From 3d62dc3382734986f27ee9434755d1109a633627 Mon Sep 17 00:00:00 2001
From: fredrik <fredrik.johansson@gmail.com>
Date: Thu, 23 Sep 2021 20:26:00 +0200
Subject: [PATCH] small improvement for barnes_g

---
 acb/barnes_g.c      |  7 +++++++
 arb_fpwrap/fpwrap.c | 34 +++++++++++++++++++---------------
 2 files changed, 26 insertions(+), 15 deletions(-)

diff --git a/acb/barnes_g.c b/acb/barnes_g.c
index 3bf96759..c531e766 100644
--- a/acb/barnes_g.c
+++ b/acb/barnes_g.c
@@ -108,6 +108,10 @@ acb_log_barnes_g(acb_t res, const acb_t z, slong prec)
 void
 acb_barnes_g(acb_t res, const acb_t z, slong prec)
 {
+    int real;
+
+    real = acb_is_real(z);
+
     if (acb_is_int(z))
     {
         if (arb_is_nonpositive(acb_realref(z)))
@@ -126,5 +130,8 @@ acb_barnes_g(acb_t res, const acb_t z, slong prec)
 
     _acb_log_barnes_g_zeta(res, z, prec);
     acb_exp(res, res, prec);
+
+    if (real)
+        arb_zero(acb_imagref(res));
 }
 
diff --git a/arb_fpwrap/fpwrap.c b/arb_fpwrap/fpwrap.c
index e4c0038f..4200b0f9 100644
--- a/arb_fpwrap/fpwrap.c
+++ b/arb_fpwrap/fpwrap.c
@@ -691,10 +691,7 @@ _arb_barnes_g(arb_t res, const arb_t x, slong prec)
     acb_init(u);
     acb_set_arb(t, x);
     acb_barnes_g(u, t, prec);
-    if (acb_is_real(u))
-        arb_set(res, acb_realref(u));
-    else
-        arb_indeterminate(res);
+    arb_set(res, acb_realref(u));
     acb_clear(t);
     acb_clear(u);
 }
@@ -702,17 +699,24 @@ _arb_barnes_g(arb_t res, const arb_t x, slong prec)
 static void
 _arb_log_barnes_g(arb_t res, const arb_t x, slong prec)
 {
-    acb_t t, u;
-    acb_init(t);
-    acb_init(u);
-    acb_set_arb(t, x);
-    acb_log_barnes_g(u, t, prec);
-    if (acb_is_real(u))
-        arb_set(res, acb_realref(u));
-    else
+    if (!arb_is_positive(x))
+    {
         arb_indeterminate(res);
-    acb_clear(t);
-    acb_clear(u);
+    }
+    else
+    {
+        acb_t t, u;
+        acb_init(t);
+        acb_init(u);
+        acb_set_arb(t, x);
+        acb_log_barnes_g(u, t, prec);
+        if (acb_is_real(u))
+            arb_set(res, acb_realref(u));
+        else
+            arb_indeterminate(res);
+        acb_clear(t);
+        acb_clear(u);
+    }
 }
 
 DEF_DOUBLE_FUN_1(barnes_g, _arb_barnes_g)
@@ -835,7 +839,7 @@ DEF_CDOUBLE_FUN_2(hermite_h, acb_hypgeom_hermite_h)
 /* todo: fresnel (with flags) */
 /* todo: functions with multiple outputs */
 /* todo: incomplete gamma, exp integrals... */
+/* todo: airy zeros */
 /* legendre_p, legendre_q, +roots, spherharm */
 /* todo: pfqs */
 
-