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-rw-r--r--ChangeLog14
-rw-r--r--NEWS2
-rw-r--r--math/libm-test.inc39
-rw-r--r--math/s_csqrt.c26
-rw-r--r--math/s_csqrtf.c26
-rw-r--r--math/s_csqrtl.c26
-rw-r--r--sysdeps/i386/fpu/libm-test-ulps28
-rw-r--r--sysdeps/x86_64/fpu/libm-test-ulps30
8 files changed, 166 insertions, 25 deletions
diff --git a/ChangeLog b/ChangeLog
index 0a4d181d2c..599399240f 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,17 @@
+2012-07-05 Joseph Myers <joseph@codesourcery.com>
+
+ [BZ #14157]
+ [BZ #14331]
+ * math/s_csqrt.c (__csqrt): Avoid multiplying by 0.5 where this
+ could result in spurious underflow. Scale down values above
+ DBL_MAX / 4.0 instead of DBL_MAX / 2.0.
+ * math/s_csqrtf.c (__csqrtf): Likewise.
+ * math/s_csqrtl.c (__csqrtl): Likewise.
+ * math/libm-test.inc (csqrt_test): Add more tests. Do not allow
+ spurious underflow.
+ * sysdeps/i386/fpu/libm-test-ulps: Update.
+ * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
2012-07-04 Andreas Schwab <schwab@linux-m68k.org>
* catgets/Makefile ($(objpfx)de.msg): Use xopen-msg.awk instead of
diff --git a/NEWS b/NEWS
index e49e4ea829..06df26fef6 100644
--- a/NEWS
+++ b/NEWS
@@ -9,7 +9,7 @@ Version 2.17
* The following bugs are resolved with this release:
- 14283, 14328
+ 14157, 14283, 14328, 14331
Version 2.16
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 514ad063b1..6adbb61dbc 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -3213,18 +3213,51 @@ csqrt_test (void)
TEST_c_c (csqrt, 0x1p-149L, 0x1p-149L, 4.112805464342778798097003462770175200803e-23L, 1.703579802732953750368659735601389709551e-23L);
TEST_c_c (csqrt, 0x1p-147L, 0x1p-147L, 8.225610928685557596194006925540350401606e-23L, 3.407159605465907500737319471202779419102e-23L);
+ TEST_c_c (csqrt, plus_zero, 0x1p-149L, 2.646977960169688559588507814623881131411e-23L, 2.646977960169688559588507814623881131411e-23L);
+ TEST_c_c (csqrt, 0x1p-50L, 0x1p-149L, 2.980232238769531250000000000000000000000e-8L, 2.350988701644575015937473074444491355637e-38L);
+#ifdef TEST_FLOAT
+ TEST_c_c (csqrt, 0x1p+127L, 0x1p-149L, 1.304381782533278221234957180625250836888e19L, plus_zero, UNDERFLOW_EXCEPTION);
+#endif
+ TEST_c_c (csqrt, 0x1p-149L, 0x1p+127L, 9.223372036854775808000000000000000000000e18L, 9.223372036854775808000000000000000000000e18L);
+ TEST_c_c (csqrt, 0x1.000002p-126L, 0x1.000002p-126L, 1.191195773697904627170323731331667740087e-19L, 4.934094449071842328766868579214125217132e-20L);
+ TEST_c_c (csqrt, -0x1.000002p-126L, -0x1.000002p-126L, 4.934094449071842328766868579214125217132e-20L, -1.191195773697904627170323731331667740087e-19L);
+
#ifndef TEST_FLOAT
TEST_c_c (csqrt, 0x1.fffffffffffffp+1023L, 0x1.fffffffffffffp+1023L, 1.473094556905565378990473658199034571917e+154L, 6.101757441282702188537080005372547713595e+153L);
TEST_c_c (csqrt, 0x1.fffffffffffffp+1023L, 0x1p+1023L, 1.379778091031440685006200821918878702861e+154L, 3.257214233483129514781233066898042490248e+153L);
- /* Bug 14157: spurious exception may occur. */
- TEST_c_c (csqrt, 0x1p-1074L, 0x1p-1074L, 2.442109726130830256743814843868934877597e-162L, 1.011554969366634726113090867589031782487e-162L, UNDERFLOW_EXCEPTION_OK);
- TEST_c_c (csqrt, 0x1p-1073L, 0x1p-1073L, 3.453664695497464982856905711457966660085e-162L, 1.430554756764195530630723976279903095110e-162L, UNDERFLOW_EXCEPTION_OK);
