path: root/common/pffft.cpp

//$ nobt

/* Copyright (c) 2013  Julien Pommier ( pommier@modartt.com )
 * Copyright (c) 2023  Christopher Robinson
 *
 * Based on original fortran 77 code from FFTPACKv4 from NETLIB
 * (http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
 * of NCAR, in 1985.
 *
 * As confirmed by the NCAR fftpack software curators, the following
 * FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
 * released under the same terms.
 *
 * FFTPACK license:
 *
 * http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
 *
 * Copyright (c) 2004 the University Corporation for Atmospheric
 * Research ("UCAR"). All rights reserved. Developed by NCAR's
 * Computational and Information Systems Laboratory, UCAR,
 * www.cisl.ucar.edu.
 *
 * Redistribution and use of the Software in source and binary forms,
 * with or without modification, is permitted provided that the
 * following conditions are met:
 *
 * - Neither the names of NCAR's Computational and Information Systems
 * Laboratory, the University Corporation for Atmospheric Research,
 * nor the names of its sponsors or contributors may be used to
 * endorse or promote products derived from this Software without
 * specific prior written permission.
 *
 * - Redistributions of source code must retain the above copyright
 * notices, this list of conditions, and the disclaimer below.
 *
 * - Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions, and the disclaimer below in the
 * documentation and/or other materials provided with the
 * distribution.
 *
 * THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
 * HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
 * SOFTWARE.
 *
 *
 * PFFFT : a Pretty Fast FFT.
 *
 * This file is largerly based on the original FFTPACK implementation, modified
 * in order to take advantage of SIMD instructions of modern CPUs.
 */

#include "pffft.h"

#include <array>
#include <assert.h>
#include <cmath>
#include <cstring>
#include <stdio.h>
#include <stdlib.h>
#include <vector>

#include "albit.h"
#include "almalloc.h"
#include "alnumbers.h"
#include "opthelpers.h"
#include "vector.h"

#if defined(__GNUC__)
#define ALWAYS_INLINE(return_type) inline return_type __attribute__ ((always_inline))
#define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
#define RESTRICT __restrict

#elif defined(_MSC_VER)

#define ALWAYS_INLINE(return_type) __forceinline return_type
#define NEVER_INLINE(return_type) __declspec(noinline) return_type
#define RESTRICT __restrict

#else

#define ALWAYS_INLINE(return_type) inline return_type
#define NEVER_INLINE(return_type) return_type
#define RESTRICT
#endif


/* Vector support macros: the rest of the code is independent of
 * SSE/Altivec/NEON -- adding support for other platforms with 4-element
 * vectors should be limited to these macros
 */

/* Define PFFFT_SIMD_DISABLE if you want to use scalar code instead of SIMD code */
//#define PFFFT_SIMD_DISABLE

#ifndef PFFFT_SIMD_DISABLE
/*
 * Altivec support macros
 */
#if defined(__ppc__) || defined(__ppc64__) || defined(__powerpc__) || defined(__powerpc64__)
typedef vector float v4sf;
#define SIMD_SZ 4
#define VZERO() ((vector float) vec_splat_u8(0))
#define VMUL(a,b) vec_madd(a,b, VZERO())
#define VADD(a,b) vec_add(a,b)
#define VMADD(a,b,c) vec_madd(a,b,c)
#define VSUB(a,b) vec_sub(a,b)
#define LD_PS1(p) vec_splats(p)
inline v4sf vset4(float a, float b, float c, float d)
{
    /* There a more efficient way to do this? */
    alignas(16) std::array<float,4> vals{{a, b, c, d}};
    return vec_ld(0, vals.data());
}
#define VSET4 vset4
#define VINSERT0(v, a) vec_insert((a), (v), 0)
#define VEXTRACT0(v) vec_extract((v), 0)
#define INTERLEAVE2(in1, in2, out1, out2) do { v4sf tmp__ = vec_mergeh(in1, in2); out2 = vec_mergel(in1, in2); out1 = tmp__; } while(0)
#define UNINTERLEAVE2(in1, in2, out1, out2) do {                           \
    vector unsigned char vperm1 =  (vector unsigned char)(0,1,2,3,8,9,10,11,16,17,18,19,24,25,26,27); \
    vector unsigned char vperm2 =  (vector unsigned char)(4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31); \
    v4sf tmp__ = vec_perm(in1, in2, vperm1); out2 = vec_perm(in1, in2, vperm2); out1 = tmp__; \
} while(0)
#define VTRANSPOSE4(x0,x1,x2,x3) do {           \
    v4sf y0 = vec_mergeh(x0, x2);               \
    v4sf y1 = vec_mergel(x0, x2);               \
    v4sf y2 = vec_mergeh(x1, x3);               \
    v4sf y3 = vec_mergel(x1, x3);               \
    x0 = vec_mergeh(y0, y2);                    \
    x1 = vec_mergel(y0, y2);                    \
    x2 = vec_mergeh(y1, y3);                    \
    x3 = vec_mergel(y1, y3);                    \
} while(0)
#define VSWAPHL(a,b) vec_perm(a,b, (vector unsigned char)(16,17,18,19,20,21,22,23,8,9,10,11,12,13,14,15))
#define VALIGNED(ptr) ((reinterpret_cast<uintptr_t>(ptr) & 0xF) == 0)

/*
 * SSE1 support macros
 */
#elif defined(__x86_64__) || defined(__SSE__) || defined(_M_X64) || \
    (defined(_M_IX86_FP) && _M_IX86_FP >= 1)

#include <xmmintrin.h>
typedef __m128 v4sf;
#define SIMD_SZ 4 // 4 floats by simd vector -- this is pretty much hardcoded in the preprocess/finalize functions anyway so you will have to work if you want to enable AVX with its 256-bit vectors.
#define VZERO _mm_setzero_ps
#define VMUL _mm_mul_ps
#define VADD _mm_add_ps
#define VMADD(a,b,c) _mm_add_ps(_mm_mul_ps(a,b), c)
#define VSUB _mm_sub_ps
#define LD_PS1 _mm_set1_ps
#define VSET4 _mm_setr_ps
#define VINSERT0(v, a) _mm_move_ss((v), _mm_set_ss(a))
#define VEXTRACT0 _mm_cvtss_f32
#define INTERLEAVE2(in1, in2, out1, out2) do { v4sf tmp__ = _mm_unpacklo_ps(in1, in2); out2 = _mm_unpackhi_ps(in1, in2); out1 = tmp__; } while(0)
#define UNINTERLEAVE2(in1, in2, out1, out2) do { v4sf tmp__ = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(2,0,2,0)); out2 = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(3,1,3,1)); out1 = tmp__; } while(0)
#define VTRANSPOSE4 _MM_TRANSPOSE4_PS
#define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))
#define VALIGNED(ptr) ((reinterpret_cast<uintptr_t>(ptr) & 0xF) == 0)

/*
 * ARM NEON support macros
 */
#elif defined(__ARM_NEON) || defined(__aarch64__) || defined(__arm64)

#include <arm_neon.h>
typedef float32x4_t v4sf;
#define SIMD_SZ 4
#define VZERO() vdupq_n_f32(0)
#define VMUL vmulq_f32
#define VADD vaddq_f32
#define VMADD(a,b,c) vmlaq_f32(c,a,b)
#define VSUB vsubq_f32
#define LD_PS1 vdupq_n_f32
inline v4sf vset4(float a, float b, float c, float d)
{
    float32x4_t ret{vmovq_n_f32(a)};
    ret = vsetq_lane_f32(b, ret, 1);
    ret = vsetq_lane_f32(c, ret, 2);
    ret = vsetq_lane_f32(d, ret, 3);
    return ret;
}
#define VSET4 vset4
#define VINSERT0(v, a) vsetq_lane_f32((a), (v), 0)
#define VEXTRACT0(v) vgetq_lane_f32((v), 0)
#define INTERLEAVE2(in1, in2, out1, out2) do { float32x4x2_t tmp__ = vzipq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; } while(0)
#define UNINTERLEAVE2(in1, in2, out1, out2) do { float32x4x2_t tmp__ = vuzpq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; } while(0)
#define VTRANSPOSE4(x0,x1,x2,x3) do {                                   \
    float32x4x2_t t0_ = vzipq_f32(x0, x2);                              \
    float32x4x2_t t1_ = vzipq_f32(x1, x3);                              \
    float32x4x2_t u0_ = vzipq_f32(t0_.val[0], t1_.val[0]);              \
    float32x4x2_t u1_ = vzipq_f32(t0_.val[1], t1_.val[1]);              \
    x0 = u0_.val[0]; x1 = u0_.val[1]; x2 = u1_.val[0]; x3 = u1_.val[1]; \
} while(0)
// marginally faster version
//#define VTRANSPOSE4(x0,x1,x2,x3) { asm("vtrn.32 %q0, %q1;\n vtrn.32 %q2,%q3\n vswp %f0,%e2\n vswp %f1,%e3" : "+w"(x0), "+w"(x1), "+w"(x2), "+w"(x3)::); }
#define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))
#define VALIGNED(ptr) ((reinterpret_cast<uintptr_t>(ptr) & 0x3) == 0)

/*
 * Generic GCC vector macros
 */
#elif defined(__GNUC__)

using v4sf [[gnu::vector_size(16), gnu::aligned(16)]] = float;
#define SIMD_SZ 4
#define VZERO() v4sf{0,0,0,0}
#define VMUL(a,b) ((a) * (b))
#define VADD(a,b) ((a) + (b))
#define VMADD(a,b,c) ((a)*(b) + (c))
#define VSUB(a,b) ((a) - (b))

constexpr v4sf ld_ps1(float a) noexcept { return v4sf{a, a, a, a}; }
#define LD_PS1 ld_ps1
#define VSET4(a, b, c, d) v4sf{(a), (b), (c), (d)}
[[gnu::always_inline]] inline v4sf vinsert0(v4sf v, float a) noexcept
{ return v4sf{a, v[1], v[2], v[3]}; }
#define VINSERT0 vinsert0
#define VEXTRACT0(v) ((v)[0])

[[gnu::always_inline]] inline v4sf unpacklo(v4sf a, v4sf b) noexcept
{ return v4sf{a[0], b[0], a[1], b[1]}; }
[[gnu::always_inline]] inline v4sf unpackhi(v4sf a, v4sf b) noexcept
{ return v4sf{a[2], b[2], a[3], b[3]}; }

[[gnu::always_inline]] inline void interleave2(v4sf in1, v4sf in2, v4sf &out1, v4sf &out2) noexcept
{
    v4sf tmp__{unpacklo(in1, in2)};
    out2 = unpackhi(in1, in2);
    out1 = tmp__;
}
#define INTERLEAVE2 interleave2

[[gnu::always_inline]] inline void uninterleave2(v4sf in1, v4sf in2, v4sf &out1, v4sf &out2) noexcept
{
    v4sf tmp__{in1[0], in1[2], in2[0], in2[2]};
    out2 = v4sf{in1[1], in1[3], in2[1], in2[3]};
    out1 = tmp__;
}
#define UNINTERLEAVE2 uninterleave2

[[gnu::always_inline]] inline void vtranspose4(v4sf &x0, v4sf &x1, v4sf &x2, v4sf &x3) noexcept
{
    v4sf tmp0{unpacklo(x0, x1)};
    v4sf tmp2{unpacklo(x2, x3)};
    v4sf tmp1{unpackhi(x0, x1)};
    v4sf tmp3{unpackhi(x2, x3)};
    x0 = v4sf{tmp0[0], tmp0[1], tmp2[0], tmp2[1]};
    x1 = v4sf{tmp0[2], tmp0[3], tmp2[2], tmp2[3]};
    x2 = v4sf{tmp1[0], tmp1[1], tmp3[0], tmp3[1]};
    x3 = v4sf{tmp1[2], tmp1[3], tmp3[2], tmp3[3]};
}
#define VTRANSPOSE4 vtranspose4

[[gnu::always_inline]] inline v4sf vswaphl(v4sf a, v4sf b) noexcept
{ return v4sf{b[0], b[1], a[2], a[3]}; }
#define VSWAPHL vswaphl

#define VALIGNED(ptr) ((reinterpret_cast<uintptr_t>(ptr) & 0xF) == 0)

