Fix catan, catanh inaccuracy through use of log (bug 15394).

diff --git a/ChangeLog b/ChangeLog
index 2d44b8ed60003fda3974cd129ffde3ff493b4c4b..c3404acd8269c85086a8f5a1d9cc0c183fae1412 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,19 @@
+2013-04-24  Joseph Myers  <joseph@codesourcery.com>
+
+       [BZ #15394]
+       * math/s_catan.c (__catan): Calculate imaginary part of result
+       with log1p not log unless computing log of number close to 0.
+       * math/s_catanf.c (__catanf): Likewise.
+       * math/s_catanl.c (__catanl): Likewise.
+       * math/s_catanh.c (__catanh): Calculate real part of result with
+       log1p not log unless computing log of number close to 0.
+       * math/s_catanhf.c (__catanhf): Likewise.
+       * math/s_catanhl.c (__catanhl): Likewise.
+       * math/libm-test.inc (catan_test): Add more tests.
+       (catanh_test): Likewise.
+       * sysdeps/i386/fpu/libm-test-ulps: Update.
+       * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2013-04-24  Siddhesh Poyarekar  <siddhesh@redhat.com>
 
        * benchtests/Makefile: Mention files in which fast and slow

diff --git a/NEWS b/NEWS
index a1aeb42550b74f42e8e830dcd5808898c437fb15..e5c4f908ef4b3d3507833d0e506b47073c0029ce 100644 (file)
--- a/NEWS
+++ b/NEWS
@@ -14,7 +14,7 @@ Version 2.18
   14888, 14920, 14964, 14981, 14982, 14985, 14994, 14996, 15003, 15006,
   15020, 15023, 15036, 15054, 15055, 15062, 15078, 15160, 15214, 15232,
   15234, 15283, 15285, 15287, 15304, 15305, 15307, 15309, 15327, 15330,
-  15335, 15336, 15337, 15342, 15346, 15361.
+  15335, 15336, 15337, 15342, 15346, 15361, 15394.
 
 * CVE-2013-0242 Buffer overrun in regexp matcher has been fixed (Bugzilla
   #15078).

diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0049fcda38ab3e12e06213c9f24536dd61173821..447b6037ae5c3529d1c4d25dc73ceccc6c69015d 100644 (file)
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -4299,6 +4299,35 @@ catan_test (void)
 
   TEST_c_c (catan, qnan_value, qnan_value, qnan_value, qnan_value);
 
