use dft convol for smooth integers

acb_dft.h

@@ -37,6 +37,7 @@ void acb_dft_prod(acb_ptr w, acb_srcptr v, slong * cyc, slong num, slong prec);
 void acb_dft_convol_naive(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec);
 void acb_dft_convol_dft(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec);
 void acb_dft_convol_rad2(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec);
+void acb_dft_convol(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec);
 
 #define CRT_MAX 15
 typedef struct

acb_dft/convol.c

@@ -0,0 +1,35 @@
+/*
+    Copyright (C) 2016 Pascal Molin
+
+    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_dft.h"
+
+static int use_dft(slong len, slong prec)
+{
+    slong l2 = len;
+    while (l2 >= 16) l2 >>= 1;
+    if (l2 < 11)
+    {
+        while (!(len & 1)) len >>= 1;
+        while (len % 3 == 0) len /= 3;
+        while (len % 5 == 0) len /= 5;
+        while (len % 7 == 0) len /= 7;
+        return (len == 1);
+    }
+    return 0;
+}
+
+void acb_dft_convol(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec)
+{
+    if (use_dft(len, prec))
+        acb_dft_convol_dft(w, f, g, len, prec);
+    else
+        acb_dft_convol_rad2(w, f, g, len, prec);
+}

acb_dft/profile/p-convol.c

@@ -26,16 +26,18 @@ int main(int argc, char *argv[])
     flint_rand_t state;
     slong r, nr;
 
-    int l, nf = 3;
-    do_f func[3] = {
+    int l, nf = 4;
+    do_f func[4] = {
         acb_dft_convol_naive,
         acb_dft_convol_dft,
         acb_dft_convol_rad2,
+        acb_dft_convol,
     };
-    char * name[3] = {
+    char * name[4] = {
         "naive",
         "dft",
-        "rad2"
+        "rad2",
+        "default"
     };
 
     int i, ni = 14;

doc/source/acb_dft.rst

@@ -141,6 +141,8 @@ For functions `f` and `g` on `G` we consider the convolution
 
 .. function:: void acb_dft_convol_rad2(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec)
 
+.. function:: void acb_dft_convol(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec)
+
    Sets *w* to the convolution of *f* and *g* of length *len*.
 
    The *naive* version simply uses the definition.
@@ -153,3 +155,6 @@ For functions `f` and `g` on `G` we consider the convolution
       \widehat{f \star g}(\chi) = \hat f(\chi)\hat g(\chi)
 
    to compute it using three radix 2 FFT.
+
+   The default version uses radix 2 FFT unless *len* is a product of small
+   primes where a non padded fft is faster.