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Fix erfcf spurious underflows (bug 18217).
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The flt-32 implementation of erfcf produces spurious underflow
exceptions for some arguments close to 0, because of calculations
squaring the argument and then multiplying by small constants.  This
patch fixes this by adjusting the threshold for arguments for which
the result is so close to 1 that 1 - x will give the right result from
2**-56 to 2**-26.  (If 1 - x * 2/sqrt(pi) were used, the errors would be
on the order of x^3 and a much larger threshold could be used.)

Tested for x86_64 and x86.

	[BZ #18217]
	* sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Use 2**-26 not 2**-56
	as threshold for returning 1 - x.
	* math/auto-libm-test-in: Add more tests of erfc.
	* math/auto-libm-test-out: Regenerated.
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Joseph Myers committed May 15, 2015
1 parent 9a71f1f commit fbc68f0
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8 changes: 8 additions & 0 deletions ChangeLog
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@@ -1,3 +1,11 @@
2015-05-15 Joseph Myers <joseph@codesourcery.com>

[BZ #18217]
* sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Use 2**-26 not 2**-56
as threshold for returning 1 - x.
* math/auto-libm-test-in: Add more tests of erfc.
* math/auto-libm-test-out: Regenerated.

2015-05-14 Joseph Myers <joseph@codesourcery.com>

[BZ #18196]
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4 changes: 2 additions & 2 deletions NEWS
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Expand Up @@ -16,8 +16,8 @@ Version 2.22
17964, 17965, 17967, 17969, 17978, 17987, 17991, 17996, 17998, 17999,
18007, 18019, 18020, 18029, 18030, 18032, 18036, 18038, 18039, 18042,
18043, 18046, 18047, 18068, 18080, 18093, 18100, 18104, 18110, 18111,
18125, 18128, 18138, 18185, 18196, 18197, 18206, 18210, 18211, 18247,
18287, 18319, 18333, 18346, 18397, 18409.
18125, 18128, 18138, 18185, 18196, 18197, 18206, 18210, 18211, 18217,
18247, 18287, 18319, 18333, 18346, 18397, 18409.

* Cache information can be queried via sysconf() function on s390 e.g. with
_SC_LEVEL1_ICACHE_SIZE as argument.
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2 changes: 2 additions & 0 deletions math/auto-libm-test-in
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Expand Up @@ -1129,6 +1129,8 @@ erf -0x1.3a0d48p+0

