diff --git a/acb/div.c b/acb/div.c
index 670882ff..5f7ff278 100644
--- a/acb/div.c
+++ b/acb/div.c
@@ -79,7 +79,7 @@ acb_div(acb_t z, const acb_t x, const acb_t y, slong prec)
     }
     else
     {
-        if (prec > 256 && acb_bits(y) <= prec / 2)
+        if (prec > 256 && acb_bits(y) <= prec / 2 && acb_is_exact(y))
         {
             arb_t t, u, v;
 
diff --git a/acb/inv.c b/acb/inv.c
index 9f91b006..31544008 100644
--- a/acb/inv.c
+++ b/acb/inv.c
@@ -1,5 +1,5 @@
 /*
-    Copyright (C) 2013 Fredrik Johansson
+    Copyright (C) 2017 Fredrik Johansson
 
     This file is part of Arb.
 
@@ -11,44 +11,189 @@
 
 #include "acb.h"
 
-void
-acb_inv(acb_t z, const acb_t x, slong prec)
+static void
+_arb_arf_div_rounded_den(arb_t res, const arf_t x, const arf_t y, int yinexact, slong prec)
 {
-#define a acb_realref(x)
-#define b acb_imagref(x)
-#define c acb_realref(z)
-#define d acb_imagref(z)
+    int inexact = arf_div(arb_midref(res), x, y, prec, ARB_RND);
 
-    if (arb_is_zero(b))
+    if (yinexact && !arf_is_special(arb_midref(res)))
+        arf_mag_set_ulp(arb_radref(res), arb_midref(res), prec - 1);
+    else if (inexact)
+        arf_mag_set_ulp(arb_radref(res), arb_midref(res), prec);
+    else
+        mag_zero(arb_radref(res));
+}
+
+static void
+_arb_arf_div_rounded_den_add_err(arb_t res, const arf_t x, const arf_t y, int yinexact, slong prec)
+{
+    int inexact = arf_div(arb_midref(res), x, y, prec, ARB_RND);
+
+    if (yinexact && !arf_is_special(arb_midref(res)))
+        arf_mag_add_ulp(arb_radref(res), arb_radref(res), arb_midref(res), prec - 1);
+    else if (inexact)
+        arf_mag_add_ulp(arb_radref(res), arb_radref(res), arb_midref(res), prec);
+}
+
+void
+acb_inv(acb_t res, const acb_t z, slong prec)
+{
+    mag_t am, bm;
+    slong hprec;
+
+#define a arb_midref(acb_realref(z))
+#define b arb_midref(acb_imagref(z))
+#define x arb_radref(acb_realref(z))
+#define y arb_radref(acb_imagref(z))
+
+    /* choose precision for the floating-point approximation of a^2+b^2 so
+       that the double rounding result in less than
+       2 ulp error; also use at least MAG_BITS bits since the
+       value will be recycled for error bounds */
+    hprec = FLINT_MAX(prec + 3, MAG_BITS);
+
+    if (arb_is_zero(acb_imagref(z)))
     {
-        arb_inv(c, a, prec);
-        arb_zero(d);
+        arb_inv(acb_realref(res), acb_realref(z), prec);
+        arb_zero(acb_imagref(res));
+        return;
     }
-    else if (arb_is_zero(a))
+
+    if (arb_is_zero(acb_realref(z)))
     {
-        arb_inv(d, b, prec);
-        arb_neg(d, d);
-        arb_zero(c);
+        arb_inv(acb_imagref(res), acb_imagref(z), prec);
+        arb_neg(acb_imagref(res), acb_imagref(res));
+        arb_zero(acb_realref(res));
+        return;
+    }
+
+    if (!acb_is_finite(z))
+    {
+        acb_indeterminate(res);
+        return;
+    }
+
+    if (mag_is_zero(x) && mag_is_zero(y))
+    {
+        int inexact;
+
+        arf_t a2b2;
+        arf_init(a2b2);
+
+        inexact = arf_sosq(a2b2, a, b, hprec, ARF_RND_DOWN);
+
+        if (arf_is_special(a2b2))
+        {
+            acb_indeterminate(res);
+        }
+        else
+        {
+            _arb_arf_div_rounded_den(acb_realref(res), a, a2b2, inexact, prec);
+            _arb_arf_div_rounded_den(acb_imagref(res), b, a2b2, inexact, prec);
+            arf_neg(arb_midref(acb_imagref(res)), arb_midref(acb_imagref(res)));
+        }
+
+        arf_clear(a2b2);
+        return;
+    }
+
+    mag_init(am);
+    mag_init(bm);
+
+    /* first bound |a|-x, |b|-y */
+    arb_get_mag_lower(am, acb_realref(z));
+    arb_get_mag_lower(bm, acb_imagref(z));
+
+    if ((mag_is_zero(am) && mag_is_zero(bm)))
+    {
+        acb_indeterminate(res);
     }
     else
     {
-        arb_t t;
-        arb_init(t);
+        /*
+        The propagated error in the real part is given exactly by
 
