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.

diff --git a/ChangeLog b/ChangeLog
index dee1967ba558ccd81a5b04e195666e260a06b30d..a7f879af23bf5e1d5cd3a3550d934a1e4745aff1 100644 (file)
--- 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 d1032510fb440426fab55afa70f44e21bff72bb6..42ebdd1af6ec4dc267b2878005a34c508b1f3fb8 100644 (file)
--- 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 9bae9d55703c601c5c03b367dbb0e4c6aff2ed9e..cf7fc359b0749ecf351759503169b95c43f71bee 100644 (file)
--- 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 9f80736e86accc11a4ad0083b67d000f4e929325..556b83382206ddcc310fe7b4b4417a72cea11b22 100644 (file)
--- 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 948a756df773e48559a594b7e012b8c1ac2e15d6..30f0a8f5296ba440089ffc815383cfd3c54df7e0 100644 (file)
--- 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 f3e3a8e6fc46e98a33ef2afd88a1c2f6c7015c0c..0b75a7ea2a5afb4c93645541a28039e5057d82ba 100644 (file)
--- 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);