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+/********************************************************************
+ * *
+ * THIS FILE IS PART OF THE OggTheora SOFTWARE CODEC SOURCE CODE. *
+ * USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS *
+ * GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
+ * IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. *
+ * *
+ * THE Theora SOURCE CODE IS COPYRIGHT (C) 2002-2009 *
+ * by the Xiph.Org Foundation and contributors http://www.xiph.org/ *
+ * *
+ ********************************************************************
+
+ function:
+ last mod: $Id: idct.c 17410 2010-09-21 21:53:48Z tterribe $
+
+ ********************************************************************/
+
+#include <string.h>
+#include "internal.h"
+#include "dct.h"
+
+/*Performs an inverse 8 point Type-II DCT transform.
+ The output is scaled by a factor of 2 relative to the orthonormal version of
+ the transform.
+ _y: The buffer to store the result in.
+ Data will be placed in every 8th entry (e.g., in a column of an 8x8
+ block).
+ _x: The input coefficients.
+ The first 8 entries are used (e.g., from a row of an 8x8 block).*/
+static void idct8(ogg_int16_t *_y,const ogg_int16_t _x[8]){
+ ogg_int32_t t[8];
+ ogg_int32_t r;
+ /*Stage 1:*/
+ /*0-1 butterfly.*/
+ t[0]=OC_C4S4*(ogg_int16_t)(_x[0]+_x[4])>>16;
+ t[1]=OC_C4S4*(ogg_int16_t)(_x[0]-_x[4])>>16;
+ /*2-3 rotation by 6pi/16.*/
+ t[2]=(OC_C6S2*_x[2]>>16)-(OC_C2S6*_x[6]>>16);
+ t[3]=(OC_C2S6*_x[2]>>16)+(OC_C6S2*_x[6]>>16);
+ /*4-7 rotation by 7pi/16.*/
+ t[4]=(OC_C7S1*_x[1]>>16)-(OC_C1S7*_x[7]>>16);
+ /*5-6 rotation by 3pi/16.*/
+ t[5]=(OC_C3S5*_x[5]>>16)-(OC_C5S3*_x[3]>>16);
+ t[6]=(OC_C5S3*_x[5]>>16)+(OC_C3S5*_x[3]>>16);
+ t[7]=(OC_C1S7*_x[1]>>16)+(OC_C7S1*_x[7]>>16);
+ /*Stage 2:*/
+ /*4-5 butterfly.*/
+ r=t[4]+t[5];
+ t[5]=OC_C4S4*(ogg_int16_t)(t[4]-t[5])>>16;
+ t[4]=r;
+ /*7-6 butterfly.*/
+ r=t[7]+t[6];
+ t[6]=OC_C4S4*(ogg_int16_t)(t[7]-t[6])>>16;
+ t[7]=r;
+ /*Stage 3:*/
+ /*0-3 butterfly.*/
+ r=t[0]+t[3];
+ t[3]=t[0]-t[3];
+ t[0]=r;
+ /*1-2 butterfly.*/
+ r=t[1]+t[2];
+ t[2]=t[1]-t[2];
+ t[1]=r;
+ /*6-5 butterfly.*/
+ r=t[6]+t[5];
+ t[5]=t[6]-t[5];
+ t[6]=r;
+ /*Stage 4:*/
+ /*0-7 butterfly.*/
+ _y[0<<3]=(ogg_int16_t)(t[0]+t[7]);
+ /*1-6 butterfly.*/
+ _y[1<<3]=(ogg_int16_t)(t[1]+t[6]);
+ /*2-5 butterfly.*/
+ _y[2<<3]=(ogg_int16_t)(t[2]+t[5]);
+ /*3-4 butterfly.*/
+ _y[3<<3]=(ogg_int16_t)(t[3]+t[4]);
+ _y[4<<3]=(ogg_int16_t)(t[3]-t[4]);
+ _y[5<<3]=(ogg_int16_t)(t[2]-t[5]);
+ _y[6<<3]=(ogg_int16_t)(t[1]-t[6]);
+ _y[7<<3]=(ogg_int16_t)(t[0]-t[7]);
+}
+
+/*Performs an inverse 8 point Type-II DCT transform.
