diff --git a/acb/rsqrt.c b/acb/rsqrt.c
index aa0e6e8f..9f8c86b9 100644
--- a/acb/rsqrt.c
+++ b/acb/rsqrt.c
@@ -22,15 +22,6 @@ arb_get_mag_reverse(mag_t res, const arb_t x)
     mag_clear(t);
 }
 
-void
-mag_add_ui_lower(mag_t res, const mag_t x, ulong y)
-{
-    mag_t t;
-    mag_init(t);
-    mag_set_ui_lower(t, y);  /* no need to free */
-    mag_add_lower(res, x, t);
-}
-
 /* upper bound for re(rsqrt(x+yi)) / |rsqrt(x+yi)|,
    given upper bound for x, lower bound for y */
 void
diff --git a/mag.h b/mag.h
index 1e7a018a..300d30e7 100644
--- a/mag.h
+++ b/mag.h
@@ -294,6 +294,7 @@ void mag_add(mag_t z, const mag_t x, const mag_t y);
 void mag_add_lower(mag_t z, const mag_t x, const mag_t y);
 
 void mag_add_ui(mag_t z, const mag_t x, ulong y);
+void mag_add_ui_lower(mag_t res, const mag_t x, ulong y);
 
 void mag_add_ui_2exp_si(mag_t z, const mag_t x, ulong y, slong e);
 
diff --git a/mag/add_ui.c b/mag/add_ui.c
index 449b04b3..4da504aa 100644
--- a/mag/add_ui.c
+++ b/mag/add_ui.c
@@ -20,4 +20,12 @@ mag_add_ui(mag_t y, const mag_t x, ulong k)
     mag_add(y, x, t);
 }
 
+void
+mag_add_ui_lower(mag_t res, const mag_t x, ulong k)
+{
+    mag_t t;
+    mag_init(t);
+    mag_set_ui_lower(t, k);  /* no need to free */
+    mag_add_lower(res, x, t);
+}
 
diff --git a/mag/root.c b/mag/root.c
index a085db05..5635c2f0 100644
--- a/mag/root.c
+++ b/mag/root.c
@@ -38,6 +38,9 @@ mag_root(mag_t y, const mag_t x, ulong n)
         fmpz_init_set_ui(e, MAG_BITS);
         fmpz_init(f);
 
+        /* We evaluate exp(log(1+2^(kn)x)/n) 2^-k where k is chosen
+           so that 2^(kn) x ~= 2^30. TODO: this rewriting is probably
+           unnecessary with the new exp/log functions. */
         fmpz_sub(e, e, MAG_EXPREF(x));
         fmpz_cdiv_q_ui(e, e, n);
         fmpz_mul_ui(f, e, n);