+ TEST_c_c (csqrt, 0x1p-1074L, 0x1p-1074L, 2.442109726130830256743814843868934877597e-162L, 1.011554969366634726113090867589031782487e-162L);
+ TEST_c_c (csqrt, 0x1p-1073L, 0x1p-1073L, 3.453664695497464982856905711457966660085e-162L, 1.430554756764195530630723976279903095110e-162L);
+
+ TEST_c_c (csqrt, plus_zero, 0x1p-1074L, 1.571727784702628688909515672805082228285e-162L, 1.571727784702628688909515672805082228285e-162L);
+ TEST_c_c (csqrt, 0x1p-500L, 0x1p-1074L, 5.527147875260444560247265192192255725514e-76L, 4.469444793151709302716387622440056066334e-249L);
+#if defined TEST_DOUBLE || (defined TEST_LDOUBLE && LDBL_MAX_EXP == 1024)
+ TEST_c_c (csqrt, 0x1p+1023L, 0x1p-1074L, 9.480751908109176726832526455652159260085e153L, plus_zero, UNDERFLOW_EXCEPTION);
+#endif
+ TEST_c_c (csqrt, 0x1p-1074L, 0x1p+1023L, 6.703903964971298549787012499102923063740e153L, 6.703903964971298549787012499102923063740e153L);
+ TEST_c_c (csqrt, 0x1.0000000000001p-1022L, 0x1.0000000000001p-1022L, 1.638872094839911521020410942677082920935e-154L, 6.788430486774966350907249113759995429568e-155L);
+ TEST_c_c (csqrt, -0x1.0000000000001p-1022L, -0x1.0000000000001p-1022L, 6.788430486774966350907249113759995429568e-155L, -1.638872094839911521020410942677082920935e-154L);
#endif
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
TEST_c_c (csqrt, 0x1.fp+16383L, 0x1.fp+16383L, 1.179514222452201722651836720466795901016e+2466L, 4.885707879516577666702435054303191575148e+2465L);
TEST_c_c (csqrt, 0x1.fp+16383L, 0x1p+16383L, 1.106698967236475180613254276996359485630e+2466L, 2.687568007603946993388538156299100955642e+2465L);
TEST_c_c (csqrt, 0x1p-16440L, 0x1p-16441L, 3.514690655930285351254618340783294558136e-2475L, 8.297059146828716918029689466551384219370e-2476L);
+
+ TEST_c_c (csqrt, plus_zero, 0x1p-16445L, 4.269191686890197837775136325621239761720e-2476L, 4.269191686890197837775136325621239761720e-2476L);
+ TEST_c_c (csqrt, 0x1p-5000L, 0x1p-16445L, 2.660791472672778409283210520357607795518e-753L, 6.849840675828785164910701384823702064234e-4199L);
+ TEST_c_c (csqrt, 0x1p+16383L, 0x1p-16445L, 7.712754032630730034273323365543179095045e2465L, plus_zero, UNDERFLOW_EXCEPTION);
+ TEST_c_c (csqrt, 0x1p-16445L, 0x1p+16383L, 5.453740678097079647314921223668914312241e2465L, 5.453740678097079647314921223668914312241e2465L);
+ TEST_c_c (csqrt, 0x1.0000000000000002p-16382L, 0x1.0000000000000002p-16382L, 2.014551439675644900131815801350165472778e-2466L, 8.344545284118961664300307045791497724440e-2467L);
+ TEST_c_c (csqrt, -0x1.0000000000000002p-16382L, -0x1.0000000000000002p-16382L, 8.344545284118961664300307045791497724440e-2467L, -2.014551439675644900131815801350165472778e-2466L);
+
+# if LDBL_MANT_DIG >= 113
+ TEST_c_c (csqrt, plus_zero, 0x1p-16494L, 1.799329752913293143453817328207572571442e-2483L, 1.799329752913293143453817328207572571442e-2483L);
+ TEST_c_c (csqrt, 0x1p-5000L, 0x1p-16494L, 2.660791472672778409283210520357607795518e-753L, 1.216776133331049643422030716668249905907e-4213L);
+ TEST_c_c (csqrt, 0x1p+16383L, 0x1p-16494L, 7.712754032630730034273323365543179095045e2465L, plus_zero, UNDERFLOW_EXCEPTION);
+ TEST_c_c (csqrt, 0x1p-16494L, 0x1p+16383L, 5.453740678097079647314921223668914312241e2465L, 5.453740678097079647314921223668914312241e2465L);
