text: /*
  
  This file is part of FFTS -- The Fastest Fourier Transform in the South
  
  Copyright (c) 2012, Anthony M. Blake <amb@anthonix.com>
  Copyright (c) 2012, The University of Waikato
  Copyright (c) 2015 - 2018, Jukka Ojanen <jukka.ojanen@kolumbus.fi>
  
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
  * Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.
  * Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.
  * Neither the name of the organization nor the
  names of its contributors may be used to endorse or promote products
  derived from this software without specific prior written permission.
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
  ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  DISCLAIMED. IN NO EVENT SHALL ANTHONY M. BLAKE BE LIABLE FOR ANY
  DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
  */
  
  #include "ffts_real.h"
  #include "ffts_cpu.h"
  #include "ffts_internal.h"
  #include "ffts_trig.h"
  
  #ifdef HAVE_NEON
  #include <arm_neon.h>
  #elif HAVE_SSE
  #include <xmmintrin.h>
  
  /* check if have SSE3 intrinsics */
  #ifdef HAVE_PMMINTRIN_H
  #include <pmmintrin.h>
  #elif HAVE_INTRIN_H
  #include <intrin.h>
  #endif
  
  /* avoid using negative zero as some configurations have problems with those */
  static const FFTS_ALIGN(16) unsigned int sign_mask_even[4] = {
      0x80000000, 0, 0x80000000, 0
  };
  static const FFTS_ALIGN(16) unsigned int sign_mask_odd[4] = {
      0, 0x80000000, 0, 0x80000000
  };
  #endif
  
  static void
  ffts_free_1d_real(ffts_plan_t *p)
  {
      if (p->B) {
          ffts_aligned_free(p->B);
      }
  
      if (p->A) {
          ffts_aligned_free(p->A);
      }
  
      if (p->buf) {
          ffts_aligned_free(p->buf);
      }
  
      if (p->plans[0]) {
          ffts_free(p->plans[0]);
      }
  
      free(p);
  }
  
  #undef __ARM_NEON__
  #ifdef __ARM_NEON__
  static void
  ffts_execute_1d_real_neon(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT out =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(output);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      float *p_buf0 = buf;
      float *p_buf1 = buf + N - 2;
      float *p_out = out;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      p->plans[0]->transform(p->plans[0], input, buf);
  
      buf[N + 0] = buf[0];
      buf[N + 1] = buf[1];
  
      for (i = 0; i < N; i += 4) {
          __asm__ __volatile__ (
              "vld1.32 {q8},  [%[pa]]!\n\t"
              "vld1.32 {q9},  [%[pb]]!\n\t"
              "vld1.32 {q10}, [%[buf0]]!\n\t"
              "vld1.32 {q11}, [%[buf1]]\n\t"
              "sub %[buf1], %[buf1], #16\n\t"
  
              "vdup.32 d26, d16[1]\n\t"
              "vdup.32 d27, d17[1]\n\t"
              "vdup.32 d24, d16[0]\n\t"
              "vdup.32 d25, d17[0]\n\t"
  
              "vdup.32 d30, d23[1]\n\t"
              "vdup.32 d31, d22[1]\n\t"
              "vdup.32 d28, d23[0]\n\t"
              "vdup.32 d29, d22[0]\n\t"
  
              "vmul.f32 q13, q13, q10\n\t"
              "vmul.f32 q15, q15, q9\n\t"
              "vmul.f32 q12, q12, q10\n\t"
              "vmul.f32 q14, q14, q9\n\t"
              "vrev64.f32 q13, q13\n\t"
              "vrev64.f32 q15, q15\n\t"
  
              "vtrn.32 d26, d27\n\t"
              "vtrn.32 d30, d31\n\t"
              "vneg.f32 d26, d26\n\t"
              "vneg.f32 d31, d31\n\t"
              "vtrn.32 d26, d27\n\t"
              "vtrn.32 d30, d31\n\t"
  
