MAINT: move pocketfft .py/.so to `_pocketfft`

These aren't public, and should have been added with underscores.

1 files changed, 0 insertions, 2406 deletions

diff --git a/numpy/fft/pocketfft.c b/numpy/fft/pocketfft.c
deleted file mode 100644
index 9d1218e6b..000000000
--- a/numpy/fft/pocketfft.c
+++ /dev/null
@@ -1,2406 +0,0 @@
-/*
- * This file is part of pocketfft.
- * Licensed under a 3-clause BSD style license - see LICENSE.md
- */
-
-/*
- *  Main implementation file.
- *
- *  Copyright (C) 2004-2018 Max-Planck-Society
- *  \author Martin Reinecke
- */
-
-#include <math.h>
-#include <string.h>
-#include <stdlib.h>
-
-#include "npy_config.h"
-#define restrict NPY_RESTRICT
-
-#define RALLOC(type,num) \
-  ((type *)malloc((num)*sizeof(type)))
-#define DEALLOC(ptr) \
-  do { free(ptr); (ptr)=NULL; } while(0)
-
-#define SWAP(a,b,type) \
-  do { type tmp_=(a); (a)=(b); (b)=tmp_; } while(0)
-
-#ifdef __GNUC__
-#define NOINLINE __attribute__((noinline))
-#define WARN_UNUSED_RESULT __attribute__ ((warn_unused_result))
-#else
-#define NOINLINE
-#define WARN_UNUSED_RESULT
-#endif
-
-struct cfft_plan_i;
-typedef struct cfft_plan_i * cfft_plan;
-struct rfft_plan_i;
-typedef struct rfft_plan_i * rfft_plan;
-
-// adapted from https://stackoverflow.com/questions/42792939/
-// CAUTION: this function only works for arguments in the range [-0.25; 0.25]!
-static void my_sincosm1pi (double a, double *restrict res)
-  {
-  double s = a * a;
-  /* Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
-  double r =     -1.0369917389758117e-4;
-  r = fma (r, s,  1.9294935641298806e-3);
-  r = fma (r, s, -2.5806887942825395e-2);
-  r = fma (r, s,  2.3533063028328211e-1);
-  r = fma (r, s, -1.3352627688538006e+0);
-  r = fma (r, s,  4.0587121264167623e+0);
-  r = fma (r, s, -4.9348022005446790e+0);
-  double c = r*s;
-  /* Approximate sin(pi*x) for x in [-0.25,0.25] */
-  r =             4.6151442520157035e-4;
-  r = fma (r, s, -7.3700183130883555e-3);
-  r = fma (r, s,  8.2145868949323936e-2);
-  r = fma (r, s, -5.9926452893214921e-1);
-  r = fma (r, s,  2.5501640398732688e+0);
-  r = fma (r, s, -5.1677127800499516e+0);
-  s = s * a;
-  r = r * s;
-  s = fma (a, 3.1415926535897931e+0, r);
-  res[0] = c;
-  res[1] = s;
-  }
-
-NOINLINE static void calc_first_octant(size_t den, double * restrict res)
-  {
-  size_t n = (den+4)>>3;
-  if (n==0) return;
-  res[0]=1.; res[1]=0.;
-  if (n==1) return;
-  size_t l1=(size_t)sqrt(n);
-  for (size_t i=1; i<l1; ++i)
-    my_sincosm1pi((2.*i)/den,&res[2*i]);
-  size_t start=l1;
-  while(start<n)
-    {
-    double cs[2];
-    my_sincosm1pi((2.*start)/den,cs);
-    res[2*start] = cs[0]+1.;
-    res[2*start+1] = cs[1];
-    size_t end = l1;
-    if (start+end>n) end = n-start;
-    for (size_t i=1; i<end; ++i)
-      {
-      double csx[2]={res[2*i], res[2*i+1]};
-      res[2*(start+i)] = ((cs[0]*csx[0] - cs[1]*csx[1] + cs[0]) + csx[0]) + 1.;
-      res[2*(start+i)+1] = (cs[0]*csx[1] + cs[1]*csx[0]) + cs[1] + csx[1];
-      }
-    start += l1;
-    }
-  for (size_t i=1; i<l1; ++i)
-    res[2*i] += 1.;
-  }
-
-NOINLINE static void calc_first_quadrant(size_t n, double * restrict res)
-  {
-  double * restrict p = res+n;
-  calc_first_octant(n<<1, p);
-  size_t ndone=(n+2)>>2;
-  size_t i=0, idx1=0, idx2=2*ndone-2;
-  for (; i+1<ndone; i+=2, idx1+=2, idx2-=2)
-    {
-    res[idx1]   = p[2*i];
-    res[idx1+1] = p[2*i+1];
-    res[idx2]   = p[2*i+3];
-    res[idx2+1] = p[2*i+2];
-    }
-  if (i!=ndone)
-    {
-    res[idx1  ] = p[2*i];
-    res[idx1+1] = p[2*i+1];
-    }
-  }
-
-NOINLINE static void calc_first_half(size_t n, double * restrict res)
-  {
-  int ndone=(n+1)>>1;
-  double * p = res+n-1;
-  calc_first_octant(n<<2, p);
-  int i4=0, in=n, i=0;
-  for (; i4<=in-i4; ++i, i4+=4) // octant 0
-    {
-    res[2*i] = p[2*i4]; res[2*i+1] = p[2*i4+1];
-    }
-  for (; i4-in <= 0; ++i, i4+=4) // octant 1
-    {
-    int xm = in-i4;
-    res[2*i] = p[2*xm+1]; res[2*i+1] = p[2*xm];
-    }
-  for (; i4<=3*in-i4; ++i, i4+=4) // octant 2
-    {
-    int xm = i4-in;
-    res[2*i] = -p[2*xm+1]; res[2*i+1] = p[2*xm];
-    }
-  for (; i<ndone; ++i, i4+=4) // octant 3
-    {
-    int xm = 2*in-i4;
-    res[2*i] = -p[2*xm]; res[2*i+1] = p[2*xm+1];
-    }
-  }
-
-NOINLINE static void fill_first_quadrant(size_t n, double * restrict res)
-  {
-  const double hsqt2 = 0.707106781186547524400844362104849;
-  size_t quart = n>>2;
-  if ((n&7)==0)
-    res[quart] = res[quart+1] = hsqt2;
-  for (size_t i=2, j=2*quart-2; i<quart; i+=2, j-=2)
-    {
-    res[j  ] = res[i+1];
-    res[j+1] = res[i  ];
-    }
-  }
-
-NOINLINE static void fill_first_half(size_t n, double * restrict res)
-  {
-  size_t half = n>>1;
-  if ((n&3)==0)
-    for (size_t i=0; i<half; i+=2)
-      {
-      res[i+half]   = -res[i+1];
-      res[i+half+1] =  res[i  ];
-      }
-  else
-    for (size_t i=2, j=2*half-2; i<half; i+=2, j-=2)
-      {
-      res[j  ] = -res[i  ];
-      res[j+1] =  res[i+1];
-      }
-  }
-
-NOINLINE static void fill_second_half(size_t n, double * restrict res)
-  {
-  if ((n&1)==0)
-    for (size_t i=0; i<n; ++i)
-      res[i+n] = -res[i];
-  else
-    for (size_t i=2, j=2*n-2; i<n; i+=2, j-=2)
-      {
-      res[j  ] =  res[i  ];
-      res[j+1] = -res[i+1];
-      }
-  }
-
-NOINLINE static void sincos_2pibyn_half(size_t n, double * restrict res)
-  {
-  if ((n&3)==0)
-    {
-    calc_first_octant(n, res);
-    fill_first_quadrant(n, res);
-    fill_first_half(n, res);
-    }
-  else if ((n&1)==0)
-    {
-    calc_first_quadrant(n, res);
-    fill_first_half(n, res);
-    }
-  else
-    calc_first_half(n, res);
-  }
-
-NOINLINE static void sincos_2pibyn(size_t n, double * restrict res)
-  {
-  sincos_2pibyn_half(n, res);
-  fill_second_half(n, res);
-  }
-
-NOINLINE static size_t largest_prime_factor (size_t n)
-  {
-  size_t res=1;
-  size_t tmp;
-  while (((tmp=(n>>1))<<1)==n)
-    { res=2; n=tmp; }
-
-  size_t limit=(size_t)sqrt(n+0.01);
-  for (size_t x=3; x<=limit; x+=2)
-  while (((tmp=(n/x))*x)==n)
-    {
-    res=x;
-    n=tmp;
-    limit=(size_t)sqrt(n+0.01);
-    }
-  if (n>1) res=n;
-
-  return res;
-  }
-
-NOINLINE static double cost_guess (size_t n)
-  {
-  const double lfp=1.1; // penalty for non-hardcoded larger factors
-  size_t ni=n;
-  double result=0.;
-  size_t tmp;
-  while (((tmp=(n>>1))<<1)==n)
-    { result+=2; n=tmp; }
-
-  size_t limit=(size_t)sqrt(n+0.01);
-  for (size_t x=3; x<=limit; x+=2)
-  while ((tmp=(n/x))*x==n)
-    {
-    result+= (x<=5) ? x : lfp*x; // penalize larger prime factors
-    n=tmp;
-    limit=(size_t)sqrt(n+0.01);
-    }
-  if (n>1) result+=(n<=5) ? n : lfp*n;
-
-  return result*ni;
-  }
-
-/* returns the smallest composite of 2, 3, 5, 7 and 11 which is >= n */
-NOINLINE static size_t good_size(size_t n)
-  {
-  if (n<=6) 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;
-  return bestfac;
-  }
-
-typedef struct cmplx {
-  double r,i;
-} cmplx;
-
-#define NFCT 25
-typedef struct cfftp_fctdata
-  {
-  size_t fct;
-  cmplx *tw, *tws;
-  } cfftp_fctdata;
-
-typedef struct cfftp_plan_i
-  {
-  size_t length, nfct;
-  cmplx *mem;
-  cfftp_fctdata fct[NFCT];
-  } cfftp_plan_i;
-typedef struct cfftp_plan_i * cfftp_plan;
-
-#define PMC(a,b,c,d) { a.r=c.r+d.r; a.i=c.i+d.i; b.r=c.r-d.r; b.i=c.i-d.i; }
-#define ADDC(a,b,c) { a.r=b.r+c.r; a.i=b.i+c.i; }
-#define SCALEC(a,b) { a.r*=b; a.i*=b; }
-#define ROT90(a) { double tmp_=a.r; a.r=-a.i; a.i=tmp_; }
-#define ROTM90(a) { double tmp_=-a.r; a.r=a.i; a.i=tmp_; }
-#define CH(a,b,c) ch[(a)+ido*((b)+l1*(c))]
-#define CC(a,b,c) cc[(a)+ido*((b)+cdim*(c))]
-#define WA(x,i) wa[(i)-1+(x)*(ido-1)]
-/* a = b*c */
-#define A_EQ_B_MUL_C(a,b,c) { a.r=b.r*c.r-b.i*c.i; a.i=b.r*c.i+b.i*c.r; }
-/* a = conj(b)*c*/
-#define A_EQ_CB_MUL_C(a,b,c) { a.r=b.r*c.r+b.i*c.i; a.i=b.r*c.i-b.i*c.r; }
-
-#define PMSIGNC(a,b,c,d) { a.r=c.r+sign*d.r; a.i=c.i+sign*d.i; b.r=c.r-sign*d.r; b.i=c.i-sign*d.i; }
-/* a = b*c */
-#define MULPMSIGNC(a,b,c) { a.r=b.r*c.r-sign*b.i*c.i; a.i=b.r*c.i+sign*b.i*c.r; }
-/* a *= b */
-#define MULPMSIGNCEQ(a,b) { double xtmp=a.r; a.r=b.r*a.r-sign*b.i*a.i; a.i=b.r*a.i+sign*b.i*xtmp; }
-
-NOINLINE static void pass2b (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=2;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      PMC (CH(0,k,0),CH(0,k,1),CC(0,0,k),CC(0,1,k))
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      PMC (CH(0,k,0),CH(0,k,1),CC(0,0,k),CC(0,1,k))
-      for (size_t i=1; i<ido; ++i)
-        {
-        cmplx t;
-        PMC (CH(i,k,0),t,CC(i,0,k),CC(i,1,k))
-        A_EQ_B_MUL_C (CH(i,k,1),WA(0,i),t)
-        }
-      }
-  }
-
-NOINLINE static void pass2f (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=2;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      PMC (CH(0,k,0),CH(0,k,1),CC(0,0,k),CC(0,1,k))
