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423 lines
17 KiB
C
423 lines
17 KiB
C
/********************************************************************
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* *
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* THIS FILE IS PART OF THE OggTheora SOFTWARE CODEC SOURCE CODE. *
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* USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS *
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* GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
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* IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. *
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* *
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* THE Theora SOURCE CODE IS COPYRIGHT (C) 2002-2009 *
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* by the Xiph.Org Foundation http://www.xiph.org/ *
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* *
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********************************************************************
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function:
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last mod: $Id: fdct.c 16503 2009-08-22 18:14:02Z giles $
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********************************************************************/
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#include "encint.h"
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#include "dct.h"
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/*Performs a forward 8 point Type-II DCT transform.
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The output is scaled by a factor of 2 from the orthonormal version of the
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transform.
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_y: The buffer to store the result in.
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Data will be placed the first 8 entries (e.g., in a row of an 8x8 block).
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_x: The input coefficients.
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Every 8th entry is used (e.g., from a column of an 8x8 block).*/
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static void oc_fdct8(ogg_int16_t _y[8],const ogg_int16_t *_x){
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int t0;
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int t1;
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int t2;
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int t3;
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int t4;
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int t5;
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int t6;
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int t7;
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int r;
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int s;
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int u;
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int v;
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/*Stage 1:*/
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/*0-7 butterfly.*/
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t0=_x[0<<3]+(int)_x[7<<3];
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t7=_x[0<<3]-(int)_x[7<<3];
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/*1-6 butterfly.*/
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t1=_x[1<<3]+(int)_x[6<<3];
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t6=_x[1<<3]-(int)_x[6<<3];
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/*2-5 butterfly.*/
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t2=_x[2<<3]+(int)_x[5<<3];
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t5=_x[2<<3]-(int)_x[5<<3];
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/*3-4 butterfly.*/
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t3=_x[3<<3]+(int)_x[4<<3];
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t4=_x[3<<3]-(int)_x[4<<3];
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/*Stage 2:*/
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/*0-3 butterfly.*/
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r=t0+t3;
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t3=t0-t3;
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t0=r;
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/*1-2 butterfly.*/
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r=t1+t2;
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t2=t1-t2;
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t1=r;
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/*6-5 butterfly.*/
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r=t6+t5;
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t5=t6-t5;
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t6=r;
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/*Stages 3 and 4 are where all the approximation occurs.
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These are chosen to be as close to an exact inverse of the approximations
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made in the iDCT as possible, while still using mostly 16-bit arithmetic.
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We use some 16x16->32 signed MACs, but those still commonly execute in 1
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cycle on a 16-bit DSP.
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For example, s=(27146*t5+0x4000>>16)+t5+(t5!=0) is an exact inverse of
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t5=(OC_C4S4*s>>16).
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That is, applying the latter to the output of the former will recover t5
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exactly (over the valid input range of t5, -23171...23169).
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We increase the rounding bias to 0xB500 in this particular case so that
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errors inverting the subsequent butterfly are not one-sided (e.g., the
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mean error is very close to zero).
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The (t5!=0) term could be replaced simply by 1, but we want to send 0 to 0.