              "vadd.f32 q12, q12, q14\n\t"
              "vadd.f32 q13, q13, q15\n\t"
              "vadd.f32 q12, q12, q13\n\t"
              "vst1.32 {q12}, [%[pout]]!\n\t"
              : [buf0] "+r" (p_buf0), [buf1] "+r" (p_buf1), [pout] "+r" (p_out)
              : [pa] "r" (A), [pb] "r" (B) 
              : "memory", "q8", "q9", "q10", "q11", "q12", "q13", "q14", "q15"
          );
      }
  
      out[N + 0] = buf[0] - buf[1];
      out[N + 1] = 0.0f;
  }
  #endif
  
  #if HAVE_SSE3
  static void
  ffts_execute_1d_real_sse3(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT out =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(output);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      p->plans[0]->transform(p->plans[0], input, buf);
  
      buf[N + 0] = buf[0];
      buf[N + 1] = buf[1];
  
      if (FFTS_UNLIKELY(N <= 8)) {
          __m128 t0 = _mm_load_ps(buf);
          __m128 t1 = _mm_load_ps(buf + N - 4);
          __m128 t2 = _mm_load_ps(A);
          __m128 t3 = _mm_load_ps(B);
  
          _mm_store_ps(out, _mm_add_ps(_mm_addsub_ps(
              _mm_mul_ps(t0, _mm_moveldup_ps(t2)),
              _mm_mul_ps(_mm_shuffle_ps(t0, t0, _MM_SHUFFLE(2,3,0,1)),
              _mm_movehdup_ps(t2))), _mm_addsub_ps(
              _mm_mul_ps(_mm_shuffle_ps(t0, t1, _MM_SHUFFLE(3,3,1,1)),
              _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,3,0,1))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t1, _MM_SHUFFLE(2,2,0,0)), t3))));
  
          if (N == 8) {
              t2 = _mm_load_ps(A + 4);
              t3 = _mm_load_ps(B + 4);
  
              _mm_store_ps(out + 4, _mm_add_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t2)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t2))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t1, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t0, _MM_SHUFFLE(2,2,0,0)), t3))));
          }
      } else {
          __m128 t0 = _mm_load_ps(buf);
  
          for (i = 0; i < N; i += 16) {
              __m128 t1 = _mm_load_ps(buf + i);
              __m128 t2 = _mm_load_ps(buf + N - i - 4);
              __m128 t3 = _mm_load_ps(A + i);
              __m128 t4 = _mm_load_ps(B + i);
  
              _mm_store_ps(out + i, _mm_add_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t0 = _mm_load_ps(buf + N - i - 8);
              t1 = _mm_load_ps(buf + i + 4);
              t3 = _mm_load_ps(A + i + 4);
              t4 = _mm_load_ps(B + i + 4);
  
              _mm_store_ps(out + i + 4, _mm_add_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t1 = _mm_load_ps(buf + i + 8);
              t2 = _mm_load_ps(buf + N - i - 12);
              t3 = _mm_load_ps(A + i + 8);
              t4 = _mm_load_ps(B + i + 8);
  
              _mm_store_ps(out + i + 8, _mm_add_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t0 = _mm_load_ps(buf + N - i - 16);
              t1 = _mm_load_ps(buf + i + 12);
              t3 = _mm_load_ps(A + i + 12);
              t4 = _mm_load_ps(B + i + 12);
  
              _mm_store_ps(out + i + 12, _mm_add_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4))));
          }
      }
  
      out[N + 0] = buf[0] - buf[1];
      out[N + 1] = 0.0f;
  }
  #endif
  
  #ifdef HAVE_SSE
  static void
  ffts_execute_1d_real_sse(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT out =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(output);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      p->plans[0]->transform(p->plans[0], input, buf);
  
      if (FFTS_UNLIKELY(N <= 8)) {
          __m128 c0 = _mm_load_ps((const float*) sign_mask_even);
          __m128 t0 = _mm_load_ps(buf);
          __m128 t1 = _mm_load_ps(buf + N - 4);
          __m128 t2 = _mm_load_ps(A);
          __m128 t3 = _mm_load_ps(B);
  
