Improve erfc accuracy.

8 files changed, 60 insertions, 7 deletions

diff --git a/ChangeLog b/ChangeLog
index a2e0d6c137..297d1b5c8e 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,17 @@
+2012-03-01  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #2541]
+	[BZ #4108]
+	* sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Mask out one more bit
+	before squaring exponent.
+	* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfcl): Mask out whole
+	bottom long double and 27 bits of top long double before squaring
+	exponent.
+	* math/libm-test.inc (erfc_test): Add more tests.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/powerpc/fpu/libm-test-ulps: Likewise.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2012-03-01  Kai Tietz  <ktietz@redhat.com>
 
 	* soft-fp/soft-fp.h (_FP_STRUCT_LAYOUT): New macro.
diff --git a/NEWS b/NEWS
index 8ac5c7b949..6c0bc4acab 100644
--- a/NEWS
+++ b/NEWS
@@ -9,11 +9,11 @@ Version 2.16
 
 * The following bugs are resolved with this release:
 
-  174, 350, 411, 2547, 2548, 3335, 3992, 4026, 4596, 4822, 5077, 5461, 5805,
-  5993, 6884, 6907, 9739, 9902, 10110, 10140, 10210, 11174, 11322, 11365,
-  11494, 12047, 13058, 13525, 13526, 13527, 13528, 13529, 13530, 13531,
-  13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559, 13583, 13618,
-  13637, 13695, 13704, 13706, 13738, 13786
+  174, 350, 411, 2541, 2547, 2548, 3335, 3992, 4026, 4108, 4596, 4822, 5077,
+  5461, 5805, 5993, 6884, 6907, 9739, 9902, 10110, 10140, 10210, 11174,
+  11322, 11365, 11494, 12047, 13058, 13525, 13526, 13527, 13528, 13529,
+  13530, 13531, 13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559,
+  13583, 13618, 13637, 13695, 13704, 13706, 13738, 13786
 
 * ISO C11 support:
 
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 3510b61303..9f7d4896d8 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -2478,12 +2478,18 @@ erfc_test (void)
   TEST_f_f (erfc, 0.75L, 0.288844366346484868401062165408589223L);
   TEST_f_f (erfc, 1.25L, 0.0770998717435417698634765188027188596L);
   TEST_f_f (erfc, 2.0L, 0.00467773498104726583793074363274707139L);
+  TEST_f_f (erfc, 0x1.f7303cp+1L, 2.705500297238986897105236321218861842255e-8L);
   TEST_f_f (erfc, 4.125L, 0.542340079956506600531223408575531062e-8L);
+  TEST_f_f (erfc, 0x1.ffa002p+2L, 1.233585992097580296336099501489175967033e-29L);
+  TEST_f_f (erfc, 0x1.ffffc8p+2L, 1.122671365033056305522366683719541099329e-29L);
 #ifdef TEST_LDOUBLE
   /* The result can only be represented in long double.  */
 # if LDBL_MIN_10_EXP < -319
   TEST_f_f (erfc, 27.0L, 0.523704892378925568501606768284954709e-318L);
 # endif
+# if LDBL_MANT_DIG >= 106
+  TEST_f_f (erfc, 0x1.ffff56789abcdef0123456789a8p+2L, 1.123161416304655390092138725253789378459e-29L);
+# endif
 #endif
 
   END (erfc);
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 18097a51c6..56293973dd 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -422,6 +422,17 @@ idouble: 1
 Test "erfc (0.75) == 0.288844366346484868401062165408589223":
 float: 1
 ifloat: 1
+Test "erfc (0x1.f7303cp+1) == 2.705500297238986897105236321218861842255e-8":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "erfc (0x1.ffa002p+2) == 1.233585992097580296336099501489175967033e-29":
+ildouble: 1
+ldouble: 1
+Test "erfc (0x1.ffffc8p+2) == 1.122671365033056305522366683719541099329e-29":
+double: 1
+idouble: 1
 Test "erfc (1.25) == 0.0770998717435417698634765188027188596":
 ildouble: 1
 ldouble: 1
diff --git a/sysdeps/ieee754/flt-32/s_erff.c b/sysdeps/ieee754/flt-32/s_erff.c
index 576618309b..8a0610d5c5 100644
--- a/sysdeps/ieee754/flt-32/s_erff.c
+++ b/sysdeps/ieee754/flt-32/s_erff.c
@@ -200,7 +200,7 @@ float __erfcf(float x)
 				sb5+s*(sb6+s*sb7))))));
 	    }
 	    GET_FLOAT_WORD(ix,x);
-	    SET_FLOAT_WORD(z,ix&0xfffff000);
+	    SET_FLOAT_WORD(z,ix&0xffffe000);
 	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
 			__ieee754_expf((z-x)*(z+x)+R/S);
 	    if(hx>0) return r/x; else return two-r/x;
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
index 85cdbe0ff8..8868f7e1cf 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c
@@ -920,7 +920,8 @@ __erfcl (long double x)
 	}
       u.value = x;
       u.parts32.w3 = 0;
-      u.parts32.w2 &= 0xffffe000;
+      u.parts32.w2 = 0;
+      u.parts32.w1 &= 0xf8000000;
       z = u.value;
       r = __ieee754_expl (-z * z - 0.5625) *
 	__ieee754_expl ((z - x) * (z + x) + p);
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index 589bae1227..00e994ce7a 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -422,6 +422,15 @@ idouble: 1
 Test "erfc (0.75) == 0.288844366346484868401062165408589223":
 float: 1
 ifloat: 1
+Test "erfc (0x1.f7303cp+1) == 2.705500297238986897105236321218861842255e-8":
+double: 1
+idouble: 1
+Test "erfc (0x1.ffa002p+2) == 1.233585992097580296336099501489175967033e-29":
+float: 1
+ifloat: 1
+Test "erfc (0x1.ffff56789abcdef0123456789a8p+2) == 1.123161416304655390092138725253789378459e-29":
+ildouble: 1
+ldouble: 1
 Test "erfc (2.0) == 0.00467773498104726583793074363274707139":
 double: 1
 idouble: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index eb67e91b97..dac90babad 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -467,6 +467,16 @@ double: 1
 idouble: 1
 
 # erfc
+Test "erfc (0x1.f7303cp+1) == 2.705500297238986897105236321218861842255e-8":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "erfc (0x1.ffa002p+2) == 1.233585992097580296336099501489175967033e-29":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "erfc (1.25) == 0.0770998717435417698634765188027188596":
 ildouble: 1
 ldouble: 1
@@ -1251,7 +1261,9 @@ idouble: 1
 
 Function: "erfc":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1