Merge ffts_small with ffts_static, and define small transforms "fully" constant

1 files changed, 534 insertions, 50 deletions

diff --git a/src/ffts_static.c b/src/ffts_static.c
index 7a0bf4a..701cca8 100644
--- a/src/ffts_static.c
+++ b/src/ffts_static.c
@@ -38,80 +38,220 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
 #include <assert.h>
 
-static const FFTS_ALIGN(16) float ffts_constants_32f[16] = {
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-    -0.70710678118654746171500846685376f,
-     0.70710678118654746171500846685376f,
-    -0.70710678118654746171500846685376f,
-     0.70710678118654746171500846685376f,
+static const FFTS_ALIGN(16) float ffts_constants_small_32f[24] = {
      1.0f,
      1.0f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+    -0.0f,
      0.0f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+     1.0f,
+     1.0f,
+     0.9238795325112867561281831893967882868224166258636425f,
+     0.9238795325112867561281831893967882868224166258636425f,
+
+    -0.0f,
      0.0f,
-    -0.70710678118654746171500846685376f,
-     0.70710678118654746171500846685376f
+    -0.3826834323650897717284599840303988667613445624856270f,
+     0.3826834323650897717284599840303988667613445624856270f,
+
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.3826834323650897717284599840303988667613445624856270f,
+     0.3826834323650897717284599840303988667613445624856270f,
+
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.9238795325112867561281831893967882868224166258636425f,
+     0.9238795325112867561281831893967882868224166258636425f
 };
 
-static const FFTS_ALIGN(16) float ffts_constants_inv_32f[16] = {
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654746171500846685376f,
-    -0.70710678118654746171500846685376f,
-     0.70710678118654746171500846685376f,
-    -0.70710678118654746171500846685376f,
+static const FFTS_ALIGN(16) double ffts_constants_small_64f[24] = {
+     1.0,
+     1.0,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
+    -0.0,
+     0.0,
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
+     1.0,
+     1.0,
+     0.9238795325112867561281831893967882868224166258636425,
+     0.9238795325112867561281831893967882868224166258636425,
+
+    -0.0,
+     0.0,
+    -0.3826834323650897717284599840303988667613445624856270,
+     0.3826834323650897717284599840303988667613445624856270,
+
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.3826834323650897717284599840303988667613445624856270,
+     0.3826834323650897717284599840303988667613445624856270,
+
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.9238795325112867561281831893967882868224166258636425,
+     0.9238795325112867561281831893967882868224166258636425
+};
+
+static const FFTS_ALIGN(16) float ffts_constants_small_inv_32f[24] = {
      1.0f,
      1.0f,
-     0.70710678118654757273731092936941f,
-     0.70710678118654757273731092936941f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
      0.0f,
+    -0.0f,
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+
+     1.0f,
+     1.0f,
+     0.9238795325112867561281831893967882868224166258636425f,
+     0.9238795325112867561281831893967882868224166258636425f,
+
      0.0f,
-     0.70710678118654746171500846685376f,
-    -0.70710678118654746171500846685376f
+    -0.0f,
+     0.3826834323650897717284599840303988667613445624856270f,
+    -0.3826834323650897717284599840303988667613445624856270f,
+
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.3826834323650897717284599840303988667613445624856270f,
+     0.3826834323650897717284599840303988667613445624856270f,
+
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.9238795325112867561281831893967882868224166258636425f,
+    -0.9238795325112867561281831893967882868224166258636425f
+};
+
+static const FFTS_ALIGN(16) double ffts_constants_small_inv_64f[24] = {
+     1.0,
+     1.0,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
+     0.0,
+    -0.0,
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740,
+
+     1.0,
+     1.0,
+     0.9238795325112867561281831893967882868224166258636425,
+     0.9238795325112867561281831893967882868224166258636425,
+
+     0.0,
+    -0.0,
+     0.3826834323650897717284599840303988667613445624856270,
+    -0.3826834323650897717284599840303988667613445624856270,
+
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.3826834323650897717284599840303988667613445624856270,
+     0.3826834323650897717284599840303988667613445624856270,
+
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.9238795325112867561281831893967882868224166258636425,
+    -0.9238795325112867561281831893967882868224166258636425
+};
+
+static const FFTS_ALIGN(16) float ffts_constants_32f[16] = {
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+     1.0f,
+     1.0f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+     0.0f,
+     0.0f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f
 };
 