+  TEST_c_c (catan, 0x1p50L, 0.0L, 1.570796326794895731052901991514519103193L, 0.0L);
+  TEST_c_c (catan, 0x1p50L, -0.0L, 1.570796326794895731052901991514519103193L, -0.0L);
+  TEST_c_c (catan, -0x1p50L, 0.0L, -1.570796326794895731052901991514519103193L, 0.0L);
+  TEST_c_c (catan, -0x1p50L, -0.0L, -1.570796326794895731052901991514519103193L, -0.0L);
+  TEST_c_c (catan, 0.0L, 0x1p50L, 1.570796326794896619231321691639751442099L, 8.881784197001252323389053344728897997441e-16L);
+  TEST_c_c (catan, -0.0L, 0x1p50L, -1.570796326794896619231321691639751442099L, 8.881784197001252323389053344728897997441e-16L);
+  TEST_c_c (catan, 0.0L, -0x1p50L, 1.570796326794896619231321691639751442099L, -8.881784197001252323389053344728897997441e-16L);
+  TEST_c_c (catan, -0.0L, -0x1p50L, -1.570796326794896619231321691639751442099L, -8.881784197001252323389053344728897997441e-16L);
+#ifndef TEST_FLOAT
+  TEST_c_c (catan, 0x1p500L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
+  TEST_c_c (catan, 0x1p500L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
+  TEST_c_c (catan, -0x1p500L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
+  TEST_c_c (catan, -0x1p500L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
+  TEST_c_c (catan, 0.0L, 0x1p500L, 1.570796326794896619231321691639751442099L, 3.054936363499604682051979393213617699789e-151L);
+  TEST_c_c (catan, -0.0L, 0x1p500L, -1.570796326794896619231321691639751442099L, 3.054936363499604682051979393213617699789e-151L);
+  TEST_c_c (catan, 0.0L, -0x1p500L, 1.570796326794896619231321691639751442099L, -3.054936363499604682051979393213617699789e-151L);
+  TEST_c_c (catan, -0.0L, -0x1p500L, -1.570796326794896619231321691639751442099L, -3.054936363499604682051979393213617699789e-151L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (catan, 0x1p5000L, 0.0L, 1.570796326794896619231321691639751442099L, 0.0L);
+  TEST_c_c (catan, 0x1p5000L, -0.0L, 1.570796326794896619231321691639751442099L, -0.0L);
+  TEST_c_c (catan, -0x1p5000L, 0.0L, -1.570796326794896619231321691639751442099L, 0.0L);
+  TEST_c_c (catan, -0x1p5000L, -0.0L, -1.570796326794896619231321691639751442099L, -0.0L);
+  TEST_c_c (catan, 0.0L, 0x1p5000L, 1.570796326794896619231321691639751442099L, 7.079811261048172892385615158694057552948e-1506L);
+  TEST_c_c (catan, -0.0L, 0x1p5000L, -1.570796326794896619231321691639751442099L, 7.079811261048172892385615158694057552948e-1506L);
+  TEST_c_c (catan, 0.0L, -0x1p5000L, 1.570796326794896619231321691639751442099L, -7.079811261048172892385615158694057552948e-1506L);
+  TEST_c_c (catan, -0.0L, -0x1p5000L, -1.570796326794896619231321691639751442099L, -7.079811261048172892385615158694057552948e-1506L);
+#endif
+
   TEST_c_c (catan, 0.75L, 1.25L, 1.10714871779409050301706546017853704L, 0.549306144334054845697622618461262852L);
   TEST_c_c (catan, -2, -3, -1.4099210495965755225306193844604208L, -0.22907268296853876629588180294200276L);
 
@@ -4365,6 +4394,35 @@ catanh_test (void)
 
   TEST_c_c (catanh, qnan_value, qnan_value, qnan_value, qnan_value);
 
+  TEST_c_c (catanh, 0x1p50L, 0.0L, 8.881784197001252323389053344728897997441e-16L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0x1p50L, -0.0L, 8.881784197001252323389053344728897997441e-16L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p50L, 0.0L, -8.881784197001252323389053344728897997441e-16L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p50L, -0.0L, -8.881784197001252323389053344728897997441e-16L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0.0L, 0x1p50L, 0.0L, 1.570796326794895731052901991514519103193L);
+  TEST_c_c (catanh, -0.0L, 0x1p50L, -0.0L, 1.570796326794895731052901991514519103193L);
+  TEST_c_c (catanh, 0.0L, -0x1p50L, 0.0L, -1.570796326794895731052901991514519103193L);
+  TEST_c_c (catanh, -0.0L, -0x1p50L, -0.0L, -1.570796326794895731052901991514519103193L);
+#ifndef TEST_FLOAT
+  TEST_c_c (catanh, 0x1p500L, 0.0L, 3.054936363499604682051979393213617699789e-151L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0x1p500L, -0.0L, 3.054936363499604682051979393213617699789e-151L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p500L, 0.0L, -3.054936363499604682051979393213617699789e-151L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p500L, -0.0L, -3.054936363499604682051979393213617699789e-151L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0.0L, 0x1p500L, 0.0L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0.0L, 0x1p500L, -0.0L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0.0L, -0x1p500L, 0.0L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0.0L, -0x1p500L, -0.0L, -1.570796326794896619231321691639751442099L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (catanh, 0x1p5000L, 0.0L, 7.079811261048172892385615158694057552948e-1506L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0x1p5000L, -0.0L, 7.079811261048172892385615158694057552948e-1506L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p5000L, 0.0L, -7.079811261048172892385615158694057552948e-1506L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0x1p5000L, -0.0L, -7.079811261048172892385615158694057552948e-1506L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0.0L, 0x1p5000L, 0.0L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0.0L, 0x1p5000L, -0.0L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, 0.0L, -0x1p5000L, 0.0L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (catanh, -0.0L, -0x1p5000L, -0.0L, -1.570796326794896619231321691639751442099L);
+#endif
+
   TEST_c_c (catanh, 0.75L, 1.25L, 0.261492138795671927078652057366532140L, 0.996825126463918666098902241310446708L);
   TEST_c_c (catanh, -2, -3, -0.14694666622552975204743278515471595L, -1.3389725222944935611241935759091443L);
 

