From f4d9bfb3a986f2c25ec023426b4fb222130af75f Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <nsz@port70.net>
Date: Thu, 5 Sep 2013 16:57:46 +0000
Subject: math: fix atanh (overflow and underflow issues)

in atanh exception handling was left to the called log functions,
but the argument to those functions could underflow or overflow.

use double_t and float_t to avoid some useless stores on x86
---
 src/math/atanh.c  | 18 +++++++++++++-----
 src/math/atanhf.c | 18 +++++++++++++-----
 src/math/atanhl.c | 15 +++++++++++----
 3 files changed, 37 insertions(+), 14 deletions(-)

diff --git a/src/math/atanh.c b/src/math/atanh.c
index 84a84c69..63a035d7 100644
--- a/src/math/atanh.c
+++ b/src/math/atanh.c
@@ -6,16 +6,24 @@ double atanh(double x)
 	union {double f; uint64_t i;} u = {.f = x};
 	unsigned e = u.i >> 52 & 0x7ff;
 	unsigned s = u.i >> 63;
+	double_t y;
 
 	/* |x| */
 	u.i &= (uint64_t)-1/2;
-	x = u.f;
+	y = u.f;
 
 	if (e < 0x3ff - 1) {
-		/* |x| < 0.5, up to 1.7ulp error */
-		x = 0.5*log1p(2*x + 2*x*x/(1-x));
+		if (e < 0x3ff - 32) {
+			/* handle underflow */
+			if (e == 0)
+				FORCE_EVAL((float)y);
+		} else {
+			/* |x| < 0.5, up to 1.7ulp error */
+			y = 0.5*log1p(2*y + 2*y*y/(1-y));
+		}
 	} else {
-		x = 0.5*log1p(2*x/(1-x));
+		/* avoid overflow */
+		y = 0.5*log1p(2*(y/(1-y)));
 	}
-	return s ? -x : x;
+	return s ? -y : y;
 }
diff --git a/src/math/atanhf.c b/src/math/atanhf.c
index ca106efc..65f07c0f 100644
--- a/src/math/atanhf.c
+++ b/src/math/atanhf.c
@@ -5,16 +5,24 @@ float atanhf(float x)
 {
 	union {float f; uint32_t i;} u = {.f = x};
 	unsigned s = u.i >> 31;
+	float_t y;
 
 	/* |x| */
 	u.i &= 0x7fffffff;
-	x = u.f;
+	y = u.f;
 
 	if (u.i < 0x3f800000 - (1<<23)) {
-		/* |x| < 0.5, up to 1.7ulp error */
-		x = 0.5f*log1pf(2*x + 2*x*x/(1-x));
+		if (u.i < 0x3f800000 - (32<<23)) {
+			/* handle underflow */
+			if (u.i < (1<<23))
+				FORCE_EVAL((float)(y*y));
+		} else {
+			/* |x| < 0.5, up to 1.7ulp error */
+			y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
+		}
 	} else {
-		x = 0.5f*log1pf(2*x/(1-x));
+		/* avoid overflow */
+		y = 0.5f*log1pf(2*(y/(1-y)));
 	}
-	return s ? -x : x;
+	return s ? -y : y;
 }
diff --git a/src/math/atanhl.c b/src/math/atanhl.c
index 72a1e345..f63d60b1 100644
--- a/src/math/atanhl.c
+++ b/src/math/atanhl.c
@@ -17,11 +17,18 @@ long double atanhl(long double x)
 	u.i.se = e;
 	x = u.f;
 
-	if (e < 0x3fff - 1) {
-		/* |x| < 0.5, up to 1.7ulp error */
-		x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+	if (e < 0x3ff - 1) {
+		if (e < 0x3ff - LDBL_MANT_DIG/2) {
+			/* handle underflow */
+			if (e == 0)
+				FORCE_EVAL((float)x);
+		} else {
+			/* |x| < 0.5, up to 1.7ulp error */
+			x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+		}
 	} else {
-		x = 0.5*log1pl(2*x/(1-x));
+		/* avoid overflow */
+		x = 0.5*log1pl(2*(x/(1-x)));
 	}
 	return s ? -x : x;
 }
-- 
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