diff --git a/src/math/special/atanh.h b/src/math/special/atanh.h
index 42cb08e..8d1cf8e 100644
--- a/src/math/special/atanh.h
+++ b/src/math/special/atanh.h
@@ -7,3 +7,8 @@ T(RN,                  0x1p+0,                     inf,          0x0p+0, DIVBYZE
 T(RN,                 -0x1p+0,                    -inf,          0x0p+0, DIVBYZERO)
 T(RN,             0x1.0001p+0,                     nan,          0x0p+0, INVALID)
 T(RN,            -0x1.0001p+0,                     nan,          0x0p+0, INVALID)
+T(RN,                 0x1p-66,                 0x1p-66,          0x0p+0, INEXACT)
+T(RN,               0x1p-1000,               0x1p-1000,          0x0p+0, INEXACT)
+T(RN,               0x1p-1024,               0x1p-1024,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,              -0x1p-1024,              -0x1p-1024,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,               0x1p+1023,                     nan,          0x0p+0, INVALID)
diff --git a/src/math/special/atanhf.h b/src/math/special/atanhf.h
index e1c9aed..55a6bfb 100644
--- a/src/math/special/atanhf.h
+++ b/src/math/special/atanhf.h
@@ -7,3 +7,8 @@ T(RN,          0x1p+0,             inf,          0x0p+0, DIVBYZERO)
 T(RN,         -0x1p+0,            -inf,          0x0p+0, DIVBYZERO)
 T(RN,     0x1.0001p+0,             nan,          0x0p+0, INVALID)
 T(RN,    -0x1.0001p+0,             nan,          0x0p+0, INVALID)
+T(RN,         0x1p-66,         0x1p-66,          0x0p+0, INEXACT)
+T(RN,        0x1p-100,        0x1p-100,          0x0p+0, INEXACT)
+T(RN,        0x1p-128,        0x1p-128,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,       -0x1p-128,       -0x1p-128,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,        0x1p+127,             nan,          0x0p+0, INVALID)
diff --git a/src/math/special/atanhl.h b/src/math/special/atanhl.h
index 3ad80b1..5468164 100644
--- a/src/math/special/atanhl.h
+++ b/src/math/special/atanhl.h
@@ -7,3 +7,8 @@ T(RN,                        0x1p+0L,                            inf,          0
 T(RN,                       -0x1p+0L,                           -inf,          0x0p+0, DIVBYZERO)
 T(RN,                   0x1.0001p+0L,                            nan,          0x0p+0, INVALID)
 T(RN,                  -0x1.0001p+0L,                            nan,          0x0p+0, INVALID)
+T(RN,                       0x1p-66L,                       0x1p-66L,          0x0p+0, INEXACT)
+T(RN,                    0x1p-16000L,                    0x1p-16000L,          0x0p+0, INEXACT)
+T(RN,                    0x1p-16384L,                    0x1p-16384L,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,                   -0x1p-16384L,                   -0x1p-16384L,          0x0p+0, INEXACT|UNDERFLOW)
+T(RN,                    0x1p+16383L,                            nan,          0x0p+0, INVALID)