#else

#warning "building with simd disabled !\n";
#define PFFFT_SIMD_DISABLE // fallback to scalar code
#endif

#endif /* PFFFT_SIMD_DISABLE */

// fallback mode for situations where SIMD is not available, use scalar mode instead
#ifdef PFFFT_SIMD_DISABLE
typedef float v4sf;
#define SIMD_SZ 1
#define VZERO() 0.f
#define VMUL(a,b) ((a)*(b))
#define VADD(a,b) ((a)+(b))
#define VMADD(a,b,c) ((a)*(b)+(c))
#define VSUB(a,b) ((a)-(b))
#define LD_PS1(p) (p)
#define VALIGNED(ptr) ((reinterpret_cast<uintptr_t>(ptr) & 0x3) == 0)
#endif

// shortcuts for complex multiplications
#define VCPLXMUL(ar,ai,br,bi) do { v4sf tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VSUB(ar,VMUL(ai,bi)); ai=VMADD(ai,br,tmp); } while(0)
#define VCPLXMULCONJ(ar,ai,br,bi) do { v4sf tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VMADD(ai,bi,ar); ai=VSUB(VMUL(ai,br),tmp); } while(0)

#if !defined(PFFFT_SIMD_DISABLE)

#define assertv4(v,f0,f1,f2,f3) assert(v##_f[0] == (f0) && v##_f[1] == (f1) && v##_f[2] == (f2) && v##_f[3] == (f3))

/* detect bugs with the vector support macros */
void validate_pffft_simd()
{
    using float4 = std::array<float,4>;
    static constexpr float f[16]{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};

    float4 a0_f, a1_f, a2_f, a3_f, t_f, u_f;
    v4sf a0_v, a1_v, a2_v, a3_v, t_v, u_v;
    std::memcpy(&a0_v, f, 4*sizeof(float));
    std::memcpy(&a1_v, f+4, 4*sizeof(float));
    std::memcpy(&a2_v, f+8, 4*sizeof(float));
    std::memcpy(&a3_v, f+12, 4*sizeof(float));

    t_v = a0_v; u_v = a1_v;
    t_v = VZERO(); t_f = al::bit_cast<float4>(t_v);
    printf("VZERO=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]); assertv4(t, 0, 0, 0, 0);
    t_v = VADD(a1_v, a2_v); t_f = al::bit_cast<float4>(t_v);
    printf("VADD(4:7,8:11)=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]); assertv4(t, 12, 14, 16, 18);
    t_v = VMUL(a1_v, a2_v); t_f = al::bit_cast<float4>(t_v);
    printf("VMUL(4:7,8:11)=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]); assertv4(t, 32, 45, 60, 77);
    t_v = VMADD(a1_v, a2_v,a0_v); t_f = al::bit_cast<float4>(t_v);
    printf("VMADD(4:7,8:11,0:3)=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]); assertv4(t, 32, 46, 62, 80);

    INTERLEAVE2(a1_v,a2_v,t_v,u_v); t_f = al::bit_cast<float4>(t_v); u_f = al::bit_cast<float4>(u_v);
    printf("INTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3], u_f[0], u_f[1], u_f[2], u_f[3]);
    assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);
    UNINTERLEAVE2(a1_v,a2_v,t_v,u_v); t_f = al::bit_cast<float4>(t_v); u_f = al::bit_cast<float4>(u_v);
    printf("UNINTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3], u_f[0], u_f[1], u_f[2], u_f[3]);
    assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);

    t_v=LD_PS1(f[15]); t_f = al::bit_cast<float4>(t_v);
    printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]);
    assertv4(t, 15, 15, 15, 15);
    t_v = VSWAPHL(a1_v, a2_v); t_f = al::bit_cast<float4>(t_v);
    printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t_f[0], t_f[1], t_f[2], t_f[3]);
    assertv4(t, 8, 9, 6, 7);
    VTRANSPOSE4(a0_v, a1_v, a2_v, a3_v);
    a0_f = al::bit_cast<float4>(a0_v);
    a1_f = al::bit_cast<float4>(a1_v);
    a2_f = al::bit_cast<float4>(a2_v);
    a3_f = al::bit_cast<float4>(a3_v);
    printf("VTRANSPOSE4(0:3,4:7,8:11,12:15)=[%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g]\n",
          a0_f[0], a0_f[1], a0_f[2], a0_f[3], a1_f[0], a1_f[1], a1_f[2], a1_f[3],
          a2_f[0], a2_f[1], a2_f[2], a2_f[3], a3_f[0], a3_f[1], a3_f[2], a3_f[3]);
    assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);
}
#endif //!PFFFT_SIMD_DISABLE

/* SSE and co like 16-bytes aligned pointers */
#define MALLOC_V4SF_ALIGNMENT 64 // with a 64-byte alignment, we are even aligned on L2 cache lines...

void *pffft_aligned_malloc(size_t nb_bytes)
{ return al_malloc(MALLOC_V4SF_ALIGNMENT, nb_bytes); }

void pffft_aligned_free(void *p) { al_free(p); }

int pffft_simd_size() { return SIMD_SZ; }

/*
  passf2 and passb2 has been merged here, fsign = -1 for passf2, +1 for passb2
*/
static NEVER_INLINE(void) passf2_ps(const int ido, const int l1, const v4sf *cc, v4sf *ch,
    const float *wa1, const float fsign)
{
    const int l1ido{l1*ido};
    if(ido <= 2)
    {
        for(int k{0};k < l1ido;k += ido, ch += ido, cc += 2*ido)
        {
            ch[0]         = VADD(cc[0], cc[ido+0]);
            ch[l1ido]     = VSUB(cc[0], cc[ido+0]);
            ch[1]         = VADD(cc[1], cc[ido+1]);
            ch[l1ido + 1] = VSUB(cc[1], cc[ido+1]);
        }
    }
    else
    {
        const v4sf vsign{LD_PS1(fsign)};
        for(int k{0};k < l1ido;k += ido, ch += ido, cc += 2*ido)
        {
            for(int i{0};i < ido-1;i += 2)
            {
                v4sf tr2{VSUB(cc[i+0], cc[i+ido+0])};
                v4sf ti2{VSUB(cc[i+1], cc[i+ido+1])};
                v4sf wr{LD_PS1(wa1[i])}, wi{VMUL(vsign, LD_PS1(wa1[i+1]))};
                ch[i]   = VADD(cc[i+0], cc[i+ido+0]);
                ch[i+1] = VADD(cc[i+1], cc[i+ido+1]);
                VCPLXMUL(tr2, ti2, wr, wi);
                ch[i+l1ido]   = tr2;
                ch[i+l1ido+1] = ti2;
            }
        }
    }
}

/*
  passf3 and passb3 has been merged here, fsign = -1 for passf3, +1 for passb3
*/
static NEVER_INLINE(void) passf3_ps(const int ido, const int l1, const v4sf *cc, v4sf *ch,
    const float *wa1, const float *wa2, const float fsign)
{
    assert(ido > 2);

    const v4sf vtaur{LD_PS1(-0.5f)};
    const v4sf vtaui{LD_PS1(0.866025403784439f*fsign)};
    const int l1ido{l1*ido};
    for(int k{0};k < l1ido;k += ido, cc += 3*ido, ch +=ido)
    {
        for(int i{0};i < ido-1;i += 2)
        {
            v4sf tr2{VADD(cc[i+ido], cc[i+2*ido])};
            v4sf cr2{VADD(cc[i], VMUL(vtaur,tr2))};
            ch[i]  = VADD(cc[i], tr2);
            v4sf ti2{VADD(cc[i+ido+1], cc[i+2*ido+1])};
            v4sf ci2{VADD(cc[i    +1], VMUL(vtaur,ti2))};
            ch[i+1] = VADD(cc[i+1], ti2);
            v4sf cr3{VMUL(vtaui, VSUB(cc[i+ido], cc[i+2*ido]))};
            v4sf ci3{VMUL(vtaui, VSUB(cc[i+ido+1], cc[i+2*ido+1]))};
            v4sf dr2{VSUB(cr2, ci3)};
            v4sf dr3{VADD(cr2, ci3)};
            v4sf di2{VADD(ci2, cr3)};
            v4sf di3{VSUB(ci2, cr3)};
            float wr1{wa1[i]}, wi1{fsign*wa1[i+1]}, wr2{wa2[i]}, wi2{fsign*wa2[i+1]};
            VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
            ch[i+l1ido] = dr2;
            ch[i+l1ido + 1] = di2;
            VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
            ch[i+2*l1ido] = dr3;
            ch[i+2*l1ido+1] = di3;
        }
    }
} /* passf3 */

static NEVER_INLINE(void) passf4_ps(const int ido, const int l1, const v4sf *cc, v4sf *ch,
    const float *wa1, const float *wa2, const float *wa3, const float fsign)
{
    /* fsign == -1 for forward transform and +1 for backward transform */
    const v4sf vsign{LD_PS1(fsign)};
    const int l1ido{l1*ido};
    if(ido == 2)
    {
        for(int k{0};k < l1ido;k += ido, ch += ido, cc += 4*ido)
        {
            v4sf tr1{VSUB(cc[0], cc[2*ido + 0])};
            v4sf tr2{VADD(cc[0], cc[2*ido + 0])};
            v4sf ti1{VSUB(cc[1], cc[2*ido + 1])};
            v4sf ti2{VADD(cc[1], cc[2*ido + 1])};
            v4sf ti4{VMUL(VSUB(cc[1*ido + 0], cc[3*ido + 0]), vsign)};
            v4sf tr4{VMUL(VSUB(cc[3*ido + 1], cc[1*ido + 1]), vsign)};
            v4sf tr3{VADD(cc[ido + 0], cc[3*ido + 0])};
            v4sf ti3{VADD(cc[ido + 1], cc[3*ido + 1])};

            ch[0*l1ido + 0] = VADD(tr2, tr3);
            ch[0*l1ido + 1] = VADD(ti2, ti3);
            ch[1*l1ido + 0] = VADD(tr1, tr4);
            ch[1*l1ido + 1] = VADD(ti1, ti4);
            ch[2*l1ido + 0] = VSUB(tr2, tr3);
            ch[2*l1ido + 1] = VSUB(ti2, ti3);
            ch[3*l1ido + 0] = VSUB(tr1, tr4);
            ch[3*l1ido + 1] = VSUB(ti1, ti4);
        }
    }
    else
    {
        for(int k{0};k < l1ido;k += ido, ch+=ido, cc += 4*ido)
        {
            for(int i{0};i < ido-1;i+=2)
            {
                v4sf tr1{VSUB(cc[i + 0], cc[i + 2*ido + 0])};
                v4sf tr2{VADD(cc[i + 0], cc[i + 2*ido + 0])};
                v4sf ti1{VSUB(cc[i + 1], cc[i + 2*ido + 1])};
                v4sf ti2{VADD(cc[i + 1], cc[i + 2*ido + 1])};
                v4sf tr4{VMUL(VSUB(cc[i + 3*ido + 1], cc[i + 1*ido + 1]), vsign)};
                v4sf ti4{VMUL(VSUB(cc[i + 1*ido + 0], cc[i + 3*ido + 0]), vsign)};
                v4sf tr3{VADD(cc[i + ido + 0], cc[i + 3*ido + 0])};
                v4sf ti3{VADD(cc[i + ido + 1], cc[i + 3*ido + 1])};

                ch[i] = VADD(tr2, tr3);
                v4sf cr3{VSUB(tr2, tr3)};
                ch[i + 1] = VADD(ti2, ti3);
                v4sf ci3{VSUB(ti2, ti3)};

                v4sf cr2{VADD(tr1, tr4)};
                v4sf cr4{VSUB(tr1, tr4)};
                v4sf ci2{VADD(ti1, ti4)};
                v4sf ci4{VSUB(ti1, ti4)};
                float wr1{wa1[i]}, wi1{fsign*wa1[i+1]};
                VCPLXMUL(cr2, ci2, LD_PS1(wr1), LD_PS1(wi1));
                float wr2{wa2[i]}, wi2{fsign*wa2[i+1]};
                ch[i + l1ido] = cr2;
                ch[i + l1ido + 1] = ci2;