 static const FFTS_ALIGN(16) double ffts_constants_64f[16] = {
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-    -0.70710678118654746171500846685376,
-     0.70710678118654746171500846685376,
-    -0.70710678118654746171500846685376,
-     0.70710678118654746171500846685376,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
      1.0,
      1.0,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
      0.0,
      0.0,
-    -0.70710678118654746171500846685376,
-     0.70710678118654746171500846685376
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740
+};
+
+static const FFTS_ALIGN(16) float ffts_constants_inv_32f[16] = {
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f,
+
+     1.0f,
+     1.0f,
+     0.7071067811865475244008443621048490392848359376884740f,
+     0.7071067811865475244008443621048490392848359376884740f,
+
+     0.0f,
+     0.0f,
+     0.7071067811865475244008443621048490392848359376884740f,
+    -0.7071067811865475244008443621048490392848359376884740f
 };
 
 static const FFTS_ALIGN(16) double ffts_constants_inv_64f[16] = {
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
-     0.70710678118654746171500846685376,
-    -0.70710678118654746171500846685376,
-     0.70710678118654746171500846685376,
-    -0.70710678118654746171500846685376,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740,
+
      1.0,
      1.0,
-     0.70710678118654757273731092936941,
-     0.70710678118654757273731092936941,
+     0.7071067811865475244008443621048490392848359376884740,
+     0.7071067811865475244008443621048490392848359376884740,
+
      0.0,
      0.0,
-     0.70710678118654746171500846685376,
-    -0.70710678118654746171500846685376
+     0.7071067811865475244008443621048490392848359376884740,
+    -0.7071067811865475244008443621048490392848359376884740
 };
 
 static FFTS_INLINE void
@@ -425,6 +565,350 @@ ffts_static_firstpass_odd_32f(float *const FFTS_RESTRICT out,
     }
 }
 