          _mm_store_ps(out, _mm_add_ps(_mm_add_ps(_mm_add_ps(
              _mm_mul_ps(t0, _mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2,2,0,0))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t0, _MM_SHUFFLE(2,3,0,1)),
              _mm_xor_ps(_mm_shuffle_ps(t2, t2, _MM_SHUFFLE(3,3,1,1)), c0))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t1, _MM_SHUFFLE(2,2,0,0)), t3)),
              _mm_mul_ps(_mm_shuffle_ps(t0, t1, _MM_SHUFFLE(3,3,1,1)),
              _mm_shuffle_ps(_mm_xor_ps(t3, c0), _mm_xor_ps(t3, c0),
              _MM_SHUFFLE(2,3,0,1)))));
  
          if (N == 8) {
              t2 = _mm_load_ps(A + 4);
              t3 = _mm_load_ps(B + 4);
  
              _mm_store_ps(out + 4, _mm_add_ps(_mm_add_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t2, t2, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t0, _MM_SHUFFLE(2,2,0,0)), t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(_mm_xor_ps(t3, c0), _mm_xor_ps(t3, c0),
                  _MM_SHUFFLE(2,3,0,1)))));
          }
      } else {
          __m128 c0 = _mm_load_ps((const float*) sign_mask_even);
          __m128 t0 = _mm_load_ps(buf);
  
          for (i = 0; i < N; i += 16) {
              __m128 t1 = _mm_load_ps(buf + i);
              __m128 t2 = _mm_load_ps(buf + N - i - 4);
              __m128 t3 = _mm_load_ps(A + i);
              __m128 t4 = _mm_load_ps(B + i);
  
              _mm_store_ps(out + i, _mm_add_ps(_mm_add_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4)),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(_mm_xor_ps(t4, c0), _mm_xor_ps(t4, c0),
                  _MM_SHUFFLE(2,3,0,1)))));
  
              t0 = _mm_load_ps(buf + N - i - 8);
              t1 = _mm_load_ps(buf + i + 4);
              t3 = _mm_load_ps(A + i + 4);
              t4 = _mm_load_ps(B + i + 4);
  
              _mm_store_ps(out + i + 4, _mm_add_ps(_mm_add_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4)),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(_mm_xor_ps(t4, c0), _mm_xor_ps(t4, c0),
                  _MM_SHUFFLE(2,3,0,1)))));
  
              t1 = _mm_load_ps(buf + i + 8);
              t2 = _mm_load_ps(buf + N - i - 12);
              t3 = _mm_load_ps(A + i + 8);
              t4 = _mm_load_ps(B + i + 8);
  
              _mm_store_ps(out + i + 8, _mm_add_ps(_mm_add_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4)),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(_mm_xor_ps(t4, c0), _mm_xor_ps(t4, c0),
                  _MM_SHUFFLE(2,3,0,1)))));
  
              t0 = _mm_load_ps(buf + N - i - 16);
              t1 = _mm_load_ps(buf + i + 12);
              t3 = _mm_load_ps(A + i + 12);
              t4 = _mm_load_ps(B + i + 12);
  
              _mm_store_ps(out + i + 12, _mm_add_ps(_mm_add_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4)),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(_mm_xor_ps(t4, c0), _mm_xor_ps(t4, c0),
                  _MM_SHUFFLE(2,3,0,1)))));
          }
      }
  
      out[N + 0] = buf[0] - buf[1];
      out[N + 1] = 0.0f;
  }
  #endif
  
  static void
  ffts_execute_1d_real(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT out =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(output);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      p->plans[0]->transform(p->plans[0], input, buf);
  
      buf[N + 0] = buf[0];
      buf[N + 1] = buf[1];
  
      for (i = 0; i < N/2; i++) {
          out[2*i + 0] =
              buf[    2*i + 0] * A[2*i + 0] - buf[    2*i + 1] * A[2*i + 1] +
              buf[N - 2*i + 0] * B[2*i + 0] + buf[N - 2*i + 1] * B[2*i + 1];
          out[2*i + 1] =
              buf[    2*i + 1] * A[2*i + 0] + buf[    2*i + 0] * A[2*i + 1] +
              buf[N - 2*i + 0] * B[2*i + 1] - buf[N - 2*i + 1] * B[2*i + 0];
      }
  