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      PMC (CH(0,k,0),CH(0,k,1),CC(0,0,k),CC(0,1,k))
-      for (size_t i=1; i<ido; ++i)
-        {
-        cmplx t;
-        PMC (CH(i,k,0),t,CC(i,0,k),CC(i,1,k))
-        A_EQ_CB_MUL_C (CH(i,k,1),WA(0,i),t)
-        }
-      }
-  }
-
-#define PREP3(idx) \
-        cmplx t0 = CC(idx,0,k), t1, t2; \
-        PMC (t1,t2,CC(idx,1,k),CC(idx,2,k)) \
-        CH(idx,k,0).r=t0.r+t1.r; \
-        CH(idx,k,0).i=t0.i+t1.i;
-#define PARTSTEP3a(u1,u2,twr,twi) \
-        { \
-        cmplx ca,cb; \
-        ca.r=t0.r+twr*t1.r; \
-        ca.i=t0.i+twr*t1.i; \
-        cb.i=twi*t2.r; \
-        cb.r=-(twi*t2.i); \
-        PMC(CH(0,k,u1),CH(0,k,u2),ca,cb) \
-        }
-
-#define PARTSTEP3b(u1,u2,twr,twi) \
-        { \
-        cmplx ca,cb,da,db; \
-        ca.r=t0.r+twr*t1.r; \
-        ca.i=t0.i+twr*t1.i; \
-        cb.i=twi*t2.r; \
-        cb.r=-(twi*t2.i); \
-        PMC(da,db,ca,cb) \
-        A_EQ_B_MUL_C (CH(i,k,u1),WA(u1-1,i),da) \
-        A_EQ_B_MUL_C (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-NOINLINE static void pass3b (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=3;
-  const double tw1r=-0.5, tw1i= 0.86602540378443864676;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP3(0)
-      PARTSTEP3a(1,2,tw1r,tw1i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP3(0)
-      PARTSTEP3a(1,2,tw1r,tw1i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP3(i)
-        PARTSTEP3b(1,2,tw1r,tw1i)
-        }
-      }
-  }
-#define PARTSTEP3f(u1,u2,twr,twi) \
-        { \
-        cmplx ca,cb,da,db; \
-        ca.r=t0.r+twr*t1.r; \
-        ca.i=t0.i+twr*t1.i; \
-        cb.i=twi*t2.r; \
-        cb.r=-(twi*t2.i); \
-        PMC(da,db,ca,cb) \
-        A_EQ_CB_MUL_C (CH(i,k,u1),WA(u1-1,i),da) \
-        A_EQ_CB_MUL_C (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-NOINLINE static void pass3f (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=3;
-  const double tw1r=-0.5, tw1i= -0.86602540378443864676;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP3(0)
-      PARTSTEP3a(1,2,tw1r,tw1i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP3(0)
-      PARTSTEP3a(1,2,tw1r,tw1i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP3(i)
-        PARTSTEP3f(1,2,tw1r,tw1i)
-        }
-      }
-  }
-
-NOINLINE static void pass4b (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=4;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      cmplx t1, t2, t3, t4;
-      PMC(t2,t1,CC(0,0,k),CC(0,2,k))
-      PMC(t3,t4,CC(0,1,k),CC(0,3,k))
-      ROT90(t4)
-      PMC(CH(0,k,0),CH(0,k,2),t2,t3)
-      PMC(CH(0,k,1),CH(0,k,3),t1,t4)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      cmplx t1, t2, t3, t4;
-      PMC(t2,t1,CC(0,0,k),CC(0,2,k))
-      PMC(t3,t4,CC(0,1,k),CC(0,3,k))
-      ROT90(t4)
-      PMC(CH(0,k,0),CH(0,k,2),t2,t3)
-      PMC(CH(0,k,1),CH(0,k,3),t1,t4)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        cmplx c2, c3, c4, t1, t2, t3, t4;
-        cmplx cc0=CC(i,0,k), cc1=CC(i,1,k),cc2=CC(i,2,k),cc3=CC(i,3,k);
-        PMC(t2,t1,cc0,cc2)
-        PMC(t3,t4,cc1,cc3)
-        ROT90(t4)
-        cmplx wa0=WA(0,i), wa1=WA(1,i),wa2=WA(2,i);
-        PMC(CH(i,k,0),c3,t2,t3)
-        PMC(c2,c4,t1,t4)
-        A_EQ_B_MUL_C (CH(i,k,1),wa0,c2)
-        A_EQ_B_MUL_C (CH(i,k,2),wa1,c3)
-        A_EQ_B_MUL_C (CH(i,k,3),wa2,c4)
-        }
-      }
-  }
-NOINLINE static void pass4f (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=4;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      cmplx t1, t2, t3, t4;
-      PMC(t2,t1,CC(0,0,k),CC(0,2,k))
-      PMC(t3,t4,CC(0,1,k),CC(0,3,k))
-      ROTM90(t4)
-      PMC(CH(0,k,0),CH(0,k,2),t2,t3)
-      PMC(CH(0,k,1),CH(0,k,3),t1,t4)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      cmplx t1, t2, t3, t4;
-      PMC(t2,t1,CC(0,0,k),CC(0,2,k))
-      PMC(t3,t4,CC(0,1,k),CC(0,3,k))
-      ROTM90(t4)
-      PMC(CH(0,k,0),CH(0,k,2),t2,t3)
-      PMC (CH(0,k,1),CH(0,k,3),t1,t4)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        cmplx c2, c3, c4, t1, t2, t3, t4;
-        cmplx cc0=CC(i,0,k), cc1=CC(i,1,k),cc2=CC(i,2,k),cc3=CC(i,3,k);
-        PMC(t2,t1,cc0,cc2)
-        PMC(t3,t4,cc1,cc3)
-        ROTM90(t4)
-        cmplx wa0=WA(0,i), wa1=WA(1,i),wa2=WA(2,i);
-        PMC(CH(i,k,0),c3,t2,t3)
-        PMC(c2,c4,t1,t4)
-        A_EQ_CB_MUL_C (CH(i,k,1),wa0,c2)
-        A_EQ_CB_MUL_C (CH(i,k,2),wa1,c3)
-        A_EQ_CB_MUL_C (CH(i,k,3),wa2,c4)
-        }
-      }
-  }
-
-#define PREP5(idx) \
-        cmplx t0 = CC(idx,0,k), t1, t2, t3, t4; \
-        PMC (t1,t4,CC(idx,1,k),CC(idx,4,k)) \
-        PMC (t2,t3,CC(idx,2,k),CC(idx,3,k)) \
-        CH(idx,k,0).r=t0.r+t1.r+t2.r; \
-        CH(idx,k,0).i=t0.i+t1.i+t2.i;
-
-#define PARTSTEP5a(u1,u2,twar,twbr,twai,twbi) \
-        { \
-        cmplx ca,cb; \
-        ca.r=t0.r+twar*t1.r+twbr*t2.r; \
-        ca.i=t0.i+twar*t1.i+twbr*t2.i; \
-        cb.i=twai*t4.r twbi*t3.r; \
-        cb.r=-(twai*t4.i twbi*t3.i); \
-        PMC(CH(0,k,u1),CH(0,k,u2),ca,cb) \
-        }
-
-#define PARTSTEP5b(u1,u2,twar,twbr,twai,twbi) \
-        { \
-        cmplx ca,cb,da,db; \
-        ca.r=t0.r+twar*t1.r+twbr*t2.r; \
-        ca.i=t0.i+twar*t1.i+twbr*t2.i; \
-        cb.i=twai*t4.r twbi*t3.r; \
-        cb.r=-(twai*t4.i twbi*t3.i); \
-        PMC(da,db,ca,cb) \
-        A_EQ_B_MUL_C (CH(i,k,u1),WA(u1-1,i),da) \
-        A_EQ_B_MUL_C (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-NOINLINE static void pass5b (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=5;
-  const double tw1r= 0.3090169943749474241,
-               tw1i= 0.95105651629515357212,
-               tw2r= -0.8090169943749474241,
-               tw2i= 0.58778525229247312917;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP5(0)
-      PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
-      PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP5(0)
-      PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
-      PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP5(i)
-        PARTSTEP5b(1,4,tw1r,tw2r,+tw1i,+tw2i)
-        PARTSTEP5b(2,3,tw2r,tw1r,+tw2i,-tw1i)
-        }
-      }
-  }
-#define PARTSTEP5f(u1,u2,twar,twbr,twai,twbi) \
-        { \
-        cmplx ca,cb,da,db; \
-        ca.r=t0.r+twar*t1.r+twbr*t2.r; \
-        ca.i=t0.i+twar*t1.i+twbr*t2.i; \
-        cb.i=twai*t4.r twbi*t3.r; \
-        cb.r=-(twai*t4.i twbi*t3.i); \
-        PMC(da,db,ca,cb) \
-        A_EQ_CB_MUL_C (CH(i,k,u1),WA(u1-1,i),da) \
-        A_EQ_CB_MUL_C (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-NOINLINE static void pass5f (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa)
-  {
-  const size_t cdim=5;
-  const double tw1r= 0.3090169943749474241,
-               tw1i= -0.95105651629515357212,
-               tw2r= -0.8090169943749474241,
-               tw2i= -0.58778525229247312917;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP5(0)
-      PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
-      PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP5(0)
-      PARTSTEP5a(1,4,tw1r,tw2r,+tw1i,+tw2i)
-      PARTSTEP5a(2,3,tw2r,tw1r,+tw2i,-tw1i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP5(i)
-        PARTSTEP5f(1,4,tw1r,tw2r,+tw1i,+tw2i)
-        PARTSTEP5f(2,3,tw2r,tw1r,+tw2i,-tw1i)
-        }
-      }
-  }
-
-#define PREP7(idx) \
-        cmplx t1 = CC(idx,0,k), t2, t3, t4, t5, t6, t7; \
-        PMC (t2,t7,CC(idx,1,k),CC(idx,6,k)) \
-        PMC (t3,t6,CC(idx,2,k),CC(idx,5,k)) \
-        PMC (t4,t5,CC(idx,3,k),CC(idx,4,k)) \
-        CH(idx,k,0).r=t1.r+t2.r+t3.r+t4.r; \
-        CH(idx,k,0).i=t1.i+t2.i+t3.i+t4.i;
-
-#define PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,out1,out2) \
-        { \
-        cmplx ca,cb; \
-        ca.r=t1.r+x1*t2.r+x2*t3.r+x3*t4.r; \
-        ca.i=t1.i+x1*t2.i+x2*t3.i+x3*t4.i; \
-        cb.i=y1*t7.r y2*t6.r y3*t5.r; \
-        cb.r=-(y1*t7.i y2*t6.i y3*t5.i); \
-        PMC(out1,out2,ca,cb) \
-        }
-#define PARTSTEP7a(u1,u2,x1,x2,x3,y1,y2,y3) \
-        PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,CH(0,k,u1),CH(0,k,u2))
-#define PARTSTEP7(u1,u2,x1,x2,x3,y1,y2,y3) \
-        { \
-        cmplx da,db; \
-        PARTSTEP7a0(u1,u2,x1,x2,x3,y1,y2,y3,da,db) \
-        MULPMSIGNC (CH(i,k,u1),WA(u1-1,i),da) \
-        MULPMSIGNC (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-
-NOINLINE static void pass7(size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa, const int sign)
-  {
-  const size_t cdim=7;
-  const double tw1r= 0.623489801858733530525,
-               tw1i= sign * 0.7818314824680298087084,
-               tw2r= -0.222520933956314404289,
-               tw2i= sign * 0.9749279121818236070181,
-               tw3r= -0.9009688679024191262361,
-               tw3i= sign * 0.4338837391175581204758;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP7(0)
