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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.
This commit is contained in:
Joseph Myers
parent
b57525f1a3
commit
b59549574e
@ -1,3 +1,12 @@
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2015-06-23 Joseph Myers <joseph@codesourcery.com>
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[BZ #18219]
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* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce
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threshold on absolute value of exponent for which scaling is used.
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* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
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* math/auto-libm-test-in: Add more tests of exp2.
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* math/auto-libm-test-out: Regenerated.
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2015-06-23 Dmitry V. Levin <ldv@altlinux.org>
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2015-06-23 Dmitry V. Levin <ldv@altlinux.org>
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[BZ #17977]
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[BZ #17977]
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12
NEWS
12
NEWS
@ -18,12 +18,12 @@ Version 2.22
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17991, 17996, 17998, 17999, 18007, 18019, 18020, 18029, 18030, 18032,
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17991, 17996, 17998, 17999, 18007, 18019, 18020, 18029, 18030, 18032,
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18034, 18036, 18038, 18039, 18042, 18043, 18046, 18047, 18049, 18068,
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18034, 18036, 18038, 18039, 18042, 18043, 18046, 18047, 18049, 18068,
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18080, 18093, 18100, 18104, 18110, 18111, 18116, 18125, 18128, 18138,
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18080, 18093, 18100, 18104, 18110, 18111, 18116, 18125, 18128, 18138,
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18185, 18196, 18197, 18206, 18210, 18211, 18217, 18220, 18221, 18234,
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18185, 18196, 18197, 18206, 18210, 18211, 18217, 18219, 18220, 18221,
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18244, 18247, 18287, 18319, 18324, 18333, 18346, 18397, 18409, 18410,
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18234, 18244, 18247, 18287, 18319, 18324, 18333, 18346, 18397, 18409,
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18412, 18418, 18422, 18434, 18444, 18468, 18469, 18470, 18479, 18483,
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18410, 18412, 18418, 18422, 18434, 18444, 18468, 18469, 18470, 18479,
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18495, 18496, 18497, 18498, 18507, 18512, 18513, 18519, 18520, 18522,
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18483, 18495, 18496, 18497, 18498, 18507, 18512, 18513, 18519, 18520,
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18527, 18528, 18529, 18530, 18532, 18533, 18534, 18536, 18539, 18540,
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18522, 18527, 18528, 18529, 18530, 18532, 18533, 18534, 18536, 18539,
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18542, 18544, 18545, 18546, 18547, 18553, 18558, 18569.
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18540, 18542, 18544, 18545, 18546, 18547, 18553, 18558, 18569.
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* Cache information can be queried via sysconf() function on s390 e.g. with
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* Cache information can be queried via sysconf() function on s390 e.g. with
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_SC_LEVEL1_ICACHE_SIZE as argument.
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_SC_LEVEL1_ICACHE_SIZE as argument.
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@ -1271,9 +1271,16 @@ exp2 max
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exp2 -max
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exp2 -max
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exp2 0.75
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exp2 0.75
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exp2 100.5
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exp2 100.5
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exp2 -116.5
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exp2 -123.5
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exp2 -124.5
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exp2 -125.5
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exp2 127
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exp2 127
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exp2 -149
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exp2 -149
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exp2 1000.25
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exp2 1000.25
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exp2 -1019.5
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exp2 -1020.5
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exp2 -1021.5
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exp2 1023
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exp2 1023
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exp2 -1074
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exp2 -1074
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exp2 16383
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exp2 16383
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@ -106691,6 +106691,106 @@ exp2 100.5
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= exp2 tonearest ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
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= exp2 tonearest ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
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= exp2 towardzero ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
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= exp2 towardzero ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p+100L : inexact-ok
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= exp2 upward ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ebp+100L : inexact-ok
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= exp2 upward ldbl-128ibm 0x6.48p+4L : 0x1.6a09e667f3bcc908b2fb1366ebp+100L : inexact-ok
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exp2 -116.5
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= exp2 downward flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
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= exp2 tonearest flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