-        arb_mul(t, a, a, prec);
-        arb_addmul(t, b, b, prec);
+             (a+x')/((a+x')^2+(b+y'))^2 - a/(a^2+b^2) = P / Q,
 
-        arb_div(c, a, t, prec);
-        arb_div(d, b, t, prec);
+             P = [(b^2-a^2) x' - a (x'^2+y'^2 + 2y'b)]
+             Q = [(a^2+b^2)((a+x')^2+(b+y')^2)]
 
-        arb_neg(d, d);
+        where |x'| <= x and |y'| <= y, and analogously for the imaginary part.
+        */
+        mag_t t, u, v, w;
+        arf_t a2b2;
+        int inexact;
 
-        arb_clear(t);
+        mag_init(t);
+        mag_init(u);
+        mag_init(v);
+        mag_init(w);
+
+        arf_init(a2b2);
+
+        inexact = arf_sosq(a2b2, a, b, hprec, ARF_RND_DOWN);
+
+        /* compute denominator */
+        /* t = (|a|-x)^2 + (|b|-x)^2 (lower bound) */
+        mag_mul_lower(t, am, am);
+        mag_mul_lower(u, bm, bm);
+        mag_add_lower(t, t, u);
+        /* u = a^2 + b^2 (lower bound) */
+        arf_get_mag_lower(u, a2b2);
+        /* t = ((|a|-x)^2 + (|b|-x)^2)(a^2 + b^2) (lower bound) */
+        mag_mul_lower(t, t, u);
+
+        /* compute numerator */
+        /* real: |a^2-b^2| x  + |a| ((x^2 + y^2) + 2 |b| y)) */
+        /* imag: |a^2-b^2| y  + |b| ((x^2 + y^2) + 2 |a| x)) */
+        /* am, bm = upper bounds for a, b */
+        arf_get_mag(am, a);
+        arf_get_mag(bm, b);
+
+        /* v = x^2 + y^2 */
+        mag_mul(v, x, x);
+        mag_addmul(v, y, y);
+
+        /* u = |a| ((x^2 + y^2) + 2 |b| y) */
+        mag_mul_2exp_si(u, bm, 1);
+        mag_mul(u, u, y);
+        mag_add(u, u, v);
+        mag_mul(u, u, am);
+
+        /* v = |b| ((x^2 + y^2) + 2 |a| x) */
+        mag_mul_2exp_si(w, am, 1);
+        mag_addmul(v, w, x);
+        mag_mul(v, v, bm);
+
+        /* w = |b^2 - a^2| (upper bound) */
+        if (arf_cmpabs(a, b) >= 0)
+            mag_mul(w, am, am);
+        else
+            mag_mul(w, bm, bm);
+
+        mag_addmul(u, w, x);
+        mag_addmul(v, w, y);
+
+        mag_div(arb_radref(acb_realref(res)), u, t);
+        mag_div(arb_radref(acb_imagref(res)), v, t);
+
+        _arb_arf_div_rounded_den_add_err(acb_realref(res), a, a2b2, inexact, prec);
+        _arb_arf_div_rounded_den_add_err(acb_imagref(res), b, a2b2, inexact, prec);
+        arf_neg(arb_midref(acb_imagref(res)), arb_midref(acb_imagref(res)));
+
+        mag_clear(t);
+        mag_clear(u);
+        mag_clear(v);
+        mag_clear(w);
+
+        arf_clear(a2b2);
     }
 