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The fDCT of an all-zeros block will still not be zero, because of the
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biases we added at the very beginning of the process, but it will be close
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enough that it is guaranteed to round to zero.*/
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/*Stage 3:*/
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/*4-5 butterfly.*/
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s=(27146*t5+0xB500>>16)+t5+(t5!=0)>>1;
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r=t4+s;
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t5=t4-s;
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t4=r;
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/*7-6 butterfly.*/
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s=(27146*t6+0xB500>>16)+t6+(t6!=0)>>1;
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r=t7+s;
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t6=t7-s;
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t7=r;
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/*Stage 4:*/
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/*0-1 butterfly.*/
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r=(27146*t0+0x4000>>16)+t0+(t0!=0);
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s=(27146*t1+0xB500>>16)+t1+(t1!=0);
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u=r+s>>1;
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v=r-u;
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_y[0]=u;
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_y[4]=v;
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/*3-2 rotation by 6pi/16*/
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u=(OC_C6S2*t2+OC_C2S6*t3+0x6CB7>>16)+(t3!=0);
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s=(OC_C6S2*u>>16)-t2;
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v=(s*21600+0x2800>>18)+s+(s!=0);
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_y[2]=u;
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_y[6]=v;
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/*6-5 rotation by 3pi/16*/
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u=(OC_C5S3*t6+OC_C3S5*t5+0x0E3D>>16)+(t5!=0);
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s=t6-(OC_C5S3*u>>16);
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v=(s*26568+0x3400>>17)+s+(s!=0);
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_y[5]=u;
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_y[3]=v;
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/*7-4 rotation by 7pi/16*/
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u=(OC_C7S1*t4+OC_C1S7*t7+0x7B1B>>16)+(t7!=0);
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s=(OC_C7S1*u>>16)-t4;
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v=(s*20539+0x3000>>20)+s+(s!=0);
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_y[1]=u;
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_y[7]=v;
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}
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void oc_enc_fdct8x8(const oc_enc_ctx *_enc,ogg_int16_t _y[64],
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const ogg_int16_t _x[64]){
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(*_enc->opt_vtable.fdct8x8)(_y,_x);
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}
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/*Performs a forward 8x8 Type-II DCT transform.
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The output is scaled by a factor of 4 relative to the orthonormal version
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of the transform.
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_y: The buffer to store the result in.
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This may be the same as _x.
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_x: The input coefficients. */
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void oc_enc_fdct8x8_c(ogg_int16_t _y[64],const ogg_int16_t _x[64]){
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const ogg_int16_t *in;
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ogg_int16_t *end;
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ogg_int16_t *out;
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ogg_int16_t w[64];
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int i;
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/*Add two extra bits of working precision to improve accuracy; any more and
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we could overflow.*/
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for(i=0;i<64;i++)w[i]=_x[i]<<2;
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/*These biases correct for some systematic error that remains in the full
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fDCT->iDCT round trip.*/
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w[0]+=(w[0]!=0)+1;
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w[1]++;
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w[8]--;
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/*Transform columns of w into rows of _y.*/
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for(in=w,out=_y,end=out+64;out<end;in++,out+=8)oc_fdct8(out,in);
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/*Transform columns of _y into rows of w.*/
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for(in=_y,out=w,end=out+64;out<end;in++,out+=8)oc_fdct8(out,in);
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/*Round the result back to the external working precision (which is still
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scaled by four relative to the orthogonal result).
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TODO: We should just update the external working precision.*/
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for(i=0;i<64;i++)_y[i]=w[i]+2>>2;
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}
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/*This does not seem to outperform simple LFE border padding before MC.
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It yields higher PSNR, but much higher bitrate usage.*/
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#if 0
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typedef struct oc_extension_info oc_extension_info;
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/*Information needed to pad boundary blocks.
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We multiply each row/column by an extension matrix that fills in the padding
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values as a linear combination of the active values, so that an equivalent
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number of coefficients are forced to zero.
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This costs at most 16 multiplies, the same as a 1-D fDCT itself, and as
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little as 7 multiplies.
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We compute the extension matrices for every possible shape in advance, as
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there are only 35.
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The coefficients for all matrices are stored in a single array to take
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advantage of the overlap and repetitiveness of many of the shapes.
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A similar technique is applied to the offsets into this array.
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This reduces the required table storage by about 48%.
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See tools/extgen.c for details.
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We could conceivably do the same for all 256 possible shapes.*/
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struct oc_extension_info{
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/*The mask of the active pixels in the shape.*/
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short mask;
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/*The number of active pixels in the shape.*/
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short na;
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/*The extension matrix.