      out[N + 0] = buf[0] - buf[1];
      out[N + 1] = 0.0f;
  }
  
  #ifdef __ARM_NEON__
  static void
  ffts_execute_1d_real_inv_neon(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT in =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(input);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      float *p_buf0 = in;
      float *p_buf1 = in + N - 2;
      float *p_out = buf;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      for (i = 0; i < N/2; i += 2) {
          __asm__ __volatile__ (
              "vld1.32 {q8},  [%[pa]]!\n\t"
              "vld1.32 {q9},  [%[pb]]!\n\t"
              "vld1.32 {q10}, [%[buf0]]!\n\t"
              "vld1.32 {q11}, [%[buf1]]\n\t"
              "sub %[buf1], %[buf1], #16\n\t"
  
              "vdup.32 d26, d16[1]\n\t"
              "vdup.32 d27, d17[1]\n\t"
              "vdup.32 d24, d16[0]\n\t"
              "vdup.32 d25, d17[0]\n\t"
  
              "vdup.32 d30, d23[1]\n\t"
              "vdup.32 d31, d22[1]\n\t"
              "vdup.32 d28, d23[0]\n\t"
              "vdup.32 d29, d22[0]\n\t"
  
              "vmul.f32 q13, q13, q10\n\t"
              "vmul.f32 q15, q15, q9\n\t"
              "vmul.f32 q12, q12, q10\n\t"
              "vmul.f32 q14, q14, q9\n\t"
              "vrev64.f32 q13, q13\n\t"
              "vrev64.f32 q15, q15\n\t"
  
              "vtrn.32 d26, d27\n\t"
              "vtrn.32 d28, d29\n\t"
              "vneg.f32 d27, d27\n\t"
              "vneg.f32 d29, d29\n\t"
              "vtrn.32 d26, d27\n\t"
              "vtrn.32 d28, d29\n\t"
  
              "vadd.f32 q12, q12, q14\n\t"
              "vsub.f32 q13, q13, q15\n\t"
              "vadd.f32 q12, q12, q13\n\t"
              "vst1.32 {q12}, [%[pout]]!\n\t"
              : [buf0] "+r" (p_buf0), [buf1] "+r" (p_buf1), [pout] "+r" (p_out)
              : [pa] "r" (A), [pb] "r" (B)
              : "memory", "q8", "q9", "q10", "q11", "q12", "q13", "q14", "q15"
          );
      }
  
      p->plans[0]->transform(p->plans[0], buf, output);
  }
  #endif
  
  #if HAVE_SSE3
  static void
  ffts_execute_1d_real_inv_sse3(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT in =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(input);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      if (FFTS_UNLIKELY(N <= 8)) {
          __m128 t0 = _mm_loadl_pi(_mm_setzero_ps(), (const __m64*) &in[N]);
          __m128 t1 = _mm_load_ps(in);
          __m128 t2 = _mm_load_ps(in + N - 4);
          __m128 t3 = _mm_load_ps(A);
          __m128 t4 = _mm_load_ps(B);
  
          _mm_store_ps(buf, _mm_sub_ps(_mm_addsub_ps(
              _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
              _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
              _mm_movehdup_ps(t3))), _mm_addsub_ps(
              _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
              _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4))));
  
          if (N == 8) {
              t3 = _mm_load_ps(A + 4);
              t4 = _mm_load_ps(B + 4);
  
              _mm_store_ps(buf + 4, _mm_sub_ps(_mm_addsub_ps(
                  _mm_mul_ps(t2, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t2, t1, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t1, _MM_SHUFFLE(2,2,0,0)), t4))));
          }
      } else {
          __m128 t0 = _mm_loadl_pi(_mm_setzero_ps(), (const __m64*) &in[N]);
  
          for (i = 0; i < N; i += 16) {
              __m128 t1 = _mm_load_ps(in + i);
              __m128 t2 = _mm_load_ps(in + N - i - 4);
              __m128 t3 = _mm_load_ps(A + i);
              __m128 t4 = _mm_load_ps(B + i);
  