+ TEST_c_c (csqrt, 0x1.0000000000000000000000000001p-16382L, 0x1.0000000000000000000000000001p-16382L, 2.014551439675644900022606748976158925145e-2466L, 8.344545284118961663847948339519226074126e-2467L);
+ TEST_c_c (csqrt, -0x1.0000000000000000000000000001p-16382L, -0x1.0000000000000000000000000001p-16382L, 8.344545284118961663847948339519226074126e-2467L, -2.014551439675644900022606748976158925145e-2466L);
+# endif
#endif
END (csqrt, complex);
diff --git a/math/s_csqrt.c b/math/s_csqrt.c
index 002ea5fdc2..f4d0f998e5 100644
--- a/math/s_csqrt.c
+++ b/math/s_csqrt.c
@@ -75,7 +75,11 @@ __csqrt (__complex__ double x)
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
- double r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
+ double r;
+ if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
+ r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
+ else
+ r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
__real__ res = r;
__imag__ res = __copysign (r, __imag__ x);
@@ -85,13 +89,21 @@ __csqrt (__complex__ double x)
double d, r, s;
int scale = 0;
- if (fabs (__real__ x) > DBL_MAX / 2.0
- || fabs (__imag__ x) > DBL_MAX / 2.0)
+ if (fabs (__real__ x) > DBL_MAX / 4.0)
{
scale = 1;
__real__ x = __scalbn (__real__ x, -2 * scale);
__imag__ x = __scalbn (__imag__ x, -2 * scale);
}
+ else if (fabs (__imag__ x) > DBL_MAX / 4.0)
+ {
+ scale = 1;
+ if (fabs (__real__ x) >= 4.0 * DBL_MIN)
+ __real__ x = __scalbn (__real__ x, -2 * scale);
+ else
+ __real__ x = 0.0;
+ __imag__ x = __scalbn (__imag__ x, -2 * scale);
+ }
else if (fabs (__real__ x) < DBL_MIN
&& fabs (__imag__ x) < DBL_MIN)
{
@@ -105,13 +117,13 @@ __csqrt (__complex__ double x)
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
- r = __ieee754_sqrt (0.5 * d + 0.5 * __real__ x);
- s = (0.5 * __imag__ x) / r;
+ r = __ieee754_sqrt (0.5 * (d + __real__ x));
+ s = 0.5 * (__imag__ x / r);
}
else
{
- s = __ieee754_sqrt (0.5 * d - 0.5 * __real__ x);
- r = fabs ((0.5 * __imag__ x) / s);
+ s = __ieee754_sqrt (0.5 * (d - __real__ x));
+ r = fabs (0.5 * (__imag__ x / s));
}
if (scale)
diff --git a/math/s_csqrtf.c b/math/s_csqrtf.c
index 6539ba2249..5a274fd87b 100644
--- a/math/s_csqrtf.c
+++ b/math/s_csqrtf.c
@@ -75,7 +75,11 @@ __csqrtf (__complex__ float x)
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
- float r = __ieee754_sqrtf (0.5 * fabsf (__imag__ x));
+ float r;
+ if (fabsf (__imag__ x) >= 2.0f * FLT_MIN)
+ r = __ieee754_sqrtf (0.5f * fabsf (__imag__ x));
+ else
+ r = 0.5f * __ieee754_sqrtf (2.0f * fabsf (__imag__ x));
__real__ res = r;
__imag__ res = __copysignf (r, __imag__ x);
@@ -85,13 +89,21 @@ __csqrtf (__complex__ float x)
float d, r, s;
int scale = 0;
- if (fabsf (__real__ x) > FLT_MAX / 2.0f
- || fabsf (__imag__ x) > FLT_MAX / 2.0f)
+ if (fabsf (__real__ x) > FLT_MAX / 4.0f)
{
scale = 1;
__real__ x = __scalbnf (__real__ x, -2 * scale);
__imag__ x = __scalbnf (__imag__ x, -2 * scale);
}
+ else if (fabsf (__imag__ x) > FLT_MAX / 4.0f)
+ {
+ scale = 1;
+ if (fabsf (__real__ x) >= 4.0f * FLT_MIN)
+ __real__ x = __scalbnf (__real__ x, -2 * scale);
+ else
+ __real__ x = 0.0f;
+ __imag__ x = __scalbnf (__imag__ x, -2 * scale);
+ }
else if (fabsf (__real__ x) < FLT_MIN
&& fabsf (__imag__ x) < FLT_MIN)
{
@@ -105,13 +117,13 @@ __csqrtf (__complex__ float x)
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
- r = __ieee754_sqrtf (0.5f * d + 0.5f * __real__ x);
- s = (0.5f * __imag__ x) / r;
