Transcendental functions for 'long double', from Paolo Bonzini.

[gnulib.git] / lib / sinl.c

diff --git a/lib/sinl.c b/lib/sinl.c
new file mode 100644 (file)
index 0000000..3bec0bb
--- /dev/null
+++ b/lib/sinl.c
@@ -0,0 +1,101 @@
+/* s_sinl.c -- long double version of s_sin.c.
+ * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* sinl(x)
+ * Return sine function of x.
+ *
+ * kernel function:
+ *     __kernel_sinl           ... sine function on [-pi/4,pi/4]
+ *     __kernel_cosl           ... cose function on [-pi/4,pi/4]
+ *     __ieee754_rem_pio2l     ... argument reduction routine
+ *
+ * Method.
+ *      Let S,C and T denote the sin, cos and tan respectively on
+ *     [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ *     in [-pi/4 , +pi/4], and let n = k mod 4.
+ *     We have
+ *
+ *          n        sin(x)      cos(x)        tan(x)
+ *     ----------------------------------------------------------
+ *         0          S           C             T
+ *         1          C          -S            -1/T
+ *         2         -S          -C             T
+ *         3         -C           S            -1/T
+ *     ----------------------------------------------------------
+ *
+ * Special cases:
+ *      Let trig be any of sin, cos, or tan.
+ *      trig(+-INF)  is NaN, with signals;
+ *      trig(NaN)    is that NaN;
+ *
+ * Accuracy:
+ *     TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include <math.h>
+
+#include "mathl.h"
+
+#include "trigl.h"
+#include "trigl.c"
+#include "sincosl.c"
+
+long double
+sinl (long double x)
+{
+  long double y[2], z = 0.0L;
+  int n;
+
+  /* |x| ~< pi/4 */
+  if (x >= -0.7853981633974483096156608458198757210492 &&
+      x <= 0.7853981633974483096156608458198757210492)
+    return kernel_sinl (x, z, 0);
+
+    /* sinl(Inf or NaN) is NaN, sinl(0) is 0 */
+  else if (x + x == x || x != x)
+    return x - x;              /* NaN */
+
+  /* argument reduction needed */
+  else
+    {
+      n = ieee754_rem_pio2l (x, y);
+      switch (n & 3)
+       {
+       case 0:
+         return kernel_sinl (y[0], y[1], 1);
+       case 1:
+         return kernel_cosl (y[0], y[1]);
+       case 2:
+         return -kernel_sinl (y[0], y[1], 1);
+       default:
+         return -kernel_cosl (y[0], y[1]);
+       }
+    }
+}
+
+#if 0
+int
+main ()
+{
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *29));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *2));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *30));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *4));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *32));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *2/3));
+  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *4/3));
+}
+#endif