erfc 0.0
erfc -0
erfc 0x1p-55
erfc -0x1p-55
erfc 0.125
erfc 0.75
erfc 1.25
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50 changes: 50 additions & 0 deletions math/auto-libm-test-out
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Expand Up @@ -101555,6 +101555,56 @@ erfc -0
= erfc tonearest ldbl-128ibm -0x0p+0L : 0x1p+0L : inexact-ok
= erfc towardzero ldbl-128ibm -0x0p+0L : 0x1p+0L : inexact-ok
= erfc upward ldbl-128ibm -0x0p+0L : 0x1p+0L : inexact-ok
erfc 0x1p-55
= erfc downward flt-32 0x2p-56f : 0xf.fffffp-4f : inexact-ok
= erfc tonearest flt-32 0x2p-56f : 0x1p+0f : inexact-ok
= erfc towardzero flt-32 0x2p-56f : 0xf.fffffp-4f : inexact-ok
= erfc upward flt-32 0x2p-56f : 0x1p+0f : inexact-ok
= erfc downward dbl-64 0x2p-56 : 0xf.ffffffffffff8p-4 : inexact-ok
= erfc tonearest dbl-64 0x2p-56 : 0x1p+0 : inexact-ok
= erfc towardzero dbl-64 0x2p-56 : 0xf.ffffffffffff8p-4 : inexact-ok
= erfc upward dbl-64 0x2p-56 : 0x1p+0 : inexact-ok
= erfc downward ldbl-96-intel 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc tonearest ldbl-96-intel 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc towardzero ldbl-96-intel 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc upward ldbl-96-intel 0x2p-56L : 0xf.ffffffffffffdbfp-4L : inexact-ok
= erfc downward ldbl-96-m68k 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc tonearest ldbl-96-m68k 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc towardzero ldbl-96-m68k 0x2p-56L : 0xf.ffffffffffffdbep-4L : inexact-ok
= erfc upward ldbl-96-m68k 0x2p-56L : 0xf.ffffffffffffdbfp-4L : inexact-ok
= erfc downward ldbl-128 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac925d8p-4L : inexact-ok
= erfc tonearest ldbl-128 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac925ep-4L : inexact-ok
= erfc towardzero ldbl-128 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac925d8p-4L : inexact-ok
= erfc upward ldbl-128 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac925ep-4L : inexact-ok
= erfc downward ldbl-128ibm 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac924p-4L : inexact-ok
= erfc tonearest ldbl-128ibm 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac924p-4L : inexact-ok
= erfc towardzero ldbl-128ibm 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac924p-4L : inexact-ok
= erfc upward ldbl-128ibm 0x2p-56L : 0xf.ffffffffffffdbe4515f7ac928p-4L : inexact-ok
erfc -0x1p-55
= erfc downward flt-32 -0x2p-56f : 0x1p+0f : inexact-ok
= erfc tonearest flt-32 -0x2p-56f : 0x1p+0f : inexact-ok
= erfc towardzero flt-32 -0x2p-56f : 0x1p+0f : inexact-ok
= erfc upward flt-32 -0x2p-56f : 0x1.000002p+0f : inexact-ok
= erfc downward dbl-64 -0x2p-56 : 0x1p+0 : inexact-ok
= erfc tonearest dbl-64 -0x2p-56 : 0x1p+0 : inexact-ok
= erfc towardzero dbl-64 -0x2p-56 : 0x1p+0 : inexact-ok
= erfc upward dbl-64 -0x2p-56 : 0x1.0000000000001p+0 : inexact-ok
= erfc downward ldbl-96-intel -0x2p-56L : 0x1.000000000000024p+0L : inexact-ok
= erfc tonearest ldbl-96-intel -0x2p-56L : 0x1.0000000000000242p+0L : inexact-ok
= erfc towardzero ldbl-96-intel -0x2p-56L : 0x1.000000000000024p+0L : inexact-ok
= erfc upward ldbl-96-intel -0x2p-56L : 0x1.0000000000000242p+0L : inexact-ok
= erfc downward ldbl-96-m68k -0x2p-56L : 0x1.000000000000024p+0L : inexact-ok
= erfc tonearest ldbl-96-m68k -0x2p-56L : 0x1.0000000000000242p+0L : inexact-ok
= erfc towardzero ldbl-96-m68k -0x2p-56L : 0x1.000000000000024p+0L : inexact-ok
= erfc upward ldbl-96-m68k -0x2p-56L : 0x1.0000000000000242p+0L : inexact-ok
= erfc downward ldbl-128 -0x2p-56L : 0x1.0000000000000241baea08536da2p+0L : inexact-ok
= erfc tonearest ldbl-128 -0x2p-56L : 0x1.0000000000000241baea08536da2p+0L : inexact-ok
= erfc towardzero ldbl-128 -0x2p-56L : 0x1.0000000000000241baea08536da2p+0L : inexact-ok
= erfc upward ldbl-128 -0x2p-56L : 0x1.0000000000000241baea08536da3p+0L : inexact-ok
= erfc downward ldbl-128ibm -0x2p-56L : 0x1.0000000000000241baea08536d8p+0L : inexact-ok
= erfc tonearest ldbl-128ibm -0x2p-56L : 0x1.0000000000000241baea08536d8p+0L : inexact-ok
= erfc towardzero ldbl-128ibm -0x2p-56L : 0x1.0000000000000241baea08536d8p+0L : inexact-ok
= erfc upward ldbl-128ibm -0x2p-56L : 0x1.0000000000000241baea08536ep+0L : inexact-ok
erfc 0.125
= erfc downward flt-32 0x2p-4f : 0xd.c143cp-4f : inexact-ok
= erfc tonearest flt-32 0x2p-4f : 0xd.c143dp-4f : inexact-ok
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2 changes: 1 addition & 1 deletion sysdeps/ieee754/flt-32/s_erff.c
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Expand Up @@ -169,7 +169,7 @@ float __erfcf(float x)
}

if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x23800000) /* |x|<2**-56 */
if(ix < 0x32800000) /* |x|<2**-26 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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