fhi, 9.8279372324732906796E-1 ,985e,407b,b4d9,940f, 0, .FB985E940FB4D9) +vc(at1flo,-3.5540295636764633916E-18 ,1edc,a383,eaea,34d6, -57,-.831EDC34D6EAEA) +vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2) +vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2) +vc(a1, 3.3333333333333473730E-1 ,aaaa,3faa,ab75,aaaa, -1, .AAAAAAAAAAAB75) +vc(a2, -2.0000000000017730678E-1 ,cccc,bf4c,946e,cccd, -2,-.CCCCCCCCCD946E) +vc(a3, 1.4285714286694640301E-1 ,4924,3f12,4262,9274, -2, .92492492744262) +vc(a4, -1.1111111135032672795E-1 ,8e38,bee3,6292,ebc6, -3,-.E38E38EBC66292) +vc(a5, 9.0909091380563043783E-2 ,2e8b,3eba,d70c,b31b, -3, .BA2E8BB31BD70C) +vc(a6, -7.6922954286089459397E-2 ,89c8,be9d,7f18,27c3, -3,-.9D89C827C37F18) +vc(a7, 6.6663180891693915586E-2 ,86b4,3e88,9e58,ae37, -3, .8886B4AE379E58) +vc(a8, -5.8772703698290408927E-2 ,bba5,be70,a942,8481, -4,-.F0BBA58481A942) +vc(a9, 5.2170707402812969804E-2 ,b0f3,3e55,13ab,a1ab, -4, .D5B0F3A1AB13AB) +vc(a10, -4.4895863157820361210E-2 ,e4b9,be37,048f,7fd1, -4,-.B7E4B97FD1048F) +vc(a11, 3.3006147437343875094E-2 ,3174,3e07,2d87,3cf7, -4, .8731743CF72D87) +vc(a12, -1.4614844866464185439E-2 ,731a,bd6f,76d9,2f34, -6,-.EF731A2F3476D9) + +ic(athfhi, 4.6364760900080609352E-1 , -2, 1.DAC670561BB4F) +ic(athflo, 4.6249969567426939759E-18 , -58, 1.5543B8F253271) +ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18) +ic(at1fhi, 9.8279372324732905408E-1 , -1, 1.F730BD281F69B) +ic(at1flo,-2.4407677060164810007E-17 , -56, -1.C23DFEFEAE6B5) +ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18) +ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18) +ic(a1, 3.3333333333333942106E-1 , -2, 1.55555555555C3) +ic(a2, -1.9999999999979536924E-1 , -3, -1.9999999997CCD) +ic(a3, 1.4285714278004377209E-1 , -3, 1.24924921EC1D7) +ic(a4, -1.1111110579344973814E-1 , -4, -1.C71C7059AF280) +ic(a5, 9.0908906105474668324E-2 , -4, 1.745CE5AA35DB2) +ic(a6, -7.6919217767468239799E-2 , -4, -1.3B0FA54BEC400) +ic(a7, 6.6614695906082474486E-2 , -4, 1.10DA924597FFF) +ic(a8, -5.8358371008508623523E-2 , -5, -1.DE125FDDBD793) +ic(a9, 4.9850617156082015213E-2 , -5, 1.9860524BDD807) +ic(a10, -3.6700606902093604877E-2 , -5, -1.2CA6C04C6937A) +ic(a11, 1.6438029044759730479E-2 , -6, 1.0D52174A1BB54) + +#ifdef vccast +#define athfhi vccast(athfhi) +#define athflo vccast(athflo) +#define PIo4 vccast(PIo4) +#define at1fhi vccast(at1fhi) +#define at1flo vccast(at1flo) +#define PIo2 vccast(PIo2) +#define PI vccast(PI) +#define a1 vccast(a1) +#define a2 vccast(a2) +#define a3 vccast(a3) +#define a4 vccast(a4) +#define a5 vccast(a5) +#define a6 vccast(a6) +#define a7 vccast(a7) +#define a8 vccast(a8) +#define a9 vccast(a9) +#define a10 vccast(a10) +#define a11 vccast(a11) +#define a12 vccast(a12) +#endif + +double atan2(y,x) +double y,x; +{ + static const double zero=0, one=1, small=1.0E-9, big=1.0E18; + double t,z,signy,signx,hi,lo; + int 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)); +} |