[musl] [PATCH] math: avoid internal overflow in expm1l.c

[Szabolcs Nagy <nsz@port70.net>]

the ld80 expm1l implementation in c tries to compute

  2^k q + 2^k - 1

but 2^k can overflow (when k==16384) while q is small and negative.
then the result should be finite, but the code gives nan. to avoid the
overflow use

  2 (2^(k-1) q + 2^(k-1) - 0.5).

note: this implementation is not used on x86 currently.
---
 src/math/expm1l.c | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/math/expm1l.c b/src/math/expm1l.c
index d1715078..79795dc0 100644
--- a/src/math/expm1l.c
+++ b/src/math/expm1l.c
@@ -109,9 +109,9 @@ long double expm1l(long double x)
 
 	/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
 	 We have qx = exp(remainder ln 2) - 1, so
-	 exp(x) - 1  =  2^k (qx + 1) - 1  =  2^k qx + 2^k - 1.  */
-	px = scalbnl(1.0, k);
-	x = px * qx + (px - 1.0);
+	 exp(x) - 1  =  2^k (qx + 1) - 1  =  2 (2^(k-1) qx + 2^(k-1) - 0.5).  */
+	px = scalbnl(1.0, k-1);
+	x = 2*(px * qx + (px - 0.5));
 	return x;
 }
 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
-- 
2.29.2