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This is (8-na)xna*/
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const ogg_int16_t *const *ext;
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/*The pixel indices: na active pixels followed by 8-na padding pixels.*/
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unsigned char pi[8];
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/*The coefficient indices: na unconstrained coefficients followed by 8-na
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coefficients to be forced to zero.*/
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unsigned char ci[8];
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};
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/*The number of shapes we need.*/
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#define OC_NSHAPES (35)
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static const ogg_int16_t OC_EXT_COEFFS[229]={
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0x7FFF,0xE1F8,0x6903,0xAA79,0x5587,0x7FFF,0x1E08,0x7FFF,
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0x5587,0xAA79,0x6903,0xE1F8,0x7FFF,0x0000,0x0000,0x0000,
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0x7FFF,0x0000,0x0000,0x7FFF,0x8000,0x7FFF,0x0000,0x0000,
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0x7FFF,0xE1F8,0x1E08,0xB0A7,0xAA1D,0x337C,0x7FFF,0x4345,
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0x2267,0x4345,0x7FFF,0x337C,0xAA1D,0xB0A7,0x8A8C,0x4F59,
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0x03B4,0xE2D6,0x7FFF,0x2CF3,0x7FFF,0xE2D6,0x03B4,0x4F59,
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0x8A8C,0x1103,0x7AEF,0x5225,0xDF60,0xC288,0xDF60,0x5225,
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0x7AEF,0x1103,0x668A,0xD6EE,0x3A16,0x0E6C,0xFA07,0x0E6C,
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0x3A16,0xD6EE,0x668A,0x2A79,0x2402,0x980F,0x50F5,0x4882,
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0x50F5,0x980F,0x2402,0x2A79,0xF976,0x2768,0x5F22,0x2768,
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0xF976,0x1F91,0x76C1,0xE9AE,0x76C1,0x1F91,0x7FFF,0xD185,
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0x0FC8,0xD185,0x7FFF,0x4F59,0x4345,0xED62,0x4345,0x4F59,
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0xF574,0x5D99,0x2CF3,0x5D99,0xF574,0x5587,0x3505,0x30FC,
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0xF482,0x953C,0xEAC4,0x7FFF,0x4F04,0x7FFF,0xEAC4,0x953C,
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0xF482,0x30FC,0x4F04,0x273D,0xD8C3,0x273D,0x1E09,0x61F7,
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0x1E09,0x273D,0xD8C3,0x273D,0x4F04,0x30FC,0xA57E,0x153C,
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0x6AC4,0x3C7A,0x1E08,0x3C7A,0x6AC4,0x153C,0xA57E,0x7FFF,
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0xA57E,0x5A82,0x6AC4,0x153C,0xC386,0xE1F8,0xC386,0x153C,
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0x6AC4,0x5A82,0xD8C3,0x273D,0x7FFF,0xE1F7,0x7FFF,0x273D,
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0xD8C3,0x4F04,0x30FC,0xD8C3,0x273D,0xD8C3,0x30FC,0x4F04,
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0x1FC8,0x67AD,0x1853,0xE038,0x1853,0x67AD,0x1FC8,0x4546,
