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authorJoseph Myers <joseph@codesourcery.com>2015-06-23 14:35:18 +0000
committerJoseph Myers <joseph@codesourcery.com>2015-06-23 14:35:18 +0000
commitb59549574efeeecf124de05c9183c120eaaa56f0 (patch)
treeae18151390fc556d7ad3fa74246b032ce9dd6db8
parentb57525f1a376149840f740a31535681c07152ba4 (diff)
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Fix exp2, exp2f spurious underflows (bug 18219).
The dbl-64 and flt-32 implementations of exp2 functions produce spurious underflow exceptions. The underlying reason is the same in both cases: the computation works as (2^a - 1)*2^b + 2^b for suitably chosen a and b, where a has small magnitude so 2^a - 1 can be computed with a low-degree polynomial approximation, and (2^a - 1)*2^b can underflow even when the final result does not. This patch fixes this by adjusting the threshold for when scaling is used to avoid intermediate underflow so it works for any possible value of a where the final result would not underflow. Tested for x86_64 and x86. [BZ #18219] * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce threshold on absolute value of exponent for which scaling is used. * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise. * math/auto-libm-test-in: Add more tests of exp2. * math/auto-libm-test-out: Regenerated.
-rw-r--r--ChangeLog9
-rw-r--r--NEWS12
-rw-r--r--math/auto-libm-test-in7
-rw-r--r--math/auto-libm-test-out175
-rw-r--r--sysdeps/ieee754/dbl-64/e_exp2.c4
-rw-r--r--sysdeps/ieee754/flt-32/e_exp2f.c4
6 files changed, 203 insertions, 8 deletions
diff --git a/ChangeLog b/ChangeLog
index dee1967ba5..a7f879af23 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+2015-06-23 Joseph Myers <joseph@codesourcery.com>
+
+ [BZ #18219]
+ * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce
+ threshold on absolute value of exponent for which scaling is used.
+ * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
+ * math/auto-libm-test-in: Add more tests of exp2.
+ * math/auto-libm-test-out: Regenerated.
+
2015-06-23 Dmitry V. Levin <ldv@altlinux.org>
[BZ #17977]
diff --git a/NEWS b/NEWS
index d1032510fb..42ebdd1af6 100644
--- a/NEWS
+++ b/NEWS
@@ -18,12 +18,12 @@ Version 2.22
17991, 17996, 17998, 17999, 18007, 18019, 18020, 18029, 18030, 18032,
18034, 18036, 18038, 18039, 18042, 18043, 18046, 18047, 18049, 18068,
18080, 18093, 18100, 18104, 18110, 18111, 18116, 18125, 18128, 18138,
- 18185, 18196, 18197, 18206, 18210, 18211, 18217, 18220, 18221, 18234,
- 18244, 18247, 18287, 18319, 18324, 18333, 18346, 18397, 18409, 18410,
- 18412, 18418, 18422, 18434, 18444, 18468, 18469, 18470, 18479, 18483,
- 18495, 18496, 18497, 18498, 18507, 18512, 18513, 18519, 18520, 18522,
- 18527, 18528, 18529, 18530, 18532, 18533, 18534, 18536, 18539, 18540,
- 18542, 18544, 18545, 18546, 18547, 18553, 18558, 18569.
+ 18185, 18196, 18197, 18206, 18210, 18211, 18217, 18219, 18220, 18221,
+ 18234, 18244, 18247, 18287, 18319, 18324, 18333, 18346, 18397, 18409,
+ 18410, 18412, 18418, 18422, 18434, 18444, 18468, 18469, 18470, 18479,
+ 18483, 18495, 18496, 18497, 18498, 18507, 18512, 18513, 18519, 18520,
+ 18522, 18527, 18528, 18529, 18530, 18532, 18533, 18534, 18536, 18539,
+ 18540, 18542, 18544, 18545, 18546, 18547, 18553, 18558, 18569.
* Cache information can be queried via sysconf() function on s390 e.g. with
_SC_LEVEL1_ICACHE_SIZE as argument.