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= exp2 towardzero flt-32 -0x7.48p+4f : 0xb.504f3p-120f : inexact-ok
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= exp2 upward flt-32 -0x7.48p+4f : 0xb.504f4p-120f : inexact-ok
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= exp2 downward dbl-64 -0x7.48p+4 : 0xb.504f333f9de6p-120 : inexact-ok
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= exp2 tonearest dbl-64 -0x7.48p+4 : 0xb.504f333f9de68p-120 : inexact-ok
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= exp2 towardzero dbl-64 -0x7.48p+4 : 0xb.504f333f9de6p-120 : inexact-ok
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= exp2 upward dbl-64 -0x7.48p+4 : 0xb.504f333f9de68p-120 : inexact-ok
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= exp2 downward ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 tonearest ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 towardzero ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 upward ldbl-96-intel -0x7.48p+4L : 0xb.504f333f9de6485p-120L : inexact-ok
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= exp2 downward ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 tonearest ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 towardzero ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6484p-120L : inexact-ok
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= exp2 upward ldbl-96-m68k -0x7.48p+4L : 0xb.504f333f9de6485p-120L : inexact-ok
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= exp2 downward ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
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= exp2 tonearest ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
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= exp2 towardzero ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754a8p-120L : inexact-ok
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= exp2 upward ldbl-128 -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754bp-120L : inexact-ok
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= exp2 downward ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
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= exp2 tonearest ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
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= exp2 towardzero ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3754p-120L : inexact-ok
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= exp2 upward ldbl-128ibm -0x7.48p+4L : 0xb.504f333f9de6484597d89b3758p-120L : inexact-ok
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exp2 -123.5
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= exp2 downward flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
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= exp2 tonearest flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
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= exp2 towardzero flt-32 -0x7.b8p+4f : 0x1.6a09e6p-124f : inexact-ok
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= exp2 upward flt-32 -0x7.b8p+4f : 0x1.6a09e8p-124f : inexact-ok
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= exp2 downward dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bccp-124 : inexact-ok
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= exp2 tonearest dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bcdp-124 : inexact-ok
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= exp2 towardzero dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bccp-124 : inexact-ok
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= exp2 upward dbl-64 -0x7.b8p+4 : 0x1.6a09e667f3bcdp-124 : inexact-ok
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= exp2 downward ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 tonearest ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 towardzero ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 upward ldbl-96-intel -0x7.b8p+4L : 0x1.6a09e667f3bcc90ap-124L : inexact-ok
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= exp2 downward ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 tonearest ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 towardzero ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc908p-124L : inexact-ok
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= exp2 upward ldbl-96-m68k -0x7.b8p+4L : 0x1.6a09e667f3bcc90ap-124L : inexact-ok
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= exp2 downward ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
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= exp2 tonearest ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
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= exp2 towardzero ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea95p-124L : inexact-ok
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= exp2 upward ldbl-128 -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea96p-124L : inexact-ok
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= exp2 downward ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
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= exp2 tonearest ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
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= exp2 towardzero ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ea8p-124L : inexact-ok
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= exp2 upward ldbl-128ibm -0x7.b8p+4L : 0x1.6a09e667f3bcc908b2fb1366ebp-124L : inexact-ok
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exp2 -124.5
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= exp2 downward flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
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= exp2 tonearest flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
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= exp2 towardzero flt-32 -0x7.c8p+4f : 0xb.504f3p-128f : inexact-ok
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= exp2 upward flt-32 -0x7.c8p+4f : 0xb.504f4p-128f : inexact-ok
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= exp2 downward dbl-64 -0x7.c8p+4 : 0xb.504f333f9de6p-128 : inexact-ok
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= exp2 tonearest dbl-64 -0x7.c8p+4 : 0xb.504f333f9de68p-128 : inexact-ok
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= exp2 towardzero dbl-64 -0x7.c8p+4 : 0xb.504f333f9de6p-128 : inexact-ok
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= exp2 upward dbl-64 -0x7.c8p+4 : 0xb.504f333f9de68p-128 : inexact-ok
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= exp2 downward ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 tonearest ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 towardzero ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 upward ldbl-96-intel -0x7.c8p+4L : 0xb.504f333f9de6485p-128L : inexact-ok