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0xE038,0x1FC8,0x3ABA,0x1FC8,0xE038,0x4546,0x3505,0x5587,
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0xF574,0xBC11,0x78F4,0x4AFB,0xE6F3,0x4E12,0x3C11,0xF8F4,
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0x4AFB,0x3C7A,0xF88B,0x3C11,0x78F4,0xCAFB,0x7FFF,0x08CC,
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0x070C,0x236D,0x5587,0x236D,0x070C,0xF88B,0x3C7A,0x4AFB,
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0xF8F4,0x3C11,0x7FFF,0x153C,0xCAFB,0x153C,0x7FFF,0x1E08,
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0xE1F8,0x7FFF,0x08CC,0x7FFF,0xCAFB,0x78F4,0x3C11,0x4E12,
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0xE6F3,0x4AFB,0x78F4,0xBC11,0xFE3D,0x7FFF,0xFE3D,0x2F3A,
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0x7FFF,0x2F3A,0x89BC,0x7FFF,0x89BC
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};
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static const ogg_int16_t *const OC_EXT_ROWS[96]={
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OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 0,
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OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 0,OC_EXT_COEFFS+ 6,
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OC_EXT_COEFFS+ 27,OC_EXT_COEFFS+ 38,OC_EXT_COEFFS+ 43,OC_EXT_COEFFS+ 32,
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OC_EXT_COEFFS+ 49,OC_EXT_COEFFS+ 58,OC_EXT_COEFFS+ 67,OC_EXT_COEFFS+ 71,
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OC_EXT_COEFFS+ 62,OC_EXT_COEFFS+ 53,OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 15,
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OC_EXT_COEFFS+ 14,OC_EXT_COEFFS+ 13,OC_EXT_COEFFS+ 76,OC_EXT_COEFFS+ 81,
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OC_EXT_COEFFS+ 86,OC_EXT_COEFFS+ 91,OC_EXT_COEFFS+ 96,OC_EXT_COEFFS+ 98,
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OC_EXT_COEFFS+ 93,OC_EXT_COEFFS+ 88,OC_EXT_COEFFS+ 83,OC_EXT_COEFFS+ 78,
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OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 15,OC_EXT_COEFFS+ 15,OC_EXT_COEFFS+ 12,
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OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 15,OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 15,
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OC_EXT_COEFFS+ 15,OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 103,OC_EXT_COEFFS+ 108,
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OC_EXT_COEFFS+ 126,OC_EXT_COEFFS+ 16,OC_EXT_COEFFS+ 137,OC_EXT_COEFFS+ 141,
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OC_EXT_COEFFS+ 20,OC_EXT_COEFFS+ 130,OC_EXT_COEFFS+ 113,OC_EXT_COEFFS+ 116,
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OC_EXT_COEFFS+ 146,OC_EXT_COEFFS+ 153,OC_EXT_COEFFS+ 160,OC_EXT_COEFFS+ 167,
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OC_EXT_COEFFS+ 170,OC_EXT_COEFFS+ 163,OC_EXT_COEFFS+ 156,OC_EXT_COEFFS+ 149,
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OC_EXT_COEFFS+ 119,OC_EXT_COEFFS+ 122,OC_EXT_COEFFS+ 174,OC_EXT_COEFFS+ 177,
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OC_EXT_COEFFS+ 182,OC_EXT_COEFFS+ 187,OC_EXT_COEFFS+ 192,OC_EXT_COEFFS+ 197,