                VCPLXMUL(cr3, ci3, LD_PS1(wr2), LD_PS1(wi2));
                float wr3{wa3[i]}, wi3{fsign*wa3[i+1]};
                ch[i + 2*l1ido] = cr3;
                ch[i + 2*l1ido + 1] = ci3;

                VCPLXMUL(cr4, ci4, LD_PS1(wr3), LD_PS1(wi3));
                ch[i + 3*l1ido] = cr4;
                ch[i + 3*l1ido + 1] = ci4;
            }
        }
    }
} /* passf4 */

/*
 * passf5 and passb5 has been merged here, fsign = -1 for passf5, +1 for passb5
 */
static NEVER_INLINE(void) passf5_ps(const int ido, const int l1, const v4sf *cc, v4sf *ch,
    const float *wa1, const float *wa2, const float *wa3, const float *wa4, const float fsign)
{
    const v4sf vtr11{LD_PS1(0.309016994374947f)};
    const v4sf vtr12{LD_PS1(-0.809016994374947f)};
    const v4sf vti11{LD_PS1(0.951056516295154f*fsign)};
    const v4sf vti12{LD_PS1(0.587785252292473f*fsign)};

#define cc_ref(a_1,a_2) cc[(a_2-1)*ido + (a_1) + 1]
#define ch_ref(a_1,a_3) ch[(a_3-1)*l1*ido + (a_1) + 1]

    assert(ido > 2);
    for(int k{0};k < l1;++k, cc += 5*ido, ch += ido)
    {
        for(int i{0};i < ido-1;i += 2)
        {
            v4sf ti5{VSUB(cc_ref(i  , 2), cc_ref(i  , 5))};
            v4sf ti2{VADD(cc_ref(i  , 2), cc_ref(i  , 5))};
            v4sf ti4{VSUB(cc_ref(i  , 3), cc_ref(i  , 4))};
            v4sf ti3{VADD(cc_ref(i  , 3), cc_ref(i  , 4))};
            v4sf tr5{VSUB(cc_ref(i-1, 2), cc_ref(i-1, 5))};
            v4sf tr2{VADD(cc_ref(i-1, 2), cc_ref(i-1, 5))};
            v4sf tr4{VSUB(cc_ref(i-1, 3), cc_ref(i-1, 4))};
            v4sf tr3{VADD(cc_ref(i-1, 3), cc_ref(i-1, 4))};
            ch_ref(i-1, 1) = VADD(cc_ref(i-1, 1), VADD(tr2, tr3));
            ch_ref(i  , 1) = VADD(cc_ref(i  , 1), VADD(ti2, ti3));
            v4sf cr2{VADD(cc_ref(i-1, 1), VADD(VMUL(vtr11, tr2),VMUL(vtr12, tr3)))};
            v4sf ci2{VADD(cc_ref(i  , 1), VADD(VMUL(vtr11, ti2),VMUL(vtr12, ti3)))};
            v4sf cr3{VADD(cc_ref(i-1, 1), VADD(VMUL(vtr12, tr2),VMUL(vtr11, tr3)))};
            v4sf ci3{VADD(cc_ref(i  , 1), VADD(VMUL(vtr12, ti2),VMUL(vtr11, ti3)))};
            v4sf cr5{VADD(VMUL(vti11, tr5), VMUL(vti12, tr4))};
            v4sf ci5{VADD(VMUL(vti11, ti5), VMUL(vti12, ti4))};
            v4sf cr4{VSUB(VMUL(vti12, tr5), VMUL(vti11, tr4))};
            v4sf ci4{VSUB(VMUL(vti12, ti5), VMUL(vti11, ti4))};
            v4sf dr3{VSUB(cr3, ci4)};
            v4sf dr4{VADD(cr3, ci4)};
            v4sf di3{VADD(ci3, cr4)};
            v4sf di4{VSUB(ci3, cr4)};
            v4sf dr5{VADD(cr2, ci5)};
            v4sf dr2{VSUB(cr2, ci5)};
            v4sf di5{VSUB(ci2, cr5)};
            v4sf di2{VADD(ci2, cr5)};
            float wr1{wa1[i]}, wi1{fsign*wa1[i+1]}, wr2{wa2[i]}, wi2{fsign*wa2[i+1]};
            float wr3{wa3[i]}, wi3{fsign*wa3[i+1]}, wr4{wa4[i]}, wi4{fsign*wa4[i+1]};
            VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
            ch_ref(i - 1, 2) = dr2;
            ch_ref(i, 2)     = di2;
            VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
            ch_ref(i - 1, 3) = dr3;
            ch_ref(i, 3)     = di3;
            VCPLXMUL(dr4, di4, LD_PS1(wr3), LD_PS1(wi3));
            ch_ref(i - 1, 4) = dr4;
            ch_ref(i, 4)     = di4;
            VCPLXMUL(dr5, di5, LD_PS1(wr4), LD_PS1(wi4));
            ch_ref(i - 1, 5) = dr5;
            ch_ref(i, 5)     = di5;
        }
    }
#undef ch_ref
#undef cc_ref
}

static NEVER_INLINE(void) radf2_ps(const int ido, const int l1, const v4sf *RESTRICT cc,
    v4sf *RESTRICT ch, const float *wa1)
{
    const int l1ido{l1*ido};
    for(int k{0};k < l1ido;k += ido)
    {
        v4sf a{cc[k]}, b{cc[k + l1ido]};
        ch[2*k] = VADD(a, b);
        ch[2*(k+ido)-1] = VSUB(a, b);
    }
    if(ido < 2)
        return;
    if(ido != 2)
    {
        for(int k{0};k < l1ido;k += ido)
        {
            for(int i{2};i < ido;i += 2)
            {
                v4sf tr2{cc[i - 1 + k + l1ido]}, ti2{cc[i + k + l1ido]};
                v4sf br{cc[i - 1 + k]}, bi{cc[i + k]};
                VCPLXMULCONJ(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
                ch[i + 2*k] = VADD(bi, ti2);
                ch[2*(k+ido) - i] = VSUB(ti2, bi);
                ch[i - 1 + 2*k] = VADD(br, tr2);
                ch[2*(k+ido) - i -1] = VSUB(br, tr2);
            }
        }
        if((ido&1) == 1)
            return;
    }
    const v4sf minus_one{LD_PS1(-1.0f)};
    for(int k{0};k < l1ido;k += ido)
    {
        ch[2*k + ido] = VMUL(minus_one, cc[ido-1 + k + l1ido]);
        ch[2*k + ido-1] = cc[k + ido-1];
    }
} /* radf2 */


static NEVER_INLINE(void) radb2_ps(const int ido, const int l1, const v4sf *cc, v4sf *ch,
    const float *wa1)
{
    const int l1ido{l1*ido};
    for(int k{0};k < l1ido;k += ido)
    {
        v4sf a{cc[2*k]};
        v4sf b{cc[2*(k+ido) - 1]};
        ch[k] = VADD(a, b);
        ch[k + l1ido] = VSUB(a, b);
    }
    if(ido < 2)
        return;
    if(ido != 2)
    {
        for(int k{0};k < l1ido;k += ido)
        {
            for(int i{2};i < ido;i += 2)
            {
                v4sf a{cc[i-1 + 2*k]};
                v4sf b{cc[2*(k + ido) - i - 1]};
                v4sf c{cc[i+0 + 2*k]};
                v4sf d{cc[2*(k + ido) - i + 0]};
                ch[i-1 + k] = VADD(a, b);
                v4sf tr2{VSUB(a, b)};
                ch[i+0 + k] = VSUB(c, d);
                v4sf ti2{VADD(c, d)};
                VCPLXMUL(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
                ch[i-1 + k + l1ido] = tr2;
                ch[i+0 + k + l1ido] = ti2;
            }
        }
        if((ido&1) == 1)
            return;
    }
    const v4sf minus_two{LD_PS1(-2.0f)};
    for(int k{0};k < l1ido;k += ido)
    {
        v4sf a{cc[2*k + ido-1]};
        v4sf b{cc[2*k + ido]};
        ch[k + ido-1] = VADD(a,a);
        ch[k + ido-1 + l1ido] = VMUL(minus_two, b);
    }
} /* radb2 */

static void radf3_ps(const int ido, const int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
    const float *wa1, const float *wa2)
{
    const v4sf vtaur{LD_PS1(-0.5f)};
    const v4sf vtaui{LD_PS1(0.866025403784439f)};
    for(int k{0};k < l1;++k)
    {
        v4sf cr2{VADD(cc[(k + l1)*ido], cc[(k + 2*l1)*ido])};
        ch[3*k*ido] = VADD(cc[k*ido], cr2);
        ch[(3*k+2)*ido] = VMUL(vtaui, VSUB(cc[(k + l1*2)*ido], cc[(k + l1)*ido]));
        ch[ido-1 + (3*k + 1)*ido] = VADD(cc[k*ido], VMUL(vtaur, cr2));
    }
    if(ido == 1)
        return;
    for(int k{0};k < l1;++k)
    {
        for(int i{2};i < ido;i += 2)
        {
            const int ic{ido - i};
            v4sf wr1{LD_PS1(wa1[i - 2])};
            v4sf wi1{LD_PS1(wa1[i - 1])};
            v4sf dr2{cc[i - 1 + (k + l1)*ido]};
            v4sf di2{cc[i + (k + l1)*ido]};
            VCPLXMULCONJ(dr2, di2, wr1, wi1);

            v4sf wr2{LD_PS1(wa2[i - 2])};
            v4sf wi2{LD_PS1(wa2[i - 1])};
            v4sf dr3{cc[i - 1 + (k + l1*2)*ido]};
            v4sf di3{cc[i + (k + l1*2)*ido]};
            VCPLXMULCONJ(dr3, di3, wr2, wi2);

            v4sf cr2{VADD(dr2, dr3)};
            v4sf ci2{VADD(di2, di3)};
            ch[i - 1 + 3*k*ido] = VADD(cc[i - 1 + k*ido], cr2);
            ch[i + 3*k*ido] = VADD(cc[i + k*ido], ci2);
            v4sf tr2{VADD(cc[i - 1 + k*ido], VMUL(vtaur, cr2))};
            v4sf ti2{VADD(cc[i + k*ido], VMUL(vtaur, ci2))};
            v4sf tr3{VMUL(vtaui, VSUB(di2, di3))};
            v4sf ti3{VMUL(vtaui, VSUB(dr3, dr2))};
            ch[i - 1 + (3*k + 2)*ido] = VADD(tr2, tr3);
            ch[ic - 1 + (3*k + 1)*ido] = VSUB(tr2, tr3);
            ch[i + (3*k + 2)*ido] = VADD(ti2, ti3);
            ch[ic + (3*k + 1)*ido] = VSUB(ti3, ti2);
        }
    }
} /* radf3 */


static void radb3_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch, const float *wa1,
    const float *wa2)
{
    static constexpr float taur{-0.5f};
    static constexpr float taui{0.866025403784439f};
    static constexpr float taui_2{taui*2.0f};

    const v4sf vtaur{LD_PS1(taur)};
    const v4sf vtaui_2{LD_PS1(taui_2)};
    for(int k{0};k < l1;++k)
    {
        v4sf tr2 = cc[ido-1 + (3*k + 1)*ido];
        tr2 = VADD(tr2,tr2);
        v4sf cr2 = VMADD(vtaur, tr2, cc[3*k*ido]);
        ch[k*ido] = VADD(cc[3*k*ido], tr2);
        v4sf ci3 = VMUL(vtaui_2, cc[(3*k + 2)*ido]);
        ch[(k + l1)*ido] = VSUB(cr2, ci3);
        ch[(k + 2*l1)*ido] = VADD(cr2, ci3);
    }
    if(ido == 1)
        return;
    const v4sf vtaui{LD_PS1(taui)};
    for(int k{0};k < l1;++k)
    {
        for(int i{2};i < ido;i += 2)
        {
            const int ic{ido - i};
            v4sf tr2{VADD(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido])};
            v4sf cr2{VMADD(vtaur, tr2, cc[i - 1 + 3*k*ido])};
            ch[i - 1 + k*ido] = VADD(cc[i - 1 + 3*k*ido], tr2);
            v4sf ti2{VSUB(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido])};
            v4sf ci2{VMADD(vtaur, ti2, cc[i + 3*k*ido])};
            ch[i + k*ido] = VADD(cc[i + 3*k*ido], ti2);
            v4sf cr3{VMUL(vtaui, VSUB(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]))};
            v4sf ci3{VMUL(vtaui, VADD(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]))};
            v4sf dr2{VSUB(cr2, ci3)};
            v4sf dr3{VADD(cr2, ci3)};
            v4sf di2{VADD(ci2, cr3)};
            v4sf di3{VSUB(ci2, cr3)};
            VCPLXMUL(dr2, di2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
            ch[i - 1 + (k + l1)*ido] = dr2;
            ch[i + (k + l1)*ido] = di2;
            VCPLXMUL(dr3, di3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
            ch[i - 1 + (k + 2*l1)*ido] = dr3;
            ch[i + (k + 2*l1)*ido] = di3;
        }
    }
} /* radb3 */