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= exp2 downward ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 tonearest ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 towardzero ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6484p-128L : inexact-ok
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= exp2 upward ldbl-96-m68k -0x7.c8p+4L : 0xb.504f333f9de6485p-128L : inexact-ok
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= exp2 downward ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
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= exp2 tonearest ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
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= exp2 towardzero ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754a8p-128L : inexact-ok
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= exp2 upward ldbl-128 -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754bp-128L : inexact-ok
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= exp2 downward ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
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= exp2 tonearest ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
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= exp2 towardzero ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3754p-128L : inexact-ok
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= exp2 upward ldbl-128ibm -0x7.c8p+4L : 0xb.504f333f9de6484597d89b3758p-128L : inexact-ok
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exp2 -125.5
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= exp2 downward flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
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= exp2 tonearest flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
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= exp2 towardzero flt-32 -0x7.d8p+4f : 0x5.a82798p-128f : inexact-ok
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= exp2 upward flt-32 -0x7.d8p+4f : 0x5.a827ap-128f : inexact-ok
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= exp2 downward dbl-64 -0x7.d8p+4 : 0x5.a827999fcef3p-128 : inexact-ok
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= exp2 tonearest dbl-64 -0x7.d8p+4 : 0x5.a827999fcef34p-128 : inexact-ok
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= exp2 towardzero dbl-64 -0x7.d8p+4 : 0x5.a827999fcef3p-128 : inexact-ok
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= exp2 upward dbl-64 -0x7.d8p+4 : 0x5.a827999fcef34p-128 : inexact-ok
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= exp2 downward ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 tonearest ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 towardzero ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 upward ldbl-96-intel -0x7.d8p+4L : 0x5.a827999fcef32428p-128L : inexact-ok
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= exp2 downward ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 tonearest ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 towardzero ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef3242p-128L : inexact-ok
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= exp2 upward ldbl-96-m68k -0x7.d8p+4L : 0x5.a827999fcef32428p-128L : inexact-ok
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= exp2 downward ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
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= exp2 tonearest ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
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= exp2 towardzero ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa54p-128L : inexact-ok
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= exp2 upward ldbl-128 -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baa58p-128L : inexact-ok
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= exp2 downward ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
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= exp2 tonearest ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
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= exp2 towardzero ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9baap-128L : inexact-ok
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= exp2 upward ldbl-128ibm -0x7.d8p+4L : 0x5.a827999fcef32422cbec4d9bacp-128L : inexact-ok
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exp2 127
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exp2 127
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= exp2 downward flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
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= exp2 downward flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
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= exp2 tonearest flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
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= exp2 tonearest flt-32 0x7.fp+4f : 0x8p+124f : inexact-ok
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@ -106766,6 +106866,81 @@ exp2 1000.25
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= exp2 tonearest ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305c8p+1000L : inexact-ok
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= 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 towardzero ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305c8p+1000L : inexact-ok
|
||||||
= exp2 upward ldbl-128ibm 0x3.e84p+8L : 0x1.306fe0a31b7152de8d5a46305dp+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 1023
|
||||||
= exp2 downward flt-32 0x3.ffp+8f : 0xf.fffffp+124f : inexact-ok overflow errno-erange-ok
|
= 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
|
= exp2 tonearest flt-32 0x3.ffp+8f : plus_infty : inexact-ok overflow errno-erange
|
||||||
|
|||||||
@ -96,7 +96,9 @@ __ieee754_exp2 (double x)
|
|||||||
/* 3. Compute ex2 = 2^(t/512+e+ex). */
|
/* 3. Compute ex2 = 2^(t/512+e+ex). */
|
||||||
ex2_u.d = exp2_accuratetable[tval & 511];
|
ex2_u.d = exp2_accuratetable[tval & 511];
|
||||||
tval >>= 9;
|
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;
|
ex2_u.ieee.exponent += tval >> unsafe;
|
||||||
scale_u.d = 1.0;
|
scale_u.d = 1.0;
|
||||||
scale_u.ieee.exponent += tval - (tval >> unsafe);
|
scale_u.ieee.exponent += tval - (tval >> unsafe);
|
||||||
|
|||||||
@ -89,7 +89,9 @@ __ieee754_exp2f (float x)
|
|||||||
/* 3. Compute ex2 = 2^(t/255+e+ex). */
|
/* 3. Compute ex2 = 2^(t/255+e+ex). */
|
||||||
ex2_u.f = __exp2f_atable[tval & 255];
|
ex2_u.f = __exp2f_atable[tval & 255];
|
||||||
tval >>= 8;
|
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;
|
ex2_u.ieee.exponent += tval >> unsafe;
|
||||||
scale_u.f = 1.0;
|
scale_u.f = 1.0;
|
||||||
scale_u.ieee.exponent += tval - (tval >> unsafe);
|
scale_u.ieee.exponent += tval - (tval >> unsafe);
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user