+void
+ffts_small_2_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    ffts_cpx_32f t0, t1, r0, r1;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[2];
+    t1[1] = din[3];
+
+    r0[0] = t0[0] + t1[0];
+    r0[1] = t0[1] + t1[1];
+    r1[0] = t0[0] - t1[0];
+    r1[1] = t0[1] - t1[1];
+
+    dout[0] = r0[0];
+    dout[1] = r0[1];
+    dout[2] = r1[0];
+    dout[3] = r1[1];
+}
+
+void
+ffts_small_2_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    ffts_cpx_64f t0, t1, r0, r1;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[2];
+    t1[1] = din[3];
+
+    r0[0] = t0[0] + t1[0];
+    r0[1] = t0[1] + t1[1];
+    r1[0] = t0[0] - t1[0];
+    r1[1] = t0[1] - t1[1];
+
+    dout[0] = r0[0];
+    dout[1] = r0[1];
+    dout[2] = r1[0];
+    dout[3] = r1[1];
+}
+
+void
+ffts_small_forward4_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    ffts_cpx_32f t0, t1, t2, t3, t4, t5, t6, t7;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[4];
+    t1[1] = din[5];
+    t2[0] = din[2];
+    t2[1] = din[3];
+    t3[0] = din[6];
+    t3[1] = din[7];
+
+    t4[0] = t0[0] + t1[0];
+    t4[1] = t0[1] + t1[1];
+    t5[0] = t0[0] - t1[0];
+    t5[1] = t0[1] - t1[1];
+    t6[0] = t2[0] + t3[0];
+    t6[1] = t2[1] + t3[1];
+    t7[0] = t2[0] - t3[0];
+    t7[1] = t2[1] - t3[1];
+
+    dout[0] = t4[0] + t6[0];
+    dout[1] = t4[1] + t6[1];
+    dout[4] = t4[0] - t6[0];
+    dout[5] = t4[1] - t6[1];
+    dout[2] = t5[0] + t7[1];
+    dout[3] = t5[1] - t7[0];
+    dout[6] = t5[0] - t7[1];
+    dout[7] = t5[1] + t7[0];
+}
+
+void
+ffts_small_forward4_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    ffts_cpx_64f t0, t1, t2, t3, t4, t5, t6, t7;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[4];
+    t1[1] = din[5];
+    t2[0] = din[2];
+    t2[1] = din[3];
+    t3[0] = din[6];
+    t3[1] = din[7];
+
+    t4[0] = t0[0] + t1[0];
+    t4[1] = t0[1] + t1[1];
+    t5[0] = t0[0] - t1[0];
+    t5[1] = t0[1] - t1[1];
+    t6[0] = t2[0] + t3[0];
+    t6[1] = t2[1] + t3[1];
+    t7[0] = t2[0] - t3[0];
+    t7[1] = t2[1] - t3[1];
+
+    dout[0] = t4[0] + t6[0];
+    dout[1] = t4[1] + t6[1];
+    dout[4] = t4[0] - t6[0];
+    dout[5] = t4[1] - t6[1];
+    dout[2] = t5[0] + t7[1];
+    dout[3] = t5[1] - t7[0];
+    dout[6] = t5[0] - t7[1];
+    dout[7] = t5[1] + t7[0];
+}
+
+void
+ffts_small_backward4_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    ffts_cpx_32f t0, t1, t2, t3, t4, t5, t6, t7;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[4];
+    t1[1] = din[5];
+    t2[0] = din[2];
+    t2[1] = din[3];
+    t3[0] = din[6];
+    t3[1] = din[7];
+
+    t4[0] = t0[0] + t1[0];
+    t4[1] = t0[1] + t1[1];
+    t5[0] = t0[0] - t1[0];
+    t5[1] = t0[1] - t1[1];
+    t6[0] = t2[0] + t3[0];
+    t6[1] = t2[1] + t3[1];
+    t7[0] = t2[0] - t3[0];
+    t7[1] = t2[1] - t3[1];
+
+    dout[0] = t4[0] + t6[0];
+    dout[1] = t4[1] + t6[1];
+    dout[4] = t4[0] - t6[0];
+    dout[5] = t4[1] - t6[1];
+    dout[2] = t5[0] - t7[1];
+    dout[3] = t5[1] + t7[0];
+    dout[6] = t5[0] + t7[1];
+    dout[7] = t5[1] - t7[0];
+}
+
+void
+ffts_small_backward4_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    ffts_cpx_64f t0, t1, t2, t3, t4, t5, t6, t7;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    t0[0] = din[0];
+    t0[1] = din[1];
+    t1[0] = din[4];
+    t1[1] = din[5];
+    t2[0] = din[2];
+    t2[1] = din[3];
+    t3[0] = din[6];
+    t3[1] = din[7];
+
+    t4[0] = t0[0] + t1[0];
+    t4[1] = t0[1] + t1[1];
+    t5[0] = t0[0] - t1[0];
+    t5[1] = t0[1] - t1[1];
+    t6[0] = t2[0] + t3[0];
+    t6[1] = t2[1] + t3[1];
+    t7[0] = t2[0] - t3[0];
+    t7[1] = t2[1] - t3[1];
+
+    dout[0] = t4[0] + t6[0];
+    dout[1] = t4[1] + t6[1];
+    dout[4] = t4[0] - t6[0];
+    dout[5] = t4[1] - t6[1];
+    dout[2] = t5[0] - t7[1];
+    dout[3] = t5[1] + t7[0];
+    dout[6] = t5[0] + t7[1];
+    dout[7] = t5[1] - t7[0];
+}
+
+void
+ffts_small_forward8_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *FFTS_RESTRICT lut = ffts_constants_small_32f;
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7;
+    
+    /* unreferenced parameter */
+    (void) p;
+
+    V4SF_L_4_2(0, din, din+8, din+4, din+12, &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_K_N(0, V4SF_LD(lut), V4SF_LD(lut + 4), &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_S_4(r0_1, r2_3, r4_5, r6_7, dout+0, dout+4, dout+8, dout+12);
+}
+
+void
+ffts_small_forward8_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7;
+    double *LUT8 = (double*) p->ws + p->ws_is[0];
