Fix casinh spurious underflows away from [-i,i] (bug 15062).

8 files changed, 528 insertions, 1 deletions

diff --git a/ChangeLog b/ChangeLog
index 7c88a4f..89e47ab 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,17 @@
+2013-01-31  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #15062]
+	* math/k_casinh.c (__kernel_casinh): Compute real and imaginary
+	parts of result separately when argument is not close to line from
+	-i to i and one part of argument is small.
+	* math/k_casinhf.c (__kernel_casinhf): Likewise.
+	* math/k_casinhl.c (__kernel_casinhl): Likewise.
+	* math/libm-test.inc (cacos_test): Add more tests.
+	(casin_test): Likewise.
+	(casinh_test): Likewise.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2013-01-31  David S. Miller  <davem@davemloft.net>
 
 	* po/de.po: Update from translation team.
diff --git a/NEWS b/NEWS
index 9a039d8..8c21790 100644
--- a/NEWS
+++ b/NEWS
@@ -10,7 +10,7 @@ Version 2.18
 * The following bugs are resolved with this release:
 
   13951, 14200, 14317, 14327, 14496, 14964, 14981, 14982, 14985, 14994,
-  14996, 15003, 15020, 15023, 15036.
+  14996, 15003, 15020, 15023, 15036, 15062.
 
 
 Version 2.17
diff --git a/math/k_casinh.c b/math/k_casinh.c
index 7f98f24..41cd5ec 100644
--- a/math/k_casinh.c
+++ b/math/k_casinh.c
@@ -57,6 +57,26 @@ __kernel_casinh (__complex__ double x, int adj)
       res = __clog (y);
       __real__ res += M_LN2;
     }
+  else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
+    {
+      double s = __ieee754_hypot (1.0, rx);
+
+      __real__ res = __ieee754_log (rx + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2 (s, __imag__ x);
+      else
+	__imag__ res = __ieee754_atan2 (ix, s);
+    }
+  else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
+    {
+      double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
+
+      __real__ res = __ieee754_log (ix + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
+      else
+	__imag__ res = __ieee754_atan2 (s, rx);
+    }
   else
     {
       __real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/k_casinhf.c b/math/k_casinhf.c
index 9401636..3152ea2 100644
--- a/math/k_casinhf.c
+++ b/math/k_casinhf.c
@@ -57,6 +57,26 @@ __kernel_casinhf (__complex__ float x, int adj)
       res = __clogf (y);
       __real__ res += (float) M_LN2;
     }
+  else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
+    {
+      float s = __ieee754_hypotf (1.0f, rx);
+
+      __real__ res = __ieee754_logf (rx + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2f (s, __imag__ x);
+      else
+	__imag__ res = __ieee754_atan2f (ix, s);
+    }
+  else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
+    {
+      float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
+
+      __real__ res = __ieee754_logf (ix + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
+      else
+	__imag__ res = __ieee754_atan2f (s, rx);
+    }
   else
     {
       __real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/k_casinhl.c b/math/k_casinhl.c
index 6412979..110ae33 100644
--- a/math/k_casinhl.c
+++ b/math/k_casinhl.c
@@ -64,6 +64,26 @@ __kernel_casinhl (__complex__ long double x, int adj)
       res = __clogl (y);
       __real__ res += M_LN2l;
     }
+  else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
+    {
+      long double s = __ieee754_hypotl (1.0L, rx);
+
+      __real__ res = __ieee754_logl (rx + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2l (s, __imag__ x);
+      else
+	__imag__ res = __ieee754_atan2l (ix, s);
+    }
+  else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
+    {
+      long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
+
+      __real__ res = __ieee754_logl (ix + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
+      else
+	__imag__ res = __ieee754_atan2l (s, rx);
+    }
   else
     {
       __real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 1c2970f..6ac3cd2 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -1490,6 +1490,35 @@ cacos_test (void)
   TEST_c_c (cacos, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, -1.135753137836666928715489992987020363057e4L);
 #endif
 
