128 bit implementation of tanh.

2024-11-27 03:41:23 +08:00 · 2001-06-19 07:24:40 +00:00 · 2001-06-19 07:24:40 +00:00 · ba0fd1ba02
commit ba0fd1ba02
parent 86dbe05e18
1 changed files with 106 additions and 0 deletions
--- a/sysdeps/ieee754/ldbl-128/s_tanhl.c
+++ b/sysdeps/ieee754/ldbl-128/s_tanhl.c
@ -0,0 +1,106 @@
+/* s_tanhl.c -- long double version of s_tanh.c.
+ * Conversion to long double by Ulrich Drepper,
+ * Cygnus Support, drepper@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* Changes for 128-bit long double contributed by
+   Stephen L. Moshier <moshier@na-net.ornl.gov> */
+
+/* tanhl(x)
+ * Return the Hyperbolic Tangent of x
+ *
+ * Method :
+ *                                      x    -x
+ *                                     e  - e
+ *      0. tanhl(x) is defined to be -----------
+ *                                      x    -x
+ *                                     e  + e
+ *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
+ *      2.  0      <= x <= 2**-57 : tanhl(x) := x*(one+x)
+ *                                               -t
+ *          2**-57 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
+ *                                              t + 2
+ *                                                    2
+ *          1      <= x <=  40.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
+ *                                                  t + 2
+ *          40.0   <  x <= INF    : tanhl(x) := 1.
+ *
+ * Special cases:
+ *      tanhl(NaN) is NaN;
+ *      only tanhl(0)=0 is exact for finite argument.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L;
+#else
+static long double one = 1.0, two = 2.0, tiny = 1.0e-4900L;
+#endif
+
+#ifdef __STDC__
+long double
+__tanhl (long double x)
+#else
+long double
+__tanhl (x)
+     long double x;
+#endif
+{
+  long double t, z;
+  u_int32_t jx, ix;
+  ieee854_long_double_shape_type u;
+
+  /* Words of |x|. */
+  u.value = x;
+  jx = u.parts32.w0;
+  ix = jx & 0x7fffffff;
+  /* x is INF or NaN */
+  if (ix >= 0x7fff0000)
+    {
+      /* for NaN it's not important which branch: tanhl(NaN) = NaN */
+      if (jx & 0x80000000)
+	return one / x - one;	/* tanhl(-inf)= -1; */
+      else
+	return one / x + one;	/* tanhl(+inf)=+1 */
+    }
+
+  /* |x| < 40 */
+  if (ix < 0x40044000)
+    {
+      if (u.value == 0)
+	return x;		/* x == +- 0 */
+      if (ix < 0x3fc60000)	/* |x| < 2^-57 */
+	return x * (one + tiny); /* tanh(small) = small */
+      u.parts32.w0 = ix;	/* Absolute value of x.  */
+      if (ix >= 0x3fff0000)
+	{			/* |x| >= 1  */
+	  t = __expm1l (two * u.value);
+	  z = one - two / (t + two);
+	}
+      else
+	{
+	  t = __expm1l (-two * u.value);
+	  z = -t / (t + two);
+	}
+      /* |x| > 40, return +-1 */
+    }
+  else
+    {
+      z = one - tiny;		/* raised inexact flag */
+    }
+  return (jx & 0x80000000) ? -z : z;
+}
+weak_alias (__tanhl, tanhl)