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OC_EXT_COEFFS+ 202,OC_EXT_COEFFS+ 207,OC_EXT_COEFFS+ 210,OC_EXT_COEFFS+ 215,
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OC_EXT_COEFFS+ 179,OC_EXT_COEFFS+ 189,OC_EXT_COEFFS+ 24,OC_EXT_COEFFS+ 204,
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OC_EXT_COEFFS+ 184,OC_EXT_COEFFS+ 194,OC_EXT_COEFFS+ 212,OC_EXT_COEFFS+ 199,
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OC_EXT_COEFFS+ 217,OC_EXT_COEFFS+ 100,OC_EXT_COEFFS+ 134,OC_EXT_COEFFS+ 135,
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OC_EXT_COEFFS+ 135,OC_EXT_COEFFS+ 12,OC_EXT_COEFFS+ 15,OC_EXT_COEFFS+ 134,
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OC_EXT_COEFFS+ 134,OC_EXT_COEFFS+ 135,OC_EXT_COEFFS+ 220,OC_EXT_COEFFS+ 223,
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OC_EXT_COEFFS+ 226,OC_EXT_COEFFS+ 227,OC_EXT_COEFFS+ 224,OC_EXT_COEFFS+ 221
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};
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static const oc_extension_info OC_EXTENSION_INFO[OC_NSHAPES]={
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{0x7F,7,OC_EXT_ROWS+ 0,{0,1,2,3,4,5,6,7},{0,1,2,4,5,6,7,3}},
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{0xFE,7,OC_EXT_ROWS+ 7,{1,2,3,4,5,6,7,0},{0,1,2,4,5,6,7,3}},
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{0x3F,6,OC_EXT_ROWS+ 8,{0,1,2,3,4,5,7,6},{0,1,3,4,6,7,5,2}},
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{0xFC,6,OC_EXT_ROWS+ 10,{2,3,4,5,6,7,1,0},{0,1,3,4,6,7,5,2}},
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{0x1F,5,OC_EXT_ROWS+ 12,{0,1,2,3,4,7,6,5},{0,2,3,5,7,6,4,1}},
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{0xF8,5,OC_EXT_ROWS+ 15,{3,4,5,6,7,2,1,0},{0,2,3,5,7,6,4,1}},
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{0x0F,4,OC_EXT_ROWS+ 18,{0,1,2,3,7,6,5,4},{0,2,4,6,7,5,3,1}},
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{0xF0,4,OC_EXT_ROWS+ 18,{4,5,6,7,3,2,1,0},{0,2,4,6,7,5,3,1}},
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{0x07,3,OC_EXT_ROWS+ 22,{0,1,2,7,6,5,4,3},{0,3,6,7,5,4,2,1}},
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{0xE0,3,OC_EXT_ROWS+ 27,{5,6,7,4,3,2,1,0},{0,3,6,7,5,4,2,1}},
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{0x03,2,OC_EXT_ROWS+ 32,{0,1,7,6,5,4,3,2},{0,4,7,6,5,3,2,1}},
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{0xC0,2,OC_EXT_ROWS+ 32,{6,7,5,4,3,2,1,0},{0,4,7,6,5,3,2,1}},
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{0x01,1,OC_EXT_ROWS+ 0,{0,7,6,5,4,3,2,1},{0,7,6,5,4,3,2,1}},
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{0x80,1,OC_EXT_ROWS+ 0,{7,6,5,4,3,2,1,0},{0,7,6,5,4,3,2,1}},
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{0x7E,6,OC_EXT_ROWS+ 42,{1,2,3,4,5,6,7,0},{0,1,2,5,6,7,4,3}},
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{0x7C,5,OC_EXT_ROWS+ 44,{2,3,4,5,6,7,1,0},{0,1,4,5,7,6,3,2}},
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{0x3E,5,OC_EXT_ROWS+ 47,{1,2,3,4,5,7,6,0},{0,1,4,5,7,6,3,2}},
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{0x78,4,OC_EXT_ROWS+ 50,{3,4,5,6,7,2,1,0},{0,4,5,7,6,3,2,1}},
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{0x3C,4,OC_EXT_ROWS+ 54,{2,3,4,5,7,6,1,0},{0,3,4,7,6,5,2,1}},
