Improve good_size and export to python

- Optimises good_size by reducing search space
- Adds real variant for finding 5-smooth numbers
- Exports good_size to python

pocketfft_hdronly.h

@@ -456,17 +456,58 @@ struct util // hack to avoid duplicate symbols
     }
 
   /* returns the smallest composite of 2, 3, 5, 7 and 11 which is >= n */
-  static POCKETFFT_NOINLINE size_t good_size(size_t n)
+  static POCKETFFT_NOINLINE size_t good_size_cmplx(size_t n)
     {
     if (n<=12) return n;
 
     size_t bestfac=2*n;
-    for (size_t f2=1; f2<bestfac; f2*=2)
-      for (size_t f23=f2; f23<bestfac; f23*=3)
-        for (size_t f235=f23; f235<bestfac; f235*=5)
-          for (size_t f2357=f235; f2357<bestfac; f2357*=7)
-            for (size_t f235711=f2357; f235711<bestfac; f235711*=11)
-              if (f235711>=n) bestfac=f235711;
+    for (size_t f11=1; f11<bestfac; f11*=11)
+      for (size_t f117=f11; f117<bestfac; f117*=7)
+        for (size_t f1175=f117; f1175<bestfac; f1175*=5)
+          {
+          size_t x=f1175;
+          while (x<n) x*=2;
+          for (;;)
+            {
+            if (x<n)
+              x*=3;
+            else if (x>n)
+              {
+              if (x<bestfac) bestfac=x;
+              if (x&1) break;
+              x>>=1;
+              }
+            else
+              return n;
+            }
+          }
+    return bestfac;
+    }
+
+  /* returns the smallest composite of 2, 3, 5 which is >= n */
+  static POCKETFFT_NOINLINE size_t good_size_real(size_t n)
+    {
+    if (n<=6) return n;
+
+    size_t bestfac=2*n;
+    for (size_t f5=1; f5<bestfac; f5*=5)
+      {
+      size_t x = f5;
+      while (x<n) x *= 2;
+      for (;;)
+        {
+        if (x<n)
+          x*=3;
+        else if (x>n)
+          {
+          if (x<bestfac) bestfac=x;
+          if (x&1) break;
+          x>>=1;
+          }
+        else
+          return n;
+        }
+      }
     return bestfac;
     }
 
@@ -2154,7 +2195,7 @@ template<typename T0> class fftblue
 
   public:
     POCKETFFT_NOINLINE fftblue(size_t length)
-      : n(length), n2(util::good_size(n*2-1)), plan(n2), mem(n+n2),
+      : n(length), n2(util::good_size_cmplx(n*2-1)), plan(n2), mem(n+n2),
         bk(mem.data()), bkf(mem.data()+n)
       {
       /* initialize b_k */
@@ -2235,7 +2276,7 @@ template<typename T0> class pocketfft_c
         return;
         }
       double comp1 = util::cost_guess(length);
-      double comp2 = 2*util::cost_guess(util::good_size(2*length-1));
+      double comp2 = 2*util::cost_guess(util::good_size_cmplx(2*length-1));
       comp2*=1.5; /* fudge factor that appears to give good overall performance */
       if (comp2<comp1) // use Bluestein
         blueplan=unique_ptr<fftblue<T0>>(new fftblue<T0>(length));
@@ -2275,7 +2316,7 @@ template<typename T0> class pocketfft_r
         return;
         }
       double comp1 = 0.5*util::cost_guess(length);
-      double comp2 = 2*util::cost_guess(util::good_size(2*length-1));
+      double comp2 = 2*util::cost_guess(util::good_size_cmplx(2*length-1));
       comp2*=1.5; /* fudge factor that appears to give good overall performance */
       if (comp2<comp1) // use Bluestein
         blueplan=unique_ptr<fftblue<T0>>(new fftblue<T0>(length));

pypocketfft.cc

@@ -377,6 +377,12 @@ py::array genuine_hartley(const py::array &in, const py::object &axes_,
   DISPATCH(in, f64, f32, flong, complex2hartley, (in, tmp, axes_, out_))
   }
 
+size_t good_size(size_t n, bool real)
+  {
+  using namespace pocketfft::detail;
+  return real ? util::good_size_real(n) : util::good_size_cmplx(n);
+  }
+
 const char *pypocketfft_DS = R"""(Fast Fourier and Hartley transforms.
 
 This module supports
@@ -662,6 +668,22 @@ numpy.ndarray (same shape and data type as `a`)
     The transformed data
 )""";
 
+const char * good_size_DS = R"""(Returns a good length to pad an FFT to.
+
+Parameters
+----------
+n : int
+    Minimum transform length
+real : bool, optional
+    True if either input or output of FFT should be fully real.
+
+Returns
+-------
+out : int
+    The smallest fast size >= n
+
+)""";
+
 } // unnamed namespace
 
 PYBIND11_MODULE(pypocketfft, m)
@@ -685,4 +707,5 @@ PYBIND11_MODULE(pypocketfft, m)
     "out"_a=None, "nthreads"_a=1);
   m.def("dst", dst, dst_DS, "a"_a, "type"_a, "axes"_a=None, "inorm"_a=0,
     "out"_a=None, "nthreads"_a=1);
+  m.def("good_size", good_size, good_size_DS, "n"_a, "real"_a=false);
   }