-      PARTSTEP7a(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
-      PARTSTEP7a(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
-      PARTSTEP7a(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP7(0)
-      PARTSTEP7a(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
-      PARTSTEP7a(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
-      PARTSTEP7a(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP7(i)
-        PARTSTEP7(1,6,tw1r,tw2r,tw3r,+tw1i,+tw2i,+tw3i)
-        PARTSTEP7(2,5,tw2r,tw3r,tw1r,+tw2i,-tw3i,-tw1i)
-        PARTSTEP7(3,4,tw3r,tw1r,tw2r,+tw3i,-tw1i,+tw2i)
-        }
-      }
-  }
-
-#define PREP11(idx) \
-        cmplx t1 = CC(idx,0,k), t2, t3, t4, t5, t6, t7, t8, t9, t10, t11; \
-        PMC (t2,t11,CC(idx,1,k),CC(idx,10,k)) \
-        PMC (t3,t10,CC(idx,2,k),CC(idx, 9,k)) \
-        PMC (t4,t9 ,CC(idx,3,k),CC(idx, 8,k)) \
-        PMC (t5,t8 ,CC(idx,4,k),CC(idx, 7,k)) \
-        PMC (t6,t7 ,CC(idx,5,k),CC(idx, 6,k)) \
-        CH(idx,k,0).r=t1.r+t2.r+t3.r+t4.r+t5.r+t6.r; \
-        CH(idx,k,0).i=t1.i+t2.i+t3.i+t4.i+t5.i+t6.i;
-
-#define PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,out1,out2) \
-        { \
-        cmplx ca,cb; \
-        ca.r=t1.r+x1*t2.r+x2*t3.r+x3*t4.r+x4*t5.r+x5*t6.r; \
-        ca.i=t1.i+x1*t2.i+x2*t3.i+x3*t4.i+x4*t5.i+x5*t6.i; \
-        cb.i=y1*t11.r y2*t10.r y3*t9.r y4*t8.r y5*t7.r; \
-        cb.r=-(y1*t11.i y2*t10.i y3*t9.i y4*t8.i y5*t7.i ); \
-        PMC(out1,out2,ca,cb) \
-        }
-#define PARTSTEP11a(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
-        PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,CH(0,k,u1),CH(0,k,u2))
-#define PARTSTEP11(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \
-        { \
-        cmplx da,db; \
-        PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,da,db) \
-        MULPMSIGNC (CH(i,k,u1),WA(u1-1,i),da) \
-        MULPMSIGNC (CH(i,k,u2),WA(u2-1,i),db) \
-        }
-
-NOINLINE static void pass11 (size_t ido, size_t l1, const cmplx * restrict cc,
-  cmplx * restrict ch, const cmplx * restrict wa, const int sign)
-  {
-  const size_t cdim=11;
-  const double tw1r =        0.8412535328311811688618,
-               tw1i = sign * 0.5406408174555975821076,
-               tw2r =        0.4154150130018864255293,
-               tw2i = sign * 0.9096319953545183714117,
-               tw3r =       -0.1423148382732851404438,
-               tw3i = sign * 0.9898214418809327323761,
-               tw4r =       -0.6548607339452850640569,
-               tw4i = sign * 0.755749574354258283774,
-               tw5r =       -0.9594929736144973898904,
-               tw5i = sign * 0.2817325568414296977114;
-
-  if (ido==1)
-    for (size_t k=0; k<l1; ++k)
-      {
-      PREP11(0)
-      PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
-      PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
-      PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
-      PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
-      PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
-      }
-  else
-    for (size_t k=0; k<l1; ++k)
-      {
-      {
-      PREP11(0)
-      PARTSTEP11a(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
-      PARTSTEP11a(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
-      PARTSTEP11a(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
-      PARTSTEP11a(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
-      PARTSTEP11a(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
-      }
-      for (size_t i=1; i<ido; ++i)
-        {
-        PREP11(i)
-        PARTSTEP11(1,10,tw1r,tw2r,tw3r,tw4r,tw5r,+tw1i,+tw2i,+tw3i,+tw4i,+tw5i)
-        PARTSTEP11(2, 9,tw2r,tw4r,tw5r,tw3r,tw1r,+tw2i,+tw4i,-tw5i,-tw3i,-tw1i)
-        PARTSTEP11(3, 8,tw3r,tw5r,tw2r,tw1r,tw4r,+tw3i,-tw5i,-tw2i,+tw1i,+tw4i)
-        PARTSTEP11(4, 7,tw4r,tw3r,tw1r,tw5r,tw2r,+tw4i,-tw3i,+tw1i,+tw5i,-tw2i)
-        PARTSTEP11(5, 6,tw5r,tw1r,tw4r,tw2r,tw3r,+tw5i,-tw1i,+tw4i,-tw2i,+tw3i)
-        }
-      }
-  }
-
-#define CX(a,b,c) cc[(a)+ido*((b)+l1*(c))]
-#define CX2(a,b) cc[(a)+idl1*(b)]
-#define CH2(a,b) ch[(a)+idl1*(b)]
-
-NOINLINE static int passg (size_t ido, size_t ip, size_t l1,
-  cmplx * restrict cc, cmplx * restrict ch, const cmplx * restrict wa,
-  const cmplx * restrict csarr, const int sign)
-  {
-  const size_t cdim=ip;
-  size_t ipph = (ip+1)/2;
-  size_t idl1 = ido*l1;
-
-  cmplx * restrict wal=RALLOC(cmplx,ip);
-  if (!wal) return -1;
-  wal[0]=(cmplx){1.,0.};
-  for (size_t i=1; i<ip; ++i)
-    wal[i]=(cmplx){csarr[i].r,sign*csarr[i].i};
-
-  for (size_t k=0; k<l1; ++k)
-    for (size_t i=0; i<ido; ++i)
-      CH(i,k,0) = CC(i,0,k);
-  for (size_t j=1, jc=ip-1; j<ipph; ++j, --jc)
-    for (size_t k=0; k<l1; ++k)
-      for (size_t i=0; i<ido; ++i)
-        PMC(CH(i,k,j),CH(i,k,jc),CC(i,j,k),CC(i,jc,k))
-  for (size_t k=0; k<l1; ++k)
-    for (size_t i=0; i<ido; ++i)
-      {
-      cmplx tmp = CH(i,k,0);
-      for (size_t j=1; j<ipph; ++j)
-        ADDC(tmp,tmp,CH(i,k,j))
-      CX(i,k,0) = tmp;
-      }
-  for (size_t l=1, lc=ip-1; l<ipph; ++l, --lc)
-    {
-    // j=0
-    for (size_t ik=0; ik<idl1; ++ik)
-      {
-      CX2(ik,l).r = CH2(ik,0).r+wal[l].r*CH2(ik,1).r+wal[2*l].r*CH2(ik,2).r;
-      CX2(ik,l).i = CH2(ik,0).i+wal[l].r*CH2(ik,1).i+wal[2*l].r*CH2(ik,2).i;
-      CX2(ik,lc).r=-wal[l].i*CH2(ik,ip-1).i-wal[2*l].i*CH2(ik,ip-2).i;
-      CX2(ik,lc).i=wal[l].i*CH2(ik,ip-1).r+wal[2*l].i*CH2(ik,ip-2).r;
-      }
-
-    size_t iwal=2*l;
-    size_t j=3, jc=ip-3;
-    for (; j<ipph-1; j+=2, jc-=2)
-      {
-      iwal+=l; if (iwal>ip) iwal-=ip;
-      cmplx xwal=wal[iwal];
-      iwal+=l; if (iwal>ip) iwal-=ip;
-      cmplx xwal2=wal[iwal];
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        CX2(ik,l).r += CH2(ik,j).r*xwal.r+CH2(ik,j+1).r*xwal2.r;
-        CX2(ik,l).i += CH2(ik,j).i*xwal.r+CH2(ik,j+1).i*xwal2.r;
-        CX2(ik,lc).r -= CH2(ik,jc).i*xwal.i+CH2(ik,jc-1).i*xwal2.i;
-        CX2(ik,lc).i += CH2(ik,jc).r*xwal.i+CH2(ik,jc-1).r*xwal2.i;
-        }
-      }
-    for (; j<ipph; ++j, --jc)
-      {
-      iwal+=l; if (iwal>ip) iwal-=ip;
-      cmplx xwal=wal[iwal];
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        CX2(ik,l).r += CH2(ik,j).r*xwal.r;
-        CX2(ik,l).i += CH2(ik,j).i*xwal.r;
-        CX2(ik,lc).r -= CH2(ik,jc).i*xwal.i;
-        CX2(ik,lc).i += CH2(ik,jc).r*xwal.i;
-        }
-      }
-    }
-  DEALLOC(wal);
-
-  // shuffling and twiddling
-  if (ido==1)
-    for (size_t j=1, jc=ip-1; j<ipph; ++j, --jc)
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        cmplx t1=CX2(ik,j), t2=CX2(ik,jc);
-        PMC(CX2(ik,j),CX2(ik,jc),t1,t2)
-        }
-  else
-    {
-    for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)
-      for (size_t k=0; k<l1; ++k)
-        {
-        cmplx t1=CX(0,k,j), t2=CX(0,k,jc);
-        PMC(CX(0,k,j),CX(0,k,jc),t1,t2)
-        for (size_t i=1; i<ido; ++i)
-          {
-          cmplx x1, x2;
-          PMC(x1,x2,CX(i,k,j),CX(i,k,jc))
-          size_t idij=(j-1)*(ido-1)+i-1;
-          MULPMSIGNC (CX(i,k,j),wa[idij],x1)
-          idij=(jc-1)*(ido-1)+i-1;
-          MULPMSIGNC (CX(i,k,jc),wa[idij],x2)
-          }
-        }
-    }
-  return 0;
-  }
-
-#undef CH2
-#undef CX2
-#undef CX
-
-NOINLINE WARN_UNUSED_RESULT static int pass_all(cfftp_plan plan, cmplx c[], double fct,
-  const int sign)
-  {
-  if (plan->length==1) return 0;
-  size_t len=plan->length;
-  size_t l1=1, nf=plan->nfct;
-  cmplx *ch = RALLOC(cmplx, len);
-  if (!ch) return -1;
-  cmplx *p1=c, *p2=ch;
-
-  for(size_t k1=0; k1<nf; k1++)
-    {
-    size_t ip=plan->fct[k1].fct;
-    size_t l2=ip*l1;
-    size_t ido = len/l2;
-    if     (ip==4)
-      sign>0 ? pass4b (ido, l1, p1, p2, plan->fct[k1].tw)
-             : pass4f (ido, l1, p1, p2, plan->fct[k1].tw);
-    else if(ip==2)
-      sign>0 ? pass2b (ido, l1, p1, p2, plan->fct[k1].tw)
-             : pass2f (ido, l1, p1, p2, plan->fct[k1].tw);
-    else if(ip==3)
-      sign>0 ? pass3b (ido, l1, p1, p2, plan->fct[k1].tw)
-             : pass3f (ido, l1, p1, p2, plan->fct[k1].tw);
-    else if(ip==5)
-      sign>0 ? pass5b (ido, l1, p1, p2, plan->fct[k1].tw)
-             : pass5f (ido, l1, p1, p2, plan->fct[k1].tw);
-    else if(ip==7)  pass7 (ido, l1, p1, p2, plan->fct[k1].tw, sign);
-    else if(ip==11) pass11(ido, l1, p1, p2, plan->fct[k1].tw, sign);
-    else
-      {
-      if (passg(ido, ip, l1, p1, p2, plan->fct[k1].tw, plan->fct[k1].tws, sign))
-        { DEALLOC(ch); return -1; }
-      SWAP(p1,p2,cmplx *);
-      }
-    SWAP(p1,p2,cmplx *);
-    l1=l2;
-    }
-  if (p1!=c)
-    {
-    if (fct!=1.)
-      for (size_t i=0; i<len; ++i)
-        {
-        c[i].r = ch[i].r*fct;
-        c[i].i = ch[i].i*fct;
-        }
-    else
-      memcpy (c,p1,len*sizeof(cmplx));
-    }
-  else
-    if (fct!=1.)
