/* (C) 2008 Jean-Marc Valin, CSIRO
*/
/*
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   are met:
   
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   notice, this list of conditions and the following disclaimer in the
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   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
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*/

/* This is a simple MDCT implementation that uses a N/4 complex FFT
   to do most of the work. It should be relatively straightforward to
   plug in pretty much and FFT here.
   
   This replaces the Vorbis FFT (and uses the exact same API), which 
   was a bit too messy and that was ending up duplicating code 
   (might as well use the same FFT everywhere).
   
   The algorithm is similar to (and inspired from) Fabrice Bellard's
   MDCT implementation in FFMPEG, but has differences in signs, ordering
   and scaling in many places. 
*/

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "mdct.h"
#include "kfft_double.h"
#include <math.h>
#include "os_support.h"
#include "mathops.h"
#include "stack_alloc.h"

#ifndef M_PI
#define M_PI 3.141592653
#endif

void mdct_init(mdct_lookup *l,int N)
{
   int i;
   int N2;
   l->n = N;
   N2 = N>>1;
   l->kfft = cpx32_fft_alloc(N>>2);
   l->trig = (kiss_twiddle_scalar*)celt_alloc(N2*sizeof(kiss_twiddle_scalar));
   /* We have enough points that sine isn't necessary */
#if defined(FIXED_POINT)
#if defined(DOUBLE_PRECISION) & !defined(MIXED_PRECISION)
   for (i=0;i<N2;i++)
      l->trig[i] = SAMP_MAX*cos(2*M_PI*(i+1./8.)/N);
#else
   for (i=0;i<N2;i++)
      l->trig[i] = TRIG_UPSCALE*celt_cos_norm(DIV32(ADD32(SHL32(EXTEND32(i),17),16386),N));
#endif
#else
   for (i=0;i<N2;i++)
      l->trig[i] = cos(2*M_PI*(i+1./8.)/N);
#endif
}

void mdct_clear(mdct_lookup *l)
{
   cpx32_fft_free(l->kfft);
   celt_free(l->trig);
}

void mdct_forward(const mdct_lookup *l, kiss_fft_scalar *in, kiss_fft_scalar * restrict out, const celt_word16_t *window, int overlap)
{
   int i;
   int N, N2, N4;
   VARDECL(kiss_fft_scalar, f);
   SAVE_STACK;
   N = l->n;
   N2 = N>>1;
   N4 = N>>2;
   ALLOC(f, N2, kiss_fft_scalar);
   
   /* Consider the input to be compused of four blocks: [a, b, c, d] */
   /* Window, shuffle, fold */
   {
      /* Temp pointers to make it really clear to the compiler what we're doing */
      const kiss_fft_scalar * restrict xp1 = in+(overlap>>1);
      const kiss_fft_scalar * restrict xp2 = in+N2-1+(overlap>>1);
      kiss_fft_scalar * restrict yp = out;
      const celt_word16_t * restrict wp1 = window+(overlap>>1);
      const celt_word16_t * restrict wp2 = window+(overlap>>1)-1;
      for(i=0;i<(overlap>>2);i++)
      {
         /* Real part arranged as -d-cR, Imag part arranged as -b+aR*/
         *yp++ = MULT16_32_Q15(*wp2, xp1[N2]) + MULT16_32_Q15(*wp1,*xp2);
         *yp++ = MULT16_32_Q15(*wp1, *xp1)    - MULT16_32_Q15(*wp2, xp2[-N2]);
         xp1+=2;
         xp2-=2;
         wp1+=2;
         wp2-=2;
      }
      wp1 = window;
      wp2 = window+overlap-1;
      for(;i<N4-(overlap>>2);i++)
      {
         /* Real part arranged as a-bR, Imag part arranged as -c-dR */
         *yp++ = *xp2;
         *yp++ = *xp1;
         xp1+=2;
         xp2-=2;
      }
      for(;i<N4;i++)
      {
         /* Real part arranged as a-bR, Imag part arranged as -c-dR */
         *yp++ =  -MULT16_32_Q15(*wp1, xp1[-N2]) + MULT16_32_Q15(*wp2, *xp2);
         *yp++ = MULT16_32_Q15(*wp2, *xp1)     + MULT16_32_Q15(*wp1, xp2[N2]);
         xp1+=2;
         xp2-=2;
         wp1+=2;
         wp2-=2;
      }
   }
   /* Pre-rotation */
   {
      kiss_fft_scalar * restrict yp = out;
      kiss_fft_scalar *t = &l->trig[0];
      for(i=0;i<N4;i++)
      {
         kiss_fft_scalar re, im;
         re = yp[0];
         im = yp[1];
         *yp++ = -S_MUL(re,t[0])  +  S_MUL(im,t[N4]);
         *yp++ = -S_MUL(im,t[0])  -  S_MUL(re,t[N4]);
         t++;
      }
   }

   /* N/4 complex FFT, down-scales by 4/N */
   cpx32_fft(l->kfft, out, f, N4);

