split-radix FFT

c is 1.9x faster than previous c (on various x86 cpus), sse is 1.6x faster than previous sse.

Originally committed as revision 14698 to svn://svn.ffmpeg.org/ffmpeg/trunk

1 files changed, 245 insertions, 126 deletions

diff --git a/libavcodec/fft.c b/libavcodec/fft.c
index 47e9e062f4..7b0d3b3b61 100644
--- a/libavcodec/fft.c
+++ b/libavcodec/fft.c
@@ -1,6 +1,8 @@
 /*
  * FFT/IFFT transforms
+ * Copyright (c) 2008 Loren Merritt
  * Copyright (c) 2002 Fabrice Bellard.
+ * Partly based on libdjbfft by D. J. Bernstein
  *
  * This file is part of FFmpeg.
  *
@@ -26,6 +28,36 @@
 
 #include "dsputil.h"
 
+/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
+DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
+DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
+static FFTSample *ff_cos_tabs[] = {
+    ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
+    ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
+};
+
+static int split_radix_permutation(int i, int n, int inverse)
+{
+    int m;
+    if(n <= 2) return i&1;
+    m = n >> 1;
+    if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
+    m >>= 1;
+    if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
+    else                  return split_radix_permutation(i, m, inverse)*4 - 1;
+}
+
 /**
  * The size of the FFT is 2^nbits. If inverse is TRUE, inverse FFT is
  * done
@@ -34,12 +66,15 @@ int ff_fft_init(FFTContext *s, int nbits, int inverse)
 {
     int i, j, m, n;
     float alpha, c1, s1, s2;
-    int shuffle = 0;
+    int split_radix = 1;
     int av_unused has_vectors;
 
+    if (nbits < 2 || nbits > 16)
+        goto fail;
     s->nbits = nbits;
     n = 1 << nbits;
 
+    s->tmp_buf = NULL;
     s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
     if (!s->exptab)
         goto fail;
@@ -50,50 +85,62 @@ int ff_fft_init(FFTContext *s, int nbits, int inverse)
 
     s2 = inverse ? 1.0 : -1.0;
 
-    for(i=0;i<(n/2);i++) {
-        alpha = 2 * M_PI * (float)i / (float)n;
-        c1 = cos(alpha);
-        s1 = sin(alpha) * s2;
-        s->exptab[i].re = c1;
-        s->exptab[i].im = s1;
-    }
+    s->fft_permute = ff_fft_permute_c;
     s->fft_calc = ff_fft_calc_c;
     s->imdct_calc = ff_imdct_calc;
     s->imdct_half = ff_imdct_half;
     s->exptab1 = NULL;
 
-#ifdef HAVE_MMX
+#if defined HAVE_MMX && defined HAVE_YASM
     has_vectors = mm_support();
-    shuffle = 1;
-    if (has_vectors & MM_3DNOWEXT) {
-        /* 3DNowEx for K7/K8 */
+    if (has_vectors & MM_SSE) {
+        /* SSE for P3/P4/K8 */
+        s->imdct_calc = ff_imdct_calc_sse;
+        s->imdct_half = ff_imdct_half_sse;
+        s->fft_permute = ff_fft_permute_sse;
+        s->fft_calc = ff_fft_calc_sse;
+    } else if (has_vectors & MM_3DNOWEXT) {
+        /* 3DNowEx for K7 */
         s->imdct_calc = ff_imdct_calc_3dn2;
         s->imdct_half = ff_imdct_half_3dn2;
         s->fft_calc = ff_fft_calc_3dn2;
     } else if (has_vectors & MM_3DNOW) {
         /* 3DNow! for K6-2/3 */
         s->fft_calc = ff_fft_calc_3dn;
-    } else if (has_vectors & MM_SSE) {
-        /* SSE for P3/P4 */
-        s->imdct_calc = ff_imdct_calc_sse;
-        s->imdct_half = ff_imdct_half_sse;
-        s->fft_calc = ff_fft_calc_sse;
-    } else {
-        shuffle = 0;
     }
 #elif defined HAVE_ALTIVEC && !defined ALTIVEC_USE_REFERENCE_C_CODE
     has_vectors = mm_support();
     if (has_vectors & MM_ALTIVEC) {
         s->fft_calc = ff_fft_calc_altivec;
-        shuffle = 1;
+        split_radix = 0;
     }
 #endif
 
-    /* compute constant table for HAVE_SSE version */
-    if (shuffle) {
+    if (split_radix) {
+        for(j=4; j<=nbits; j++) {
+            int m = 1<<j;
+            double freq = 2*M_PI/m;
+            FFTSample *tab = ff_cos_tabs[j-4];
+            for(i=0; i<=m/4; i++)
+                tab[i] = cos(i*freq);
+            for(i=1; i<m/4; i++)
+                tab[m/2-i] = tab[i];
+        }
+        for(i=0; i<n; i++)
+            s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
+        s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
+    } else {
         int np, nblocks, np2, l;
         FFTComplex *q;
 
