From 9916182253deeb400d9b022e30056a4ac9a01b18 Mon Sep 17 00:00:00 2001
From: fredrik <fredrik.johansson@gmail.com>
Date: Sun, 19 Sep 2021 12:56:03 +0200
Subject: [PATCH] use table for const_euler at low prec

---
 arb/const_euler.c | 29 ++++++++++++++++++++++++++++-
 1 file changed, 28 insertions(+), 1 deletion(-)

diff --git a/arb/const_euler.c b/arb/const_euler.c
index bbfcc2fb..90fa4279 100644
--- a/arb/const_euler.c
+++ b/arb/const_euler.c
@@ -11,6 +11,7 @@
 
 #include "arb.h"
 #include "hypgeom.h"
+#include "arb_hypgeom.h"
 
 typedef struct
 {
@@ -333,5 +334,31 @@ arb_const_euler_eval(arb_t res, slong prec)
     euler_bsplit_clear(sum);
 }
 
-ARB_DEF_CACHED_CONSTANT(arb_const_euler, arb_const_euler_eval)
+ARB_DEF_CACHED_CONSTANT(arb_const_euler_brent_mcmillan, arb_const_euler_eval)
+
+extern const mp_limb_t arb_hypgeom_gamma_tab_limbs[];
+
+void
+arb_const_euler(arb_t res, slong prec)
+{
+    if (prec < ARB_HYPGEOM_GAMMA_TAB_PREC - 16)
+    {
+        slong exp;
+        mp_size_t n;
+
+        n = ARB_HYPGEOM_GAMMA_TAB_PREC / FLINT_BITS;
+
+        /* just reading the table is known to give the correct rounding */
+        _arf_set_round_mpn(arb_midref(res), &exp, arb_hypgeom_gamma_tab_limbs + n, n, 0, prec, ARF_RND_NEAR);
+        _fmpz_set_si_small(ARF_EXPREF(arb_midref(res)), exp);
+
+        /* 1/2 ulp error */
+        _fmpz_set_si_small(MAG_EXPREF(arb_radref(res)), exp - prec);
+        MAG_MAN(arb_radref(res)) = MAG_ONE_HALF;
+    }
+    else
+    {
+        arb_const_euler_brent_mcmillan(res, prec);
+    }
+}