+    mag_clear(am);
+    mag_clear(bm);
 #undef a
 #undef b
-#undef c
-#undef d
+#undef x
+#undef y
 }
 
diff --git a/acb/test/t-inv.c b/acb/test/t-inv.c
new file mode 100644
index 00000000..e49c3889
--- /dev/null
+++ b/acb/test/t-inv.c
@@ -0,0 +1,150 @@
+/*
+    Copyright (C) 2012 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb.h"
+
+static void
+acb_inv_naive(acb_t z, const acb_t x, slong prec)
+{
+#define a acb_realref(x)
+#define b acb_imagref(x)
+#define c acb_realref(z)
+#define d acb_imagref(z)
+
+    if (arb_is_zero(b))
+    {
+        arb_inv(c, a, prec);
+        arb_zero(d);
+    }
+    else if (arb_is_zero(a))
+    {
+        arb_inv(d, b, prec);
+        arb_neg(d, d);
+        arb_zero(c);
+    }
+    else
+    {
+        arb_t t;
+        arb_init(t);
+
+        arb_mul(t, a, a, prec);
+        arb_addmul(t, b, b, prec);
+
+        arb_div(c, a, t, prec);
+        arb_div(d, b, t, prec);
+
+        arb_neg(d, d);
+
+        arb_clear(t);
+    }
+
+#undef a
+#undef b
+#undef c
+#undef d
+}
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("inv....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
+    {
+        acb_t a, b, c, d, e, f;
+        arf_t t;
+        slong prec;
+
+        acb_init(a);
+        acb_init(b);
+        acb_init(c);
+        acb_init(d);
+        acb_init(e);
+        acb_init(f);
+        arf_init(t);
+
+        prec = 2 + n_randint(state, 1000);
+
+        acb_randtest_special(a, state, 1 + n_randint(state, 1000), 100);
+        acb_randtest_special(b, state, 1 + n_randint(state, 1000), 100);
+
+        acb_inv(b, a, prec);
+        acb_inv_naive(c, a, prec);
+
+        if (!acb_overlaps(b, c))
+        {
+            flint_printf("FAIL: overlap\n\n");
+            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
+            flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
+            flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
+            abort();
+        }
+
+        acb_set(c, a);
+        acb_inv(c, c, prec);
+
+        if (!acb_equal(b, c))
+        {
+            flint_printf("FAIL: aliasing\n\n");
+            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
+            flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
+            flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
+            abort();
+        }
+
+        acb_randtest(a, state, 1 + n_randint(state, 1000), 10);
+        acb_randtest(b, state, 1 + n_randint(state, 1000), 10);
+
+        acb_zero(d);
+        arf_set_mag(t, arb_radref(acb_realref(a)));
+        if (n_randint(state, 2))
+            arf_neg(t, t);
+        arf_add(arb_midref(acb_realref(d)),
+            arb_midref(acb_realref(a)), t, ARF_PREC_EXACT, ARF_RND_DOWN);
+
+        arf_set_mag(t, arb_radref(acb_imagref(a)));
+        if (n_randint(state, 2))
+            arf_neg(t, t);
+        arf_add(arb_midref(acb_imagref(d)),
+            arb_midref(acb_imagref(a)), t, ARF_PREC_EXACT, ARF_RND_DOWN);
+
+        acb_inv(b, a, 2 + n_randint(state, 1000));
+        acb_inv(d, d, 2 + n_randint(state, 1000));
+
+        if (!acb_overlaps(b, d))
+        {
+            flint_printf("FAIL: corner test\n\n");
+            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
+            flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
+            flint_printf("d = "); acb_printd(d, 30); flint_printf("\n\n");
+            abort();
+        }
+
+        acb_clear(a);
+        acb_clear(b);
+        acb_clear(c);
+        acb_clear(d);
+        acb_clear(e);
+        acb_clear(f);
+        arf_clear(t);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+