+  TEST_c_c (cacos, 0x1.fp-129L, 1.5L, 1.570796326794896619231321691639751442097L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 0x1.fp-129L, -1.5L, 1.570796326794896619231321691639751442097L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-129L, 1.5L, 1.570796326794896619231321691639751442100L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-129L, -1.5L, 1.570796326794896619231321691639751442100L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 1.5L, 0x1.fp-129L, 2.546345110742945032959687790021055102355e-39L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (cacos, -1.5L, 0x1.fp-129L, 3.141592653589793238462643383279502884195L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (cacos, 1.5L, -0x1.fp-129L, 2.546345110742945032959687790021055102355e-39L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (cacos, -1.5L, -0x1.fp-129L, 3.141592653589793238462643383279502884195L, 9.624236501192068949955178268487368462704e-1L);
+#ifndef TEST_FLOAT
+  TEST_c_c (cacos, 0x1.fp-1025L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 0x1.fp-1025L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-1025L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-1025L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 1.5L, 0x1.fp-1025L, 4.819934639999230680322935210539402497827e-309L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (cacos, -1.5L, 0x1.fp-1025L, 3.141592653589793238462643383279502884197L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (cacos, 1.5L, -0x1.fp-1025L, 4.819934639999230680322935210539402497827e-309L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (cacos, -1.5L, -0x1.fp-1025L, 3.141592653589793238462643383279502884197L, 9.624236501192068949955178268487368462704e-1L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+  TEST_c_c (cacos, 0x1.fp-16385L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 0x1.fp-16385L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-16385L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, -0x1.fp-16385L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+  TEST_c_c (cacos, 1.5L, 0x1.fp-16385L, 7.282957076134209141226696333885150260319e-4933L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (cacos, -1.5L, 0x1.fp-16385L, 3.141592653589793238462643383279502884197L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (cacos, 1.5L, -0x1.fp-16385L, 7.282957076134209141226696333885150260319e-4933L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (cacos, -1.5L, -0x1.fp-16385L, 3.141592653589793238462643383279502884197L, 9.624236501192068949955178268487368462704e-1L);
+#endif
+
   TEST_c_c (cacos, 0.75L, 1.25L, 1.11752014915610270578240049553777969L, -1.13239363160530819522266333696834467L);
   TEST_c_c (cacos, -2, -3, 2.1414491111159960199416055713254211L, 1.9833870299165354323470769028940395L);
 
@@ -1772,6 +1801,35 @@ casin_test (void)
   TEST_c_c (casin, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, 1.135753137836666928715489992987020363057e4L);
 #endif
 
+  TEST_c_c (casin, 0x1.fp-129L, 1.5L, 1.579176199917649005841160751101628985741e-39L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casin, 0x1.fp-129L, -1.5L, 1.579176199917649005841160751101628985741e-39L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casin, -0x1.fp-129L, 1.5L, -1.579176199917649005841160751101628985741e-39L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casin, -0x1.fp-129L, -1.5L, -1.579176199917649005841160751101628985741e-39L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casin, 1.5L, 0x1.fp-129L, 1.570796326794896619231321691639751442096L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, 0x1.fp-129L, -1.570796326794896619231321691639751442096L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, 1.5L, -0x1.fp-129L, 1.570796326794896619231321691639751442096L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, -0x1.fp-129L, -1.570796326794896619231321691639751442096L, -9.624236501192068949955178268487368462704e-1L);
+#ifndef TEST_FLOAT
+  TEST_c_c (casin, 0x1.fp-1025L, 1.5L, 2.989196569048182929051881765490354365918e-309L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casin, 0x1.fp-1025L, -1.5L, 2.989196569048182929051881765490354365918e-309L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casin, -0x1.fp-1025L, 1.5L, -2.989196569048182929051881765490354365918e-309L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casin, -0x1.fp-1025L, -1.5L, -2.989196569048182929051881765490354365918e-309L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casin, 1.5L, 0x1.fp-1025L, 1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, 0x1.fp-1025L, -1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, 1.5L, -0x1.fp-1025L, 1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, -0x1.fp-1025L, -1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+  TEST_c_c (casin, 0x1.fp-16385L, 1.5L, 4.516698239814521372306784062043266700598e-4933L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casin, 0x1.fp-16385L, -1.5L, 4.516698239814521372306784062043266700598e-4933L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casin, -0x1.fp-16385L, 1.5L, -4.516698239814521372306784062043266700598e-4933L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casin, -0x1.fp-16385L, -1.5L, -4.516698239814521372306784062043266700598e-4933L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casin, 1.5L, 0x1.fp-16385L, 1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, 0x1.fp-16385L, -1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, 1.5L, -0x1.fp-16385L, 1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+  TEST_c_c (casin, -1.5L, -0x1.fp-16385L, -1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+#endif
+
   TEST_c_c (casin, 0.75L, 1.25L, 0.453276177638793913448921196101971749L, 1.13239363160530819522266333696834467L);
   TEST_c_c (casin, -2, -3, -0.57065278432109940071028387968566963L, -1.9833870299165354323470769028940395L);
 