-      for (size_t i=0; i<len; ++i)
-        {
-        c[i].r *= fct;
-        c[i].i *= fct;
-        }
-  DEALLOC(ch);
-  return 0;
-  }
-
-#undef PMSIGNC
-#undef A_EQ_B_MUL_C
-#undef A_EQ_CB_MUL_C
-#undef MULPMSIGNC
-#undef MULPMSIGNCEQ
-
-#undef WA
-#undef CC
-#undef CH
-#undef ROT90
-#undef SCALEC
-#undef ADDC
-#undef PMC
-
-NOINLINE WARN_UNUSED_RESULT
-static int cfftp_forward(cfftp_plan plan, double c[], double fct)
-  { return pass_all(plan,(cmplx *)c, fct, -1); }
-
-NOINLINE WARN_UNUSED_RESULT
-static int cfftp_backward(cfftp_plan plan, double c[], double fct)
-  { return pass_all(plan,(cmplx *)c, fct, 1); }
-
-NOINLINE WARN_UNUSED_RESULT
-static int cfftp_factorize (cfftp_plan plan)
-  {
-  size_t length=plan->length;
-  size_t nfct=0;
-  while ((length%4)==0)
-    { if (nfct>=NFCT) return -1; plan->fct[nfct++].fct=4; length>>=2; }
-  if ((length%2)==0)
-    {
-    length>>=1;
-    // factor 2 should be at the front of the factor list
-    if (nfct>=NFCT) return -1;
-    plan->fct[nfct++].fct=2;
-    SWAP(plan->fct[0].fct, plan->fct[nfct-1].fct,size_t);
-    }
-  size_t maxl=(size_t)(sqrt((double)length))+1;
-  for (size_t divisor=3; (length>1)&&(divisor<maxl); divisor+=2)
-    if ((length%divisor)==0)
-      {
-      while ((length%divisor)==0)
-        {
-        if (nfct>=NFCT) return -1;
-        plan->fct[nfct++].fct=divisor;
-        length/=divisor;
-        }
-      maxl=(size_t)(sqrt((double)length))+1;
-      }
-  if (length>1) plan->fct[nfct++].fct=length;
-  plan->nfct=nfct;
-  return 0;
-  }
-
-NOINLINE static size_t cfftp_twsize (cfftp_plan plan)
-  {
-  size_t twsize=0, l1=1;
-  for (size_t k=0; k<plan->nfct; ++k)
-    {
-    size_t ip=plan->fct[k].fct, ido= plan->length/(l1*ip);
-    twsize+=(ip-1)*(ido-1);
-    if (ip>11)
-      twsize+=ip;
-    l1*=ip;
-    }
-  return twsize;
-  }
-
-NOINLINE WARN_UNUSED_RESULT static int cfftp_comp_twiddle (cfftp_plan plan)
-  {
-  size_t length=plan->length;
-  double *twid = RALLOC(double, 2*length);
-  if (!twid) return -1;
-  sincos_2pibyn(length, twid);
-  size_t l1=1;
-  size_t memofs=0;
-  for (size_t k=0; k<plan->nfct; ++k)
-    {
-    size_t ip=plan->fct[k].fct, ido= length/(l1*ip);
-    plan->fct[k].tw=plan->mem+memofs;
-    memofs+=(ip-1)*(ido-1);
-    for (size_t j=1; j<ip; ++j)
-      for (size_t i=1; i<ido; ++i)
-        {
-        plan->fct[k].tw[(j-1)*(ido-1)+i-1].r = twid[2*j*l1*i];
-        plan->fct[k].tw[(j-1)*(ido-1)+i-1].i = twid[2*j*l1*i+1];
-        }
-    if (ip>11)
-      {
-      plan->fct[k].tws=plan->mem+memofs;
-      memofs+=ip;
-      for (size_t j=0; j<ip; ++j)
-        {
-        plan->fct[k].tws[j].r = twid[2*j*l1*ido];
-        plan->fct[k].tws[j].i = twid[2*j*l1*ido+1];
-        }
-      }
-    l1*=ip;
-    }
-  DEALLOC(twid);
-  return 0;
-  }
-
-static cfftp_plan make_cfftp_plan (size_t length)
-  {
-  if (length==0) return NULL;
-  cfftp_plan plan = RALLOC(cfftp_plan_i,1);
-  if (!plan) return NULL;
-  plan->length=length;
-  plan->nfct=0;
-  for (size_t i=0; i<NFCT; ++i)
-    plan->fct[i]=(cfftp_fctdata){0,0,0};
-  plan->mem=0;
-  if (length==1) return plan;
-  if (cfftp_factorize(plan)!=0) { DEALLOC(plan); return NULL; }
-  size_t tws=cfftp_twsize(plan);
-  plan->mem=RALLOC(cmplx,tws);
-  if (!plan->mem) { DEALLOC(plan); return NULL; }
-  if (cfftp_comp_twiddle(plan)!=0)
-    { DEALLOC(plan->mem); DEALLOC(plan); return NULL; }
-  return plan;
-  }
-
-static void destroy_cfftp_plan (cfftp_plan plan)
-  {
-  DEALLOC(plan->mem);
-  DEALLOC(plan);
-  }
-
-typedef struct rfftp_fctdata
-  {
-  size_t fct;
-  double *tw, *tws;
-  } rfftp_fctdata;
-
-typedef struct rfftp_plan_i
-  {
-  size_t length, nfct;
-  double *mem;
-  rfftp_fctdata fct[NFCT];
-  } rfftp_plan_i;
-typedef struct rfftp_plan_i * rfftp_plan;
-
-#define WA(x,i) wa[(i)+(x)*(ido-1)]
-#define PM(a,b,c,d) { a=c+d; b=c-d; }
-/* (a+ib) = conj(c+id) * (e+if) */
-#define MULPM(a,b,c,d,e,f) { a=c*e+d*f; b=c*f-d*e; }
-
-#define CC(a,b,c) cc[(a)+ido*((b)+l1*(c))]
-#define CH(a,b,c) ch[(a)+ido*((b)+cdim*(c))]
-
-NOINLINE static void radf2 (size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=2;
-
-  for (size_t k=0; k<l1; k++)
-    PM (CH(0,0,k),CH(ido-1,1,k),CC(0,k,0),CC(0,k,1))
-  if ((ido&1)==0)
-    for (size_t k=0; k<l1; k++)
-      {
-      CH(    0,1,k) = -CC(ido-1,k,1);
-      CH(ido-1,0,k) =  CC(ido-1,k,0);
-      }
-  if (ido<=2) return;
-  for (size_t k=0; k<l1; k++)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double tr2, ti2;
-      MULPM (tr2,ti2,WA(0,i-2),WA(0,i-1),CC(i-1,k,1),CC(i,k,1))
-      PM (CH(i-1,0,k),CH(ic-1,1,k),CC(i-1,k,0),tr2)
-      PM (CH(i  ,0,k),CH(ic  ,1,k),ti2,CC(i  ,k,0))
-      }
-  }
-
-NOINLINE static void radf3(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=3;
-  static const double taur=-0.5, taui=0.86602540378443864676;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double cr2=CC(0,k,1)+CC(0,k,2);
-    CH(0,0,k) = CC(0,k,0)+cr2;
-    CH(0,2,k) = taui*(CC(0,k,2)-CC(0,k,1));
-    CH(ido-1,1,k) = CC(0,k,0)+taur*cr2;
-    }
-  if (ido==1) return;
-  for (size_t k=0; k<l1; k++)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double di2, di3, dr2, dr3;
-      MULPM (dr2,di2,WA(0,i-2),WA(0,i-1),CC(i-1,k,1),CC(i,k,1)) // d2=conj(WA0)*CC1
-      MULPM (dr3,di3,WA(1,i-2),WA(1,i-1),CC(i-1,k,2),CC(i,k,2)) // d3=conj(WA1)*CC2
-      double cr2=dr2+dr3; // c add
-      double ci2=di2+di3;
-      CH(i-1,0,k) = CC(i-1,k,0)+cr2; // c add
-      CH(i  ,0,k) = CC(i  ,k,0)+ci2;
-      double tr2 = CC(i-1,k,0)+taur*cr2; // c add
-      double ti2 = CC(i  ,k,0)+taur*ci2;
-      double tr3 = taui*(di2-di3);  // t3 = taui*i*(d3-d2)?
-      double ti3 = taui*(dr3-dr2);
-      PM(CH(i-1,2,k),CH(ic-1,1,k),tr2,tr3) // PM(i) = t2+t3
-      PM(CH(i  ,2,k),CH(ic  ,1,k),ti3,ti2) // PM(ic) = conj(t2-t3)
-      }
-  }
-
-NOINLINE static void radf4(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=4;
-  static const double hsqt2=0.70710678118654752440;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double tr1,tr2;
-    PM (tr1,CH(0,2,k),CC(0,k,3),CC(0,k,1))
-    PM (tr2,CH(ido-1,1,k),CC(0,k,0),CC(0,k,2))
-    PM (CH(0,0,k),CH(ido-1,3,k),tr2,tr1)
-    }
-  if ((ido&1)==0)
-    for (size_t k=0; k<l1; k++)
-      {
-      double ti1=-hsqt2*(CC(ido-1,k,1)+CC(ido-1,k,3));
-      double tr1= hsqt2*(CC(ido-1,k,1)-CC(ido-1,k,3));
-      PM (CH(ido-1,0,k),CH(ido-1,2,k),CC(ido-1,k,0),tr1)
-      PM (CH(    0,3,k),CH(    0,1,k),ti1,CC(ido-1,k,2))
-      }
-  if (ido<=2) return;
-  for (size_t k=0; k<l1; k++)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
-      MULPM(cr2,ci2,WA(0,i-2),WA(0,i-1),CC(i-1,k,1),CC(i,k,1))
-      MULPM(cr3,ci3,WA(1,i-2),WA(1,i-1),CC(i-1,k,2),CC(i,k,2))
-      MULPM(cr4,ci4,WA(2,i-2),WA(2,i-1),CC(i-1,k,3),CC(i,k,3))
-      PM(tr1,tr4,cr4,cr2)
-      PM(ti1,ti4,ci2,ci4)
-      PM(tr2,tr3,CC(i-1,k,0),cr3)
-      PM(ti2,ti3,CC(i  ,k,0),ci3)
-      PM(CH(i-1,0,k),CH(ic-1,3,k),tr2,tr1)
-      PM(CH(i  ,0,k),CH(ic  ,3,k),ti1,ti2)
-      PM(CH(i-1,2,k),CH(ic-1,1,k),tr3,ti4)
-      PM(CH(i  ,2,k),CH(ic  ,1,k),tr4,ti3)
-      }
-  }
-
-NOINLINE static void radf5(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=5;
-  static const double tr11= 0.3090169943749474241, ti11=0.95105651629515357212,
-                      tr12=-0.8090169943749474241, ti12=0.58778525229247312917;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double cr2, cr3, ci4, ci5;
-    PM (cr2,ci5,CC(0,k,4),CC(0,k,1))
-    PM (cr3,ci4,CC(0,k,3),CC(0,k,2))
-    CH(0,0,k)=CC(0,k,0)+cr2+cr3;
-    CH(ido-1,1,k)=CC(0,k,0)+tr11*cr2+tr12*cr3;
-    CH(0,2,k)=ti11*ci5+ti12*ci4;
-    CH(ido-1,3,k)=CC(0,k,0)+tr12*cr2+tr11*cr3;
-    CH(0,4,k)=ti12*ci5-ti11*ci4;
-    }
-  if (ido==1) return;
-  for (size_t k=0; k<l1;++k)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      double ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3,