static NEVER_INLINE(void) radf4_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
        const float *RESTRICT wa1, const float * RESTRICT wa2, const float *RESTRICT wa3)
{
    const int l1ido{l1*ido};
    {
        const v4sf *RESTRICT cc_ = cc, *RESTRICT cc_end = cc + l1ido;
        v4sf *RESTRICT ch_ = ch;
        while(cc != cc_end)
        {
            // this loop represents between 25% and 40% of total radf4_ps cost !
            v4sf a0{cc[0]}, a1{cc[l1ido]};
            v4sf a2{cc[2*l1ido]}, a3{cc[3*l1ido]};
            v4sf tr1{VADD(a1, a3)};
            v4sf tr2{VADD(a0, a2)};
            ch[2*ido-1] = VSUB(a0, a2);
            ch[2*ido  ] = VSUB(a3, a1);
            ch[0      ] = VADD(tr1, tr2);
            ch[4*ido-1] = VSUB(tr2, tr1);
            cc += ido; ch += 4*ido;
        }
        cc = cc_;
        ch = ch_;
    }
    if(ido < 2)
        return;
    if(ido != 2)
    {
        for(int k{0};k < l1ido;k += ido)
        {
            const v4sf *RESTRICT pc{cc + 1 + k};
            for(int i{2};i < ido;i += 2, pc += 2)
            {
                const int ic{ido - i};

                v4sf cr2{pc[1*l1ido+0]};
                v4sf ci2{pc[1*l1ido+1]};
                v4sf wr{LD_PS1(wa1[i - 2])};
                v4sf wi{LD_PS1(wa1[i - 1])};
                VCPLXMULCONJ(cr2,ci2,wr,wi);

                v4sf cr3{pc[2*l1ido+0]};
                v4sf ci3{pc[2*l1ido+1]};
                wr = LD_PS1(wa2[i-2]);
                wi = LD_PS1(wa2[i-1]);
                VCPLXMULCONJ(cr3, ci3, wr, wi);

                v4sf cr4{pc[3*l1ido]};
                v4sf ci4{pc[3*l1ido+1]};
                wr = LD_PS1(wa3[i-2]);
                wi = LD_PS1(wa3[i-1]);
                VCPLXMULCONJ(cr4, ci4, wr, wi);

                /* at this point, on SSE, five of "cr2 cr3 cr4 ci2 ci3 ci4" should be loaded in registers */

                v4sf tr1{VADD(cr2,cr4)};
                v4sf tr4{VSUB(cr4,cr2)};
                v4sf tr2{VADD(pc[0],cr3)};
                v4sf tr3{VSUB(pc[0],cr3)};
                ch[i - 1 + 4*k] = VADD(tr1,tr2);
                ch[ic - 1 + 4*k + 3*ido] = VSUB(tr2,tr1); // at this point tr1 and tr2 can be disposed
                v4sf ti1{VADD(ci2,ci4)};
                v4sf ti4{VSUB(ci2,ci4)};
                ch[i - 1 + 4*k + 2*ido] = VADD(ti4,tr3);
                ch[ic - 1 + 4*k + 1*ido] = VSUB(tr3,ti4); // dispose tr3, ti4
                v4sf ti2{VADD(pc[1],ci3)};
                v4sf ti3{VSUB(pc[1],ci3)};
                ch[i + 4*k] = VADD(ti1, ti2);
                ch[ic + 4*k + 3*ido] = VSUB(ti1, ti2);
                ch[i + 4*k + 2*ido] = VADD(tr4, ti3);
                ch[ic + 4*k + 1*ido] = VSUB(tr4, ti3);
            }
        }
        if((ido&1) == 1)
            return;
    }
    const v4sf minus_hsqt2{LD_PS1(al::numbers::sqrt2_v<float> * -0.5f)};
    for(int k{0};k < l1ido;k += ido)
    {
        v4sf a{cc[ido-1 + k + l1ido]}, b{cc[ido-1 + k + 3*l1ido]};
        v4sf c{cc[ido-1 + k]}, d{cc[ido-1 + k + 2*l1ido]};
        v4sf ti1{VMUL(minus_hsqt2, VADD(a, b))};
        v4sf tr1{VMUL(minus_hsqt2, VSUB(b, a))};
        ch[ido-1 + 4*k] = VADD(tr1, c);
        ch[ido-1 + 4*k + 2*ido] = VSUB(c, tr1);
        ch[4*k + 1*ido] = VSUB(ti1, d);
        ch[4*k + 3*ido] = VADD(ti1, d);
    }
} /* radf4 */


static NEVER_INLINE(void) radb4_ps(const int ido, const int l1, const v4sf * RESTRICT cc,
    v4sf *RESTRICT ch, const float *RESTRICT wa1, const float *RESTRICT wa2,
    const float *RESTRICT wa3)
{
    const v4sf two{LD_PS1(2.0f)};
    const int l1ido{l1*ido};
    {
        const v4sf *RESTRICT cc_{cc}, *RESTRICT ch_end{ch + l1ido};
        v4sf *ch_{ch};
        while(ch != ch_end)
        {
            v4sf a{cc[0]}, b{cc[4*ido-1]};
            v4sf c{cc[2*ido]}, d{cc[2*ido-1]};
            v4sf tr3{VMUL(two,d)};
            v4sf tr2{VADD(a,b)};
            v4sf tr1{VSUB(a,b)};
            v4sf tr4{VMUL(two,c)};
            ch[0*l1ido] = VADD(tr2, tr3);
            ch[2*l1ido] = VSUB(tr2, tr3);
            ch[1*l1ido] = VSUB(tr1, tr4);
            ch[3*l1ido] = VADD(tr1, tr4);

            cc += 4*ido; ch += ido;
        }
        cc = cc_; ch = ch_;
    }
    if(ido < 2)
        return;
    if(ido != 2)
    {
        for(int k{0};k < l1ido;k += ido)
        {
            const v4sf *RESTRICT pc{cc - 1 + 4*k};
            v4sf *RESTRICT ph{ch + k + 1};
            for(int i{2};i < ido;i += 2)
            {
                v4sf tr1{VSUB(pc[i], pc[4*ido - i])};
                v4sf tr2{VADD(pc[i], pc[4*ido - i])};
                v4sf ti4{VSUB(pc[2*ido + i], pc[2*ido - i])};
                v4sf tr3{VADD(pc[2*ido + i], pc[2*ido - i])};
                ph[0] = VADD(tr2, tr3);
                v4sf cr3{VSUB(tr2, tr3)};

                v4sf ti3{VSUB(pc[2*ido + i + 1], pc[2*ido - i + 1])};
                v4sf tr4{VADD(pc[2*ido + i + 1], pc[2*ido - i + 1])};
                v4sf cr2{VSUB(tr1, tr4)};
                v4sf cr4{VADD(tr1, tr4)};

                v4sf ti1{VADD(pc[i + 1], pc[4*ido - i + 1])};
                v4sf ti2{VSUB(pc[i + 1], pc[4*ido - i + 1])};

                ph[1] = VADD(ti2, ti3); ph += l1ido;
                v4sf ci3{VSUB(ti2, ti3)};
                v4sf ci2{VADD(ti1, ti4)};
                v4sf ci4{VSUB(ti1, ti4)};
                VCPLXMUL(cr2, ci2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
                ph[0] = cr2;
                ph[1] = ci2; ph += l1ido;
                VCPLXMUL(cr3, ci3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
                ph[0] = cr3;
                ph[1] = ci3; ph += l1ido;
                VCPLXMUL(cr4, ci4, LD_PS1(wa3[i-2]), LD_PS1(wa3[i-1]));
                ph[0] = cr4;
                ph[1] = ci4; ph = ph - 3*l1ido + 2;
            }
        }
        if((ido&1) == 1)
            return;
    }
    const v4sf minus_sqrt2{LD_PS1(-1.414213562373095f)};
    for(int k{0};k < l1ido;k += ido)
    {
        const int i0{4*k + ido};
        v4sf c{cc[i0-1]}, d{cc[i0 + 2*ido-1]};
        v4sf a{cc[i0+0]}, b{cc[i0 + 2*ido+0]};
        v4sf tr1{VSUB(c,d)};
        v4sf tr2{VADD(c,d)};
        v4sf ti1{VADD(b,a)};
        v4sf ti2{VSUB(b,a)};
        ch[ido-1 + k + 0*l1ido] = VADD(tr2,tr2);
        ch[ido-1 + k + 1*l1ido] = VMUL(minus_sqrt2, VSUB(ti1, tr1));
        ch[ido-1 + k + 2*l1ido] = VADD(ti2, ti2);
        ch[ido-1 + k + 3*l1ido] = VMUL(minus_sqrt2, VADD(ti1, tr1));
    }
} /* radb4 */

static void radf5_ps(const int ido, const int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
    const float *wa1, const float *wa2, const float *wa3, const float *wa4)
{
    const v4sf tr11{LD_PS1(0.309016994374947f)};
    const v4sf ti11{LD_PS1(0.951056516295154f)};
    const v4sf tr12{LD_PS1(-0.809016994374947f)};
    const v4sf ti12{LD_PS1(0.587785252292473f)};

#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
#define ch_ref(a_1,a_2,a_3) ch[((a_3)*5 + (a_2))*ido + a_1]

    /* Parameter adjustments */
    const int ch_offset{1 + ido * 6};
    ch -= ch_offset;
    const int cc_offset{1 + ido * (1 + l1)};
    cc -= cc_offset;

    /* Function Body */
    for(int k{1};k <= l1;++k)
    {
        v4sf cr2{VADD(cc_ref(1, k, 5), cc_ref(1, k, 2))};
        v4sf ci5{VSUB(cc_ref(1, k, 5), cc_ref(1, k, 2))};
        v4sf cr3{VADD(cc_ref(1, k, 4), cc_ref(1, k, 3))};
        v4sf ci4{VSUB(cc_ref(1, k, 4), cc_ref(1, k, 3))};
        ch_ref(1, 1, k) = VADD(cc_ref(1, k, 1), VADD(cr2, cr3));
        ch_ref(ido, 2, k) = VADD(cc_ref(1, k, 1), VADD(VMUL(tr11, cr2), VMUL(tr12, cr3)));
        ch_ref(1, 3, k) = VADD(VMUL(ti11, ci5), VMUL(ti12, ci4));
        ch_ref(ido, 4, k) = VADD(cc_ref(1, k, 1), VADD(VMUL(tr12, cr2), VMUL(tr11, cr3)));
        ch_ref(1, 5, k) = VSUB(VMUL(ti12, ci5), VMUL(ti11, ci4));
        //printf("pffft: radf5, k=%d ch_ref=%f, ci4=%f\n", k, ch_ref(1, 5, k), ci4);
    }
    if(ido == 1)
      return;

