initial check-in, version 0.5.0 v0.5.0

1 files changed, 120 insertions, 0 deletions

diff --git a/src/math/e_atan2.c b/src/math/e_atan2.c
new file mode 100644
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+++ b/src/math/e_atan2.c
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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(-,-) */
+        }
+}