+ The output is scaled by a factor of 2 relative to the orthonormal version of
+ the transform.
+ _y: The buffer to store the result in.
+ Data will be placed in every 8th entry (e.g., in a column of an 8x8
+ block).
+ _x: The input coefficients.
+ Only the first 4 entries are used.
+ The other 4 are assumed to be 0.*/
+static void idct8_4(ogg_int16_t *_y,const ogg_int16_t _x[8]){
+ ogg_int32_t t[8];
+ ogg_int32_t r;
+ /*Stage 1:*/
+ t[0]=OC_C4S4*_x[0]>>16;
+ t[2]=OC_C6S2*_x[2]>>16;
+ t[3]=OC_C2S6*_x[2]>>16;
+ t[4]=OC_C7S1*_x[1]>>16;
+ t[5]=-(OC_C5S3*_x[3]>>16);
+ t[6]=OC_C3S5*_x[3]>>16;
+ t[7]=OC_C1S7*_x[1]>>16;
+ /*Stage 2:*/
+ r=t[4]+t[5];
+ t[5]=OC_C4S4*(ogg_int16_t)(t[4]-t[5])>>16;
+ t[4]=r;
+ r=t[7]+t[6];
+ t[6]=OC_C4S4*(ogg_int16_t)(t[7]-t[6])>>16;
+ t[7]=r;
+ /*Stage 3:*/
+ t[1]=t[0]+t[2];
+ t[2]=t[0]-t[2];
+ r=t[0]+t[3];
+ t[3]=t[0]-t[3];
+ t[0]=r;
+ r=t[6]+t[5];
+ t[5]=t[6]-t[5];
+ t[6]=r;
+ /*Stage 4:*/
+ _y[0<<3]=(ogg_int16_t)(t[0]+t[7]);
+ _y[1<<3]=(ogg_int16_t)(t[1]+t[6]);
+ _y[2<<3]=(ogg_int16_t)(t[2]+t[5]);
+ _y[3<<3]=(ogg_int16_t)(t[3]+t[4]);
+ _y[4<<3]=(ogg_int16_t)(t[3]-t[4]);
+ _y[5<<3]=(ogg_int16_t)(t[2]-t[5]);
+ _y[6<<3]=(ogg_int16_t)(t[1]-t[6]);
+ _y[7<<3]=(ogg_int16_t)(t[0]-t[7]);
+}
+
+/*Performs an inverse 8 point Type-II DCT transform.
+ The output is scaled by a factor of 2 relative to the orthonormal version of
+ the transform.
+ _y: The buffer to store the result in.
+ Data will be placed in every 8th entry (e.g., in a column of an 8x8
+ block).
+ _x: The input coefficients.
+ Only the first 3 entries are used.
+ The other 5 are assumed to be 0.*/
+static void idct8_3(ogg_int16_t *_y,const ogg_int16_t _x[8]){
+ ogg_int32_t t[8];
+ ogg_int32_t r;
+ /*Stage 1:*/
+ t[0]=OC_C4S4*_x[0]>>16;
+ t[2]=OC_C6S2*_x[2]>>16;
+ t[3]=OC_C2S6*_x[2]>>16;
+ t[4]=OC_C7S1*_x[1]>>16;
+ t[7]=OC_C1S7*_x[1]>>16;
+ /*Stage 2:*/
+ t[5]=OC_C4S4*t[4]>>16;
+ t[6]=OC_C4S4*t[7]>>16;
+ /*Stage 3:*/
+ t[1]=t[0]+t[2];
+ t[2]=t[0]-t[2];
+ r=t[0]+t[3];
+ t[3]=t[0]-t[3];
+ t[0]=r;
+ r=t[6]+t[5];
+ t[5]=t[6]-t[5];
+ t[6]=r;
+ /*Stage 4:*/
+ _y[0<<3]=(ogg_int16_t)(t[0]+t[7]);
+ _y[1<<3]=(ogg_int16_t)(t[1]+t[6]);
+ _y[2<<3]=(ogg_int16_t)(t[2]+t[5]);
+ _y[3<<3]=(ogg_int16_t)(t[3]+t[4]);
+ _y[4<<3]=(ogg_int16_t)(t[3]-t[4]);
+ _y[5<<3]=(ogg_int16_t)(t[2]-t[5]);
+ _y[6<<3]=(ogg_int16_t)(t[1]-t[6]);
+ _y[7<<3]=(ogg_int16_t)(t[0]-t[7]);
+}
+
+/*Performs an inverse 8 point Type-II DCT transform.
