From f399fc8dab36676d617b1fa7e1e2c70bc5ddbffa Mon Sep 17 00:00:00 2001
From: Raymond Toy <toy.raymond@gmail.com>
Date: Sat, 2 Aug 2014 14:33:26 -0700
Subject: [PATCH] Import hyperbolic functions from fdlibm, as is.

---
 src/lisp/e_cosh.c | 89 +++++++++++++++++++++++++++++++++++++++++++++++
 src/lisp/e_sinh.c | 82 +++++++++++++++++++++++++++++++++++++++++++
 src/lisp/s_tanh.c | 82 +++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 253 insertions(+)
 create mode 100644 src/lisp/e_cosh.c
 create mode 100644 src/lisp/e_sinh.c
 create mode 100644 src/lisp/s_tanh.c

diff --git a/src/lisp/e_cosh.c b/src/lisp/e_cosh.c
new file mode 100644
index 000000000..204017d84
--- /dev/null
+++ b/src/lisp/e_cosh.c
@@ -0,0 +1,89 @@
+
+/* @(#)e_cosh.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.
+ * ====================================================
+ */
+
+/* __ieee754_cosh(x)
+ * Method : 
+ * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ *	1. Replace x by |x| (cosh(x) = cosh(-x)). 
+ *	2. 
+ *		                                        [ exp(x) - 1 ]^2 
+ *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
+ *			       			           2*exp(x)
+ *
+ *		                                  exp(x) +  1/exp(x)
+ *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
+ *			       			          2
+ *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2 
+ *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
+ *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ *	cosh(x) is |x| if x is +INF, -INF, or NaN.
+ *	only cosh(0)=1 is exact for finite x.
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static const double one = 1.0, half=0.5, huge = 1.0e300;
+#else
+static double one = 1.0, half=0.5, huge = 1.0e300;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_cosh(double x)
+#else
+	double __ieee754_cosh(x)
+	double x;
+#endif
+{	
+	double t,w;
+	int ix;
+	unsigned lx;
+
+    /* High word of |x|. */
+	ix = __HI(x);
+	ix &= 0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7ff00000) return x*x;	
+
+    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+	if(ix<0x3fd62e43) {
+	    t = expm1(fabs(x));
+	    w = one+t;
+	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
+	    return one+(t*t)/(w+w);
+	}
+
+    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+	if (ix < 0x40360000) {
+		t = __ieee754_exp(fabs(x));
+		return half*t+half/t;
+	}
+
+    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
+	if (ix<0x408633CE || 
+	      (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
+	    w = __ieee754_exp(half*fabs(x));
+	    t = half*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, cosh(x) overflow */
+	return huge*huge;
+}
diff --git a/src/lisp/e_sinh.c b/src/lisp/e_sinh.c
new file mode 100644
index 000000000..8af8a11eb
--- /dev/null
+++ b/src/lisp/e_sinh.c
@@ -0,0 +1,82 @@
+
+/* @(#)e_sinh.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.
+ * ====================================================
+ */
+
+/* __ieee754_sinh(x)
+ * Method : 
+ * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ *	1. Replace x by |x| (sinh(-x) = -sinh(x)). 
+ *	2. 
+ *		                                    E + E/(E+1)
+ *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
+ *			       			        2
+ *
+ *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2 
+ *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
+ *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
+ *
+ * Special cases:
+ *	sinh(x) is |x| if x is +INF, -INF, or NaN.
+ *	only sinh(0)=0 is exact for finite x.
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static const double one = 1.0, shuge = 1.0e307;
+#else
+static double one = 1.0, shuge = 1.0e307;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_sinh(double x)
+#else
+	double __ieee754_sinh(x)
+	double x;
+#endif
+{	
+	double t,w,h;
+	int ix,jx;
+	unsigned lx;
+
+    /* High word of |x|. */
+	jx = __HI(x);
+	ix = jx&0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7ff00000) return x+x;	
+
+	h = 0.5;
+	if (jx<0) h = -h;
+    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+	if (ix < 0x40360000) {		/* |x|<22 */
+	    if (ix<0x3e300000) 		/* |x|<2**-28 */
+		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+	    t = expm1(fabs(x));
+	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
+	    return h*(t+t/(t+one));
+	}
+
+    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
+	if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
+	    w = __ieee754_exp(0.5*fabs(x));
+	    t = h*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, sinh(x) overflow */
+	return x*shuge;
+}
diff --git a/src/lisp/s_tanh.c b/src/lisp/s_tanh.c
new file mode 100644
index 000000000..7d77c2eac
--- /dev/null
+++ b/src/lisp/s_tanh.c
@@ -0,0 +1,82 @@
+
+/* @(#)s_tanh.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.
+ * ====================================================
+ */
+
+/* Tanh(x)
+ * Return the Hyperbolic Tangent of x
+ *
+ * Method :
+ *				       x    -x
+ *				      e  - e
+ *	0. tanh(x) is defined to be -----------
+ *				       x    -x
+ *				      e  + e
+ *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
+ *	2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
+ *					        -t
+ *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
+ *					       t + 2
+ *						     2
+ *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
+ *						   t + 2
+ *	    22.0   <  x <= INF    : tanh(x) := 1.
+ *
+ * Special cases:
+ *	tanh(NaN) is NaN;
+ *	only tanh(0)=0 is exact for finite argument.
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static const double one=1.0, two=2.0, tiny = 1.0e-300;
+#else
+static double one=1.0, two=2.0, tiny = 1.0e-300;
+#endif
+
+#ifdef __STDC__
+	double tanh(double x)
+#else
+	double tanh(x)
+	double x;
+#endif
+{
+	double t,z;
+	int jx,ix;
+
+    /* High word of |x|. */
+	jx = __HI(x);
+	ix = jx&0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7ff00000) { 
+	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
+	    else       return one/x-one;    /* tanh(NaN) = NaN */
+	}
+
+    /* |x| < 22 */
+	if (ix < 0x40360000) {		/* |x|<22 */
+	    if (ix<0x3c800000) 		/* |x|<2**-55 */
+		return x*(one+x);    	/* tanh(small) = small */
+	    if (ix>=0x3ff00000) {	/* |x|>=1  */
+		t = expm1(two*fabs(x));
+		z = one - two/(t+two);
+	    } else {
+	        t = expm1(-two*fabs(x));
+	        z= -t/(t+two);
+	    }
+    /* |x| > 22, return +-1 */
+	} else {
+	    z = one - tiny;		/* raised inexact flag */
+	}
+	return (jx>=0)? z: -z;
+}
-- 
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