1 files changed, 108 insertions, 0 deletions
diff --git a/libm/ldouble/arcdotl.c b/libm/ldouble/arcdotl.c
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+/*							arcdot.c
+ *
+ *	Angle between two vectors
+ *
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p[3], q[3], arcdotl();
+ *
+ * y = arcdotl( p, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * For two vectors p, q, the angle A between them is given by
+ *
+ *      p.q / (|p| |q|)  = cos A  .
+ *
+ * where "." represents inner product, "|x|" the length of vector x.
+ * If the angle is small, an expression in sin A is preferred.
+ * Set r = q - p.  Then
+ *
+ *     p.q = p.p + p.r ,
+ *
+ *     |p|^2 = p.p ,
+ *
+ *     |q|^2 = p.p + 2 p.r + r.r ,
+ *
+ *                  p.p^2 + 2 p.p p.r + p.r^2
+ *     cos^2 A  =  ----------------------------
+ *                    p.p (p.p + 2 p.r + r.r)
+ *
+ *                  p.p + 2 p.r + p.r^2 / p.p
+ *              =  --------------------------- ,
+ *                     p.p + 2 p.r + r.r
+ *
+ *     sin^2 A  =  1 - cos^2 A
+ *
+ *                   r.r - p.r^2 / p.p
+ *              =  --------------------
+ *                  p.p + 2 p.r + r.r
+ *
+ *              =   (r.r - p.r^2 / p.p) / q.q  .
+ *
+ * ACCURACY:
+ *
+ * About 1 ULP.  See arcdot.c.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double acosl ( long double );
+extern long double asinl ( long double );
+extern long double atanl ( long double );
+#else
+long double sqrtl(), acosl(), asinl(), atanl();
+#endif
+extern long double PIL;
+
+long double arcdotl(p,q)
+long double p[], q[];
+{
+long double pp, pr, qq, rr, rt, pt, qt, pq;
+int i;
+
+pq = 0.0L;
+qq = 0.0L;
+pp = 0.0L;
+pr = 0.0L;
+rr = 0.0L;
+for (i=0; i<3; i++)
+  {
+    pt = p[i];
+    qt = q[i];
+    pq += pt * qt;
+    qq += qt * qt;
+    pp += pt * pt;
+    rt = qt - pt;
+    pr += pt * rt;
+    rr += rt * rt;
+  }
+if (rr == 0.0L || pp == 0.0L || qq == 0.0L)
+  return 0.0L;
+rt = (rr - (pr * pr) / pp) / qq;
+if (rt <= 0.75L)
+  {
+    rt = sqrtl(rt);
+    qt = asinl(rt);
+    if (pq < 0.0L)
+      qt = PIL - qt;
+  }
+else
+  {
+    pt = pq / sqrtl(pp*qq);
+    qt = acosl(pt);
+  }
+return qt;
+}