From e42a977fe5dbe48ba45072ab82886e6b5a694487 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <nsz@port70.net>
Date: Sun, 16 Dec 2012 19:52:42 +0100
Subject: math: tanh.c cleanup similar to sinh, cosh

comments are kept in the double version of the function

compared to fdlibm/freebsd we partition the domain into one
more part and select different threshold points:
now the [log(5/3)/2,log(3)/2] and [log(3)/2,inf] domains
should have <1.5ulp error
(so only the last bit may be wrong, assuming good exp, expm1)

(note that log(3)/2 and log(5/3)/2 are the points where tanh
changes resolution: tanh(log(3)/2)=0.5, tanh(log(5/3)/2)=0.25)

for some x < log(5/3)/2 (~=0.2554) the error can be >1.5ulp
but it should be <2ulp
(the freebsd code had some >2ulp errors in [0.255,1])

even with the extra logic the new code produces smaller
object files
---
 src/math/tanhf.c | 70 ++++++++++++++++++++------------------------------------
 1 file changed, 25 insertions(+), 45 deletions(-)

(limited to 'src/math/tanhf.c')

diff --git a/src/math/tanhf.c b/src/math/tanhf.c
index 7cb459d0..8099ec30 100644
--- a/src/math/tanhf.c
+++ b/src/math/tanhf.c
@@ -1,55 +1,35 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_tanhf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@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.
- * ====================================================
- */
-
 #include "libm.h"
 
-static const float
-tiny = 1.0e-30,
-huge = 1.0e30;
-
 float tanhf(float x)
 {
-	float t,z;
-	int32_t jx,ix;
+	union {float f; uint32_t i;} u = {.f = x};
+	uint32_t w;
+	int sign;
+	float t;
 
-	GET_FLOAT_WORD(jx, x);
-	ix = jx & 0x7fffffff;
+	/* x = |x| */
+	sign = u.i >> 31;
+	u.i &= 0x7fffffff;
+	x = u.f;
+	w = u.i;
 
-	/* x is INF or NaN */
-	if(ix >= 0x7f800000) {
-		if (jx >= 0)
-			return 1.0f/x + 1.0f;  /* tanh(+-inf)=+-1 */
-		else
-			return 1.0f/x - 1.0f;  /* tanh(NaN) = NaN */
-	}
-
-	if (ix < 0x41100000) {  /* |x| < 9 */
-		if (ix < 0x39800000) {  /* |x| < 2**-12 */
-			/* tanh(tiny) = tiny with inexact */
-			if (huge+x > 1.0f)
-				return x;
-		}
-		if (ix >= 0x3f800000) {  /* |x|>=1  */
-			t = expm1f(2.0f*fabsf(x));
-			z = 1.0f - 2.0f/(t+2.0f);
+	if (w > 0x3f0c9f54) {
+		/* |x| > log(3)/2 ~= 0.5493 or nan */
+		if (w > 0x41200000) {
+			/* |x| > 10 */
+			t = 1 + 0/(x + 0x1p-120f);
 		} else {
-			t = expm1f(-2.0f*fabsf(x));
-			z = -t/(t+2.0f);
+			t = expm1f(2*x);
+			t = 1 - 2/(t+2);
 		}
-	} else {  /* |x| >= 9, return +-1 */
-		z = 1.0f - tiny;  /* raise inexact */
+	} else if (w > 0x3e82c578) {
+		/* |x| > log(5/3)/2 ~= 0.2554 */
+		t = expm1f(2*x);
+		t = t/(t+2);
+	} else {
+		/* |x| is small */
+		t = expm1f(-2*x);
+		t = -t/(t+2);
 	}
-	return jx >= 0 ? z : -z;
+	return sign ? -t : t;
 }
-- 
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