From 43b98b6045657666621f980bd72f3e21df60ff57 Mon Sep 17 00:00:00 2001
From: Fredrik Johansson <fredrik.johansson@gmail.com>
Date: Tue, 20 Jan 2015 16:55:15 +0100
Subject: [PATCH] optimize arb_digamma for small integers

---
 arb/digamma.c | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/arb/digamma.c b/arb/digamma.c
index 3cc6c09c..33f97eb7 100644
--- a/arb/digamma.c
+++ b/arb/digamma.c
@@ -24,6 +24,7 @@
 ******************************************************************************/
 
 #include "arb.h"
+#include "arith.h"
 
 void arb_gamma_stirling_choose_param(int * reflect, long * r, long * n,
     const arb_t x, int use_reflect, int digamma, long prec);
@@ -37,6 +38,43 @@ arb_digamma(arb_t y, const arb_t x, long prec)
     long r, n, wp;
     arb_t t, u, v;
 
+    if (arb_is_exact(x))
+    {
+        const arf_struct * mid = arb_midref(x);
+
+        if (arf_is_special(mid))
+        {
+            arb_indeterminate(y);
+            return;
+        }
+        else if (arf_is_int(mid))
+        {
+            if (arf_sgn(mid) < 0)
+            {
+                arb_indeterminate(y);
+                return;
+            }
+            else if (arf_cmpabs_ui(mid, 30 + prec / 2) < 0)
+            {
+                fmpq_t h;
+
+                arb_init(t);
+                fmpq_init(h);
+
+                /* should change to fmpq_harmonic_ui when flint upgrades */
+                arith_harmonic_number(h, arf_get_si(mid, ARF_RND_DOWN) - 1);
+                arb_set_fmpq(y, h, prec + 2);
+                arb_const_euler(t, prec + 2);
+                arb_sub(y, y, t, prec);
+
+                arb_clear(t);
+                fmpq_clear(h);
+
+                return;
+            }
+        }
+    }
+
     wp = prec + FLINT_BIT_COUNT(prec);
 
     arb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 1, wp);