+ The output is scaled by a factor of 2 relative to the orthonormal version of
+ the transform.
+ _y: The buffer to store the result in.
+ Data will be placed in every 8th entry (e.g., in a column of an 8x8
+ block).
+ _x: The input coefficients.
+ Only the first 2 entries are used.
+ The other 6 are assumed to be 0.*/
+static void idct8_2(ogg_int16_t *_y,const ogg_int16_t _x[8]){
+ ogg_int32_t t[8];
+ ogg_int32_t r;
+ /*Stage 1:*/
+ t[0]=OC_C4S4*_x[0]>>16;
+ t[4]=OC_C7S1*_x[1]>>16;
+ t[7]=OC_C1S7*_x[1]>>16;
+ /*Stage 2:*/
+ t[5]=OC_C4S4*t[4]>>16;
+ t[6]=OC_C4S4*t[7]>>16;
+ /*Stage 3:*/
+ r=t[6]+t[5];
+ t[5]=t[6]-t[5];
+ t[6]=r;
+ /*Stage 4:*/
+ _y[0<<3]=(ogg_int16_t)(t[0]+t[7]);
+ _y[1<<3]=(ogg_int16_t)(t[0]+t[6]);
+ _y[2<<3]=(ogg_int16_t)(t[0]+t[5]);
+ _y[3<<3]=(ogg_int16_t)(t[0]+t[4]);
+ _y[4<<3]=(ogg_int16_t)(t[0]-t[4]);
+ _y[5<<3]=(ogg_int16_t)(t[0]-t[5]);
+ _y[6<<3]=(ogg_int16_t)(t[0]-t[6]);
+ _y[7<<3]=(ogg_int16_t)(t[0]-t[7]);
+}
+
+/*Performs an inverse 8 point Type-II DCT transform.
+ The output is scaled by a factor of 2 relative to the orthonormal version of
+ the transform.
+ _y: The buffer to store the result in.
+ Data will be placed in every 8th entry (e.g., in a column of an 8x8
+ block).
+ _x: The input coefficients.
+ Only the first entry is used.
+ The other 7 are assumed to be 0.*/
+static void idct8_1(ogg_int16_t *_y,const ogg_int16_t _x[1]){
+ _y[0<<3]=_y[1<<3]=_y[2<<3]=_y[3<<3]=
+ _y[4<<3]=_y[5<<3]=_y[6<<3]=_y[7<<3]=(ogg_int16_t)(OC_C4S4*_x[0]>>16);
+}
+
+/*Performs an inverse 8x8 Type-II DCT transform.
+ The input is assumed to be scaled by a factor of 4 relative to orthonormal
+ version of the transform.
+ All coefficients but the first 3 in zig-zag scan order are assumed to be 0:
+ x x 0 0 0 0 0 0
+ x 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ _y: The buffer to store the result in.
+ This may be the same as _x.
+ _x: The input coefficients.*/
+static void oc_idct8x8_3(ogg_int16_t _y[64],ogg_int16_t _x[64]){
+ ogg_int16_t w[64];
+ int i;
+ /*Transform rows of x into columns of w.*/
+ idct8_2(w,_x);
+ idct8_1(w+1,_x+8);
+ /*Transform rows of w into columns of y.*/
+ for(i=0;i<8;i++)idct8_2(_y+i,w+i*8);
+ /*Adjust for the scale factor.*/
+ for(i=0;i<64;i++)_y[i]=(ogg_int16_t)(_y[i]+8>>4);
+ /*Clear input data for next block (decoder only).*/
+ if(_x!=_y)_x[0]=_x[1]=_x[8]=0;
+}
+
+/*Performs an inverse 8x8 Type-II DCT transform.