@@ -1899,6 +1957,35 @@ casinh_test (void)
   TEST_c_c (casinh, 0x1.fp16383L, 0x1.fp16383L, 1.135753137836666928715489992987020363057e4L, 7.853981633974483096156608458198757210493e-1L);
 #endif
 
+  TEST_c_c (casinh, 0x1.fp-129L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442096L);
+  TEST_c_c (casinh, 0x1.fp-129L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442096L);
+  TEST_c_c (casinh, -0x1.fp-129L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442096L);
+  TEST_c_c (casinh, -0x1.fp-129L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442096L);
+  TEST_c_c (casinh, 1.5L, 0x1.fp-129L, 1.194763217287109304111930828519090523536L, 1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casinh, -1.5L, 0x1.fp-129L, -1.194763217287109304111930828519090523536L, 1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casinh, 1.5L, -0x1.fp-129L, 1.194763217287109304111930828519090523536L, -1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+  TEST_c_c (casinh, -1.5L, -0x1.fp-129L, -1.194763217287109304111930828519090523536L, -1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+#ifndef TEST_FLOAT
+  TEST_c_c (casinh, 0x1.fp-1025L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, 0x1.fp-1025L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, -0x1.fp-1025L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, -0x1.fp-1025L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, 1.5L, 0x1.fp-1025L, 1.194763217287109304111930828519090523536L, 2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casinh, -1.5L, 0x1.fp-1025L, -1.194763217287109304111930828519090523536L, 2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casinh, 1.5L, -0x1.fp-1025L, 1.194763217287109304111930828519090523536L, -2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+  TEST_c_c (casinh, -1.5L, -0x1.fp-1025L, -1.194763217287109304111930828519090523536L, -2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+  TEST_c_c (casinh, 0x1.fp-16385L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, 0x1.fp-16385L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, -0x1.fp-16385L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, -0x1.fp-16385L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+  TEST_c_c (casinh, 1.5L, 0x1.fp-16385L, 1.194763217287109304111930828519090523536L, 4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casinh, -1.5L, 0x1.fp-16385L, -1.194763217287109304111930828519090523536L, 4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casinh, 1.5L, -0x1.fp-16385L, 1.194763217287109304111930828519090523536L, -4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+  TEST_c_c (casinh, -1.5L, -0x1.fp-16385L, -1.194763217287109304111930828519090523536L, -4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+#endif
+
   TEST_c_c (casinh, 0.75L, 1.25L, 1.03171853444778027336364058631006594L, 0.911738290968487636358489564316731207L);
   TEST_c_c (casinh, -2, -3, -1.9686379257930962917886650952454982L, -0.96465850440760279204541105949953237L);
 