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{0x1E,4,OC_EXT_ROWS+ 58,{1,2,3,4,7,6,5,0},{0,4,5,7,6,3,2,1}},
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{0x70,3,OC_EXT_ROWS+ 62,{4,5,6,7,3,2,1,0},{0,5,7,6,4,3,2,1}},
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{0x38,3,OC_EXT_ROWS+ 67,{3,4,5,7,6,2,1,0},{0,5,6,7,4,3,2,1}},
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{0x1C,3,OC_EXT_ROWS+ 72,{2,3,4,7,6,5,1,0},{0,5,6,7,4,3,2,1}},
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{0x0E,3,OC_EXT_ROWS+ 77,{1,2,3,7,6,5,4,0},{0,5,7,6,4,3,2,1}},
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{0x60,2,OC_EXT_ROWS+ 82,{5,6,7,4,3,2,1,0},{0,2,7,6,5,4,3,1}},
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{0x30,2,OC_EXT_ROWS+ 36,{4,5,7,6,3,2,1,0},{0,4,7,6,5,3,2,1}},
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{0x18,2,OC_EXT_ROWS+ 90,{3,4,7,6,5,2,1,0},{0,1,7,6,5,4,3,2}},
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{0x0C,2,OC_EXT_ROWS+ 34,{2,3,7,6,5,4,1,0},{0,4,7,6,5,3,2,1}},
|
|
{0x06,2,OC_EXT_ROWS+ 84,{1,2,7,6,5,4,3,0},{0,2,7,6,5,4,3,1}},
|
|
{0x40,1,OC_EXT_ROWS+ 0,{6,7,5,4,3,2,1,0},{0,7,6,5,4,3,2,1}},
|
|
{0x20,1,OC_EXT_ROWS+ 0,{5,7,6,4,3,2,1,0},{0,7,6,5,4,3,2,1}},
|
|
{0x10,1,OC_EXT_ROWS+ 0,{4,7,6,5,3,2,1,0},{0,7,6,5,4,3,2,1}},
|
|
{0x08,1,OC_EXT_ROWS+ 0,{3,7,6,5,4,2,1,0},{0,7,6,5,4,3,2,1}},
|
|
{0x04,1,OC_EXT_ROWS+ 0,{2,7,6,5,4,3,1,0},{0,7,6,5,4,3,2,1}},
|
|
{0x02,1,OC_EXT_ROWS+ 0,{1,7,6,5,4,3,2,0},{0,7,6,5,4,3,2,1}}
|
|
};
|
|
|
|
|
|
|
|
/*Pads a single column of a partial block and then performs a forward Type-II
|
|
DCT on the result.
|
|
The input is scaled by a factor of 4 and biased appropriately for the current
|
|
fDCT implementation.
|
|
The output is scaled by an additional factor of 2 from the orthonormal
|
|
version of the transform.
|
|
_y: The buffer to store the result in.
|
|
Data will be placed the first 8 entries (e.g., in a row of an 8x8 block).
|
|
_x: The input coefficients.
|
|
Every 8th entry is used (e.g., from a column of an 8x8 block).
|
|
_e: The extension information for the shape.*/
|
|
static void oc_fdct8_ext(ogg_int16_t _y[8],ogg_int16_t *_x,
|
|
const oc_extension_info *_e){
|
|
const unsigned char *pi;
|
|
int na;
|
|
na=_e->na;
|
|
pi=_e->pi;
|
|
if(na==1){
|
|
int ci;
|
|
/*While the branch below is still correct for shapes with na==1, we can
|
|
perform the entire transform with just 1 multiply in this case instead
|
|
of 23.*/
|
|
_y[0]=(ogg_int16_t)(OC_DIV2_16(OC_C4S4*(_x[pi[0]])));
|
|
for(ci=1;ci<8;ci++)_y[ci]=0;
|
|
}
|
|
else{
|
|
const ogg_int16_t *const *ext;
|
|
int zpi;
|
|
int api;
|
|
int nz;
|
|
/*First multiply by the extension matrix to compute the padding values.*/
|
|
nz=8-na;
|
|
ext=_e->ext;
|
|
for(zpi=0;zpi<nz;zpi++){
|
|
ogg_int32_t v;
|
|
v=0;
|
|
for(api=0;api<na;api++){
|
|
v+=ext[zpi][api]*(ogg_int32_t)(_x[pi[api]<<3]<<1);
|
|
}
|
|
_x[pi[na+zpi]<<3]=(ogg_int16_t)(v+0x8000>>16)+1>>1;
|
|
}
|
|
oc_fdct8(_y,_x);
|
|
}
|
|
}
|
|
|
|
/*Performs a forward 8x8 Type-II DCT transform on blocks which overlap the
|
|
border of the picture region.
|
|
This method ONLY works with rectangular regions.
|
|
_border: A description of which pixels are inside the border.
|
|
_y: The buffer to store the result in.
|
|
This may be the same as _x.