    const int idp2{ido + 2};
    for(int k{1};k <= l1;++k)
    {
        for(int i{3};i <= ido;i += 2)
        {
            const int ic{idp2 - i};
            v4sf dr2{LD_PS1(wa1[i-3])};
            v4sf di2{LD_PS1(wa1[i-2])};
            v4sf dr3{LD_PS1(wa2[i-3])};
            v4sf di3{LD_PS1(wa2[i-2])};
            v4sf dr4{LD_PS1(wa3[i-3])};
            v4sf di4{LD_PS1(wa3[i-2])};
            v4sf dr5{LD_PS1(wa4[i-3])};
            v4sf di5{LD_PS1(wa4[i-2])};
            VCPLXMULCONJ(dr2, di2, cc_ref(i-1, k, 2), cc_ref(i, k, 2));
            VCPLXMULCONJ(dr3, di3, cc_ref(i-1, k, 3), cc_ref(i, k, 3));
            VCPLXMULCONJ(dr4, di4, cc_ref(i-1, k, 4), cc_ref(i, k, 4));
            VCPLXMULCONJ(dr5, di5, cc_ref(i-1, k, 5), cc_ref(i, k, 5));
            v4sf cr2{VADD(dr2, dr5)};
            v4sf ci5{VSUB(dr5, dr2)};
            v4sf cr5{VSUB(di2, di5)};
            v4sf ci2{VADD(di2, di5)};
            v4sf cr3{VADD(dr3, dr4)};
            v4sf ci4{VSUB(dr4, dr3)};
            v4sf cr4{VSUB(di3, di4)};
            v4sf ci3{VADD(di3, di4)};
            ch_ref(i - 1, 1, k) = VADD(cc_ref(i - 1, k, 1), VADD(cr2, cr3));
            ch_ref(i, 1, k) = VSUB(cc_ref(i, k, 1), VADD(ci2, ci3));
            v4sf tr2{VADD(cc_ref(i - 1, k, 1), VADD(VMUL(tr11, cr2), VMUL(tr12, cr3)))};
            v4sf ti2{VSUB(cc_ref(i, k, 1), VADD(VMUL(tr11, ci2), VMUL(tr12, ci3)))};
            v4sf tr3{VADD(cc_ref(i - 1, k, 1), VADD(VMUL(tr12, cr2), VMUL(tr11, cr3)))};
            v4sf ti3{VSUB(cc_ref(i, k, 1), VADD(VMUL(tr12, ci2), VMUL(tr11, ci3)))};
            v4sf tr5{VADD(VMUL(ti11, cr5), VMUL(ti12, cr4))};
            v4sf ti5{VADD(VMUL(ti11, ci5), VMUL(ti12, ci4))};
            v4sf tr4{VSUB(VMUL(ti12, cr5), VMUL(ti11, cr4))};
            v4sf ti4{VSUB(VMUL(ti12, ci5), VMUL(ti11, ci4))};
            ch_ref(i - 1, 3, k) = VSUB(tr2, tr5);
            ch_ref(ic - 1, 2, k) = VADD(tr2, tr5);
            ch_ref(i, 3, k) = VADD(ti2, ti5);
            ch_ref(ic, 2, k) = VSUB(ti5, ti2);
            ch_ref(i - 1, 5, k) = VSUB(tr3, tr4);
            ch_ref(ic - 1, 4, k) = VADD(tr3, tr4);
            ch_ref(i, 5, k) = VADD(ti3, ti4);
            ch_ref(ic, 4, k) = VSUB(ti4, ti3);
        }
    }
#undef cc_ref
#undef ch_ref
} /* radf5 */

static void radb5_ps(const int ido, const int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
    const float *wa1, const float *wa2, const float *wa3, const float *wa4)
{
    const v4sf tr11{LD_PS1(0.309016994374947f)};
    const v4sf ti11{LD_PS1(0.951056516295154f)};
    const v4sf tr12{LD_PS1(-0.809016994374947f)};
    const v4sf ti12{LD_PS1(0.587785252292473f)};

#define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]
#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]

    /* Parameter adjustments */
    const int ch_offset{1 + ido*(1 + l1)};
    ch -= ch_offset;
    const int cc_offset{1 + ido*6};
    cc -= cc_offset;

    /* Function Body */
    for(int k{1};k <= l1;++k)
    {
        v4sf ti5{VADD(cc_ref(1, 3, k), cc_ref(1, 3, k))};
        v4sf ti4{VADD(cc_ref(1, 5, k), cc_ref(1, 5, k))};
        v4sf tr2{VADD(cc_ref(ido, 2, k), cc_ref(ido, 2, k))};
        v4sf tr3{VADD(cc_ref(ido, 4, k), cc_ref(ido, 4, k))};
        ch_ref(1, k, 1) = VADD(cc_ref(1, 1, k), VADD(tr2, tr3));
        v4sf cr2{VADD(cc_ref(1, 1, k), VADD(VMUL(tr11, tr2), VMUL(tr12, tr3)))};
        v4sf cr3{VADD(cc_ref(1, 1, k), VADD(VMUL(tr12, tr2), VMUL(tr11, tr3)))};
        v4sf ci5{VADD(VMUL(ti11, ti5), VMUL(ti12, ti4))};
        v4sf ci4{VSUB(VMUL(ti12, ti5), VMUL(ti11, ti4))};
        ch_ref(1, k, 2) = VSUB(cr2, ci5);
        ch_ref(1, k, 3) = VSUB(cr3, ci4);
        ch_ref(1, k, 4) = VADD(cr3, ci4);
        ch_ref(1, k, 5) = VADD(cr2, ci5);
    }
    if(ido == 1)
        return;

    const int idp2{ido + 2};
    for(int k{1};k <= l1;++k)
    {
        for(int i{3};i <= ido;i += 2)
        {
            const int ic{idp2 - i};
            v4sf ti5{VADD(cc_ref(i  , 3, k), cc_ref(ic  , 2, k))};
            v4sf ti2{VSUB(cc_ref(i  , 3, k), cc_ref(ic  , 2, k))};
            v4sf ti4{VADD(cc_ref(i  , 5, k), cc_ref(ic  , 4, k))};
            v4sf ti3{VSUB(cc_ref(i  , 5, k), cc_ref(ic  , 4, k))};
            v4sf tr5{VSUB(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k))};
            v4sf tr2{VADD(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k))};
            v4sf tr4{VSUB(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k))};
            v4sf tr3{VADD(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k))};
            ch_ref(i - 1, k, 1) = VADD(cc_ref(i-1, 1, k), VADD(tr2, tr3));
            ch_ref(i, k, 1) = VADD(cc_ref(i, 1, k), VADD(ti2, ti3));
            v4sf cr2{VADD(cc_ref(i-1, 1, k), VADD(VMUL(tr11, tr2), VMUL(tr12, tr3)))};
            v4sf ci2{VADD(cc_ref(i  , 1, k), VADD(VMUL(tr11, ti2), VMUL(tr12, ti3)))};
            v4sf cr3{VADD(cc_ref(i-1, 1, k), VADD(VMUL(tr12, tr2), VMUL(tr11, tr3)))};
            v4sf ci3{VADD(cc_ref(i  , 1, k), VADD(VMUL(tr12, ti2), VMUL(tr11, ti3)))};
            v4sf cr5{VADD(VMUL(ti11, tr5), VMUL(ti12, tr4))};
            v4sf ci5{VADD(VMUL(ti11, ti5), VMUL(ti12, ti4))};
            v4sf cr4{VSUB(VMUL(ti12, tr5), VMUL(ti11, tr4))};
            v4sf ci4{VSUB(VMUL(ti12, ti5), VMUL(ti11, ti4))};
            v4sf dr3{VSUB(cr3, ci4)};
            v4sf dr4{VADD(cr3, ci4)};
            v4sf di3{VADD(ci3, cr4)};
            v4sf di4{VSUB(ci3, cr4)};
            v4sf dr5{VADD(cr2, ci5)};
            v4sf dr2{VSUB(cr2, ci5)};
            v4sf di5{VSUB(ci2, cr5)};
            v4sf di2{VADD(ci2, cr5)};
            VCPLXMUL(dr2, di2, LD_PS1(wa1[i-3]), LD_PS1(wa1[i-2]));
            VCPLXMUL(dr3, di3, LD_PS1(wa2[i-3]), LD_PS1(wa2[i-2]));
            VCPLXMUL(dr4, di4, LD_PS1(wa3[i-3]), LD_PS1(wa3[i-2]));
            VCPLXMUL(dr5, di5, LD_PS1(wa4[i-3]), LD_PS1(wa4[i-2]));

            ch_ref(i-1, k, 2) = dr2; ch_ref(i, k, 2) = di2;
            ch_ref(i-1, k, 3) = dr3; ch_ref(i, k, 3) = di3;
            ch_ref(i-1, k, 4) = dr4; ch_ref(i, k, 4) = di4;
            ch_ref(i-1, k, 5) = dr5; ch_ref(i, k, 5) = di5;
        }
    }
#undef cc_ref
#undef ch_ref
} /* radb5 */

static NEVER_INLINE(v4sf *) rfftf1_ps(const int n, const v4sf *input_readonly, v4sf *work1,
    v4sf *work2, const float *wa, const int *ifac)
{
    assert(work1 != work2);

    const v4sf *in{input_readonly};
    v4sf *out{in == work2 ? work1 : work2};
    const int nf{ifac[1]};
    int l2{n};
    int iw{n-1};
    for(int k1{1};k1 <= nf;++k1)
    {
        int kh{nf - k1};
        int ip{ifac[kh + 2]};
        int l1{l2 / ip};
        int ido{n / l2};
        iw -= (ip - 1)*ido;
        switch(ip)
        {
        case 5:
            {
                int ix2{iw + ido};
                int ix3{ix2 + ido};
                int ix4{ix3 + ido};
                radf5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
            }
            break;
        case 4:
            {
                int ix2{iw + ido};
                int ix3{ix2 + ido};
                radf4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
            }
            break;
        case 3:
            {
                int ix2{iw + ido};
                radf3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
            }
            break;
        case 2:
            radf2_ps(ido, l1, in, out, &wa[iw]);
            break;
        default:
            assert(0);
            break;
        }
        l2 = l1;
        if(out == work2)
        {
            out = work1;
            in = work2;
        }
        else
        {
            out = work2;
            in = work1;
        }
    }
    return const_cast<v4sf*>(in); /* this is in fact the output .. */
} /* rfftf1 */

static NEVER_INLINE(v4sf *) rfftb1_ps(const int n, const v4sf *input_readonly, v4sf *work1,
    v4sf *work2, const float *wa, const int *ifac)
{
    assert(work1 != work2);

    const v4sf *in{input_readonly};
    v4sf *out{in == work2 ? work1 : work2};
    const int nf{ifac[1]};
    int l1{1};
    int iw{0};
    for(int k1{1};k1 <= nf;++k1)
    {
        int ip{ifac[k1 + 1]};
        int l2{ip*l1};
        int ido{n / l2};
        switch(ip)
        {
        case 5:
            {
                int ix2{iw + ido};
                int ix3{ix2 + ido};
                int ix4{ix3 + ido};
                radb5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
            }
            break;
        case 4:
            {
                int ix2{iw + ido};
                int ix3{ix2 + ido};
                radb4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
            }
            break;
        case 3:
            {
                int ix2{iw + ido};
                radb3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
            }
            break;
        case 2:
            radb2_ps(ido, l1, in, out, &wa[iw]);
            break;
        default:
            assert(0);
            break;
        }
        l1 = l2;
        iw += (ip - 1)*ido;

        if(out == work2)
        {
            out = work1;
            in = work2;
        }
        else
        {
            out = work2;
            in = work1;
        }
    }
    return const_cast<v4sf*>(in); /* this is in fact the output .. */
}

static int decompose(const int n, int *ifac, const int *ntryh)
{
    int nl{n}, nf{0};
    for(int j{0};ntryh[j];++j)
    {
        const int ntry{ntryh[j]};
        while(nl != 1)
        {
            const int nq{nl / ntry};
            const int nr{nl - ntry*nq};
            if(nr != 0)
                break;

            ifac[2+nf++] = ntry;
            nl = nq;
            if(ntry == 2 && nf != 1)
            {
                for(int i{2};i <= nf;++i)
                {
                    int ib{nf - i + 2};
                    ifac[ib + 1] = ifac[ib];
                }
                ifac[2] = 2;
            }
        }
    }
    ifac[0] = n;
    ifac[1] = nf;
    return nf;
}



static void rffti1_ps(const int n, float *wa, int *ifac)
{
    static constexpr int ntryh[]{4,2,3,5,0};