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 1525b16..fd0180f 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -275,6 +275,18 @@ ifloat: 1
 Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: cacos (-1.5 + +0 i) == pi - 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -282,9 +294,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: cacos (0.5 + +0 i) == 1.047197551196597746154214461093167628066 - 0 i":
 double: 1
 idouble: 1
@@ -303,6 +333,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442097 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442097 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -316,9 +358,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # cacosh
 Test "Real part of: cacosh (+0 + 0.5 i) == 0.4812118250596034474977589134243684231352 + pi/2 i":
@@ -502,6 +562,18 @@ ifloat: 1
 Test "Imaginary part of: casin (-0 - 1.5 i) == -0 - 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 + 1.5 i) == -2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 - 1.5 i) == -2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 + 1.5 i) == -1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 - 1.5 i) == -1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (-1.5 + +0 i) == -pi/2 + 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -509,9 +581,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casin (0.75 + 1.25 i) == 0.453276177638793913448921196101971749 + 1.13239363160530819522266333696834467 i":
 double: 1
 float: 1
@@ -524,6 +614,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: casin (0x1.fp-1025 + 1.5 i) == 2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-1025 - 1.5 i) == 2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 + 1.5 i) == 1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 - 1.5 i) == 1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -537,9 +639,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # casinh
 Test "Real part of: casinh (+0 + 1.5 i) == 0.9624236501192068949955178268487368462704 + pi/2 i":
@@ -576,6 +696,24 @@ idouble: 2
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
 double: 2
 float: 1
@@ -595,11 +733,23 @@ double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-1.5 - 0 i) == -1.194763217287109304111930828519090523536 - 0 i":
 double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i":
 double: 5
 float: 1
@@ -638,6 +788,24 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
 double: 1
 idouble: 1
@@ -657,9 +825,21 @@ ifloat: 1
 Test "Real part of: casinh (1.5 + +0 i) == 1.194763217287109304111930828519090523536 + +0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (1.5 - 0 i) == 1.194763217287109304111930828519090523536 - 0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 
 # catan
 Test "Imaginary part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 63c6aed..b828774 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -244,6 +244,24 @@ ifloat: 1
 Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Real part of: cacos (-1.0 + 0x1p50 i) == 1.570796326794897507409741391764983781004 - 3.535050620855721078027883819436759661753e1 i":
 float: 1
 ifloat: 1
@@ -257,9 +275,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i":
 float: 1
 ifloat: 1
@@ -281,6 +317,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442097 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442097 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -294,9 +342,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # cacosh
 Test "Real part of: cacosh (+0 + 0.5 i) == 0.4812118250596034474977589134243684231352 + pi/2 i":
@@ -460,6 +526,18 @@ ifloat: 1
 Test "Imaginary part of: casin (-0 - 1.5 i) == -0 - 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 + 1.5 i) == -2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 - 1.5 i) == -2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 + 1.5 i) == -1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 - 1.5 i) == -1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (-1.5 + +0 i) == -pi/2 + 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -467,9 +545,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casin (0.75 + 1.25 i) == 0.453276177638793913448921196101971749 + 1.13239363160530819522266333696834467 i":
 double: 1
 float: 1
@@ -482,6 +578,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: casin (0x1.fp-1025 + 1.5 i) == 2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-1025 - 1.5 i) == 2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 + 1.5 i) == 1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 - 1.5 i) == 1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -495,9 +603,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # casinh
 Test "Real part of: casinh (+0 + 1.5 i) == 0.9624236501192068949955178268487368462704 + pi/2 i":
@@ -534,6 +660,24 @@ idouble: 2
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
 double: 2
 float: 1
@@ -553,11 +697,23 @@ double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-1.5 - 0 i) == -1.194763217287109304111930828519090523536 - 0 i":
 double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i":
 double: 5
 float: 1
@@ -592,6 +748,24 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
 double: 1
 idouble: 1
@@ -611,9 +785,21 @@ ifloat: 1
 Test "Real part of: casinh (1.5 + +0 i) == 1.194763217287109304111930828519090523536 + +0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (1.5 - 0 i) == 1.194763217287109304111930828519090523536 - 0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 
 # catan
 Test "Real part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":