              _mm_store_ps(buf + i, _mm_sub_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t0 = _mm_load_ps(in + N - i - 8);
              t1 = _mm_load_ps(in + i + 4);
              t3 = _mm_load_ps(A + i + 4);
              t4 = _mm_load_ps(B + i + 4);
  
              _mm_store_ps(buf + i + 4, _mm_sub_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t1 = _mm_load_ps(in + i + 8);
              t2 = _mm_load_ps(in + N - i - 12);
              t3 = _mm_load_ps(A + i + 8);
              t4 = _mm_load_ps(B + i + 8);
  
              _mm_store_ps(buf + i + 8, _mm_sub_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)), t4))));
  
              t0 = _mm_load_ps(in + N - i - 16);
              t1 = _mm_load_ps(in + i + 12);
              t3 = _mm_load_ps(A + i + 12);
              t4 = _mm_load_ps(B + i + 12);
  
              _mm_store_ps(buf + i + 12, _mm_sub_ps(_mm_addsub_ps(
                  _mm_mul_ps(t1, _mm_moveldup_ps(t3)),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_movehdup_ps(t3))), _mm_addsub_ps(
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)), t4))));
          }
      }
  
      p->plans[0]->transform(p->plans[0], buf, output);
  }
  #endif
  
  #if HAVE_SSE
  static void
  ffts_execute_1d_real_inv_sse(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT in =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(input);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      if (FFTS_UNLIKELY(N <= 8)) {
          __m128 c0 = _mm_load_ps((const float*) sign_mask_odd);
          __m128 t0 = _mm_loadl_pi(_mm_setzero_ps(), (const __m64*) &in[N]);
          __m128 t1 = _mm_load_ps(in);
          __m128 t2 = _mm_load_ps(in + N - 4);
          __m128 t3 = _mm_load_ps(A);
          __m128 t4 = _mm_load_ps(B);
  
          _mm_store_ps(buf, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
              _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
              _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
              _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
              _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
              _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)),
              _mm_xor_ps(t4, c0))));
  
          if (N == 8) {
              t3 = _mm_load_ps(A + 4);
              t4 = _mm_load_ps(B + 4);
  
              _mm_store_ps(buf + 4, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
                  _mm_mul_ps(t2, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t1, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t1, _MM_SHUFFLE(2,2,0,0)),
                  _mm_xor_ps(t4, c0))));
          }
      } else {
          __m128 c0 = _mm_load_ps((const float*) sign_mask_odd);
          __m128 t0 = _mm_loadl_pi(_mm_setzero_ps(), (const __m64*) &in[N]);
  
          for (i = 0; i < N; i += 16) {
              __m128 t1 = _mm_load_ps(in + i);
              __m128 t2 = _mm_load_ps(in + N - i - 4);
              __m128 t3 = _mm_load_ps(A + i);
              __m128 t4 = _mm_load_ps(B + i);
  
              _mm_store_ps(buf + i, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)),
                  _mm_xor_ps(t4, c0))));
  
              t0 = _mm_load_ps(in + N - i - 8);
              t1 = _mm_load_ps(in + i + 4);
              t3 = _mm_load_ps(A + i + 4);
              t4 = _mm_load_ps(B + i + 4);
  
              _mm_store_ps(buf + i + 4, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)),
                  _mm_xor_ps(t4, c0))));
  
              t1 = _mm_load_ps(in + i + 8);
              t2 = _mm_load_ps(in + N - i - 12);
              t3 = _mm_load_ps(A + i + 8);
              t4 = _mm_load_ps(B + i + 8);
  
              _mm_store_ps(buf + i + 8, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
                  _mm_mul_ps(_mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2,2,0,0)),
                  _mm_xor_ps(t4, c0))));
  
              t0 = _mm_load_ps(in + N - i - 16);
              t1 = _mm_load_ps(in + i + 12);
              t3 = _mm_load_ps(A + i + 12);
              t4 = _mm_load_ps(B + i + 12);
  