+        for(i=0; i<(n/2); i++) {
+            alpha = 2 * M_PI * (float)i / (float)n;
+            c1 = cos(alpha);
+            s1 = sin(alpha) * s2;
+            s->exptab[i].re = c1;
+            s->exptab[i].im = s1;
+        }
+
         np = 1 << nbits;
         nblocks = np >> 3;
         np2 = np >> 1;
@@ -116,7 +163,6 @@ int ff_fft_init(FFTContext *s, int nbits, int inverse)
             nblocks = nblocks >> 1;
         } while (nblocks != 0);
         av_freep(&s->exptab);
-    }
 
     /* compute bit reverse table */
 
@@ -127,126 +173,35 @@ int ff_fft_init(FFTContext *s, int nbits, int inverse)
         }
         s->revtab[i]=m;
     }
+    }
+
     return 0;
  fail:
     av_freep(&s->revtab);
     av_freep(&s->exptab);
     av_freep(&s->exptab1);
+    av_freep(&s->tmp_buf);
     return -1;
 }
 
-/* butter fly op */
-#define BF(pre, pim, qre, qim, pre1, pim1, qre1, qim1) \
-{\
-  FFTSample ax, ay, bx, by;\
-  bx=pre1;\
-  by=pim1;\
-  ax=qre1;\
-  ay=qim1;\
-  pre = (bx + ax);\
-  pim = (by + ay);\
-  qre = (bx - ax);\
-  qim = (by - ay);\
-}
-
-#define MUL16(a,b) ((a) * (b))
-
-#define CMUL(pre, pim, are, aim, bre, bim) \
-{\
-   pre = (MUL16(are, bre) - MUL16(aim, bim));\
-   pim = (MUL16(are, bim) + MUL16(bre, aim));\
-}
-
-/**
- * Do a complex FFT with the parameters defined in ff_fft_init(). The
- * input data must be permuted before with s->revtab table. No
- * 1.0/sqrt(n) normalization is done.
- */
-void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
-{
-    int ln = s->nbits;
-    int j, np, np2;
-    int nblocks, nloops;
-    register FFTComplex *p, *q;
-    FFTComplex *exptab = s->exptab;
-    int l;
-    FFTSample tmp_re, tmp_im;
-
-    np = 1 << ln;
-
-    /* pass 0 */
-
-    p=&z[0];
-    j=(np >> 1);
-    do {
-        BF(p[0].re, p[0].im, p[1].re, p[1].im,
-           p[0].re, p[0].im, p[1].re, p[1].im);
-        p+=2;
-    } while (--j != 0);
-
-    /* pass 1 */
-
-
-    p=&z[0];
-    j=np >> 2;
-    if (s->inverse) {
-        do {
-            BF(p[0].re, p[0].im, p[2].re, p[2].im,
-               p[0].re, p[0].im, p[2].re, p[2].im);
-            BF(p[1].re, p[1].im, p[3].re, p[3].im,
-               p[1].re, p[1].im, -p[3].im, p[3].re);
-            p+=4;
-        } while (--j != 0);
-    } else {
-        do {
-            BF(p[0].re, p[0].im, p[2].re, p[2].im,
-               p[0].re, p[0].im, p[2].re, p[2].im);
-            BF(p[1].re, p[1].im, p[3].re, p[3].im,
-               p[1].re, p[1].im, p[3].im, -p[3].re);
-            p+=4;
-        } while (--j != 0);
-    }
-    /* pass 2 .. ln-1 */
-
-    nblocks = np >> 3;
-    nloops = 1 << 2;
-    np2 = np >> 1;
-    do {
-        p = z;
-        q = z + nloops;
-        for (j = 0; j < nblocks; ++j) {
-            BF(p->re, p->im, q->re, q->im,
-               p->re, p->im, q->re, q->im);
-
-            p++;
-            q++;
-            for(l = nblocks; l < np2; l += nblocks) {
-                CMUL(tmp_re, tmp_im, exptab[l].re, exptab[l].im, q->re, q->im);
-                BF(p->re, p->im, q->re, q->im,
-                   p->re, p->im, tmp_re, tmp_im);
-                p++;
-                q++;
-            }
-
-            p += nloops;
-            q += nloops;
-        }
-        nblocks = nblocks >> 1;
-        nloops = nloops << 1;
-    } while (nblocks != 0);
-}
-
 /**
  * Do the permutation needed BEFORE calling ff_fft_calc()
  */
-void ff_fft_permute(FFTContext *s, FFTComplex *z)
+void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
 {
     int j, k, np;
     FFTComplex tmp;
     const uint16_t *revtab = s->revtab;
+    np = 1 << s->nbits;
+
+    if (s->tmp_buf) {
+        /* TODO: handle split-radix permute in a more optimal way, probably in-place */
+        for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
+        memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
+        return;
+    }
 