diff --git a/math/s_catan.c b/math/s_catan.c
index 46c18bf2af7d37e44452c7a7023243969bf382dc..783941a72efd1a4ba13096131879496e11c72b13 100644 (file)
--- a/math/s_catan.c
+++ b/math/s_catan.c
@@ -61,7 +61,7 @@ __catan (__complex__ double x)
     }
   else
     {
-      double r2, num, den;
+      double r2, num, den, f;
 
       r2 = __real__ x * __real__ x;
 
@@ -75,7 +75,14 @@ __catan (__complex__ double x)
       den = __imag__ x - 1.0;
       den = r2 + den * den;
 
-      __imag__ res = 0.25 * __ieee754_log (num / den);
+      f = num / den;
+      if (f < 0.5)
+       __imag__ res = 0.25 * __ieee754_log (f);
+      else
+       {
+         num = 4.0 * __imag__ x;
+         __imag__ res = 0.25 * __log1p (num / den);
+       }
     }
 
   return res;

diff --git a/math/s_catanf.c b/math/s_catanf.c
index 5a432471cde08be7312dc68fdc91e018073b689e..0dc85ffc25e0e4fd6487cb867a3da5cc0a43870f 100644 (file)
--- a/math/s_catanf.c
+++ b/math/s_catanf.c
@@ -61,7 +61,7 @@ __catanf (__complex__ float x)
     }
   else
     {
-      float r2, num, den;
+      float r2, num, den, f;
 
       r2 = __real__ x * __real__ x;
 
@@ -75,7 +75,14 @@ __catanf (__complex__ float x)
       den = __imag__ x - 1.0;
       den = r2 + den * den;
 
-      __imag__ res = 0.25 * __ieee754_logf (num / den);
+      f = num / den;
+      if (f < 0.5)
+       __imag__ res = 0.25 * __ieee754_logf (f);
+      else
+       {
+         num = 4.0 * __imag__ x;
+         __imag__ res = 0.25 * __log1pf (num / den);
+       }
     }
 
   return res;

diff --git a/math/s_catanh.c b/math/s_catanh.c
index 5371f44b67778d54c1678956ec6b4e5b56ee0aa4..0ee8c64b6fa35f3ed3047558eecef223a723d15a 100644 (file)
--- a/math/s_catanh.c
+++ b/math/s_catanh.c
@@ -64,7 +64,14 @@ __catanh (__complex__ double x)
       double den = 1.0 - __real__ x;
       den = i2 + den * den;
 
-      __real__ res = 0.25 * (__ieee754_log (num) - __ieee754_log (den));
+      double f = num / den;
+      if (f < 0.5)
+       __real__ res = 0.25 * __ieee754_log (f);
+      else
+       {
+         num = 4.0 * __real__ x;
+         __real__ res = 0.25 * __log1p (num / den);
+       }
 
       den = 1 - __real__ x * __real__ x - i2;
 

diff --git a/math/s_catanhf.c b/math/s_catanhf.c
index 8385af41b0154b314d7574b225c8d847275b9538..ca9a30101e277389a1d8ba66043efd732a59526e 100644 (file)
--- a/math/s_catanhf.c
+++ b/math/s_catanhf.c
@@ -64,7 +64,14 @@ __catanhf (__complex__ float x)
       float den = 1.0 - __real__ x;
       den = i2 + den * den;
 