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 9bae9d5570..cf7fc359b0 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -1271,9 +1271,16 @@ exp2 max
exp2 -max
exp2 0.75
exp2 100.5
+exp2 -116.5
+exp2 -123.5
+exp2 -124.5
+exp2 -125.5
exp2 127
exp2 -149
exp2 1000.25
+exp2 -1019.5
+exp2 -1020.5
+exp2 -1021.5
exp2 1023
exp2 -1074
exp2 16383
diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 9f80736e86..556b833822 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -106691,6 +106691,106 @@ exp2 100.5
= exp2 tonearest ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
= exp2 towardzero ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
= exp2 upward ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ebp+100L : inexact-ok
+exp2 -116.5
+= exp2 downward flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
+= exp2 tonearest flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
+= exp2 towardzero flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
+= exp2 upward flt-32 -0x7.48p+4f : 0xb.504f4p-120f : inexact-ok
+= exp2 downward dbl-64 -0x7.48p+4 : 0xb.504f333f9de6p-120 : inexact-ok
+= exp2 tonearest dbl-64 -0x7.48p+4 : 0xb.504f333f9de68p-120 : inexact-ok
+= exp2 towardzero dbl-64 -0x7.48p+4 : 0xb.504f333f9de6p-120 : inexact-ok
+= exp2 upward dbl-64 -0x7.48p+4 : 0xb.504f333f9de68p-120 : inexact-ok
+= exp2 downward ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 upward ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6485p-120L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6485p-120L : inexact-ok
+= exp2 downward ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
+= exp2 tonearest ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
+= exp2 towardzero ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
+= exp2 upward ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754bp-120L : inexact-ok
+= exp2 downward ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
+= exp2 tonearest ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
+= exp2 towardzero ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
+= exp2 upward ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3758p-120L : inexact-ok
+exp2 -123.5
+= exp2 downward flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
+= exp2 tonearest flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
+= exp2 towardzero flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
+= exp2 upward flt-32 -0x7.b8p+4f : 0x1.6a09e8p-124f : inexact-ok
+= exp2 downward dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bccp-124 : inexact-ok
+= exp2 tonearest dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bcdp-124 : inexact-ok
+= exp2 towardzero dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bccp-124 : inexact-ok
+= exp2 upward dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bcdp-124 : inexact-ok
+= exp2 downward ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 upward ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc90ap-124L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc90ap-124L : inexact-ok
+= exp2 downward ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
+= exp2 tonearest ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
+= exp2 towardzero ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
+= exp2 upward ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea96p-124L : inexact-ok
+= exp2 downward ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
+= exp2 tonearest ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
+= exp2 towardzero ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
+= exp2 upward ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ebp-124L : inexact-ok
+exp2 -124.5
+= exp2 downward flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
+= exp2 tonearest flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
+= exp2 towardzero flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
+= exp2 upward flt-32 -0x7.c8p+4f : 0xb.504f4p-128f : inexact-ok
+= exp2 downward dbl-64 -0x7.c8p+4 : 0xb.504f333f9de6p-128 : inexact-ok
+= exp2 tonearest dbl-64 -0x7.c8p+4 : 0xb.504f333f9de68p-128 : inexact-ok
+= exp2 towardzero dbl-64 -0x7.c8p+4 : 0xb.504f333f9de6p-128 : inexact-ok
+= exp2 upward dbl-64 -0x7.c8p+4 : 0xb.504f333f9de68p-128 : inexact-ok
+= exp2 downward ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 upward ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6485p-128L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6485p-128L : inexact-ok
+= exp2 downward ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
+= exp2 tonearest ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
+= exp2 towardzero ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