-         dr4, dr5, cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;
-      size_t ic=ido-i;
-      MULPM (dr2,di2,WA(0,i-2),WA(0,i-1),CC(i-1,k,1),CC(i,k,1))
-      MULPM (dr3,di3,WA(1,i-2),WA(1,i-1),CC(i-1,k,2),CC(i,k,2))
-      MULPM (dr4,di4,WA(2,i-2),WA(2,i-1),CC(i-1,k,3),CC(i,k,3))
-      MULPM (dr5,di5,WA(3,i-2),WA(3,i-1),CC(i-1,k,4),CC(i,k,4))
-      PM(cr2,ci5,dr5,dr2)
-      PM(ci2,cr5,di2,di5)
-      PM(cr3,ci4,dr4,dr3)
-      PM(ci3,cr4,di3,di4)
-      CH(i-1,0,k)=CC(i-1,k,0)+cr2+cr3;
-      CH(i  ,0,k)=CC(i  ,k,0)+ci2+ci3;
-      tr2=CC(i-1,k,0)+tr11*cr2+tr12*cr3;
-      ti2=CC(i  ,k,0)+tr11*ci2+tr12*ci3;
-      tr3=CC(i-1,k,0)+tr12*cr2+tr11*cr3;
-      ti3=CC(i  ,k,0)+tr12*ci2+tr11*ci3;
-      MULPM(tr5,tr4,cr5,cr4,ti11,ti12)
-      MULPM(ti5,ti4,ci5,ci4,ti11,ti12)
-      PM(CH(i-1,2,k),CH(ic-1,1,k),tr2,tr5)
-      PM(CH(i  ,2,k),CH(ic  ,1,k),ti5,ti2)
-      PM(CH(i-1,4,k),CH(ic-1,3,k),tr3,tr4)
-      PM(CH(i  ,4,k),CH(ic  ,3,k),ti4,ti3)
-      }
-  }
-
-#undef CC
-#undef CH
-#define C1(a,b,c) cc[(a)+ido*((b)+l1*(c))]
-#define C2(a,b) cc[(a)+idl1*(b)]
-#define CH2(a,b) ch[(a)+idl1*(b)]
-#define CC(a,b,c) cc[(a)+ido*((b)+cdim*(c))]
-#define CH(a,b,c) ch[(a)+ido*((b)+l1*(c))]
-NOINLINE static void radfg(size_t ido, size_t ip, size_t l1,
-  double * restrict cc, double * restrict ch, const double * restrict wa,
-  const double * restrict csarr)
-  {
-  const size_t cdim=ip;
-  size_t ipph=(ip+1)/2;
-  size_t idl1 = ido*l1;
-
-  if (ido>1)
-    {
-    for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)              // 114
-      {
-      size_t is=(j-1)*(ido-1),
-             is2=(jc-1)*(ido-1);
-      for (size_t k=0; k<l1; ++k)                            // 113
-        {
-        size_t idij=is;
-        size_t idij2=is2;
-        for (size_t i=1; i<=ido-2; i+=2)                      // 112
-          {
-          double t1=C1(i,k,j ), t2=C1(i+1,k,j ),
-                 t3=C1(i,k,jc), t4=C1(i+1,k,jc);
-          double x1=wa[idij]*t1 + wa[idij+1]*t2,
-                 x2=wa[idij]*t2 - wa[idij+1]*t1,
-                 x3=wa[idij2]*t3 + wa[idij2+1]*t4,
-                 x4=wa[idij2]*t4 - wa[idij2+1]*t3;
-          C1(i  ,k,j ) = x1+x3;
-          C1(i  ,k,jc) = x2-x4;
-          C1(i+1,k,j ) = x2+x4;
-          C1(i+1,k,jc) = x3-x1;
-          idij+=2;
-          idij2+=2;
-          }
-        }
-      }
-    }
-
-  for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)                // 123
-    for (size_t k=0; k<l1; ++k)                              // 122
-      {
-      double t1=C1(0,k,j), t2=C1(0,k,jc);
-      C1(0,k,j ) = t1+t2;
-      C1(0,k,jc) = t2-t1;
-      }
-
-//everything in C
-//memset(ch,0,ip*l1*ido*sizeof(double));
-
-  for (size_t l=1,lc=ip-1; l<ipph; ++l,--lc)                 // 127
-    {
-    for (size_t ik=0; ik<idl1; ++ik)                         // 124
-      {
-      CH2(ik,l ) = C2(ik,0)+csarr[2*l]*C2(ik,1)+csarr[4*l]*C2(ik,2);
-      CH2(ik,lc) = csarr[2*l+1]*C2(ik,ip-1)+csarr[4*l+1]*C2(ik,ip-2);
-      }
-    size_t iang = 2*l;
-    size_t j=3, jc=ip-3;
-    for (; j<ipph-3; j+=4,jc-=4)              // 126
-      {
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar1=csarr[2*iang], ai1=csarr[2*iang+1];
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar2=csarr[2*iang], ai2=csarr[2*iang+1];
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar3=csarr[2*iang], ai3=csarr[2*iang+1];
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar4=csarr[2*iang], ai4=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)                       // 125
-        {
-        CH2(ik,l ) += ar1*C2(ik,j )+ar2*C2(ik,j +1)
-                     +ar3*C2(ik,j +2)+ar4*C2(ik,j +3);
-        CH2(ik,lc) += ai1*C2(ik,jc)+ai2*C2(ik,jc-1)
-                     +ai3*C2(ik,jc-2)+ai4*C2(ik,jc-3);
-        }
-      }
-    for (; j<ipph-1; j+=2,jc-=2)              // 126
-      {
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar1=csarr[2*iang], ai1=csarr[2*iang+1];
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar2=csarr[2*iang], ai2=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)                       // 125
-        {
-        CH2(ik,l ) += ar1*C2(ik,j )+ar2*C2(ik,j +1);
-        CH2(ik,lc) += ai1*C2(ik,jc)+ai2*C2(ik,jc-1);
-        }
-      }
-    for (; j<ipph; ++j,--jc)              // 126
-      {
-      iang+=l; if (iang>=ip) iang-=ip;
-      double ar=csarr[2*iang], ai=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)                       // 125
-        {
-        CH2(ik,l ) += ar*C2(ik,j );
-        CH2(ik,lc) += ai*C2(ik,jc);
-        }
-      }
-    }
-  for (size_t ik=0; ik<idl1; ++ik)                         // 101
-    CH2(ik,0) = C2(ik,0);
-  for (size_t j=1; j<ipph; ++j)                              // 129
-    for (size_t ik=0; ik<idl1; ++ik)                         // 128
-      CH2(ik,0) += C2(ik,j);
-
-// everything in CH at this point!
-//memset(cc,0,ip*l1*ido*sizeof(double));
-
-  for (size_t k=0; k<l1; ++k)                                // 131
-    for (size_t i=0; i<ido; ++i)                             // 130
-      CC(i,0,k) = CH(i,k,0);
-
-  for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)                // 137
-    {
-    size_t j2=2*j-1;
-    for (size_t k=0; k<l1; ++k)                              // 136
-      {
-      CC(ido-1,j2,k) = CH(0,k,j);
-      CC(0,j2+1,k) = CH(0,k,jc);
-      }
-    }
-
-  if (ido==1) return;
-
-  for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)                // 140
-    {
-    size_t j2=2*j-1;
-    for(size_t k=0; k<l1; ++k)                               // 139
-      for(size_t i=1, ic=ido-i-2; i<=ido-2; i+=2, ic-=2)      // 138
-        {
-        CC(i   ,j2+1,k) = CH(i  ,k,j )+CH(i  ,k,jc);
-        CC(ic  ,j2  ,k) = CH(i  ,k,j )-CH(i  ,k,jc);
-        CC(i+1 ,j2+1,k) = CH(i+1,k,j )+CH(i+1,k,jc);
-        CC(ic+1,j2  ,k) = CH(i+1,k,jc)-CH(i+1,k,j );
-        }
-    }
-  }
-#undef C1
-#undef C2
-#undef CH2
-
-#undef CH
-#undef CC
-#define CH(a,b,c) ch[(a)+ido*((b)+l1*(c))]
-#define CC(a,b,c) cc[(a)+ido*((b)+cdim*(c))]
-
-NOINLINE static void radb2(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=2;
-
-  for (size_t k=0; k<l1; k++)
-    PM (CH(0,k,0),CH(0,k,1),CC(0,0,k),CC(ido-1,1,k))
-  if ((ido&1)==0)
-    for (size_t k=0; k<l1; k++)
-      {
-      CH(ido-1,k,0) = 2.*CC(ido-1,0,k);
-      CH(ido-1,k,1) =-2.*CC(0    ,1,k);
-      }
-  if (ido<=2) return;
-  for (size_t k=0; k<l1;++k)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double ti2, tr2;
-      PM (CH(i-1,k,0),tr2,CC(i-1,0,k),CC(ic-1,1,k))
-      PM (ti2,CH(i  ,k,0),CC(i  ,0,k),CC(ic  ,1,k))
-      MULPM (CH(i,k,1),CH(i-1,k,1),WA(0,i-2),WA(0,i-1),ti2,tr2)
-      }
-  }
-
-NOINLINE static void radb3(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=3;
-  static const double taur=-0.5, taui=0.86602540378443864676;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double tr2=2.*CC(ido-1,1,k);
-    double cr2=CC(0,0,k)+taur*tr2;
-    CH(0,k,0)=CC(0,0,k)+tr2;
-    double ci3=2.*taui*CC(0,2,k);
-    PM (CH(0,k,2),CH(0,k,1),cr2,ci3);
-    }
-  if (ido==1) return;
-  for (size_t k=0; k<l1; k++)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double tr2=CC(i-1,2,k)+CC(ic-1,1,k); // t2=CC(I) + conj(CC(ic))
-      double ti2=CC(i  ,2,k)-CC(ic  ,1,k);
-      double cr2=CC(i-1,0,k)+taur*tr2;     // c2=CC +taur*t2
-      double ci2=CC(i  ,0,k)+taur*ti2;
-      CH(i-1,k,0)=CC(i-1,0,k)+tr2;         // CH=CC+t2
-      CH(i  ,k,0)=CC(i  ,0,k)+ti2;
-      double cr3=taui*(CC(i-1,2,k)-CC(ic-1,1,k));// c3=taui*(CC(i)-conj(CC(ic)))
-      double ci3=taui*(CC(i  ,2,k)+CC(ic  ,1,k));
-      double di2, di3, dr2, dr3;
-      PM(dr3,dr2,cr2,ci3) // d2= (cr2-ci3, ci2+cr3) = c2+i*c3
-      PM(di2,di3,ci2,cr3) // d3= (cr2+ci3, ci2-cr3) = c2-i*c3
-      MULPM(CH(i,k,1),CH(i-1,k,1),WA(0,i-2),WA(0,i-1),di2,dr2) // ch = WA*d2
-      MULPM(CH(i,k,2),CH(i-1,k,2),WA(1,i-2),WA(1,i-1),di3,dr3)