+ r = __ieee754_sqrtf (0.5f * (d + __real__ x));
+ s = 0.5f * (__imag__ x / r);
}
else
{
- s = __ieee754_sqrtf (0.5f * d - 0.5f * __real__ x);
- r = fabsf ((0.5f * __imag__ x) / s);
+ s = __ieee754_sqrtf (0.5f * (d - __real__ x));
+ r = fabsf (0.5f * (__imag__ x / s));
}
if (scale)
diff --git a/math/s_csqrtl.c b/math/s_csqrtl.c
index 64332f67b2..579d9768c2 100644
--- a/math/s_csqrtl.c
+++ b/math/s_csqrtl.c
@@ -75,7 +75,11 @@ __csqrtl (__complex__ long double x)
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
- long double r = __ieee754_sqrtl (0.5 * fabsl (__imag__ x));
+ long double r;
+ if (fabsl (__imag__ x) >= 2.0L * LDBL_MIN)
+ r = __ieee754_sqrtl (0.5L * fabsl (__imag__ x));
+ else
+ r = 0.5L * __ieee754_sqrtl (2.0L * fabsl (__imag__ x));
__real__ res = r;
__imag__ res = __copysignl (r, __imag__ x);
@@ -85,13 +89,21 @@ __csqrtl (__complex__ long double x)
long double d, r, s;
int scale = 0;
- if (fabsl (__real__ x) > LDBL_MAX / 2.0L
- || fabsl (__imag__ x) > LDBL_MAX / 2.0L)
+ if (fabsl (__real__ x) > LDBL_MAX / 4.0L)
{
scale = 1;
__real__ x = __scalbnl (__real__ x, -2 * scale);
__imag__ x = __scalbnl (__imag__ x, -2 * scale);
}
+ else if (fabsl (__imag__ x) > LDBL_MAX / 4.0L)
+ {
+ scale = 1;
+ if (fabsl (__real__ x) >= 4.0L * LDBL_MIN)
+ __real__ x = __scalbnl (__real__ x, -2 * scale);
+ else
+ __real__ x = 0.0L;
+ __imag__ x = __scalbnl (__imag__ x, -2 * scale);
+ }
else if (fabsl (__real__ x) < LDBL_MIN
&& fabsl (__imag__ x) < LDBL_MIN)
{
@@ -105,13 +117,13 @@ __csqrtl (__complex__ long double x)
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
- r = __ieee754_sqrtl (0.5L * d + 0.5L * __real__ x);
- s = (0.5L * __imag__ x) / r;
+ r = __ieee754_sqrtl (0.5L * (d + __real__ x));
+ s = 0.5L * (__imag__ x / r);
}
else
{
- s = __ieee754_sqrtl (0.5L * d - 0.5L * __real__ x);
- r = fabsl ((0.5L * __imag__ x) / s);
+ s = __ieee754_sqrtl (0.5L * (d - __real__ x));
+ r = fabsl (0.5L * (__imag__ x / s));
}
if (scale)
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 6f41f02bd2..97249194c7 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1374,6 +1374,30 @@ float: 1
ifloat: 1
# csqrt
+Test "Real part of: csqrt (-0x1.0000000000000002p-16382 - 0x1.0000000000000002p-16382 i) == 8.344545284118961664300307045791497724440e-2467 - 2.014551439675644900131815801350165472778e-2466 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (-0x1.0000000000000002p-16382 - 0x1.0000000000000002p-16382 i) == 8.344545284118961664300307045791497724440e-2467 - 2.014551439675644900131815801350165472778e-2466 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csqrt (-0x1.0000000000001p-1022 - 0x1.0000000000001p-1022 i) == 6.788430486774966350907249113759995429568e-155 - 1.638872094839911521020410942677082920935e-154 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csqrt (-0x1.000002p-126 - 0x1.000002p-126 i) == 4.934094449071842328766868579214125217132e-20 - 1.191195773697904627170323731331667740087e-19 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csqrt (0x1.0000000000000002p-16382 + 0x1.0000000000000002p-16382 i) == 2.014551439675644900131815801350165472778e-2466 + 8.344545284118961664300307045791497724440e-2467 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.0000000000000002p-16382 + 0x1.0000000000000002p-16382 i) == 2.014551439675644900131815801350165472778e-2466 + 8.344545284118961664300307045791497724440e-2467 