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

4 files changed, 147 insertions, 0 deletions

diff --git a/math/k_casinh.c b/math/k_casinh.c
index 7f98f24a80..41cd5ec47d 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 9401636348..3152ea2f7d 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 6412979755..110ae33dee 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 1c2970fc79..6ac3cd2d0b 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);