-      }
-  }
-
-NOINLINE static void radb4(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=4;
-  static const double sqrt2=1.41421356237309504880;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double tr1, tr2;
-    PM (tr2,tr1,CC(0,0,k),CC(ido-1,3,k))
-    double tr3=2.*CC(ido-1,1,k);
-    double tr4=2.*CC(0,2,k);
-    PM (CH(0,k,0),CH(0,k,2),tr2,tr3)
-    PM (CH(0,k,3),CH(0,k,1),tr1,tr4)
-    }
-  if ((ido&1)==0)
-    for (size_t k=0; k<l1; k++)
-      {
-      double tr1,tr2,ti1,ti2;
-      PM (ti1,ti2,CC(0    ,3,k),CC(0    ,1,k))
-      PM (tr2,tr1,CC(ido-1,0,k),CC(ido-1,2,k))
-      CH(ido-1,k,0)=tr2+tr2;
-      CH(ido-1,k,1)=sqrt2*(tr1-ti1);
-      CH(ido-1,k,2)=ti2+ti2;
-      CH(ido-1,k,3)=-sqrt2*(tr1+ti1);
-      }
-  if (ido<=2) return;
-  for (size_t k=0; k<l1;++k)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      double ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
-      size_t ic=ido-i;
-      PM (tr2,tr1,CC(i-1,0,k),CC(ic-1,3,k))
-      PM (ti1,ti2,CC(i  ,0,k),CC(ic  ,3,k))
-      PM (tr4,ti3,CC(i  ,2,k),CC(ic  ,1,k))
-      PM (tr3,ti4,CC(i-1,2,k),CC(ic-1,1,k))
-      PM (CH(i-1,k,0),cr3,tr2,tr3)
-      PM (CH(i  ,k,0),ci3,ti2,ti3)
-      PM (cr4,cr2,tr1,tr4)
-      PM (ci2,ci4,ti1,ti4)
-      MULPM (CH(i,k,1),CH(i-1,k,1),WA(0,i-2),WA(0,i-1),ci2,cr2)
-      MULPM (CH(i,k,2),CH(i-1,k,2),WA(1,i-2),WA(1,i-1),ci3,cr3)
-      MULPM (CH(i,k,3),CH(i-1,k,3),WA(2,i-2),WA(2,i-1),ci4,cr4)
-      }
-  }
-
-NOINLINE static void radb5(size_t ido, size_t l1, const double * restrict cc,
-  double * restrict ch, const double * restrict wa)
-  {
-  const size_t cdim=5;
-  static const double tr11= 0.3090169943749474241, ti11=0.95105651629515357212,
-                      tr12=-0.8090169943749474241, ti12=0.58778525229247312917;
-
-  for (size_t k=0; k<l1; k++)
-    {
-    double ti5=CC(0,2,k)+CC(0,2,k);
-    double ti4=CC(0,4,k)+CC(0,4,k);
-    double tr2=CC(ido-1,1,k)+CC(ido-1,1,k);
-    double tr3=CC(ido-1,3,k)+CC(ido-1,3,k);
-    CH(0,k,0)=CC(0,0,k)+tr2+tr3;
-    double cr2=CC(0,0,k)+tr11*tr2+tr12*tr3;
-    double cr3=CC(0,0,k)+tr12*tr2+tr11*tr3;
-    double ci4, ci5;
-    MULPM(ci5,ci4,ti5,ti4,ti11,ti12)
-    PM(CH(0,k,4),CH(0,k,1),cr2,ci5)
-    PM(CH(0,k,3),CH(0,k,2),cr3,ci4)
-    }
-  if (ido==1) return;
-  for (size_t k=0; k<l1;++k)
-    for (size_t i=2; i<ido; i+=2)
-      {
-      size_t ic=ido-i;
-      double tr2, tr3, tr4, tr5, ti2, ti3, ti4, ti5;
-      PM(tr2,tr5,CC(i-1,2,k),CC(ic-1,1,k))
-      PM(ti5,ti2,CC(i  ,2,k),CC(ic  ,1,k))
-      PM(tr3,tr4,CC(i-1,4,k),CC(ic-1,3,k))
-      PM(ti4,ti3,CC(i  ,4,k),CC(ic  ,3,k))
-      CH(i-1,k,0)=CC(i-1,0,k)+tr2+tr3;
-      CH(i  ,k,0)=CC(i  ,0,k)+ti2+ti3;
-      double cr2=CC(i-1,0,k)+tr11*tr2+tr12*tr3;
-      double ci2=CC(i  ,0,k)+tr11*ti2+tr12*ti3;
-      double cr3=CC(i-1,0,k)+tr12*tr2+tr11*tr3;
-      double ci3=CC(i  ,0,k)+tr12*ti2+tr11*ti3;
-      double ci4, ci5, cr5, cr4;
-      MULPM(cr5,cr4,tr5,tr4,ti11,ti12)
-      MULPM(ci5,ci4,ti5,ti4,ti11,ti12)
-      double dr2, dr3, dr4, dr5, di2, di3, di4, di5;
-      PM(dr4,dr3,cr3,ci4)
-      PM(di3,di4,ci3,cr4)
-      PM(dr5,dr2,cr2,ci5)
-      PM(di2,di5,ci2,cr5)
-      MULPM(CH(i,k,1),CH(i-1,k,1),WA(0,i-2),WA(0,i-1),di2,dr2)
-      MULPM(CH(i,k,2),CH(i-1,k,2),WA(1,i-2),WA(1,i-1),di3,dr3)
-      MULPM(CH(i,k,3),CH(i-1,k,3),WA(2,i-2),WA(2,i-1),di4,dr4)
-      MULPM(CH(i,k,4),CH(i-1,k,4),WA(3,i-2),WA(3,i-1),di5,dr5)
-      }
-  }
-
-#undef CC
-#undef CH
-#define CC(a,b,c) cc[(a)+ido*((b)+cdim*(c))]
-#define CH(a,b,c) ch[(a)+ido*((b)+l1*(c))]
-#define C1(a,b,c) cc[(a)+ido*((b)+l1*(c))]
-#define C2(a,b) cc[(a)+idl1*(b)]
-#define CH2(a,b) ch[(a)+idl1*(b)]
-
-NOINLINE static void radbg(size_t ido, size_t ip, size_t l1,
-  double * restrict cc, double * restrict ch, const double * restrict wa,
-  const double * restrict csarr)
-  {
-  const size_t cdim=ip;
-  size_t ipph=(ip+1)/ 2;
-  size_t idl1 = ido*l1;
-
-  for (size_t k=0; k<l1; ++k)        // 102
-    for (size_t i=0; i<ido; ++i)     // 101
-      CH(i,k,0) = CC(i,0,k);
-  for (size_t j=1, jc=ip-1; j<ipph; ++j, --jc)   // 108
-    {
-    size_t j2=2*j-1;
-    for (size_t k=0; k<l1; ++k)
-      {
-      CH(0,k,j ) = 2*CC(ido-1,j2,k);
-      CH(0,k,jc) = 2*CC(0,j2+1,k);
-      }
-    }
-
-  if (ido!=1)
-    {
-    for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)   // 111
-      {
-      size_t j2=2*j-1;
-      for (size_t k=0; k<l1; ++k)
-        for (size_t i=1, ic=ido-i-2; i<=ido-2; i+=2, ic-=2)      // 109
-          {
-          CH(i  ,k,j ) = CC(i  ,j2+1,k)+CC(ic  ,j2,k);
-          CH(i  ,k,jc) = CC(i  ,j2+1,k)-CC(ic  ,j2,k);
-          CH(i+1,k,j ) = CC(i+1,j2+1,k)-CC(ic+1,j2,k);
-          CH(i+1,k,jc) = CC(i+1,j2+1,k)+CC(ic+1,j2,k);
-          }
-      }
-    }
-  for (size_t l=1,lc=ip-1; l<ipph; ++l,--lc)
-    {
-    for (size_t ik=0; ik<idl1; ++ik)
-      {
-      C2(ik,l ) = CH2(ik,0)+csarr[2*l]*CH2(ik,1)+csarr[4*l]*CH2(ik,2);
-      C2(ik,lc) = csarr[2*l+1]*CH2(ik,ip-1)+csarr[4*l+1]*CH2(ik,ip-2);
-      }
-    size_t iang=2*l;
-    size_t j=3,jc=ip-3;
-    for(; j<ipph-3; j+=4,jc-=4)
-      {
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar1=csarr[2*iang], ai1=csarr[2*iang+1];
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar2=csarr[2*iang], ai2=csarr[2*iang+1];
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar3=csarr[2*iang], ai3=csarr[2*iang+1];
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar4=csarr[2*iang], ai4=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        C2(ik,l ) += ar1*CH2(ik,j )+ar2*CH2(ik,j +1)
-                    +ar3*CH2(ik,j +2)+ar4*CH2(ik,j +3);
-        C2(ik,lc) += ai1*CH2(ik,jc)+ai2*CH2(ik,jc-1)
-                    +ai3*CH2(ik,jc-2)+ai4*CH2(ik,jc-3);
-        }
-      }
-    for(; j<ipph-1; j+=2,jc-=2)
-      {
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar1=csarr[2*iang], ai1=csarr[2*iang+1];
-      iang+=l; if(iang>ip) iang-=ip;
-      double ar2=csarr[2*iang], ai2=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        C2(ik,l ) += ar1*CH2(ik,j )+ar2*CH2(ik,j +1);
-        C2(ik,lc) += ai1*CH2(ik,jc)+ai2*CH2(ik,jc-1);
-        }
-      }
-    for(; j<ipph; ++j,--jc)
-      {
-      iang+=l; if(iang>ip) iang-=ip;
-      double war=csarr[2*iang], wai=csarr[2*iang+1];
-      for (size_t ik=0; ik<idl1; ++ik)
-        {
-        C2(ik,l ) += war*CH2(ik,j );
-        C2(ik,lc) += wai*CH2(ik,jc);
-        }
-      }
-    }
-  for (size_t j=1; j<ipph; ++j)
-    for (size_t ik=0; ik<idl1; ++ik)
-      CH2(ik,0) += CH2(ik,j);
-  for (size_t j=1, jc=ip-1; j<ipph; ++j,--jc)   // 124
-    for (size_t k=0; k<l1; ++k)
-      {
-      CH(0,k,j ) = C1(0,k,j)-C1(0,k,jc);
-      CH(0,k,jc) = C1(0,k,j)+C1(0,k,jc);
-      }
-
-  if (ido==1) return;
-
-  for (size_t j=1, jc=ip-1; j<ipph; ++j, --jc)  // 127
-    for (size_t k=0; k<l1; ++k)
-      for (size_t i=1; i<=ido-2; i+=2)
-        {
-        CH(i  ,k,j ) = C1(i  ,k,j)-C1(i+1,k,jc);
-        CH(i  ,k,jc) = C1(i  ,k,j)+C1(i+1,k,jc);
-        CH(i+1,k,j ) = C1(i+1,k,j)+C1(i  ,k,jc);
-        CH(i+1,k,jc) = C1(i+1,k,j)-C1(i  ,k,jc);
-        }
-
-// All in CH
-
-  for (size_t j=1; j<ip; ++j)
-    {
-    size_t is = (j-1)*(ido-1);
-    for (size_t k=0; k<l1; ++k)
-      {
-      size_t idij = is;
-      for (size_t i=1; i<=ido-2; i+=2)
-        {
-        double t1=CH(i,k,j), t2=CH(i+1,k,j);
-        CH(i  ,k,j) = wa[idij]*t1-wa[idij+1]*t2;
-        CH(i+1,k,j) = wa[idij]*t2+wa[idij+1]*t1;
-        idij+=2;
-        }
-      }
-    }
-  }
-#undef C1
-#undef C2
-#undef CH2
-
-#undef CC
-#undef CH
-#undef PM
-#undef MULPM
-#undef WA
-
-static void copy_and_norm(double *c, double *p1, size_t n, double fct)
-  {
-  if (p1!=c)
-    {
-    if (fct!=1.)
-      for (size_t i=0; i<n; ++i)
-        c[i] = fct*p1[i];
-    else
-      memcpy (c,p1,n*sizeof(double));
-    }
-  else
-    if (fct!=1.)