+ The input is assumed to be scaled by a factor of 4 relative to orthonormal
+ version of the transform.
+ All coefficients but the first 10 in zig-zag scan order are assumed to be 0:
+ x x x x 0 0 0 0
+ x x x 0 0 0 0 0
+ x x 0 0 0 0 0 0
+ x 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ _y: The buffer to store the result in.
+ This may be the same as _x.
+ _x: The input coefficients.*/
+static void oc_idct8x8_10(ogg_int16_t _y[64],ogg_int16_t _x[64]){
+ ogg_int16_t w[64];
+ int i;
+ /*Transform rows of x into columns of w.*/
+ idct8_4(w,_x);
+ idct8_3(w+1,_x+8);
+ idct8_2(w+2,_x+16);
+ idct8_1(w+3,_x+24);
+ /*Transform rows of w into columns of y.*/
+ for(i=0;i<8;i++)idct8_4(_y+i,w+i*8);
+ /*Adjust for the scale factor.*/
+ for(i=0;i<64;i++)_y[i]=(ogg_int16_t)(_y[i]+8>>4);
+ /*Clear input data for next block (decoder only).*/
+ if(_x!=_y)_x[0]=_x[1]=_x[2]=_x[3]=_x[8]=_x[9]=_x[10]=_x[16]=_x[17]=_x[24]=0;
+}
+
+/*Performs an inverse 8x8 Type-II DCT transform.
+ The input is assumed to be scaled by a factor of 4 relative to orthonormal
+ version of the transform.
+ _y: The buffer to store the result in.
+ This may be the same as _x.
+ _x: The input coefficients.*/
+static void oc_idct8x8_slow(ogg_int16_t _y[64],ogg_int16_t _x[64]){
+ ogg_int16_t w[64];
+ int i;
+ /*Transform rows of x into columns of w.*/
+ for(i=0;i<8;i++)idct8(w+i,_x+i*8);
+ /*Transform rows of w into columns of y.*/
+ for(i=0;i<8;i++)idct8(_y+i,w+i*8);
+ /*Adjust for the scale factor.*/
+ for(i=0;i<64;i++)_y[i]=(ogg_int16_t)(_y[i]+8>>4);
+ if(_x!=_y)for(i=0;i<64;i++)_x[i]=0;
+}
+
+/*Performs an inverse 8x8 Type-II DCT transform.
+ The input is assumed to be scaled by a factor of 4 relative to orthonormal
+ version of the transform.*/
+void oc_idct8x8_c(ogg_int16_t _y[64],ogg_int16_t _x[64],int _last_zzi){
+ /*_last_zzi is subtly different from an actual count of the number of
+ coefficients we decoded for this block.
+ It contains the value of zzi BEFORE the final token in the block was
+ decoded.
+ In most cases this is an EOB token (the continuation of an EOB run from a
+ previous block counts), and so this is the same as the coefficient count.
+ However, in the case that the last token was NOT an EOB token, but filled
+ the block up with exactly 64 coefficients, _last_zzi will be less than 64.
+ Provided the last token was not a pure zero run, the minimum value it can
+ be is 46, and so that doesn't affect any of the cases in this routine.
+ However, if the last token WAS a pure zero run of length 63, then _last_zzi
+ will be 1 while the number of coefficients decoded is 64.
+ Thus, we will trigger the following special case, where the real
+ coefficient count would not.
+ Note also that a zero run of length 64 will give _last_zzi a value of 0,
+ but we still process the DC coefficient, which might have a non-zero value
+ due to DC prediction.
+ Although convoluted, this is arguably the correct behavior: it allows us to
+ use a smaller transform when the block ends with a long zero run instead
+ of a normal EOB token.
+ It could be smarter... multiple separate zero runs at the end of a block
+ will fool it, but an encoder that generates these really deserves what it
+ gets.
+ Needless to say we inherited this approach from VP3.*/
+ /*Then perform the iDCT.*/
+ if(_last_zzi<=3)oc_idct8x8_3(_y,_x);
+ else if(_last_zzi<=10)oc_idct8x8_10(_y,_x);
+ else oc_idct8x8_slow(_y,_x);
+}
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