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.0000000000001p-1022 + 0x1.0000000000001p-1022 i) == 1.638872094839911521020410942677082920935e-154 + 6.788430486774966350907249113759995429568e-155 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.000002p-126 + 0x1.000002p-126 i) == 1.191195773697904627170323731331667740087e-19 + 4.934094449071842328766868579214125217132e-20 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: csqrt (0x1.fffffffffffffp+1023 + 0x1p+1023 i) == 1.379778091031440685006200821918878702861e+154 + 3.257214233483129514781233066898042490248e+153 i":
ildouble: 1
ldouble: 1
@@ -3032,6 +3056,10 @@ ifloat: 1
ildouble: 2
ldouble: 2
+Function: Real part of "csqrt":
+ildouble: 1
+ldouble: 1
+
Function: Imaginary part of "csqrt":
ildouble: 1
ldouble: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 765c7a0cee..b64e52d7d8 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1222,12 +1222,40 @@ float: 1
ifloat: 1
# csqrt
+Test "Real part of: csqrt (-0x1.0000000000000002p-16382 - 0x1.0000000000000002p-16382 i) == 8.344545284118961664300307045791497724440e-2467 - 2.014551439675644900131815801350165472778e-2466 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (-0x1.0000000000000002p-16382 - 0x1.0000000000000002p-16382 i) == 8.344545284118961664300307045791497724440e-2467 - 2.014551439675644900131815801350165472778e-2466 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csqrt (-0x1.0000000000001p-1022 - 0x1.0000000000001p-1022 i) == 6.788430486774966350907249113759995429568e-155 - 1.638872094839911521020410942677082920935e-154 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csqrt (-0x1.000002p-126 - 0x1.000002p-126 i) == 4.934094449071842328766868579214125217132e-20 - 1.191195773697904627170323731331667740087e-19 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
Test "Real part of: csqrt (-2 + 3 i) == 0.89597747612983812471573375529004348 + 1.6741492280355400404480393008490519 i":
float: 1
ifloat: 1
Test "Real part of: csqrt (-2 - 3 i) == 0.89597747612983812471573375529004348 - 1.6741492280355400404480393008490519 i":
float: 1
ifloat: 1
+Test "Real part of: csqrt (0x1.0000000000000002p-16382 + 0x1.0000000000000002p-16382 i) == 2.014551439675644900131815801350165472778e-2466 + 8.344545284118961664300307045791497724440e-2467 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.0000000000000002p-16382 + 0x1.0000000000000002p-16382 i) == 2.014551439675644900131815801350165472778e-2466 + 8.344545284118961664300307045791497724440e-2467 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.0000000000001p-1022 + 0x1.0000000000001p-1022 i) == 1.638872094839911521020410942677082920935e-154 + 6.788430486774966350907249113759995429568e-155 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csqrt (0x1.000002p-126 + 0x1.000002p-126 i) == 1.191195773697904627170323731331667740087e-19 + 4.934094449071842328766868579214125217132e-20 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: csqrt (0x1.fffffep+127 + 1.0 i) == 1.844674352395372953599975585936590505260e+19 + 2.710505511993121390769065968615872097053e-20 i":
float: 1
ifloat: 1
@@ -2818,6 +2846,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
+ildouble: 1
+ldouble: 1
Function: Imaginary part of "csqrt":
double: 1
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-15 19:33:33 +0000