-      for (size_t i=0; i<n; ++i)
-        c[i] *= fct;
-  }
-
-WARN_UNUSED_RESULT
-static int rfftp_forward(rfftp_plan plan, double c[], double fct)
-  {
-  if (plan->length==1) return 0;
-  size_t n=plan->length;
-  size_t l1=n, nf=plan->nfct;
-  double *ch = RALLOC(double, n);
-  if (!ch) return -1;
-  double *p1=c, *p2=ch;
-
-  for(size_t k1=0; k1<nf;++k1)
-    {
-    size_t k=nf-k1-1;
-    size_t ip=plan->fct[k].fct;
-    size_t ido=n / l1;
-    l1 /= ip;
-    if(ip==4)
-      radf4(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==2)
-      radf2(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==3)
-      radf3(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==5)
-      radf5(ido, l1, p1, p2, plan->fct[k].tw);
-    else
-      {
-      radfg(ido, ip, l1, p1, p2, plan->fct[k].tw, plan->fct[k].tws);
-      SWAP (p1,p2,double *);
-      }
-    SWAP (p1,p2,double *);
-    }
-  copy_and_norm(c,p1,n,fct);
-  DEALLOC(ch);
-  return 0;
-  }
-
-WARN_UNUSED_RESULT
-static int rfftp_backward(rfftp_plan plan, double c[], double fct)
-  {
-  if (plan->length==1) return 0;
-  size_t n=plan->length;
-  size_t l1=1, nf=plan->nfct;
-  double *ch = RALLOC(double, n);
-  if (!ch) return -1;
-  double *p1=c, *p2=ch;
-
-  for(size_t k=0; k<nf; k++)
-    {
-    size_t ip = plan->fct[k].fct,
-           ido= n/(ip*l1);
-    if(ip==4)
-      radb4(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==2)
-      radb2(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==3)
-      radb3(ido, l1, p1, p2, plan->fct[k].tw);
-    else if(ip==5)
-      radb5(ido, l1, p1, p2, plan->fct[k].tw);
-    else
-      radbg(ido, ip, l1, p1, p2, plan->fct[k].tw, plan->fct[k].tws);
-    SWAP (p1,p2,double *);
-    l1*=ip;
-    }
-  copy_and_norm(c,p1,n,fct);
-  DEALLOC(ch);
-  return 0;
-  }
-
-WARN_UNUSED_RESULT
-static int rfftp_factorize (rfftp_plan plan)
-  {
-  size_t length=plan->length;
-  size_t nfct=0;
-  while ((length%4)==0)
-    { if (nfct>=NFCT) return -1; plan->fct[nfct++].fct=4; length>>=2; }
-  if ((length%2)==0)
-    {
-    length>>=1;
-    // factor 2 should be at the front of the factor list
-    if (nfct>=NFCT) return -1;
-    plan->fct[nfct++].fct=2;
-    SWAP(plan->fct[0].fct, plan->fct[nfct-1].fct,size_t);
-    }
-  size_t maxl=(size_t)(sqrt((double)length))+1;
-  for (size_t divisor=3; (length>1)&&(divisor<maxl); divisor+=2)
-    if ((length%divisor)==0)
-      {
-      while ((length%divisor)==0)
-        {
-        if (nfct>=NFCT) return -1;
-        plan->fct[nfct++].fct=divisor;
-        length/=divisor;
-        }
-      maxl=(size_t)(sqrt((double)length))+1;
-      }
-  if (length>1) plan->fct[nfct++].fct=length;
-  plan->nfct=nfct;
-  return 0;
-  }
-
-static size_t rfftp_twsize(rfftp_plan plan)
-  {
-  size_t twsize=0, l1=1;
-  for (size_t k=0; k<plan->nfct; ++k)
-    {
-    size_t ip=plan->fct[k].fct, ido= plan->length/(l1*ip);
-    twsize+=(ip-1)*(ido-1);
-    if (ip>5) twsize+=2*ip;
-    l1*=ip;
-    }
-  return twsize;
-  return 0;
-  }
-
-WARN_UNUSED_RESULT NOINLINE static int rfftp_comp_twiddle (rfftp_plan plan)
-  {
-  size_t length=plan->length;
-  double *twid = RALLOC(double, 2*length);
-  if (!twid) return -1;
-  sincos_2pibyn_half(length, twid);
-  size_t l1=1;
-  double *ptr=plan->mem;
-  for (size_t k=0; k<plan->nfct; ++k)
-    {
-    size_t ip=plan->fct[k].fct, ido=length/(l1*ip);
-    if (k<plan->nfct-1) // last factor doesn't need twiddles
-      {
-      plan->fct[k].tw=ptr; ptr+=(ip-1)*(ido-1);
-      for (size_t j=1; j<ip; ++j)
-        for (size_t i=1; i<=(ido-1)/2; ++i)
-          {
-          plan->fct[k].tw[(j-1)*(ido-1)+2*i-2] = twid[2*j*l1*i];
-          plan->fct[k].tw[(j-1)*(ido-1)+2*i-1] = twid[2*j*l1*i+1];
-          }
-      }
-    if (ip>5) // special factors required by *g functions
-      {
-      plan->fct[k].tws=ptr; ptr+=2*ip;
-      plan->fct[k].tws[0] = 1.;
-      plan->fct[k].tws[1] = 0.;
-      for (size_t i=1; i<=(ip>>1); ++i)
-        {
-        plan->fct[k].tws[2*i  ] = twid[2*i*(length/ip)];
-        plan->fct[k].tws[2*i+1] = twid[2*i*(length/ip)+1];
-        plan->fct[k].tws[2*(ip-i)  ] = twid[2*i*(length/ip)];
-        plan->fct[k].tws[2*(ip-i)+1] = -twid[2*i*(length/ip)+1];
-        }
-      }
-    l1*=ip;
-    }
-  DEALLOC(twid);
-  return 0;
-  }
-
-NOINLINE static rfftp_plan make_rfftp_plan (size_t length)
-  {
-  if (length==0) return NULL;
-  rfftp_plan plan = RALLOC(rfftp_plan_i,1);
-  if (!plan) return NULL;
-  plan->length=length;
-  plan->nfct=0;
-  plan->mem=NULL;
-  for (size_t i=0; i<NFCT; ++i)
-    plan->fct[i]=(rfftp_fctdata){0,0,0};
-  if (length==1) return plan;
-  if (rfftp_factorize(plan)!=0) { DEALLOC(plan); return NULL; }
-  size_t tws=rfftp_twsize(plan);
-  plan->mem=RALLOC(double,tws);
-  if (!plan->mem) { DEALLOC(plan); return NULL; }
-  if (rfftp_comp_twiddle(plan)!=0)
-    { DEALLOC(plan->mem); DEALLOC(plan); return NULL; }
-  return plan;
-  }
-
-NOINLINE static void destroy_rfftp_plan (rfftp_plan plan)
-  {
-  DEALLOC(plan->mem);
-  DEALLOC(plan);
-  }
-
-typedef struct fftblue_plan_i
-  {
-  size_t n, n2;
-  cfftp_plan plan;
-  double *mem;
-  double *bk, *bkf;
-  } fftblue_plan_i;
-typedef struct fftblue_plan_i * fftblue_plan;
-
-NOINLINE static fftblue_plan make_fftblue_plan (size_t length)
-  {
-  fftblue_plan plan = RALLOC(fftblue_plan_i,1);
-  if (!plan) return NULL;
-  plan->n = length;
-  plan->n2 = good_size(plan->n*2-1);
-  plan->mem = RALLOC(double, 2*plan->n+2*plan->n2);
-  if (!plan->mem) { DEALLOC(plan); return NULL; }
-  plan->bk  = plan->mem;
-  plan->bkf = plan->bk+2*plan->n;
-
-/* initialize b_k */
-  double *tmp = RALLOC(double,4*plan->n);
-  if (!tmp) { DEALLOC(plan->mem); DEALLOC(plan); return NULL; }
-  sincos_2pibyn(2*plan->n,tmp);
-  plan->bk[0] = 1;
-  plan->bk[1] = 0;
-
-  size_t coeff=0;
-  for (size_t m=1; m<plan->n; ++m)
-    {
-    coeff+=2*m-1;
-    if (coeff>=2*plan->n) coeff-=2*plan->n;
-    plan->bk[2*m  ] = tmp[2*coeff  ];
-    plan->bk[2*m+1] = tmp[2*coeff+1];
-    }
-
-  /* initialize the zero-padded, Fourier transformed b_k. Add normalisation. */
-  double xn2 = 1./plan->n2;
-  plan->bkf[0] = plan->bk[0]*xn2;
-  plan->bkf[1] = plan->bk[1]*xn2;
-  for (size_t m=2; m<2*plan->n; m+=2)
-    {
-    plan->bkf[m]   = plan->bkf[2*plan->n2-m]   = plan->bk[m]   *xn2;
-    plan->bkf[m+1] = plan->bkf[2*plan->n2-m+1] = plan->bk[m+1] *xn2;
-    }
-  for (size_t m=2*plan->n;m<=(2*plan->n2-2*plan->n+1);++m)
-    plan->bkf[m]=0.;
-  plan->plan=make_cfftp_plan(plan->n2);
-  if (!plan->plan)
-    { DEALLOC(tmp); DEALLOC(plan->mem); DEALLOC(plan); return NULL; }
-  if (cfftp_forward(plan->plan,plan->bkf,1.)!=0)
-    { DEALLOC(tmp); DEALLOC(plan->mem); DEALLOC(plan); return NULL; }
-  DEALLOC(tmp);
-
-  return plan;
-  }
-
-NOINLINE static void destroy_fftblue_plan (fftblue_plan plan)
-  {
-  DEALLOC(plan->mem);
-  destroy_cfftp_plan(plan->plan);
-  DEALLOC(plan);
-  }
-
-NOINLINE WARN_UNUSED_RESULT
-static int fftblue_fft(fftblue_plan plan, double c[], int isign, double fct)
-  {
-  size_t n=plan->n;
-  size_t n2=plan->n2;
-  double *bk  = plan->bk;
-  double *bkf = plan->bkf;
-  double *akf = RALLOC(double, 2*n2);
-  if (!akf) return -1;
-
-/* initialize a_k and FFT it */
-  if (isign>0)
-    for (size_t m=0; m<2*n; m+=2)
-      {
-      akf[m]   = c[m]*bk[m]   - c[m+1]*bk[m+1];
-      akf[m+1] = c[m]*bk[m+1] + c[m+1]*bk[m];
-      }
-  else
-    for (size_t m=0; m<2*n; m+=2)
-      {
-      akf[m]   = c[m]*bk[m]   + c[m+1]*bk[m+1];
-      akf[m+1] =-c[m]*bk[m+1] + c[m+1]*bk[m];
-      }
-  for (size_t m=2*n; m<2*n2; ++m)
-    akf[m]=0;
-
-  if (cfftp_forward (plan->plan,akf,fct)!=0)
-    { DEALLOC(akf); return -1; }
-
-/* do the convolution */
-  if (isign>0)
-    for (size_t m=0; m<2*n2; m+=2)
-      {
-      double im = -akf[m]*bkf[m+1] + akf[m+1]*bkf[m];
-      akf[m  ]  =  akf[m]*bkf[m]   + akf[m+1]*bkf[m+1];
-      akf[m+1]  = im;
-      }
-  else
-    for (size_t m=0; m<2*n2; m+=2)
-      {
-      double im = akf[m]*bkf[m+1] + akf[m+1]*bkf[m];
-      akf[m  ]  = akf[m]*bkf[m]   - akf[m+1]*bkf[m+1];
-      akf[m+1]  = im;
-      }
-
-/* inverse FFT */
-  if (cfftp_backward (plan->plan,akf,1.)!=0)
-    { DEALLOC(akf); return -1; }
-
-/* multiply by b_k */
-  if (isign>0)
-    for (size_t m=0; m<2*n; m+=2)
-      {
-      c[m]   = bk[m]  *akf[m] - bk[m+1]*akf[m+1];
-      c[m+1] = bk[m+1]*akf[m] + bk[m]  *akf[m+1];
-      }
-  else
-    for (size_t m=0; m<2*n; m+=2)
-      {
-      c[m]   = bk[m]  *akf[m] + bk[m+1]*akf[m+1];
-      c[m+1] =-bk[m+1]*akf[m] + bk[m]  *akf[m+1];
-      }
-  DEALLOC(akf);
-  return 0;
-  }
-
-WARN_UNUSED_RESULT
-static int cfftblue_backward(fftblue_plan plan, double c[], double fct)
-  { return fftblue_fft(plan,c,1,fct); }
-
-WARN_UNUSED_RESULT
-static int cfftblue_forward(fftblue_plan plan, double c[], double fct)
-  { return fftblue_fft(plan,c,-1,fct); }
-
-WARN_UNUSED_RESULT
-static int rfftblue_backward(fftblue_plan plan, double c[], double fct)
-  {
-  size_t n=plan->n;
-  double *tmp = RALLOC(double,2*n);
-  if (!tmp) return -1;
-  tmp[0]=c[0];
-  tmp[1]=0.;
-  memcpy (tmp+2,c+1, (n-1)*sizeof(double));
-  if ((n&1)==0) tmp[n+1]=0.;
-  for (size_t m=2; m<n; m+=2)
-    {
-    tmp[2*n-m]=tmp[m];
-    tmp[2*n-m+1]=-tmp[m+1];
-    }
-  if (fftblue_fft(plan,tmp,1,fct)!=0)
-    { DEALLOC(tmp); return -1; }
-  for (size_t m=0; m<n; ++m)
-    c[m] = tmp[2*m];
-  DEALLOC(tmp);
-  return 0;
-  }
-
-WARN_UNUSED_RESULT
-static int rfftblue_forward(fftblue_plan plan, double c[], double fct)
-  {
-  size_t n=plan->n;
-  double *tmp = RALLOC(double,2*n);
-  if (!tmp) return -1;
-  for (size_t m=0; m<n; ++m)
-    {
-    tmp[2*m] = c[m];
-    tmp[2*m+1] = 0.;
-    }
-  if (fftblue_fft(plan,tmp,-1,fct)!=0)
-    { DEALLOC(tmp); return -1; }