   /* Post-rotate */
   {
      /* Temp pointers to make it really clear to the compiler what we're doing */
      const kiss_fft_scalar * restrict fp = f;
      kiss_fft_scalar * restrict yp1 = out;
      kiss_fft_scalar * restrict yp2 = out+N2-1;
      kiss_fft_scalar *t = &l->trig[0];
      /* Temp pointers to make it really clear to the compiler what we're doing */
      for(i=0;i<N4;i++)
      {
         *yp1 = -S_MUL(fp[1],t[N4]) + S_MUL(fp[0],t[0]);
         *yp2 = -S_MUL(fp[0],t[N4]) - S_MUL(fp[1],t[0]);
         fp += 2;
         yp1 += 2;
         yp2 -= 2;
         t++;
      }
   }
   RESTORE_STACK;
}


void mdct_backward(const mdct_lookup *l, kiss_fft_scalar *in, kiss_fft_scalar * restrict out, const celt_word16_t * restrict window, int overlap)
{
   int i;
   int N, N2, N4;
   VARDECL(kiss_fft_scalar, f);
   VARDECL(kiss_fft_scalar, f2);
   SAVE_STACK;
   N = l->n;
   N2 = N>>1;
   N4 = N>>2;
   ALLOC(f, N2, kiss_fft_scalar);
   ALLOC(f2, N2, kiss_fft_scalar);
   
   /* Pre-rotate */
   {
      /* Temp pointers to make it really clear to the compiler what we're doing */
      const kiss_fft_scalar * restrict xp1 = in;
      const kiss_fft_scalar * restrict xp2 = in+N2-1;
      kiss_fft_scalar * restrict yp = f2;
      kiss_fft_scalar *t = &l->trig[0];
      for(i=0;i<N4;i++) 
      {
         *yp++ = -S_MUL(*xp2, t[0])  - S_MUL(*xp1,t[N4]);
         *yp++ =  S_MUL(*xp2, t[N4]) - S_MUL(*xp1,t[0]);
         xp1+=2;
         xp2-=2;
         t++;
      }
   }

   /* Inverse N/4 complex FFT. This one should *not* downscale even in fixed-point */
   cpx32_ifft(l->kfft, f2, f, N4);
   
   /* Post-rotate */
   {
      kiss_fft_scalar * restrict fp = f;
      kiss_fft_scalar *t = &l->trig[0];

      for(i=0;i<N4;i++)
      {
         kiss_fft_scalar re, im;
         re = fp[0];
         im = fp[1];
         /* We'd scale up by 2 here, but instead it's done when mixing the windows */
         *fp++ = S_MUL(re,*t) + S_MUL(im,t[N4]);
         *fp++ = S_MUL(im,*t) - S_MUL(re,t[N4]);
         t++;
      }
   }
   /* De-shuffle the components for the middle of the window only */
   {
      const kiss_fft_scalar * restrict fp1 = f;
      const kiss_fft_scalar * restrict fp2 = f+N2-1;
      kiss_fft_scalar * restrict yp = f2;
      for(i = 0; i < N4; i++)
      {
         *yp++ =-*fp1;
         *yp++ = *fp2;
         fp1 += 2;
         fp2 -= 2;
      }
   }

   /* Mirror on both sides for TDAC */
   {
      kiss_fft_scalar * restrict fp1 = f2+N4-1;
      kiss_fft_scalar * restrict xp1 = out+N2-1;
      kiss_fft_scalar * restrict yp1 = out+N4-overlap/2;
      const celt_word16_t * restrict wp1 = window;
      const celt_word16_t * restrict wp2 = window+overlap-1;
      for(i = 0; i< N4-overlap/2; i++)
      {
         *xp1 = *fp1;
         xp1--;
         fp1--;
      }
      for(; i < N4; i++)
      {
         kiss_fft_scalar x1;
         x1 = *fp1--;
         *yp1++ +=-MULT16_32_Q15(*wp1, x1);
         *xp1-- += MULT16_32_Q15(*wp2, x1);
         wp1++;
         wp2--;
      }
   }
   {
      kiss_fft_scalar * restrict fp2 = f2+N4;
      kiss_fft_scalar * restrict xp2 = out+N2;
      kiss_fft_scalar * restrict yp2 = out+N-1-(N4-overlap/2);
      const celt_word16_t * restrict wp1 = window;
      const celt_word16_t * restrict wp2 = window+overlap-1;
      for(i = 0; i< N4-overlap/2; i++)
      {
         *xp2 = *fp2;
         xp2++;
         fp2++;
      }
      for(; i < N4; i++)
      {
         kiss_fft_scalar x2;
         x2 = *fp2++;
         *yp2--  = MULT16_32_Q15(*wp1, x2);
         *xp2++  = MULT16_32_Q15(*wp2, x2);
         wp1++;
         wp2--;
      }
   }
   RESTORE_STACK;
}