    const int nf{decompose(n, ifac, ntryh)};
    const double argh{2.0*al::numbers::pi / n};
    int is{0};
    int nfm1{nf - 1};
    int l1{1};
    for(int k1{1};k1 <= nfm1;++k1)
    {
        const int ip{ifac[k1 + 1]};
        const int l2{l1*ip};
        const int ido{n / l2};
        const int ipm{ip - 1};
        int ld{0};
        for(int j{1};j <= ipm;++j)
        {
            int i{is}, fi{0};
            ld += l1;
            double argld{ld*argh};
            for(int ii{3};ii <= ido;ii += 2)
            {
                i += 2;
                fi += 1;
                wa[i - 2] = static_cast<float>(std::cos(fi*argld));
                wa[i - 1] = static_cast<float>(std::sin(fi*argld));
            }
            is += ido;
        }
        l1 = l2;
    }
} /* rffti1 */

void cffti1_ps(const int n, float *wa, int *ifac)
{
    static constexpr int ntryh[]{5,3,4,2,0};

    const int nf{decompose(n, ifac, ntryh)};
    const double argh{2.0*al::numbers::pi / n};
    int i{1};
    int l1{1};
    for(int k1{1};k1 <= nf;++k1)
    {
        const int ip{ifac[k1+1]};
        const int l2{l1*ip};
        const int ido{n / l2};
        const int idot{ido + ido + 2};
        const int ipm{ip - 1};
        int ld{0};
        for(int j{1};j <= ipm;++j)
        {
            int i1{i}, fi{0};
            wa[i-1] = 1;
            wa[i] = 0;
            ld += l1;
            double argld = ld*argh;
            for(int ii = 4; ii <= idot; ii += 2)
            {
                i += 2;
                fi += 1;
                wa[i-1] = static_cast<float>(std::cos(fi*argld));
                wa[i]   = static_cast<float>(std::sin(fi*argld));
            }
            if(ip > 5)
            {
                wa[i1-1] = wa[i-1];
                wa[i1] = wa[i];
            }
        }
        l1 = l2;
    }
} /* cffti1 */


v4sf *cfftf1_ps(const int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, const float *wa,
    const int *ifac, const float fsign)
{
    assert(work1 != work2);

    const v4sf *in{input_readonly};
    v4sf *out{in == work2 ? work1 : work2};
    const int nf{ifac[1]};
    int l1{1}, iw{0};
    for(int k1{2};k1 <= nf+1;++k1)
    {
        const int ip{ifac[k1]};
        const int l2{ip*l1};
        const int ido{n / l2};
        const int idot{ido + ido};
        switch(ip)
        {
        case 5:
            {
                int ix2{iw + idot};
                int ix3{ix2 + idot};
                int ix4{ix3 + idot};
                passf5_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], fsign);
            }
            break;
        case 4:
            {
                int ix2{iw + idot};
                int ix3{ix2 + idot};
                passf4_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], fsign);
            }
            break;
        case 3:
            {
                int ix2{iw + idot};
                passf3_ps(idot, l1, in, out, &wa[iw], &wa[ix2], fsign);
            }
            break;
        case 2:
            passf2_ps(idot, l1, in, out, &wa[iw], fsign);
            break;
        default:
            assert(0);
        }
        l1 = l2;
        iw += (ip - 1)*idot;
        if(out == work2)
        {
            out = work1;
            in = work2;
        }
        else
        {
            out = work2;
            in = work1;
        }
    }

    return const_cast<v4sf*>(in); /* this is in fact the output .. */
}


struct PFFFT_Setup {
    int N;
    int Ncvec; // nb of complex simd vectors (N/4 if PFFFT_COMPLEX, N/8 if PFFFT_REAL)
    int ifac[15];
    pffft_transform_t transform;

    float *twiddle; // N/4 elements
    alignas(MALLOC_V4SF_ALIGNMENT) v4sf e[1]; // N/4*3 elements
};

PFFFT_Setup *pffft_new_setup(int N, pffft_transform_t transform)
{
    assert(transform == PFFFT_REAL || transform == PFFFT_COMPLEX);
    assert(N > 0);
    /* unfortunately, the fft size must be a multiple of 16 for complex FFTs
     * and 32 for real FFTs -- a lot of stuff would need to be rewritten to
     * handle other cases (or maybe just switch to a scalar fft, I don't know..)
     */
    if(transform == PFFFT_REAL)
        assert((N%(2*SIMD_SZ*SIMD_SZ)) == 0);
    else
        assert((N%(SIMD_SZ*SIMD_SZ)) == 0);

    const auto Ncvec = static_cast<unsigned>(transform == PFFFT_REAL ? N/2 : N)/SIMD_SZ;
    const size_t storelen{offsetof(PFFFT_Setup, e[0]) + (2u*Ncvec * sizeof(v4sf))};

    void *store{al_calloc(MALLOC_V4SF_ALIGNMENT, storelen)};
    if(!store) return nullptr;

    PFFFT_Setup *s{::new(store) PFFFT_Setup{}};
    s->N = N;
    s->transform = transform;
    /* nb of complex simd vectors */
    s->Ncvec = static_cast<int>(Ncvec);
    s->twiddle = reinterpret_cast<float*>(&s->e[2u*Ncvec*(SIMD_SZ-1)/SIMD_SZ]);

    if constexpr(SIMD_SZ > 1)
    {
        al::vector<float,16> e(2u*Ncvec*(SIMD_SZ-1));
        for(int k{0};k < s->Ncvec;++k)
        {
            const size_t i{static_cast<size_t>(k) / SIMD_SZ};
            const size_t j{static_cast<size_t>(k) % SIMD_SZ};
            for(size_t m{0};m < SIMD_SZ-1;++m)
            {
                const double A = -2.0*al::numbers::pi*static_cast<double>(m+1)*k / N;
                e[(2*(i*3 + m) + 0)*SIMD_SZ + j] = static_cast<float>(std::cos(A));
                e[(2*(i*3 + m) + 1)*SIMD_SZ + j] = static_cast<float>(std::sin(A));
            }
        }
        std::memcpy(s->e, e.data(), e.size()*sizeof(float));
    }
    if(transform == PFFFT_REAL)
        rffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);
    else
        cffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);

    /* check that N is decomposable with allowed prime factors */
    int m{1};
    for(int k{0};k < s->ifac[1];++k)
        m *= s->ifac[2+k];

    if(m != N/SIMD_SZ)
    {
        pffft_destroy_setup(s);
        s = nullptr;
    }

    return s;
}


void pffft_destroy_setup(PFFFT_Setup *s)
{
    std::destroy_at(s);
    al_free(s);
}

#if !defined(PFFFT_SIMD_DISABLE)

/* [0 0 1 2 3 4 5 6 7 8] -> [0 8 7 6 5 4 3 2 1] */
static void reversed_copy(const int N, const v4sf *in, const int in_stride, v4sf *out)
{
    v4sf g0, g1;
    INTERLEAVE2(in[0], in[1], g0, g1);
    in += in_stride;

    *--out = VSWAPHL(g0, g1); // [g0l, g0h], [g1l g1h] -> [g1l, g0h]
    for(int k{1};k < N;++k)
    {
        v4sf h0, h1;
        INTERLEAVE2(in[0], in[1], h0, h1);
        in += in_stride;
        *--out = VSWAPHL(g1, h0);
        *--out = VSWAPHL(h0, h1);
        g1 = h1;
    }
    *--out = VSWAPHL(g1, g0);
}

static void unreversed_copy(const int N, const v4sf *in, v4sf *out, const int out_stride)
{
    v4sf g0{in[0]}, g1{g0};
    ++in;
    for(int k{1};k < N;++k)
    {
        v4sf h0{*in++}; v4sf h1{*in++};
        g1 = VSWAPHL(g1, h0);
        h0 = VSWAPHL(h0, h1);
        UNINTERLEAVE2(h0, g1, out[0], out[1]);
        out += out_stride;
        g1 = h1;
    }
    v4sf h0{*in++}, h1{g0};
    g1 = VSWAPHL(g1, h0);
    h0 = VSWAPHL(h0, h1);
    UNINTERLEAVE2(h0, g1, out[0], out[1]);
}

void pffft_zreorder(PFFFT_Setup *setup, const float *in, float *out, pffft_direction_t direction)
{
    assert(in != out);

    const int N{setup->N}, Ncvec{setup->Ncvec};
    const v4sf *vin{reinterpret_cast<const v4sf*>(in)};
    v4sf *vout{reinterpret_cast<v4sf*>(out)};
    if(setup->transform == PFFFT_REAL)
    {
        const int dk{N/32};
        if(direction == PFFFT_FORWARD)
        {
            for(int k{0};k < dk;++k)
            {
                INTERLEAVE2(vin[k*8 + 0], vin[k*8 + 1], vout[2*(0*dk + k) + 0], vout[2*(0*dk + k) + 1]);
                INTERLEAVE2(vin[k*8 + 4], vin[k*8 + 5], vout[2*(2*dk + k) + 0], vout[2*(2*dk + k) + 1]);
            }
            reversed_copy(dk, vin+2, 8, vout + N/SIMD_SZ/2);
            reversed_copy(dk, vin+6, 8, vout + N/SIMD_SZ);
        }
        else
        {
            for(int k=0; k < dk; ++k)
            {
                UNINTERLEAVE2(vin[2*(0*dk + k) + 0], vin[2*(0*dk + k) + 1], vout[k*8 + 0], vout[k*8 + 1]);
                UNINTERLEAVE2(vin[2*(2*dk + k) + 0], vin[2*(2*dk + k) + 1], vout[k*8 + 4], vout[k*8 + 5]);
            }
            unreversed_copy(dk, vin + N/SIMD_SZ/4, vout + N/SIMD_SZ - 6, -8);
            unreversed_copy(dk, vin + 3*N/SIMD_SZ/4, vout + N/SIMD_SZ - 2, -8);
        }
    }
    else
    {
        if(direction == PFFFT_FORWARD)
        {
            for(int k=0; k < Ncvec; ++k)
            {
                int kk = (k/4) + (k%4)*(Ncvec/4);
                INTERLEAVE2(vin[k*2], vin[k*2+1], vout[kk*2], vout[kk*2+1]);
            }
        }
        else
        {
            for(int k=0; k < Ncvec; ++k)
            {
                int kk = (k/4) + (k%4)*(Ncvec/4);
                UNINTERLEAVE2(vin[kk*2], vin[kk*2+1], vout[k*2], vout[k*2+1]);
            }
        }
    }
}

void pffft_cplx_finalize(const int Ncvec, const v4sf *in, v4sf *out, const v4sf *e)
{
    assert(in != out);

    const int dk{Ncvec/SIMD_SZ}; // number of 4x4 matrix blocks
    for(int k=0; k < dk; ++k)
    {
        v4sf r0{in[8*k+0]}, i0{in[8*k+1]};
        v4sf r1{in[8*k+2]}, i1{in[8*k+3]};
        v4sf r2{in[8*k+4]}, i2{in[8*k+5]};
        v4sf r3{in[8*k+6]}, i3{in[8*k+7]};
        VTRANSPOSE4(r0,r1,r2,r3);
        VTRANSPOSE4(i0,i1,i2,i3);
        VCPLXMUL(r1,i1,e[k*6+0],e[k*6+1]);
        VCPLXMUL(r2,i2,e[k*6+2],e[k*6+3]);
        VCPLXMUL(r3,i3,e[k*6+4],e[k*6+5]);

        v4sf sr0{VADD(r0,r2)}, dr0{VSUB(r0, r2)};
        v4sf sr1{VADD(r1,r3)}, dr1{VSUB(r1, r3)};
        v4sf si0{VADD(i0,i2)}, di0{VSUB(i0, i2)};
        v4sf si1{VADD(i1,i3)}, di1{VSUB(i1, i3)};

        /* transformation for each column is:
         *
         * [1   1   1   1   0   0   0   0]   [r0]
         * [1   0  -1   0   0  -1   0   1]   [r1]
         * [1  -1   1  -1   0   0   0   0]   [r2]
         * [1   0  -1   0   0   1   0  -1]   [r3]
         * [0   0   0   0   1   1   1   1] * [i0]
         * [0   1   0  -1   1   0  -1   0]   [i1]
         * [0   0   0   0   1  -1   1  -1]   [i2]
         * [0  -1   0   1   1   0  -1   0]   [i3]
         */

        r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);
        r1 = VADD(dr0, di1); i1 = VSUB(di0, dr1);
        r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);
        r3 = VSUB(dr0, di1); i3 = VADD(di0, dr1);

