From 0d96be37f81f192e5031b5a0153f128212c70e02 Mon Sep 17 00:00:00 2001
From: Pascal <molin.maths@gmail.com>
Date: Wed, 23 Mar 2016 18:23:19 +0100
Subject: [PATCH] add parity in char (simpler to have on logs)

---
 acb_dirichlet.h                               | 24 ++++++++++++++++++-
 acb_dirichlet/char_conrey.c                   |  3 ++-
 .../{char_is_odd.c => conrey_parity.c}        |  6 ++---
 acb_dirichlet/test/t-thetanull.c              |  2 +-
 4 files changed, 29 insertions(+), 6 deletions(-)
 rename acb_dirichlet/{char_is_odd.c => conrey_parity.c} (89%)

diff --git a/acb_dirichlet.h b/acb_dirichlet.h
index 3279cd39..fb1e7c2a 100644
--- a/acb_dirichlet.h
+++ b/acb_dirichlet.h
@@ -1,6 +1,7 @@
 /*
     Copyright (C) 2015 Jonathan Bober
     Copyright (C) 2016 Fredrik Johansson
+    Copyright (C) 2016 Pascal Molin
 
     This file is part of Arb.
 
@@ -13,6 +14,12 @@
 #ifndef ACB_DIRICHLET_H
 #define ACB_DIRICHLET_H
 
+#ifdef ACB_INLINES_C
+#define ACB_INLINE
+#else
+#define ACB_INLINE static __inline__
+#endif
+
 #include "acb.h"
 #include "dlog.h"
 
@@ -59,11 +66,14 @@ void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
 
 void acb_dirichlet_group_init(acb_dirichlet_group_t G, ulong q);
 void acb_dirichlet_group_clear(acb_dirichlet_group_t G);
+void acb_dirichlet_group_dlog_precompute(acb_dirichlet_group_t G, ulong num);
+
 
 void acb_dirichlet_conrey_init(acb_dirichlet_conrey_t x, const acb_dirichlet_group_t G);
 void acb_dirichlet_conrey_clear(acb_dirichlet_conrey_t x);
 void acb_dirichlet_conrey_print(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x);
 
+int acb_dirichlet_conrey_parity(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x);
 void acb_dirichlet_conrey_log(acb_dirichlet_conrey_t x, const acb_dirichlet_group_t G, ulong m);
 
 void acb_dirichlet_conrey_one(acb_dirichlet_conrey_t x, const acb_dirichlet_group_t G);
@@ -89,11 +99,24 @@ typedef struct
   ulong n;           /* number */
   ulong order;       /* order */
   ulong * expo;      /* reduced exponents ( order * log[k] / gcd( ) ) */
+  int parity;        /* 0 for even char, 1 for odd */
 }
 acb_dirichlet_char_struct;
 
 typedef acb_dirichlet_char_struct acb_dirichlet_char_t[1];
 
+ACB_INLINE int
+acb_dirichlet_char_order(const acb_dirichlet_char_t chi)
+{
+    return chi->order;
+}
+
+ACB_INLINE int
+acb_dirichlet_char_parity(const acb_dirichlet_char_t chi)
+{
+    return chi->parity;
+}
+
 void acb_dirichlet_char_init(acb_dirichlet_char_t chi, const acb_dirichlet_group_t G);
 void acb_dirichlet_char_clear(acb_dirichlet_char_t chi);
 void acb_dirichlet_char_print(const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi);
@@ -129,4 +152,3 @@ void acb_dirichlet_arb_quadratic_powers(arb_ptr v, slong nv, const arb_t x, slon
 #endif
 
 #endif
-
diff --git a/acb_dirichlet/char_conrey.c b/acb_dirichlet/char_conrey.c
index 8414534f..c295c011 100644
--- a/acb_dirichlet/char_conrey.c
+++ b/acb_dirichlet/char_conrey.c
@@ -33,9 +33,10 @@ acb_dirichlet_char_conrey(acb_dirichlet_char_t chi, const acb_dirichlet_group_t
   ulong k;
   chi->q = G->q;
   chi->n = x->n;
+  chi->parity = acb_dirichlet_conrey_parity(G, x);
 
   for (k = 0; k < G->num; k++)
-    chi->expo[k] = (x->log[k] * G->PHI[k]) % G->expo;
+      chi->expo[k] = (x->log[k] * G->PHI[k]) % G->expo;
 
   /* optional: divide by gcd to obtain true order */
   acb_dirichlet_char_normalize(chi, G);
diff --git a/acb_dirichlet/char_is_odd.c b/acb_dirichlet/conrey_parity.c
similarity index 89%
rename from acb_dirichlet/char_is_odd.c
rename to acb_dirichlet/conrey_parity.c
index cb5d0502..ede8aaf6 100644
--- a/acb_dirichlet/char_is_odd.c
+++ b/acb_dirichlet/conrey_parity.c
@@ -26,14 +26,14 @@
 #include "acb_dirichlet.h"
 
 int
-acb_dirichlet_char_is_odd(const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi)
+acb_dirichlet_conrey_parity(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x)
 {
-    slong k, odd = 0;
+    int k, odd = 0;
     for (k = 0; k < G->num; k++)
     {
         if (k == 1 && G->neven == 2)
             continue;
-        if (chi->expo[k] % 2 == 1)
+        if (x->log[k] % 2)
             odd = 1 - odd;
     }
     return odd;
diff --git a/acb_dirichlet/test/t-thetanull.c b/acb_dirichlet/test/t-thetanull.c
index dc7ca96a..e57889a2 100644
--- a/acb_dirichlet/test/t-thetanull.c
+++ b/acb_dirichlet/test/t-thetanull.c
@@ -100,7 +100,7 @@ int main()
             /*
             flint_printf("Theta(chi_%wu(%wu)) (m=%wu)\n", q, chi->n, m);
             */
-            tt = acb_dirichlet_char_is_odd(G, chi) ? kt : t;
+            tt = acb_dirichlet_char_parity(chi) ? kt : t;
             for (k = 1; k < nv; k++)
                 if (v[k] != CHI_NULL)
                     acb_addmul_arb(sum, z + (v[k] * m), tt + k, prec);