From 39c910fb061114e6aa5c3bf2c94b1d7262d62221 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <nsz@port70.net>
Date: Wed, 4 Sep 2013 07:51:11 +0000
Subject: math: fix underflow in exp*.c and long double handling in exp2l

* don't care about inexact flag
* use double_t and float_t (faster, smaller, more precise on x86)
* exp: underflow when result is zero or subnormal and not -inf
* exp2: underflow when result is zero or subnormal and not exact
* expm1: underflow when result is zero or subnormal
* expl: don't underflow on -inf
* exp2: fix incorrect comment
* expm1: simplify special case handling and overflow properly
* expm1: cleanup final scaling and fix negative left shift ub (twopk)
---
 src/math/exp2.c | 40 ++++++++++++++++++++--------------------
 1 file changed, 20 insertions(+), 20 deletions(-)

(limited to 'src/math/exp2.c')

diff --git a/src/math/exp2.c b/src/math/exp2.c
index 8e252280..2e078fb0 100644
--- a/src/math/exp2.c
+++ b/src/math/exp2.c
@@ -305,7 +305,7 @@ static const double tbl[TBLSIZE * 2] = {
  * Method: (accurate tables)
  *
  *   Reduce x:
- *     x = 2**k + y, for integer k and |y| <= 1/2.
+ *     x = k + y, for integer k and |y| <= 1/2.
  *     Thus we have exp2(x) = 2**k * exp2(y).
  *
  *   Reduce y:
@@ -330,41 +330,41 @@ static const double tbl[TBLSIZE * 2] = {
  */
 double exp2(double x)
 {
-	double r, t, z;
-	uint32_t hx, ix, i0;
+	double_t r, t, z;
+	uint32_t ix, i0;
+	union {double f; uint64_t i;} u = {x};
 	union {uint32_t u; int32_t i;} k;
 
 	/* Filter out exceptional cases. */
-	GET_HIGH_WORD(hx, x);
-	ix = hx & 0x7fffffff;
-	if (ix >= 0x40900000) {        /* |x| >= 1024 */
-		if (ix >= 0x7ff00000) {
-			GET_LOW_WORD(ix, x);
-			if (hx == 0xfff00000 && ix == 0) /* -inf */
-				return 0;
-			return x;
-		}
-		if (x >= 1024) {
+	ix = u.i>>32 & 0x7fffffff;
+	if (ix >= 0x408ff000) {  /* |x| >= 1022 or nan */
+		if (ix >= 0x40900000 && u.i>>63 == 0) {  /* x >= 1024 or nan */
+			/* overflow */
 			STRICT_ASSIGN(double, x, x * 0x1p1023);
 			return x;
 		}
-		if (x <= -1075) {
-			STRICT_ASSIGN(double, x, 0x1p-1000*0x1p-1000);
-			return x;
+		if (ix >= 0x7ff00000)  /* -inf or -nan */
+			return -1/x;
+		if (u.i>>63) {  /* x <= -1022 */
+			/* underflow */
+			if (x <= -1075 || x - 0x1p52 + 0x1p52 != x)
+				FORCE_EVAL((float)(-0x1p-149/x));
+			if (x <= -1075)
+				return 0;
 		}
 	} else if (ix < 0x3c900000) {  /* |x| < 0x1p-54 */
 		return 1.0 + x;
 	}
 
 	/* Reduce x, computing z, i0, and k. */
-	STRICT_ASSIGN(double, t, x + redux);
-	GET_LOW_WORD(i0, t);
+	u.f = x + redux;
+	i0 = u.i;
 	i0 += TBLSIZE / 2;
 	k.u = i0 / TBLSIZE * TBLSIZE;
 	k.i /= TBLSIZE;
 	i0 %= TBLSIZE;
-	t -= redux;
-	z = x - t;
+	u.f -= redux;
+	z = x - u.f;
 
 	/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
 	t = tbl[2*i0];       /* exp2t[i0] */
-- 
cgit v1.2.1