|
|
_x: The input pixel values.
|
|
Pixel values outside the border will be ignored.*/
|
|
void oc_fdct8x8_border(const oc_border_info *_border,
|
|
ogg_int16_t _y[64],const ogg_int16_t _x[64]){
|
|
ogg_int16_t *in;
|
|
ogg_int16_t *out;
|
|
ogg_int16_t w[64];
|
|
ogg_int64_t mask;
|
|
const oc_extension_info *cext;
|
|
const oc_extension_info *rext;
|
|
int cmask;
|
|
int rmask;
|
|
int ri;
|
|
int ci;
|
|
/*Identify the shapes of the non-zero rows and columns.*/
|
|
rmask=cmask=0;
|
|
mask=_border->mask;
|
|
for(ri=0;ri<8;ri++){
|
|
/*This aggregation is _only_ correct for rectangular masks.*/
|
|
cmask|=((mask&0xFF)!=0)<<ri;
|
|
rmask|=mask&0xFF;
|
|
mask>>=8;
|
|
}
|
|
/*Find the associated extension info for these shapes.*/
|
|
if(cmask==0xFF)cext=NULL;
|
|
else for(cext=OC_EXTENSION_INFO;cext->mask!=cmask;){
|
|
/*If we somehow can't find the shape, then just do an unpadded fDCT.
|
|
It won't be efficient, but it should still be correct.*/
|
|
if(++cext>=OC_EXTENSION_INFO+OC_NSHAPES){
|
|
oc_enc_fdct8x8_c(_y,_x);
|
|
return;
|
|
}
|
|
}
|
|
if(rmask==0xFF)rext=NULL;
|
|
else for(rext=OC_EXTENSION_INFO;rext->mask!=rmask;){
|
|
/*If we somehow can't find the shape, then just do an unpadded fDCT.
|
|
It won't be efficient, but it should still be correct.*/
|
|
if(++rext>=OC_EXTENSION_INFO+OC_NSHAPES){
|
|
oc_enc_fdct8x8_c(_y,_x);
|
|
return;
|
|
}
|
|
}
|
|
/*Add two extra bits of working precision to improve accuracy; any more and
|
|
we could overflow.*/
|
|
for(ci=0;ci<64;ci++)w[ci]=_x[ci]<<2;
|
|
/*These biases correct for some systematic error that remains in the full
|
|
fDCT->iDCT round trip.
|
|
We can safely add them before padding, since if these pixel values are
|
|
overwritten, we didn't care what they were anyway (and the unbiased values
|
|
will usually yield smaller DCT coefficient magnitudes).*/
|
|
w[0]+=(w[0]!=0)+1;
|
|
w[1]++;
|
|
w[8]--;
|
|
/*Transform the columns.
|
|
We can ignore zero columns without a problem.*/
|
|
in=w;
|
|
out=_y;
|
|
if(cext==NULL)for(ci=0;ci<8;ci++)oc_fdct8(out+(ci<<3),in+ci);
|
|
else for(ci=0;ci<8;ci++)if(rmask&(1<<ci))oc_fdct8_ext(out+(ci<<3),in+ci,cext);
|
|
/*Transform the rows.
|
|
We transform even rows that are supposedly zero, because rounding errors
|
|
may make them slightly non-zero, and this will give a more precise
|
|
reconstruction with very small quantizers.*/
|
|
in=_y;
|
|
out=w;
|
|
if(rext==NULL)for(ri=0;ri<8;ri++)oc_fdct8(out+(ri<<3),in+ri);
|
|
else for(ri=0;ri<8;ri++)oc_fdct8_ext(out+(ri<<3),in+ri,rext);
|
|
/*Round the result back to the external working precision (which is still
|
|
scaled by four relative to the orthogonal result).
|
|
TODO: We should just update the external working precision.*/
|
|
for(ci=0;ci<64;ci++)_y[ci]=w[ci]+2>>2;
|
|
}
|
|
#endif
|