+
+#if MACROS_READY
+    L_4_2(0, din, din+8, din+4, din+12, &r0_1, &r2_3, &r4_5, &r6_7);
+    K_N(0, VLD(LUT8), VLD(LUT8+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    S_4(r0_1, r2_3, r4_5, r6_7, dout+0, dout+4, dout+8, dout+12);
+#endif
+}
+
+void
+ffts_small_backward8_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *FFTS_RESTRICT lut = ffts_constants_small_inv_32f;
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    V4SF_L_4_2(1, din, din+8, din+4, din+12, &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_K_N(1, V4SF_LD(lut), V4SF_LD(lut+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_S_4(r0_1, r2_3, r4_5, r6_7, dout+0, dout+4, dout+8, dout+12);
+}
+
+void
+ffts_small_backward8_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7;
+    double *LUT8 = (double*) p->ws + p->ws_is[0];
+
+#if MACROS_READY
+    L_4_2(1, din, din+8, din+4, din+12, &r0_1, &r2_3, &r4_5, &r6_7);
+    K_N(1, VLD(LUT8), VLD(LUT8+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    S_4(r0_1, r2_3, r4_5, r6_7, dout+0, dout+4, dout+8, dout+12);
+#endif
+}
+
+void
+ffts_small_forward16_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *FFTS_RESTRICT lut = ffts_constants_small_32f;
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7, r8_9, r10_11, r12_13, r14_15;
+
+    /* unreferenced parameter */
+    (void) p;
+
+    V4SF_L_4_4(0, din+0, din+16, din+8, din+24, &r0_1, &r2_3, &r8_9, &r10_11);
+    V4SF_L_2_4(0, din+4, din+20, din+28, din+12, &r4_5, &r6_7, &r14_15, &r12_13);
+    V4SF_K_N(0, V4SF_LD(lut), V4SF_LD(lut+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_K_N(0, V4SF_LD(lut+8), V4SF_LD(lut+12), &r0_1, &r4_5, &r8_9, &r12_13);
+    V4SF_S_4(r0_1, r4_5, r8_9, r12_13, dout+0, dout+8, dout+16, dout+24);
+    V4SF_K_N(0, V4SF_LD(lut+16), V4SF_LD(lut+20), &r2_3, &r6_7, &r10_11, &r14_15);
+    V4SF_S_4(r2_3, r6_7, r10_11, r14_15, dout+4, dout+12, dout+20, dout+28);
+}
+
+void
+ffts_small_forward16_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    double *LUT8 = (double*) p->ws;
+    V4SF r0_1, r2_3, r4_5, r6_7, r8_9, r10_11, r12_13, r14_15;
+
+#ifdef MACROS_READY
+    L_4_4(0, din+0, din+16, din+8, din+24, &r0_1, &r2_3, &r8_9, &r10_11);
+    L_2_4(0, din+4, din+20, din+28, din+12, &r4_5, &r6_7, &r14_15, &r12_13);
+    K_N(0, VLD(LUT8), VLD(LUT8+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    K_N(0, VLD(LUT8+8), VLD(LUT8+12), &r0_1, &r4_5, &r8_9, &r12_13);
+    S_4(r0_1, r4_5, r8_9, r12_13, dout+0, dout+8, dout+16, dout+24);
+    K_N(0, VLD(LUT8+16), VLD(LUT8+20), &r2_3, &r6_7, &r10_11, &r14_15);
+    S_4(r2_3, r6_7, r10_11, r14_15, dout+4, dout+12, dout+20, dout+28);
+#endif
+}
+
+void
+ffts_small_backward16_32f(ffts_plan_t *p, const void *in, void *out)
+{
+    const float *FFTS_RESTRICT lut = ffts_constants_small_inv_32f;
+    const float *din = (const float*) in;
+    float *dout = (float*) out;
+    V4SF r0_1, r2_3, r4_5, r6_7, r8_9, r10_11, r12_13, r14_15;
+    
+    /* unreferenced parameter */
+    (void) p;
+
+    V4SF_L_4_4(1, din+0, din+16, din+8, din+24, &r0_1, &r2_3, &r8_9, &r10_11);
+    V4SF_L_2_4(1, din+4, din+20, din+28, din+12, &r4_5, &r6_7, &r14_15, &r12_13);
+    V4SF_K_N(1, V4SF_LD(lut), V4SF_LD(lut+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    V4SF_K_N(1, V4SF_LD(lut+8), V4SF_LD(lut+12), &r0_1, &r4_5, &r8_9, &r12_13);
+    V4SF_S_4(r0_1, r4_5, r8_9, r12_13, dout+0, dout+8, dout+16, dout+24);
+    V4SF_K_N(1, V4SF_LD(lut+16), V4SF_LD(lut+20), &r2_3, &r6_7, &r10_11, &r14_15);
+    V4SF_S_4(r2_3, r6_7, r10_11, r14_15, dout+4, dout+12, dout+20, dout+28);
+}
+
+void
+ffts_small_backward16_64f(ffts_plan_t *p, const void *in, void *out)
+{
+    const double *din = (const double*) in;
+    double *dout = (double*) out;
+    double *LUT8 = (double*) p->ws;
+    V4SF r0_1, r2_3, r4_5, r6_7, r8_9, r10_11, r12_13, r14_15;
+
+#ifdef MACROS_READY
+    L_4_4(1, din+0, din+16, din+8, din+24, &r0_1, &r2_3, &r8_9, &r10_11);
+    L_2_4(1, din+4, din+20, din+28, din+12, &r4_5, &r6_7, &r14_15, &r12_13);
+    K_N(1, VLD(LUT8), VLD(LUT8+4), &r0_1, &r2_3, &r4_5, &r6_7);
+    K_N(1, VLD(LUT8+8), VLD(LUT8+12),&r0_1, &r4_5, &r8_9, &r12_13);
+    S_4(r0_1, r4_5, r8_9, r12_13, dout+0, dout+8, dout+16, dout+24);
+    K_N(1, VLD(LUT8+16), VLD(LUT8+20), &r2_3, &r6_7, &r10_11, &r14_15);
+    S_4(r2_3, r6_7, r10_11, r14_15, dout+4, dout+12, dout+20, dout+28);
+#endif
+}
+
 static FFTS_INLINE void
 ffts_static_firstpass_even_32f(float *FFTS_RESTRICT out,
                                const float *FFTS_RESTRICT in,