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

1 files changed, 27 insertions, 65 deletions

diff --git a/src/math/tanhl.c b/src/math/tanhl.c
index 92efb20d..66559e9f 100644
--- a/src/math/tanhl.c
+++ b/src/math/tanhl.c
@@ -1,38 +1,3 @@
-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_tanhl.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/* 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**-55 : tanhl(x) := x*(one+x)
- *                                               -t
- *          2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
- *                                              t + 2
- *                                                    2
- *          1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
- *                                                  t + 2
- *          23.0   <  x <= INF    : tanhl(x) := 1.
- *
- * Special cases:
- *      tanhl(NaN) is NaN;
- *      only tanhl(0)=0 is exact for finite argument.
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -41,43 +6,40 @@ long double tanhl(long double x)
 	return tanh(x);
 }
 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double tiny = 1.0e-4900L;
-
 long double tanhl(long double x)
 {
-	long double t,z;
-	int32_t se;
-	uint32_t jj0,jj1,ix;
+	union {
+		long double f;
+		struct{uint64_t m; uint16_t se; uint16_t pad;} i;
+	} u = {.f = x};
+	unsigned ex = u.i.se & 0x7fff;
+	unsigned sign = u.i.se & 0x8000;
+	uint32_t w;
+	long double t;
 
-	/* High word of |x|. */
-	GET_LDOUBLE_WORDS(se, jj0, jj1, x);
-	ix = se & 0x7fff;
-
-	/* x is INF or NaN */
-	if (ix == 0x7fff) {
-		/* for NaN it's not important which branch: tanhl(NaN) = NaN */
-		if (se & 0x8000)
-			return 1.0/x-1.0;  /* tanhl(-inf)= -1; */
-		return 1.0/x+1.0;          /* tanhl(+inf)= +1 */
-	}
+	/* x = |x| */
+	u.i.se = ex;
+	x = u.f;
+	w = u.i.m >> 32;
 
-	/* |x| < 23 */
-	if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {
-		if ((ix|jj0|jj1) == 0) /* x == +- 0 */
-			return x;
-		if (ix < 0x3fc8)       /* |x| < 2**-55 */
-			return x*(1.0+tiny);  /* tanh(small) = small */
-		if (ix >= 0x3fff) {    /* |x| >= 1  */
-			t = expm1l(2.0*fabsl(x));
-			z = 1.0 - 2.0/(t+2.0);
+	if (ex > 0x3ffe || (ex == 0x3ffe && w > 0x8c9f53d5)) {
+		/* |x| > log(3)/2 ~= 0.5493 or nan */
+		if (ex >= 0x3fff+5) {
+			/* |x| >= 32 */
+			t = 1 + 0/(x + 0x1p-120f);
 		} else {
-			t = expm1l(-2.0*fabsl(x));
-			z = -t/(t+2.0);
+			t = expm1l(2*x);
+			t = 1 - 2/(t+2);
 		}
-	/* |x| > 23, return +-1 */
+	} else if (ex > 0x3ffd || (ex == 0x3ffd && w > 0x82c577d4)) {
+		/* |x| > log(5/3)/2 ~= 0.2554 */
+		t = expm1l(2*x);
+		t = t/(t+2);
 	} else {
-		z = 1.0 - tiny;  /* raise inexact flag */
+		/* |x| is small */
+		t = expm1l(-2*x);
+		t = -t/(t+2);
 	}
-	return se & 0x8000 ? -z : z;
+	return sign ? -t : t;
 }
 #endif