diff --git a/arf.h b/arf.h
index 30f722d7..2c193f52 100644
--- a/arf.h
+++ b/arf.h
@@ -610,8 +610,9 @@ int arf_get_mpfr(mpfr_t x, const arf_t y, mpfr_rnd_t rnd);
 void arf_set_mpfr(arf_t x, const mpfr_t y);
 
 int arf_equal(const arf_t x, const arf_t y);
-
 int arf_equal_si(const arf_t x, slong y);
+int arf_equal_ui(const arf_t x, ulong y);
+int arf_equal_d(const arf_t x, double y);
 
 ARF_INLINE void
 arf_min(arf_t z, const arf_t a, const arf_t b)
diff --git a/arf/equal.c b/arf/equal.c
index 96aa721c..09010b27 100644
--- a/arf/equal.c
+++ b/arf/equal.c
@@ -48,3 +48,19 @@ arf_equal_si(const arf_t x, slong y)
     return arf_equal(x, t); /* no need to free */
 }
 
+int
+arf_equal_ui(const arf_t x, ulong y)
+{
+    arf_t t;
+    arf_init_set_ui(t, y);
+    return arf_equal(x, t); /* no need to free */
+}
+
+int
+arf_equal_d(const arf_t x, double y)
+{
+    arf_t t;
+    arf_init(t);
+    arf_set_d(t, y);
+    return arf_equal(x, t); /* no need to free */
+}
diff --git a/arf/test/t-set_d.c b/arf/test/t-set_d.c
index 12bd3bc9..ab417926 100644
--- a/arf/test/t-set_d.c
+++ b/arf/test/t-set_d.c
@@ -37,7 +37,7 @@ int main()
         mpfr_set_d(m, x, MPFR_RNDN);
         arf_set_mpfr(z, m);
 
-        if (!arf_equal(y, z))
+        if (!arf_equal(y, z) || !arf_equal_d(y, x))
         {
             flint_printf("FAIL:\n\n");
             flint_printf("x = %.17g\n\n", x);
diff --git a/arf/test/t-set_round_ui.c b/arf/test/t-set_round_ui.c
index d18e17be..39f693f4 100644
--- a/arf/test/t-set_round_ui.c
+++ b/arf/test/t-set_round_ui.c
@@ -61,7 +61,7 @@ int main()
 
         ret2 = arf_set_round_ui(y, t, prec, rnd);
 
-        if (!arf_equal(x, y) || (ret1 != ret2))
+        if (!arf_equal(x, y) || (ret1 != ret2) || (ret2 == 0 && !arf_equal_ui(y, t)))
         {
             flint_printf("FAIL\n\n");
             flint_printf("prec = %wd", prec); flint_printf("\n\n");
@@ -81,4 +81,3 @@ int main()
     flint_printf("PASS\n");
     return EXIT_SUCCESS;
 }
-
diff --git a/doc/source/arf.rst b/doc/source/arf.rst
index 56bdcf81..c4bd7c59 100644
--- a/doc/source/arf.rst
+++ b/doc/source/arf.rst
@@ -323,11 +323,15 @@ Comparisons and bounds
 -------------------------------------------------------------------------------
 
 .. function:: int arf_equal(const arf_t x, const arf_t y)
+              int arf_equal_si(const arf_t x, slong y)
+              int arf_equal_ui(const arf_t x, ulong y)
+              int arf_equal_d(const arf_t x, double y)
 
-.. function:: int arf_equal_si(const arf_t x, slong y)
+    Returns nonzero iff *x* and *y* are exactly equal. NaN is not
+    treated specially, i.e. NaN compares as equal to itself.
 
-    Returns nonzero iff *x* and *y* are exactly equal. This function does
-    not treat NaN specially, i.e. NaN compares as equal to itself.
+    For comparison with a *double*, the values -0 and +0 are
+    both treated as zero, and all NaN values are treated as identical.
 
 .. function:: int arf_cmp(const arf_t x, const arf_t y)