              _mm_store_ps(buf + i + 12, _mm_add_ps(_mm_sub_ps(_mm_add_ps(
                  _mm_mul_ps(t1, _mm_shuffle_ps(t3, t3, _MM_SHUFFLE(2,2,0,0))),
                  _mm_mul_ps(_mm_shuffle_ps(t1, t1, _MM_SHUFFLE(2,3,0,1)),
                  _mm_xor_ps(_mm_shuffle_ps(t3, t3, _MM_SHUFFLE(3,3,1,1)), c0))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(3,3,1,1)),
                  _mm_shuffle_ps(t4, t4, _MM_SHUFFLE(2,3,0,1)))),
                  _mm_mul_ps(_mm_shuffle_ps(t2, t0, _MM_SHUFFLE(2,2,0,0)),
                  _mm_xor_ps(t4, c0))));
          }
      }
  
      p->plans[0]->transform(p->plans[0], buf, output);
  }
  #endif
  
  static void
  ffts_execute_1d_real_inv(ffts_plan_t *p, const void *input, void *output)
  {
      float *const FFTS_RESTRICT in =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_16(input);
      float *const FFTS_RESTRICT buf =
          (float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->buf);
      const float *const FFTS_RESTRICT A =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->A);
      const float *const FFTS_RESTRICT B =
          (const float *const FFTS_RESTRICT) FFTS_ASSUME_ALIGNED_32(p->B);
      const int N = (const int) p->N;
      int i;
  
      /* we know this */
      FFTS_ASSUME(N/2 > 0);
  
      for (i = 0; i < N/2; i++) {
          buf[2*i + 0] =
              in[    2*i + 0] * A[2*i + 0] + in[    2*i + 1] * A[2*i + 1] +
              in[N - 2*i + 0] * B[2*i + 0] - in[N - 2*i + 1] * B[2*i + 1];
          buf[2*i + 1] =
              in[    2*i + 1] * A[2*i + 0] - in[    2*i + 0] * A[2*i + 1] -
              in[N - 2*i + 0] * B[2*i + 1] - in[N - 2*i + 1] * B[2*i + 0];
      }
  
      p->plans[0]->transform(p->plans[0], buf, output);
  }
  
  FFTS_API ffts_plan_t*
  ffts_init_1d_real(size_t N, int sign)
  {
  #ifndef __ARM_NEON__
      int cpu_flags = ffts_cpu_detect(NULL);
  #endif
      ffts_plan_t *p;
      int invert = 0;
  
      p = (ffts_plan_t*) calloc(1, sizeof(*p) + sizeof(*p->plans));
      if (!p) {
          return NULL;
      }
  
  #ifdef __ARM_NEON__
      p->transform = (sign < 0) ? &ffts_execute_1d_real_neon : &ffts_execute_1d_real_inv;
  #else
  #ifdef HAVE_SSE3
      if (cpu_flags & FFTS_CPU_X86_SSE3) {
          p->transform = (sign < 0) ? &ffts_execute_1d_real_sse3 : &ffts_execute_1d_real_inv_sse3;
          invert = 1;
      } else
  #endif
  #ifdef HAVE_SSE
      if (cpu_flags & FFTS_CPU_X86_SSE) {
          p->transform = (sign < 0) ? &ffts_execute_1d_real_sse : &ffts_execute_1d_real_inv_sse;
      } else
  #endif
      {
          p->transform = (sign < 0) ? &ffts_execute_1d_real : &ffts_execute_1d_real_inv;
      }
  #endif
  
      p->destroy = &ffts_free_1d_real;
      p->N       = N;
      p->rank    = 1;
      p->plans   = (ffts_plan_t**) &p[1];
  
      p->plans[0] = ffts_init_1d(N/2, sign);
      if (!p->plans[0]) {
          goto cleanup;
      }
  
      p->buf = ffts_aligned_malloc(2 * ((N/2) + 1) * sizeof(float));
      if (!p->buf) {
          goto cleanup;
      }
  
      p->A = (float*) ffts_aligned_malloc(N * sizeof(float));
      if (!p->A) {
          goto cleanup;
      }
  
      p->B = (float*) ffts_aligned_malloc(N * sizeof(float));
      if (!p->B) {
          goto cleanup;
      }
  
      ffts_generate_table_1d_real_32f(p, sign, invert);
      return p;
  
  cleanup:
      ffts_free_1d_real(p);
      return NULL;
  }
  