+= exp2 upward ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754bp-128L : inexact-ok
+= exp2 downward ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
+= exp2 tonearest ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
+= exp2 towardzero ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
+= exp2 upward ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3758p-128L : inexact-ok
+exp2 -125.5
+= exp2 downward flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
+= exp2 tonearest flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
+= exp2 towardzero flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
+= exp2 upward flt-32 -0x7.d8p+4f : 0x5.a827ap-128f : inexact-ok
+= exp2 downward dbl-64 -0x7.d8p+4 : 0x5.a827999fcef3p-128 : inexact-ok
+= exp2 tonearest dbl-64 -0x7.d8p+4 : 0x5.a827999fcef34p-128 : inexact-ok
+= exp2 towardzero dbl-64 -0x7.d8p+4 : 0x5.a827999fcef3p-128 : inexact-ok
+= exp2 upward dbl-64 -0x7.d8p+4 : 0x5.a827999fcef34p-128 : inexact-ok
+= exp2 downward ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 upward ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef32428p-128L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef32428p-128L : inexact-ok
+= exp2 downward ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
+= exp2 tonearest ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
+= exp2 towardzero ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
+= exp2 upward ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa58p-128L : inexact-ok
+= exp2 downward ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
+= exp2 tonearest ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
+= exp2 towardzero ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
+= exp2 upward ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9bacp-128L : inexact-ok
exp2 127
= exp2 downward flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
= exp2 tonearest flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
@@ -106766,6 +106866,81 @@ exp2 1000.25
= exp2 tonearest ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305c8p+1000L : inexact-ok
= exp2 towardzero ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305c8p+1000L : inexact-ok
= exp2 upward ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305dp+1000L : inexact-ok
+exp2 -1019.5
+= exp2 downward flt-32 -0x3.fb8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 tonearest flt-32 -0x3.fb8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 towardzero flt-32 -0x3.fb8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 upward flt-32 -0x3.fb8p+8f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= exp2 downward dbl-64 -0x3.fb8p+8 : 0x1.6a09e667f3bccp-1020 : inexact-ok
+= exp2 tonearest dbl-64 -0x3.fb8p+8 : 0x1.6a09e667f3bcdp-1020 : inexact-ok
+= exp2 towardzero dbl-64 -0x3.fb8p+8 : 0x1.6a09e667f3bccp-1020 : inexact-ok
+= exp2 upward dbl-64 -0x3.fb8p+8 : 0x1.6a09e667f3bcdp-1020 : inexact-ok
+= exp2 downward ldbl-96-intel -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 upward ldbl-96-intel -0x3.fb8p+8L : 0x1.6a09e667f3bcc90ap-1020L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x3.fb8p+8L : 0x1.6a09e667f3bcc908p-1020L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x3.fb8p+8L : 0x1.6a09e667f3bcc90ap-1020L : inexact-ok
+= exp2 downward ldbl-128 -0x3.fb8p+8L : 0x1.6a09e667f3bcc908b2fb1366ea95p-1020L : inexact-ok
+= exp2 tonearest ldbl-128 -0x3.fb8p+8L : 0x1.6a09e667f3bcc908b2fb1366ea95p-1020L : inexact-ok
+= exp2 towardzero ldbl-128 -0x3.fb8p+8L : 0x1.6a09e667f3bcc908b2fb1366ea95p-1020L : inexact-ok
+= exp2 upward ldbl-128 -0x3.fb8p+8L : 0x1.6a09e667f3bcc908b2fb1366ea96p-1020L : inexact-ok
+= exp2 downward ldbl-128ibm -0x3.fb8p+8L : 0x1.6a09e667f3bcc8p-1020L : inexact-ok underflow errno-erange-ok
+= exp2 tonearest ldbl-128ibm -0x3.fb8p+8L : 0x1.6a09e667f3bcc8p-1020L : inexact-ok underflow errno-erange-ok
+= exp2 towardzero ldbl-128ibm -0x3.fb8p+8L : 0x1.6a09e667f3bcc8p-1020L : inexact-ok underflow errno-erange-ok
+= exp2 upward ldbl-128ibm -0x3.fb8p+8L : 0x1.6a09e667f3bcccp-1020L : inexact-ok underflow errno-erange-ok
+exp2 -1020.5
+= exp2 downward flt-32 -0x3.fc8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 tonearest flt-32 -0x3.fc8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 towardzero flt-32 -0x3.fc8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 upward flt-32 -0x3.fc8p+8f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= exp2 downward dbl-64 -0x3.fc8p+8 : 0xb.504f333f9de6p-1024 : inexact-ok
+= exp2 tonearest dbl-64 -0x3.fc8p+8 : 0xb.504f333f9de68p-1024 : inexact-ok
+= exp2 towardzero dbl-64 -0x3.fc8p+8 : 0xb.504f333f9de6p-1024 : inexact-ok
+= exp2 upward dbl-64 -0x3.fc8p+8 : 0xb.504f333f9de68p-1024 : inexact-ok