        *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;
        *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;
    }
}

void pffft_cplx_preprocess(const int Ncvec, const v4sf *in, v4sf *out, const v4sf *e)
{
    assert(in != out);

    const int dk{Ncvec/SIMD_SZ}; // number of 4x4 matrix blocks
    for(int k=0; k < dk; ++k)
    {
        v4sf r0{in[8*k+0]}, i0{in[8*k+1]};
        v4sf r1{in[8*k+2]}, i1{in[8*k+3]};
        v4sf r2{in[8*k+4]}, i2{in[8*k+5]};
        v4sf r3{in[8*k+6]}, i3{in[8*k+7]};

        v4sf sr0{VADD(r0,r2)}, dr0{VSUB(r0, r2)};
        v4sf sr1{VADD(r1,r3)}, dr1{VSUB(r1, r3)};
        v4sf si0{VADD(i0,i2)}, di0{VSUB(i0, i2)};
        v4sf si1{VADD(i1,i3)}, di1{VSUB(i1, i3)};

        r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);
        r1 = VSUB(dr0, di1); i1 = VADD(di0, dr1);
        r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);
        r3 = VADD(dr0, di1); i3 = VSUB(di0, dr1);

        VCPLXMULCONJ(r1,i1,e[k*6+0],e[k*6+1]);
        VCPLXMULCONJ(r2,i2,e[k*6+2],e[k*6+3]);
        VCPLXMULCONJ(r3,i3,e[k*6+4],e[k*6+5]);

        VTRANSPOSE4(r0,r1,r2,r3);
        VTRANSPOSE4(i0,i1,i2,i3);

        *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;
        *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;
    }
}


static ALWAYS_INLINE(void) pffft_real_finalize_4x4(const v4sf *in0, const v4sf *in1,
    const v4sf *in, const v4sf *e, v4sf *out)
{
    v4sf r0{*in0}, i0{*in1};
    v4sf r1{*in++}; v4sf i1{*in++};
    v4sf r2{*in++}; v4sf i2{*in++};
    v4sf r3{*in++}; v4sf i3{*in++};
    VTRANSPOSE4(r0,r1,r2,r3);
    VTRANSPOSE4(i0,i1,i2,i3);

    /*
     * transformation for each column is:
     *
     * [1   1   1   1   0   0   0   0]   [r0]
     * [1   0  -1   0   0  -1   0   1]   [r1]
     * [1   0  -1   0   0   1   0  -1]   [r2]
     * [1  -1   1  -1   0   0   0   0]   [r3]
     * [0   0   0   0   1   1   1   1] * [i0]
     * [0  -1   0   1  -1   0   1   0]   [i1]
     * [0  -1   0   1   1   0  -1   0]   [i2]
     * [0   0   0   0  -1   1  -1   1]   [i3]
     */

    //cerr << "matrix initial, before e , REAL:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";
    //cerr << "matrix initial, before e, IMAG :\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";

    VCPLXMUL(r1,i1,e[0],e[1]);
    VCPLXMUL(r2,i2,e[2],e[3]);
    VCPLXMUL(r3,i3,e[4],e[5]);

    //cerr << "matrix initial, real part:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";
    //cerr << "matrix initial, imag part:\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";

    v4sf sr0{VADD(r0,r2)}, dr0{VSUB(r0,r2)};
    v4sf sr1{VADD(r1,r3)}, dr1{VSUB(r3,r1)};
    v4sf si0{VADD(i0,i2)}, di0{VSUB(i0,i2)};
    v4sf si1{VADD(i1,i3)}, di1{VSUB(i3,i1)};

    r0 = VADD(sr0, sr1);
    r3 = VSUB(sr0, sr1);
    i0 = VADD(si0, si1);
    i3 = VSUB(si1, si0);
    r1 = VADD(dr0, di1);
    r2 = VSUB(dr0, di1);
    i1 = VSUB(dr1, di0);
    i2 = VADD(dr1, di0);

    *out++ = r0;
    *out++ = i0;
    *out++ = r1;
    *out++ = i1;
    *out++ = r2;
    *out++ = i2;
    *out++ = r3;
    *out++ = i3;
}

static NEVER_INLINE(void) pffft_real_finalize(const int Ncvec, const v4sf *in, v4sf *out,
    const v4sf *e)
{
    static constexpr float s{al::numbers::sqrt2_v<float>/2.0f};

    assert(in != out);
    const int dk{Ncvec/SIMD_SZ}; // number of 4x4 matrix blocks
    /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */

    const v4sf zero{VZERO()};
    const auto cr = al::bit_cast<std::array<float,SIMD_SZ>>(in[0]);
    const auto ci = al::bit_cast<std::array<float,SIMD_SZ>>(in[Ncvec*2-1]);
    pffft_real_finalize_4x4(&zero, &zero, in+1, e, out);

    /* [cr0 cr1 cr2 cr3 ci0 ci1 ci2 ci3]
     *
     * [Xr(1)]  ] [1   1   1   1   0   0   0   0]
     * [Xr(N/4) ] [0   0   0   0   1   s   0  -s]
     * [Xr(N/2) ] [1   0  -1   0   0   0   0   0]
     * [Xr(3N/4)] [0   0   0   0   1  -s   0   s]
     * [Xi(1)   ] [1  -1   1  -1   0   0   0   0]
     * [Xi(N/4) ] [0   0   0   0   0  -s  -1  -s]
     * [Xi(N/2) ] [0  -1   0   1   0   0   0   0]
     * [Xi(3N/4)] [0   0   0   0   0  -s   1  -s]
     */

    const float xr0{(cr[0]+cr[2]) + (cr[1]+cr[3])}; out[0] = VINSERT0(out[0], xr0);
    const float xi0{(cr[0]+cr[2]) - (cr[1]+cr[3])}; out[1] = VINSERT0(out[1], xi0);
    const float xr2{(cr[0]-cr[2])};                 out[4] = VINSERT0(out[4], xr2);
    const float xi2{(cr[3]-cr[1])};                 out[5] = VINSERT0(out[5], xi2);
    const float xr1{ ci[0] + s*(ci[1]-ci[3])};      out[2] = VINSERT0(out[2], xr1);
    const float xi1{-ci[2] - s*(ci[1]+ci[3])};      out[3] = VINSERT0(out[3], xi1);
    const float xr3{ ci[0] - s*(ci[1]-ci[3])};      out[6] = VINSERT0(out[6], xr3);
    const float xi3{ ci[2] - s*(ci[1]+ci[3])};      out[7] = VINSERT0(out[7], xi3);

    for(int k{1};k < dk;++k)
        pffft_real_finalize_4x4(&in[8*k-1], &in[8*k+0], in + 8*k+1, e + k*6, out + k*8);
}

static ALWAYS_INLINE(void) pffft_real_preprocess_4x4(const v4sf *in, const v4sf *e, v4sf *out,
    const bool first)
{
    v4sf r0{in[0]}, i0{in[1]}, r1{in[2]}, i1{in[3]};
    v4sf r2{in[4]}, i2{in[5]}, r3{in[6]}, i3{in[7]};

    /* transformation for each column is:
     *
     * [1   1   1   1   0   0   0   0]   [r0]
     * [1   0   0  -1   0  -1  -1   0]   [r1]
     * [1  -1  -1   1   0   0   0   0]   [r2]
     * [1   0   0  -1   0   1   1   0]   [r3]
     * [0   0   0   0   1  -1   1  -1] * [i0]
     * [0  -1   1   0   1   0   0   1]   [i1]
     * [0   0   0   0   1   1  -1  -1]   [i2]
     * [0   1  -1   0   1   0   0   1]   [i3]
     */

    v4sf sr0{VADD(r0,r3)}, dr0{VSUB(r0,r3)};
    v4sf sr1{VADD(r1,r2)}, dr1{VSUB(r1,r2)};
    v4sf si0{VADD(i0,i3)}, di0{VSUB(i0,i3)};
    v4sf si1{VADD(i1,i2)}, di1{VSUB(i1,i2)};

    r0 = VADD(sr0, sr1);
    r2 = VSUB(sr0, sr1);
    r1 = VSUB(dr0, si1);
    r3 = VADD(dr0, si1);
    i0 = VSUB(di0, di1);
    i2 = VADD(di0, di1);
    i1 = VSUB(si0, dr1);
    i3 = VADD(si0, dr1);

    VCPLXMULCONJ(r1,i1,e[0],e[1]);
    VCPLXMULCONJ(r2,i2,e[2],e[3]);
    VCPLXMULCONJ(r3,i3,e[4],e[5]);

    VTRANSPOSE4(r0,r1,r2,r3);
    VTRANSPOSE4(i0,i1,i2,i3);

    if(!first)
    {
        *out++ = r0;
        *out++ = i0;
    }
    *out++ = r1;
    *out++ = i1;
    *out++ = r2;
    *out++ = i2;
    *out++ = r3;
    *out++ = i3;
}

static NEVER_INLINE(void) pffft_real_preprocess(const int Ncvec, const v4sf *in, v4sf *out,
    const v4sf *e)
{
    static constexpr float sqrt2{al::numbers::sqrt2_v<float>};

    assert(in != out);
    const int dk{Ncvec/SIMD_SZ}; // number of 4x4 matrix blocks
    /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */

    std::array<float,SIMD_SZ> Xr, Xi;
    for(size_t k{0};k < 4;++k)
    {
        Xr[k] = VEXTRACT0(in[4*k]);
        Xi[k] = VEXTRACT0(in[4*k + 1]);
    }

    pffft_real_preprocess_4x4(in, e, out+1, true); // will write only 6 values

    /* [Xr0 Xr1 Xr2 Xr3 Xi0 Xi1 Xi2 Xi3]
     *
     * [cr0] [1   0   2   0   1   0   0   0]
     * [cr1] [1   0   0   0  -1   0  -2   0]
     * [cr2] [1   0  -2   0   1   0   0   0]
     * [cr3] [1   0   0   0  -1   0   2   0]
     * [ci0] [0   2   0   2   0   0   0   0]
     * [ci1] [0   s   0  -s   0  -s   0  -s]
     * [ci2] [0   0   0   0   0  -2   0   2]
     * [ci3] [0  -s   0   s   0  -s   0  -s]
     */
    for(int k{1};k < dk;++k)
        pffft_real_preprocess_4x4(in+8*k, e + k*6, out-1+k*8, false);

    const float cr0{(Xr[0]+Xi[0]) + 2*Xr[2]};
    const float cr1{(Xr[0]-Xi[0]) - 2*Xi[2]};
    const float cr2{(Xr[0]+Xi[0]) - 2*Xr[2]};
    const float cr3{(Xr[0]-Xi[0]) + 2*Xi[2]};
    out[0] = VSET4(cr0, cr1, cr2, cr3);
    const float ci0{     2*(Xr[1]+Xr[3])};
    const float ci1{ sqrt2*(Xr[1]-Xr[3]) - sqrt2*(Xi[1]+Xi[3])};
    const float ci2{     2*(Xi[3]-Xi[1])};
    const float ci3{-sqrt2*(Xr[1]-Xr[3]) - sqrt2*(Xi[1]+Xi[3])};
    out[2*Ncvec-1] = VSET4(ci0, ci1, ci2, ci3);
}


void pffft_transform_internal(PFFFT_Setup *setup, const v4sf *vinput, v4sf *voutput,
    v4sf *scratch, const pffft_direction_t direction, const bool ordered)
{
    assert(scratch != nullptr);
    assert(voutput != scratch);

    const int Ncvec{setup->Ncvec};
    const int nf_odd{setup->ifac[1] & 1};

