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authorRich Felker <dalias@aerifal.cx>2011-02-12 00:22:29 -0500
committerRich Felker <dalias@aerifal.cx>2011-02-12 00:22:29 -0500
commit0b44a0315b47dd8eced9f3b7f31580cf14bbfc01 (patch)
tree6eaef0d8a720fa3da580de87b647fff796fe80b3 /src/math/e_atan2.c
downloadmusl-0b44a0315b47dd8eced9f3b7f31580cf14bbfc01.tar.gz
initial check-in, version 0.5.0v0.5.0
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+
+/* @(#)e_atan2.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+/* atan2(y,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,
+ *
+ * Special cases:
+ *
+ * ATAN2((anything), NaN ) is NaN;
+ * ATAN2(NAN , (anything) ) is NaN;
+ * ATAN2(+-0, +(anything but NaN)) is +-0 ;
+ * ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ * ATAN2(+-INF,+INF ) is +-pi/4 ;
+ * ATAN2(+-INF,-INF ) is +-3pi/4;
+ * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * 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 <math.h>
+#include "math_private.h"
+
+static const double
+tiny = 1.0e-300,
+zero = 0.0,
+pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
+pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
+pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
+pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+double
+atan2(double y, double x)
+{
+ double z;
+ int32_t k,m,hx,hy,ix,iy;
+ uint32_t lx,ly;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = hx&0x7fffffff;
+ EXTRACT_WORDS(hy,ly,y);
+ iy = hy&0x7fffffff;
+ if(((ix|((lx|-lx)>>31))>0x7ff00000)||
+ ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
+ return x+y;
+ if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
+ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
+
+ /* when y = 0 */
+ if((iy|ly)==0) {
+ switch(m) {
+ case 0:
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi+tiny;/* atan(+0,-anything) = pi */
+ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+ }
+ }
+ /* when x = 0 */
+ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* when x is INF */
+ if(ix==0x7ff00000) {
+ if(iy==0x7ff00000) {
+ switch(m) {
+ case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
+ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+ case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+ case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+ }
+ } else {
+ switch(m) {
+ case 0: return zero ; /* atan(+...,+INF) */
+ case 1: return -zero ; /* atan(-...,+INF) */
+ case 2: return pi+tiny ; /* atan(+...,-INF) */
+ case 3: return -pi-tiny ; /* atan(-...,-INF) */
+ }
+ }
+ }
+ /* when y is INF */
+ if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* compute y/x */
+ k = (iy-ix)>>20;
+ if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
+ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
+ else z=atan(fabs(y/x)); /* safe to do y/x */
+ switch (m) {
+ case 0: return z ; /* atan(+,+) */
+ case 1: {
+ uint32_t zh;
+ GET_HIGH_WORD(zh,z);
+ SET_HIGH_WORD(z,zh ^ 0x80000000);
+ }
+ return z ; /* atan(-,+) */
+ case 2: return pi-(z-pi_lo);/* atan(+,-) */
+ default: /* case 3 */
+ return (z-pi_lo)-pi;/* atan(-,-) */
+ }
+}