/*
  * 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.
  *
  * FFmpeg is free software; you can redistribute it and/or

  * modify it under the terms of the GNU Lesser General Public
  * License as published by the Free Software Foundation; either

  * version 2.1 of the License, or (at your option) any later version.

  *

  * FFmpeg is distributed in the hope that it will be useful,

  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  * Lesser General Public License for more details.
  *
  * You should have received a copy of the GNU Lesser General Public

  * License along with FFmpeg; if not, write to the Free Software

  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

  */

 
 /**

  * @file

  * FFT/IFFT transforms.
  */
 

 #include <stdlib.h>
 #include <string.h>

 #include "libavutil/mathematics.h"
 #include "fft.h"

 #include "fft-internal.h"

 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */

 #if !CONFIG_HARDCODED_TABLES
 COSTABLE(16);
 COSTABLE(32);
 COSTABLE(64);
 COSTABLE(128);
 COSTABLE(256);
 COSTABLE(512);
 COSTABLE(1024);
 COSTABLE(2048);
 COSTABLE(4096);
 COSTABLE(8192);
 COSTABLE(16384);
 COSTABLE(32768);
 COSTABLE(65536);

 #endif

 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {

     NULL, NULL, NULL, NULL,

     FFT_NAME(ff_cos_16),
     FFT_NAME(ff_cos_32),
     FFT_NAME(ff_cos_64),
     FFT_NAME(ff_cos_128),
     FFT_NAME(ff_cos_256),
     FFT_NAME(ff_cos_512),
     FFT_NAME(ff_cos_1024),
     FFT_NAME(ff_cos_2048),
     FFT_NAME(ff_cos_4096),
     FFT_NAME(ff_cos_8192),
     FFT_NAME(ff_cos_16384),
     FFT_NAME(ff_cos_32768),
     FFT_NAME(ff_cos_65536),

 };
 

 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
 

 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;
 }
 

 av_cold void ff_init_ff_cos_tabs(int index)
 {
 #if !CONFIG_HARDCODED_TABLES
     int i;
     int m = 1<<index;
     double freq = 2*M_PI/m;

     FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];

     for(i=0; i<=m/4; i++)

         tab[i] = FIX15(cos(i*freq));

     for(i=1; i<m/4; i++)
         tab[m/2-i] = tab[i];
 #endif
 }
 

 static const int avx_tab[] = {
     0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
 };
 
 static int is_second_half_of_fft32(int i, int n)
 {
     if (n <= 32)
         return i >= 16;
     else if (i < n/2)
         return is_second_half_of_fft32(i, n/2);
     else if (i < 3*n/4)
         return is_second_half_of_fft32(i - n/2, n/4);
     else
         return is_second_half_of_fft32(i - 3*n/4, n/4);
 }
 
 static av_cold void fft_perm_avx(FFTContext *s)
 {
     int i;
     int n = 1 << s->nbits;
 
     for (i = 0; i < n; i += 16) {
         int k;
         if (is_second_half_of_fft32(i, n)) {
             for (k = 0; k < 16; k++)
                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
                     i + avx_tab[k];
 
         } else {
             for (k = 0; k < 16; k++) {
                 int j = i + k;
                 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
             }
         }
     }
 }
 

 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)

 {

     int i, j, n;

     if (nbits < 2 || nbits > 16)
         goto fail;

     s->nbits = nbits;
     n = 1 << nbits;
 
     s->revtab = av_malloc(n * sizeof(uint16_t));
     if (!s->revtab)
         goto fail;

     s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
     if (!s->tmp_buf)
         goto fail;

     s->inverse = inverse;

     s->fft_permutation = FF_FFT_PERM_DEFAULT;

     s->fft_permute = ff_fft_permute_c;

     s->fft_calc    = ff_fft_calc_c;

 #if CONFIG_MDCT

     s->imdct_calc  = ff_imdct_calc_c;
     s->imdct_half  = ff_imdct_half_c;

     s->mdct_calc   = ff_mdct_calc_c;

 #endif

 #if CONFIG_FFT_FLOAT

     if (ARCH_ARM)     ff_fft_init_arm(s);
     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);

     if (ARCH_X86)     ff_fft_init_x86(s);

     if (CONFIG_MDCT)  s->mdct_calcw = s->mdct_calc;

     if (HAVE_MIPSFPU) ff_fft_init_mips(s);

 #else
     if (CONFIG_MDCT)  s->mdct_calcw = ff_mdct_calcw_c;

     if (ARCH_ARM)     ff_fft_fixed_init_arm(s);

 #endif

     for(j=4; j<=nbits; j++) {
         ff_init_ff_cos_tabs(j);
     }

 
     if (s->fft_permutation == FF_FFT_PERM_AVX) {
         fft_perm_avx(s);
     } else {
         for(i=0; i<n; i++) {
             int j = i;
             if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
                 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
         }

     }

     return 0;
  fail:
     av_freep(&s->revtab);

     av_freep(&s->tmp_buf);

     return -1;
 }
 

 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)

 {

     int j, np;

     const uint16_t *revtab = s->revtab;

     np = 1 << s->nbits;

     /* 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));

 }
 

 av_cold void ff_fft_end(FFTContext *s)

 {
     av_freep(&s->revtab);

     av_freep(&s->tmp_buf);
 }
 
 #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) {\

     CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
     CMUL(t5, t6, a3.re, a3.im, wre,  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)\
 {\

     FFTDouble 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,FFT_NAME(ff_cos_##n),n4/2);\

 }
 
 static void fft4(FFTComplex *z)
 {

     FFTDouble 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)
 {

     FFTDouble t1, t2, t3, t4, t5, t6;

 
     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(t5, z[7].re, z[6].re, -z[7].re);
     BF(t6, z[7].im, z[6].im, -z[7].im);

     BUTTERFLIES(z[0],z[2],z[4],z[6]);

     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
 }
 

 #if !CONFIG_SMALL

 static void fft16(FFTComplex *z)
 {

     FFTDouble t1, t2, t3, t4, t5, t6;
     FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
     FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];

 
     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],cos_16_1,cos_16_3);
     TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,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)

 #if !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 (* const fft_dispatch[])(FFTComplex*) = {

     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 };
 

 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)

 {
     fft_dispatch[s->nbits-2](z);

 }