+= exp2 downward ldbl-96-intel -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 upward ldbl-96-intel -0x3.fc8p+8L : 0xb.504f333f9de6485p-1024L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x3.fc8p+8L : 0xb.504f333f9de6484p-1024L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x3.fc8p+8L : 0xb.504f333f9de6485p-1024L : inexact-ok
+= exp2 downward ldbl-128 -0x3.fc8p+8L : 0xb.504f333f9de6484597d89b3754a8p-1024L : inexact-ok
+= exp2 tonearest ldbl-128 -0x3.fc8p+8L : 0xb.504f333f9de6484597d89b3754a8p-1024L : inexact-ok
+= exp2 towardzero ldbl-128 -0x3.fc8p+8L : 0xb.504f333f9de6484597d89b3754a8p-1024L : inexact-ok
+= exp2 upward ldbl-128 -0x3.fc8p+8L : 0xb.504f333f9de6484597d89b3754bp-1024L : inexact-ok
+= exp2 downward ldbl-128ibm -0x3.fc8p+8L : 0xb.504f333f9de64p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 tonearest ldbl-128ibm -0x3.fc8p+8L : 0xb.504f333f9de64p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 towardzero ldbl-128ibm -0x3.fc8p+8L : 0xb.504f333f9de64p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 upward ldbl-128ibm -0x3.fc8p+8L : 0xb.504f333f9de68p-1024L : inexact-ok underflow errno-erange-ok
+exp2 -1021.5
+= exp2 downward flt-32 -0x3.fd8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 tonearest flt-32 -0x3.fd8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 towardzero flt-32 -0x3.fd8p+8f : 0x0p+0f : inexact-ok underflow errno-erange
+= exp2 upward flt-32 -0x3.fd8p+8f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= exp2 downward dbl-64 -0x3.fd8p+8 : 0x5.a827999fcef3p-1024 : inexact-ok
+= exp2 tonearest dbl-64 -0x3.fd8p+8 : 0x5.a827999fcef34p-1024 : inexact-ok
+= exp2 towardzero dbl-64 -0x3.fd8p+8 : 0x5.a827999fcef3p-1024 : inexact-ok
+= exp2 upward dbl-64 -0x3.fd8p+8 : 0x5.a827999fcef34p-1024 : inexact-ok
+= exp2 downward ldbl-96-intel -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 tonearest ldbl-96-intel -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 towardzero ldbl-96-intel -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 upward ldbl-96-intel -0x3.fd8p+8L : 0x5.a827999fcef32428p-1024L : inexact-ok
+= exp2 downward ldbl-96-m68k -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 tonearest ldbl-96-m68k -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 towardzero ldbl-96-m68k -0x3.fd8p+8L : 0x5.a827999fcef3242p-1024L : inexact-ok
+= exp2 upward ldbl-96-m68k -0x3.fd8p+8L : 0x5.a827999fcef32428p-1024L : inexact-ok
+= exp2 downward ldbl-128 -0x3.fd8p+8L : 0x5.a827999fcef32422cbec4d9baa54p-1024L : inexact-ok
+= exp2 tonearest ldbl-128 -0x3.fd8p+8L : 0x5.a827999fcef32422cbec4d9baa54p-1024L : inexact-ok
+= exp2 towardzero ldbl-128 -0x3.fd8p+8L : 0x5.a827999fcef32422cbec4d9baa54p-1024L : inexact-ok
+= exp2 upward ldbl-128 -0x3.fd8p+8L : 0x5.a827999fcef32422cbec4d9baa58p-1024L : inexact-ok
+= exp2 downward ldbl-128ibm -0x3.fd8p+8L : 0x5.a827999fcef3p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 tonearest ldbl-128ibm -0x3.fd8p+8L : 0x5.a827999fcef34p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 towardzero ldbl-128ibm -0x3.fd8p+8L : 0x5.a827999fcef3p-1024L : inexact-ok underflow errno-erange-ok
+= exp2 upward ldbl-128ibm -0x3.fd8p+8L : 0x5.a827999fcef34p-1024L : inexact-ok underflow errno-erange-ok
exp2 1023
= exp2 downward flt-32 0x3.ffp+8f : 0xf.fffffp+124f : inexact-ok overflow errno-erange-ok
= exp2 tonearest flt-32 0x3.ffp+8f : plus_infty : inexact-ok overflow errno-erange
diff --git a/sysdeps/ieee754/dbl-64/e_exp2.c b/sysdeps/ieee754/dbl-64/e_exp2.c
index 948a756df7..30f0a8f529 100644
--- a/sysdeps/ieee754/dbl-64/e_exp2.c
+++ b/sysdeps/ieee754/dbl-64/e_exp2.c
@@ -96,7 +96,9 @@ __ieee754_exp2 (double x)
/* 3. Compute ex2 = 2^(t/512+e+ex). */
ex2_u.d = exp2_accuratetable[tval & 511];
tval >>= 9;
- unsafe = abs (tval) >= -DBL_MIN_EXP - 1;
+ /* x2 is an integer multiple of 2^-54; avoid intermediate
+ underflow from the calculation of x22 * x. */
+ unsafe = abs (tval) >= -DBL_MIN_EXP - 56;
ex2_u.ieee.exponent += tval >> unsafe;
scale_u.d = 1.0;
scale_u.ieee.exponent += tval - (tval >> unsafe);
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index f3e3a8e6fc..0b75a7ea2a 100644
--- a/sysdeps/ieee754/flt-32/e_exp2f.c
+++ b/sysdeps/ieee754/flt-32/e_exp2f.c
@@ -89,7 +89,9 @@ __ieee754_exp2f (float x)
/* 3. Compute ex2 = 2^(t/255+e+ex). */
ex2_u.f = __exp2f_atable[tval & 255];
tval >>= 8;
- unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
+ /* x2 is an integer multiple of 2^-30; avoid intermediate
+ underflow from the calculation of x22 * x. */
+ unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
ex2_u.ieee.exponent += tval >> unsafe;
scale_u.f = 1.0;
scale_u.ieee.exponent += tval - (tval >> unsafe);