-  c[0] = tmp[0];
-  memcpy (c+1, tmp+2, (n-1)*sizeof(double));
-  DEALLOC(tmp);
-  return 0;
-  }
-
-typedef struct cfft_plan_i
-  {
-  cfftp_plan packplan;
-  fftblue_plan blueplan;
-  } cfft_plan_i;
-
-static cfft_plan make_cfft_plan (size_t length)
-  {
-  if (length==0) return NULL;
-  cfft_plan plan = RALLOC(cfft_plan_i,1);
-  if (!plan) return NULL;
-  plan->blueplan=0;
-  plan->packplan=0;
-  if ((length<50) || (largest_prime_factor(length)<=sqrt(length)))
-    {
-    plan->packplan=make_cfftp_plan(length);
-    if (!plan->packplan) { DEALLOC(plan); return NULL; }
-    return plan;
-    }
-  double comp1 = cost_guess(length);
-  double comp2 = 2*cost_guess(good_size(2*length-1));
-  comp2*=1.5; /* fudge factor that appears to give good overall performance */
-  if (comp2<comp1) // use Bluestein
-    {
-    plan->blueplan=make_fftblue_plan(length);
-    if (!plan->blueplan) { DEALLOC(plan); return NULL; }
-    }
-  else
-    {
-    plan->packplan=make_cfftp_plan(length);
-    if (!plan->packplan) { DEALLOC(plan); return NULL; }
-    }
-  return plan;
-  }
-
-static void destroy_cfft_plan (cfft_plan plan)
-  {
-  if (plan->blueplan)
-    destroy_fftblue_plan(plan->blueplan);
-  if (plan->packplan)
-    destroy_cfftp_plan(plan->packplan);
-  DEALLOC(plan);
-  }
-
-WARN_UNUSED_RESULT static int cfft_backward(cfft_plan plan, double c[], double fct)
-  {
-  if (plan->packplan)
-    return cfftp_backward(plan->packplan,c,fct);
-  // if (plan->blueplan)
-  return cfftblue_backward(plan->blueplan,c,fct);
-  }
-
-WARN_UNUSED_RESULT static int cfft_forward(cfft_plan plan, double c[], double fct)
-  {
-  if (plan->packplan)
-    return cfftp_forward(plan->packplan,c,fct);
-  // if (plan->blueplan)
-  return cfftblue_forward(plan->blueplan,c,fct);
-  }
-
-typedef struct rfft_plan_i
-  {
-  rfftp_plan packplan;
-  fftblue_plan blueplan;
-  } rfft_plan_i;
-
-static rfft_plan make_rfft_plan (size_t length)
-  {
-  if (length==0) return NULL;
-  rfft_plan plan = RALLOC(rfft_plan_i,1);
-  if (!plan) return NULL;
-  plan->blueplan=0;
-  plan->packplan=0;
-  if ((length<50) || (largest_prime_factor(length)<=sqrt(length)))
-    {
-    plan->packplan=make_rfftp_plan(length);
-    if (!plan->packplan) { DEALLOC(plan); return NULL; }
-    return plan;
-    }
-  double comp1 = 0.5*cost_guess(length);
-  double comp2 = 2*cost_guess(good_size(2*length-1));
-  comp2*=1.5; /* fudge factor that appears to give good overall performance */
-  if (comp2<comp1) // use Bluestein
-    {
-    plan->blueplan=make_fftblue_plan(length);
-    if (!plan->blueplan) { DEALLOC(plan); return NULL; }
-    }
-  else
-    {
-    plan->packplan=make_rfftp_plan(length);
-    if (!plan->packplan) { DEALLOC(plan); return NULL; }
-    }
-  return plan;
-  }
-
-static void destroy_rfft_plan (rfft_plan plan)
-  {
-  if (plan->blueplan)
-    destroy_fftblue_plan(plan->blueplan);
-  if (plan->packplan)
-    destroy_rfftp_plan(plan->packplan);
-  DEALLOC(plan);
-  }
-
-WARN_UNUSED_RESULT static int rfft_backward(rfft_plan plan, double c[], double fct)
-  {
-  if (plan->packplan)
-    return rfftp_backward(plan->packplan,c,fct);
-  else // if (plan->blueplan)
-    return rfftblue_backward(plan->blueplan,c,fct);
-  }
-
-WARN_UNUSED_RESULT static int rfft_forward(rfft_plan plan, double c[], double fct)
-  {
-  if (plan->packplan)
-    return rfftp_forward(plan->packplan,c,fct);
-  else // if (plan->blueplan)
-    return rfftblue_forward(plan->blueplan,c,fct);
-  }
-
-#define NPY_NO_DEPRECATED_API NPY_API_VERSION
-
-#include "Python.h"
-#include "numpy/arrayobject.h"
-
-static PyObject *
-execute_complex(PyObject *a1, int is_forward, double fct)
-{
-    PyArrayObject *data = (PyArrayObject *)PyArray_FromAny(a1,
-            PyArray_DescrFromType(NPY_CDOUBLE), 1, 0,
-            NPY_ARRAY_ENSURECOPY | NPY_ARRAY_DEFAULT |
-            NPY_ARRAY_ENSUREARRAY | NPY_ARRAY_FORCECAST,
-            NULL);
-    if (!data) return NULL;
-
-    int npts = PyArray_DIM(data, PyArray_NDIM(data) - 1);
-    cfft_plan plan=NULL;
-
-    int nrepeats = PyArray_SIZE(data)/npts;
-    double *dptr = (double *)PyArray_DATA(data);
-    int fail=0;
-    Py_BEGIN_ALLOW_THREADS;
-    NPY_SIGINT_ON;
-    plan = make_cfft_plan(npts);
-    if (!plan) fail=1;
-    if (!fail)
-      for (int i = 0; i < nrepeats; i++) {
-          int res = is_forward ?
-            cfft_forward(plan, dptr, fct) : cfft_backward(plan, dptr, fct);
-          if (res!=0) { fail=1; break; }
-          dptr += npts*2;
-      }
-    if (plan) destroy_cfft_plan(plan);
-    NPY_SIGINT_OFF;
-    Py_END_ALLOW_THREADS;
-    if (fail) {
-      Py_XDECREF(data);
-      return PyErr_NoMemory();
-    }
-    return (PyObject *)data;
-}
-
-static PyObject *
-execute_real_forward(PyObject *a1, double fct)
-{
-    rfft_plan plan=NULL;
-    int fail = 0;
-    PyArrayObject *data = (PyArrayObject *)PyArray_FromAny(a1,
-            PyArray_DescrFromType(NPY_DOUBLE), 1, 0,
-            NPY_ARRAY_DEFAULT | NPY_ARRAY_ENSUREARRAY | NPY_ARRAY_FORCECAST,
-            NULL);
-    if (!data) return NULL;
-
-    int ndim = PyArray_NDIM(data);
-    const npy_intp *odim = PyArray_DIMS(data);
-    int npts = odim[ndim - 1];
-    npy_intp *tdim=(npy_intp *)malloc(ndim*sizeof(npy_intp));
-    if (!tdim)
-      { Py_XDECREF(data); return NULL; }
-    for (int d=0; d<ndim-1; ++d)
-      tdim[d] = odim[d];
-    tdim[ndim-1] = npts/2 + 1;
-    PyArrayObject *ret = (PyArrayObject *)PyArray_Empty(ndim,
-            tdim, PyArray_DescrFromType(NPY_CDOUBLE), 0);
-    free(tdim);
-    if (!ret) fail=1;
-    if (!fail) {
-      int rstep = PyArray_DIM(ret, PyArray_NDIM(ret) - 1)*2;
-
-      int nrepeats = PyArray_SIZE(data)/npts;
-      double *rptr = (double *)PyArray_DATA(ret),
-             *dptr = (double *)PyArray_DATA(data);
-
-      Py_BEGIN_ALLOW_THREADS;
-      NPY_SIGINT_ON;
-      plan = make_rfft_plan(npts);
-      if (!plan) fail=1;
-      if (!fail)
-        for (int i = 0; i < nrepeats; i++) {
-            rptr[rstep-1] = 0.0;
-            memcpy((char *)(rptr+1), dptr, npts*sizeof(double));
-            if (rfft_forward(plan, rptr+1, fct)!=0) {fail=1; break;}
-            rptr[0] = rptr[1];
-            rptr[1] = 0.0;
-            rptr += rstep;
-            dptr += npts;
-      }
-      if (plan) destroy_rfft_plan(plan);
-      NPY_SIGINT_OFF;
-      Py_END_ALLOW_THREADS;
-    }
-    if (fail) {
-      Py_XDECREF(data);
-      Py_XDECREF(ret);
-      return PyErr_NoMemory();
-    }
-    Py_DECREF(data);
-    return (PyObject *)ret;
-}
-static PyObject *
-execute_real_backward(PyObject *a1, double fct)
-{
-    rfft_plan plan=NULL;
-    PyArrayObject *data = (PyArrayObject *)PyArray_FromAny(a1,
-            PyArray_DescrFromType(NPY_CDOUBLE), 1, 0,
-            NPY_ARRAY_DEFAULT | NPY_ARRAY_ENSUREARRAY | NPY_ARRAY_FORCECAST,
-            NULL);
-    if (!data) return NULL;
-    int npts = PyArray_DIM(data, PyArray_NDIM(data) - 1);
-    PyArrayObject *ret = (PyArrayObject *)PyArray_Empty(PyArray_NDIM(data),
-            PyArray_DIMS(data), PyArray_DescrFromType(NPY_DOUBLE), 0);
-    int fail = 0;
-    if (!ret) fail=1;
-    if (!fail) {
-      int nrepeats = PyArray_SIZE(ret)/npts;
-      double *rptr = (double *)PyArray_DATA(ret),
-             *dptr = (double *)PyArray_DATA(data);
-
-      Py_BEGIN_ALLOW_THREADS;
-      NPY_SIGINT_ON;
-      plan = make_rfft_plan(npts);
-      if (!plan) fail=1;
-      if (!fail) {
-        for (int i = 0; i < nrepeats; i++) {
-          memcpy((char *)(rptr + 1), (dptr + 2), (npts - 1)*sizeof(double));
-          rptr[0] = dptr[0];
-          if (rfft_backward(plan, rptr, fct)!=0) {fail=1; break;}
-          rptr += npts;
-          dptr += npts*2;
-        }
-      }
-      if (plan) destroy_rfft_plan(plan);
-      NPY_SIGINT_OFF;
-      Py_END_ALLOW_THREADS;
-    }
-    if (fail) {
-      Py_XDECREF(data);
-      Py_XDECREF(ret);
-      return PyErr_NoMemory();
-    }
-    Py_DECREF(data);
-    return (PyObject *)ret;
-}
-
-static PyObject *
-execute_real(PyObject *a1, int is_forward, double fct)
-{
-    return is_forward ? execute_real_forward(a1, fct)
-                      : execute_real_backward(a1, fct);
-}
-
-static const char execute__doc__[] = "";
-
-static PyObject *
-execute(PyObject *NPY_UNUSED(self), PyObject *args)
-{
-    PyObject *a1;
-    int is_real, is_forward;
-    double fct;
-
-    if(!PyArg_ParseTuple(args, "Oiid:execute", &a1, &is_real, &is_forward, &fct)) {
-        return NULL;
-    }
-
-    return is_real ? execute_real(a1, is_forward, fct)
-                   : execute_complex(a1, is_forward, fct);
-}
-
-/* List of methods defined in the module */
-
-static struct PyMethodDef methods[] = {
-    {"execute",   execute,   1, execute__doc__},
-    {NULL, NULL, 0, NULL}          /* sentinel */
-};
-
-#if PY_MAJOR_VERSION >= 3
-static struct PyModuleDef moduledef = {
-        PyModuleDef_HEAD_INIT,
-        "pocketfft_internal",
-        NULL,
-        -1,
-        methods,
-        NULL,
-        NULL,
-        NULL,
-        NULL
-};
-#endif
-
-/* Initialization function for the module */
-#if PY_MAJOR_VERSION >= 3
-#define RETVAL(x) x
-PyMODINIT_FUNC PyInit_pocketfft_internal(void)
-#else
-#define RETVAL(x)
-PyMODINIT_FUNC
-initpocketfft_internal(void)
-#endif
-{
-    PyObject *m;
-#if PY_MAJOR_VERSION >= 3
-    m = PyModule_Create(&moduledef);
-#else
-    static const char module_documentation[] = "";
-
-    m = Py_InitModule4("pocketfft_internal", methods,
-            module_documentation,
-            (PyObject*)NULL,PYTHON_API_VERSION);
-#endif
-    if (m == NULL) {
-        return RETVAL(NULL);
-    }
-
-    /* Import the array object */
-    import_array();
-
-    /* XXXX Add constants here */
-
-    return RETVAL(m);
-}