    v4sf *buff[2]{voutput, scratch};
    int ib{(nf_odd ^ ordered) ? 1 : 0};
    if(direction == PFFFT_FORWARD)
    {
        /* Swap the initial work buffer for forward FFTs, which helps avoid an
         * extra copy for output.
         */
        ib = !ib;
        if(setup->transform == PFFFT_REAL)
        {
            ib = (rfftf1_ps(Ncvec*2, vinput, buff[ib], buff[!ib], setup->twiddle, setup->ifac) == buff[1]);
            pffft_real_finalize(Ncvec, buff[ib], buff[!ib], setup->e);
        }
        else
        {
            v4sf *tmp{buff[ib]};
            for(int k=0; k < Ncvec; ++k)
                UNINTERLEAVE2(vinput[k*2], vinput[k*2+1], tmp[k*2], tmp[k*2+1]);

            ib = (cfftf1_ps(Ncvec, buff[ib], buff[!ib], buff[ib], setup->twiddle, setup->ifac, -1.0f) == buff[1]);
            pffft_cplx_finalize(Ncvec, buff[ib], buff[!ib], setup->e);
        }
        if(ordered)
            pffft_zreorder(setup, reinterpret_cast<float*>(buff[!ib]),
                reinterpret_cast<float*>(buff[ib]), PFFFT_FORWARD);
        else
            ib = !ib;
    }
    else
    {
        if(vinput == buff[ib])
            ib = !ib; // may happen when finput == foutput

        if(ordered)
        {
            pffft_zreorder(setup, reinterpret_cast<const float*>(vinput),
                reinterpret_cast<float*>(buff[ib]), PFFFT_BACKWARD);
            vinput = buff[ib];
            ib = !ib;
        }
        if(setup->transform == PFFFT_REAL)
        {
            pffft_real_preprocess(Ncvec, vinput, buff[ib], setup->e);
            ib = (rfftb1_ps(Ncvec*2, buff[ib], buff[0], buff[1], setup->twiddle, setup->ifac) == buff[1]);
        }
        else
        {
            pffft_cplx_preprocess(Ncvec, vinput, buff[ib], setup->e);
            ib = (cfftf1_ps(Ncvec, buff[ib], buff[0], buff[1],  setup->twiddle, setup->ifac, +1.0f) == buff[1]);
            for(int k{0};k < Ncvec;++k)
                INTERLEAVE2(buff[ib][k*2], buff[ib][k*2+1], buff[ib][k*2], buff[ib][k*2+1]);
        }
    }

    if(buff[ib] != voutput)
    {
        /* extra copy required -- this situation should only happen when finput == foutput */
        assert(vinput==voutput);
        for(int k{0};k < Ncvec;++k)
        {
            v4sf a{buff[ib][2*k]}, b{buff[ib][2*k+1]};
            voutput[2*k] = a; voutput[2*k+1] = b;
        }
    }
}

void pffft_zconvolve_accumulate(PFFFT_Setup *s, const float *a, const float *b, float *ab,
    float scaling)
{
    const int Ncvec{s->Ncvec};
    const v4sf *RESTRICT va{reinterpret_cast<const v4sf*>(a)};
    const v4sf *RESTRICT vb{reinterpret_cast<const v4sf*>(b)};
    v4sf *RESTRICT vab{reinterpret_cast<v4sf*>(ab)};

#ifdef __arm__
    __builtin_prefetch(va);
    __builtin_prefetch(vb);
    __builtin_prefetch(vab);
    __builtin_prefetch(va+2);
    __builtin_prefetch(vb+2);
    __builtin_prefetch(vab+2);
    __builtin_prefetch(va+4);
    __builtin_prefetch(vb+4);
    __builtin_prefetch(vab+4);
    __builtin_prefetch(va+6);
    __builtin_prefetch(vb+6);
    __builtin_prefetch(vab+6);
#ifndef __clang__
#define ZCONVOLVE_USING_INLINE_NEON_ASM
#endif
#endif

#ifndef ZCONVOLVE_USING_INLINE_ASM
    const v4sf vscal{LD_PS1(scaling)};
#endif
    const float ar1{VEXTRACT0(va[0])};
    const float ai1{VEXTRACT0(va[1])};
    const float br1{VEXTRACT0(vb[0])};
    const float bi1{VEXTRACT0(vb[1])};
    const float abr1{VEXTRACT0(vab[0])};
    const float abi1{VEXTRACT0(vab[1])};

#ifdef ZCONVOLVE_USING_INLINE_ASM // inline asm version, unfortunately miscompiled by clang 3.2, at least on ubuntu.. so this will be restricted to gcc
    const float *a_{a}, *b_{b}; float *ab_{ab};
    int N{Ncvec};
    asm volatile("mov         r8, %2                  \n"
                "vdup.f32    q15, %4                 \n"
                "1:                                  \n"
                "pld         [%0,#64]                \n"
                "pld         [%1,#64]                \n"
                "pld         [%2,#64]                \n"
                "pld         [%0,#96]                \n"
                "pld         [%1,#96]                \n"
                "pld         [%2,#96]                \n"
                "vld1.f32    {q0,q1},   [%0,:128]!         \n"
                "vld1.f32    {q4,q5},   [%1,:128]!         \n"
                "vld1.f32    {q2,q3},   [%0,:128]!         \n"
                "vld1.f32    {q6,q7},   [%1,:128]!         \n"
                "vld1.f32    {q8,q9},   [r8,:128]!          \n"

                "vmul.f32    q10, q0, q4             \n"
                "vmul.f32    q11, q0, q5             \n"
                "vmul.f32    q12, q2, q6             \n"
                "vmul.f32    q13, q2, q7             \n"
                "vmls.f32    q10, q1, q5             \n"
                "vmla.f32    q11, q1, q4             \n"
                "vld1.f32    {q0,q1}, [r8,:128]!     \n"
                "vmls.f32    q12, q3, q7             \n"
                "vmla.f32    q13, q3, q6             \n"
                "vmla.f32    q8, q10, q15            \n"
                "vmla.f32    q9, q11, q15            \n"
                "vmla.f32    q0, q12, q15            \n"
                "vmla.f32    q1, q13, q15            \n"
                "vst1.f32    {q8,q9},[%2,:128]!    \n"
                "vst1.f32    {q0,q1},[%2,:128]!    \n"
                "subs        %3, #2                  \n"
                "bne         1b                      \n"
                : "+r"(a_), "+r"(b_), "+r"(ab_), "+r"(N) : "r"(scaling) : "r8", "q0","q1","q2","q3","q4","q5","q6","q7","q8","q9", "q10","q11","q12","q13","q15","memory");

#else // default routine, works fine for non-arm cpus with current compilers

    for(int i{0};i < Ncvec;i += 2)
    {
        v4sf ar4{va[2*i+0]}, ai4{va[2*i+1]};
        v4sf br4{vb[2*i+0]}, bi4{vb[2*i+1]};
        VCPLXMUL(ar4, ai4, br4, bi4);
        vab[2*i+0] = VMADD(ar4, vscal, vab[2*i+0]);
        vab[2*i+1] = VMADD(ai4, vscal, vab[2*i+1]);
        ar4 = va[2*i+2]; ai4 = va[2*i+3];
        br4 = vb[2*i+2]; bi4 = vb[2*i+3];
        VCPLXMUL(ar4, ai4, br4, bi4);
        vab[2*i+2] = VMADD(ar4, vscal, vab[2*i+2]);
        vab[2*i+3] = VMADD(ai4, vscal, vab[2*i+3]);
    }
#endif

    if(s->transform == PFFFT_REAL)
    {
        vab[0] = VINSERT0(vab[0], abr1 + ar1*br1*scaling);
        vab[1] = VINSERT0(vab[1], abi1 + ai1*bi1*scaling);
    }
}


void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction)
{
    assert(VALIGNED(input) && VALIGNED(output) && VALIGNED(work));
    pffft_transform_internal(setup, reinterpret_cast<const v4sf*>(al::assume_aligned<16>(input)),
        reinterpret_cast<v4sf*>(al::assume_aligned<16>(output)),
        reinterpret_cast<v4sf*>(al::assume_aligned<16>(work)), direction, false);
}

void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction)
{
    assert(VALIGNED(input) && VALIGNED(output) && VALIGNED(work));
    pffft_transform_internal(setup, reinterpret_cast<const v4sf*>(al::assume_aligned<16>(input)),
        reinterpret_cast<v4sf*>(al::assume_aligned<16>(output)),
        reinterpret_cast<v4sf*>(al::assume_aligned<16>(work)), direction, true);
}

#else // defined(PFFFT_SIMD_DISABLE)

// standard routine using scalar floats, without SIMD stuff.

#define pffft_zreorder_nosimd pffft_zreorder
void pffft_zreorder_nosimd(PFFFT_Setup *setup, const float *in, float *out,
    pffft_direction_t direction)
{
    const int N{setup->N};
    if(setup->transform == PFFFT_COMPLEX)
    {
        for(int k{0};k < 2*N;++k)
            out[k] = in[k];
        return;
    }
    else if(direction == PFFFT_FORWARD)
    {
        float x_N{in[N-1]};
        for(int k{N-1};k > 1;--k)
            out[k] = in[k-1];
        out[0] = in[0];
        out[1] = x_N;
    }
    else
    {
        float x_N{in[1]};
        for(int k{1};k < N-1;++k)
            out[k] = in[k+1];
        out[0] = in[0];
        out[N-1] = x_N;
    }
}

#define pffft_transform_internal_nosimd pffft_transform_internal
void pffft_transform_internal_nosimd(PFFFT_Setup *setup, const float *input, float *output,
    float *scratch, const pffft_direction_t direction, bool ordered)
{
    const int Ncvec{setup->Ncvec};
    const int nf_odd{setup->ifac[1] & 1};

    assert(scratch != nullptr);

    /* z-domain data for complex transforms is already ordered without SIMD. */
    if(setup->transform == PFFFT_COMPLEX)
        ordered = 0;

    float *buff[2]{output, scratch};
    int ib{(nf_odd ^ ordered) ? 1 : 0};

    if(direction == PFFFT_FORWARD)
    {
        if(setup->transform == PFFFT_REAL)
            ib = (rfftf1_ps(Ncvec*2, input, buff[ib], buff[!ib], setup->twiddle, setup->ifac) == buff[1]);
        else
            ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib], setup->twiddle, setup->ifac, -1.0f) == buff[1]);
        if(ordered)
        {
            pffft_zreorder(setup, buff[ib], buff[!ib], PFFFT_FORWARD);
            ib = !ib;
        }
    }
    else
    {
        if (input == buff[ib])
            ib = !ib; // may happen when finput == foutput

        if(ordered)
        {
            pffft_zreorder(setup, input, buff[ib], PFFFT_BACKWARD);
            input = buff[ib];
            ib = !ib;
        }
        if(setup->transform == PFFFT_REAL)
            ib = (rfftb1_ps(Ncvec*2, input, buff[ib], buff[!ib],  setup->twiddle, setup->ifac) == buff[1]);
        else
            ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib], setup->twiddle, setup->ifac, +1.0f) == buff[1]);
    }
    if(buff[ib] != output)
    {
        // extra copy required -- this situation should happens only when finput == foutput
        assert(input==output);
        for(int k{0};k < Ncvec;++k)
        {
            float a{buff[ib][2*k]}, b{buff[ib][2*k+1]};
            output[2*k] = a; output[2*k+1] = b;
        }
    }
}

#define pffft_zconvolve_accumulate_nosimd pffft_zconvolve_accumulate
void pffft_zconvolve_accumulate_nosimd(PFFFT_Setup *s, const float *a, const float *b, float *ab,
    float scaling)
{
    int Ncvec = s->Ncvec;

    if(s->transform == PFFFT_REAL)
    {
        // take care of the fftpack ordering
        ab[0] += a[0]*b[0]*scaling;
        ab[2*Ncvec-1] += a[2*Ncvec-1]*b[2*Ncvec-1]*scaling;
        ++ab; ++a; ++b; --Ncvec;
    }
    for(int i=0; i < Ncvec; ++i)
    {
        float ar       = a[2*i+0], ai = a[2*i+1];
        const float br = b[2*i+0], bi = b[2*i+1];
        VCPLXMUL(ar, ai, br, bi);
        ab[2*i+0] += ar*scaling;
        ab[2*i+1] += ai*scaling;
    }
}


void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction)
{
    pffft_transform_internal(setup, input, output, work, direction, false);
}

void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction)
{
    pffft_transform_internal(setup, input, output, work, direction, true);
}

#endif // defined(PFFFT_SIMD_DISABLE)