     /* reverse */
-    np = 1 << s->nbits;
     for(j=0;j<np;j++) {
         k = revtab[j];
         if (k < j) {
@@ -262,5 +217,169 @@ void ff_fft_end(FFTContext *s)
     av_freep(&s->revtab);
     av_freep(&s->exptab);
     av_freep(&s->exptab1);
+    av_freep(&s->tmp_buf);
+}
+
+#define sqrthalf (float)M_SQRT1_2
+
+#define BF(x,y,a,b) {\
+    x = a - b;\
+    y = a + b;\
+}
+
+#define BUTTERFLIES(a0,a1,a2,a3) {\
+    BF(t3, t5, t5, t1);\
+    BF(a2.re, a0.re, a0.re, t5);\
+    BF(a3.im, a1.im, a1.im, t3);\
+    BF(t4, t6, t2, t6);\
+    BF(a3.re, a1.re, a1.re, t4);\
+    BF(a2.im, a0.im, a0.im, t6);\
+}
+
+// force loading all the inputs before storing any.
+// this is slightly slower for small data, but avoids store->load aliasing
+// for addresses separated by large powers of 2.
+#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
+    FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
+    BF(t3, t5, t5, t1);\
+    BF(a2.re, a0.re, r0, t5);\
+    BF(a3.im, a1.im, i1, t3);\
+    BF(t4, t6, t2, t6);\
+    BF(a3.re, a1.re, r1, t4);\
+    BF(a2.im, a0.im, i0, t6);\
+}
+
+#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
+    t1 = a2.re * wre + a2.im * wim;\
+    t2 = a2.im * wre - a2.re * wim;\
+    t5 = a3.re * wre - a3.im * wim;\
+    t6 = a3.im * wre + a3.re * wim;\
+    BUTTERFLIES(a0,a1,a2,a3)\
+}
+
+#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
+    t1 = a2.re;\
+    t2 = a2.im;\
+    t5 = a3.re;\
+    t6 = a3.im;\
+    BUTTERFLIES(a0,a1,a2,a3)\
+}
+
+/* z[0...8n-1], w[1...2n-1] */
+#define PASS(name)\
+static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
+{\
+    FFTSample t1, t2, t3, t4, t5, t6;\
+    int o1 = 2*n;\
+    int o2 = 4*n;\
+    int o3 = 6*n;\
+    const FFTSample *wim = wre+o1;\
+    n--;\
+\
+    TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
+    TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
+    do {\
+        z += 2;\
+        wre += 2;\
+        wim -= 2;\
+        TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
+        TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
+    } while(--n);\
+}
+
+PASS(pass)
+#undef BUTTERFLIES
+#define BUTTERFLIES BUTTERFLIES_BIG
+PASS(pass_big)
+
+#define DECL_FFT(n,n2,n4)\
+static void fft##n(FFTComplex *z)\
+{\
+    fft##n2(z);\
+    fft##n4(z+n4*2);\
+    fft##n4(z+n4*3);\
+    pass(z,ff_cos_##n,n4/2);\
+}
+
+static void fft4(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
+
+    BF(t3, t1, z[0].re, z[1].re);
+    BF(t8, t6, z[3].re, z[2].re);
+    BF(z[2].re, z[0].re, t1, t6);
+    BF(t4, t2, z[0].im, z[1].im);
+    BF(t7, t5, z[2].im, z[3].im);
+    BF(z[3].im, z[1].im, t4, t8);
+    BF(z[3].re, z[1].re, t3, t7);
+    BF(z[2].im, z[0].im, t2, t5);
+}
+
+static void fft8(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
+
+    fft4(z);
+
+    BF(t1, z[5].re, z[4].re, -z[5].re);
+    BF(t2, z[5].im, z[4].im, -z[5].im);
+    BF(t3, z[7].re, z[6].re, -z[7].re);
+    BF(t4, z[7].im, z[6].im, -z[7].im);
+    BF(t8, t1, t3, t1);
+    BF(t7, t2, t2, t4);
+    BF(z[4].re, z[0].re, z[0].re, t1);
+    BF(z[4].im, z[0].im, z[0].im, t2);
+    BF(z[6].re, z[2].re, z[2].re, t7);
+    BF(z[6].im, z[2].im, z[2].im, t8);
+
+    TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
+}
+
+#ifndef CONFIG_SMALL
+static void fft16(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6;
+
+    fft8(z);
+    fft4(z+8);
+    fft4(z+12);
+
+    TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
+    TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
+    TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
+    TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
+}
+#else
+DECL_FFT(16,8,4)
+#endif
+DECL_FFT(32,16,8)
+DECL_FFT(64,32,16)
+DECL_FFT(128,64,32)
+DECL_FFT(256,128,64)
+DECL_FFT(512,256,128)
+#ifndef CONFIG_SMALL
+#define pass pass_big
+#endif
+DECL_FFT(1024,512,256)
+DECL_FFT(2048,1024,512)
+DECL_FFT(4096,2048,1024)
+DECL_FFT(8192,4096,2048)
+DECL_FFT(16384,8192,4096)
+DECL_FFT(32768,16384,8192)
+DECL_FFT(65536,32768,16384)
+
+static void (*fft_dispatch[])(FFTComplex*) = {
+    fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
+    fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
+};
+
+/**
+ * Do a complex FFT with the parameters defined in ff_fft_init(). The
+ * input data must be permuted before with s->revtab table. No
+ * 1.0/sqrt(n) normalization is done.
+ */
+void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
+{
+    fft_dispatch[s->nbits-2](z);
 }