-      __real__ res = 0.25 * (__ieee754_logf (num) - __ieee754_logf (den));
+      float f = num / den;
+      if (f < 0.5)
+       __real__ res = 0.25 * __ieee754_logf (f);
+      else
+       {
+         num = 4.0 * __real__ x;
+         __real__ res = 0.25 * __log1pf (num / den);
+       }
 
       den = 1 - __real__ x * __real__ x - i2;
 

diff --git a/math/s_catanhl.c b/math/s_catanhl.c
index 6844f03dea6a1520f6cdb4fec914b21daebff5ee..4897c0c87165d7fa02e6581e4163889ef65b81a2 100644 (file)
--- a/math/s_catanhl.c
+++ b/math/s_catanhl.c
@@ -64,7 +64,14 @@ __catanhl (__complex__ long double x)
       long double den = 1.0 - __real__ x;
       den = i2 + den * den;
 
-      __real__ res = 0.25 * (__ieee754_logl (num) - __ieee754_logl (den));
+      long double f = num / den;
+      if (f < 0.5)
+       __real__ res = 0.25 * __ieee754_logl (f);
+      else
+       {
+         num = 4.0 * __real__ x;
+         __real__ res = 0.25 * __log1pl (num / den);
+       }
 
       den = 1 - __real__ x * __real__ x - i2;
 

diff --git a/math/s_catanl.c b/math/s_catanl.c
index 57d2e595503431d4b920c6fe2a0a87f05328a3ff..e04dba73878c55ea32308a0383364eecc54980c0 100644 (file)
--- a/math/s_catanl.c
+++ b/math/s_catanl.c
@@ -61,7 +61,7 @@ __catanl (__complex__ long double x)
     }
   else
     {
-      long double r2, num, den;
+      long double r2, num, den, f;
 
       r2 = __real__ x * __real__ x;
 
@@ -75,7 +75,14 @@ __catanl (__complex__ long double x)
       den = __imag__ x - 1.0;
       den = r2 + den * den;
 
-      __imag__ res = 0.25 * __ieee754_logl (num / den);
+      f = num / den;
+      if (f < 0.5)
+       __imag__ res = 0.25 * __ieee754_logl (f);
+      else
+       {
+         num = 4.0 * __imag__ x;
+         __imag__ res = 0.25 * __log1pl (num / den);
+       }
     }
 
   return res;

diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index fecaa94d45b33cfcc2373db856823e2dbc4cd85f..a6d9b0f2478b52570489dc131fdbdf975e080a4d 100644 (file)
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -3417,6 +3417,8 @@ ldouble: 1
 Test "Real part of: catanh (0.75 + 1.25 i) == 0.261492138795671927078652057366532140 + 0.996825126463918666098902241310446708 i":
 double: 1
 idouble: 1
+ildouble: 1
+ldouble: 1
 
 # cbrt
 Test "cbrt (-27.0) == -3.0":

diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 9c9c47344902218645097f1997b06e3de23fb3e6..2747fc51cd8f9ceda46417d23d168c288011602a 100644 (file)
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -3985,6 +3985,8 @@ ifloat: 4
 Test "Real part of: catanh (0.75 + 1.25 i) == 0.261492138795671927078652057366532140 + 0.996825126463918666098902241310446708 i":
 double: 1
 idouble: 1
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: catanh (0.75 + 1.25 i) == 0.261492138795671927078652057366532140 + 0.996825126463918666098902241310446708 i":
 float: 6
 ifloat: 6