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/*


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* jfdctint.c

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*

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* Copyright (C) 19911996, Thomas G. Lane.

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* This file is part of the Independent JPEG Group's software.

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* For conditions of distribution and use, see the accompanying README file.

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*

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* This file contains a slowbutaccurate integer implementation of the

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* forward DCT (Discrete Cosine Transform).

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*

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* A 2D DCT can be done by 1D DCT on each row followed by 1D DCT

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* on each column. Direct algorithms are also available, but they are

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* much more complex and seem not to be any faster when reduced to code.

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*

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* This implementation is based on an algorithm described in

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* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1D DCT

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* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,

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* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988991.

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* The primary algorithm described there uses 11 multiplies and 29 adds.

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* We use their alternate method with 12 multiplies and 32 adds.

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* The advantage of this method is that no data path contains more than one

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* multiplication; this allows a very simple and accurate implementation in

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* scaled fixedpoint arithmetic, with a minimal number of shifts.

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*/

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/**

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* @file jfdctint.c

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* Independent JPEG Group's slow & accurate dct.

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*/

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#include <stdlib.h> 
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#include <stdio.h> 
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#include "common.h" 
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#include "dsputil.h" 
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#define SHIFT_TEMPS

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#define DCTSIZE 8 
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#define BITS_IN_JSAMPLE 8 
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#define GLOBAL(x) x

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#define RIGHT_SHIFT(x, n) ((x) >> (n))

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#define MULTIPLY16C16(var,const) ((var)*(const)) 
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#if 1 //def USE_ACCURATE_ROUNDING 
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#define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n)  1)), n) 
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#else

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#define DESCALE(x,n) RIGHT_SHIFT(x, n)

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#endif

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/*

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* This module is specialized to the case DCTSIZE = 8.

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*/

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#if DCTSIZE != 8 
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 
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#endif

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/*

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* The poop on this scaling stuff is as follows:

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*

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* Each 1D DCT step produces outputs which are a factor of sqrt(N)

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* larger than the true DCT outputs. The final outputs are therefore

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* a factor of N larger than desired; since N=8 this can be cured by

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* a simple right shift at the end of the algorithm. The advantage of

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* this arrangement is that we save two multiplications per 1D DCT,

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* because the y0 and y4 outputs need not be divided by sqrt(N).

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* In the IJG code, this factor of 8 is removed by the quantization step

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* (in jcdctmgr.c), NOT in this module.

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*

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* We have to do addition and subtraction of the integer inputs, which

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* is no problem, and multiplication by fractional constants, which is

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* a problem to do in integer arithmetic. We multiply all the constants

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* by CONST_SCALE and convert them to integer constants (thus retaining

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* CONST_BITS bits of precision in the constants). After doing a

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* multiplication we have to divide the product by CONST_SCALE, with proper

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* rounding, to produce the correct output. This division can be done

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* cheaply as a right shift of CONST_BITS bits. We postpone shifting

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* as long as possible so that partial sums can be added together with

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* full fractional precision.

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*

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* The outputs of the first pass are scaled up by PASS1_BITS bits so that

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* they are represented to betterthanintegral precision. These outputs

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* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16bit word

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* with the recommended scaling. (For 12bit sample data, the intermediate

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* array is int32_t anyway.)

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*

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* To avoid overflow of the 32bit intermediate results in pass 2, we must

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* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis

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* shows that the values given below are the most effective.

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*/

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#if BITS_IN_JSAMPLE == 8 
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#define CONST_BITS 13 
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#define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */ 
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#else

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#define CONST_BITS 13 
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#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 
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#endif

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/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus

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* causing a lot of useless floatingpoint operations at run time.

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* To get around this we use the following precalculated constants.

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* If you change CONST_BITS you may want to add appropriate values.

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* (With a reasonable C compiler, you can just rely on the FIX() macro...)

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*/

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#if CONST_BITS == 13 
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#define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */ 
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#define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */ 
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#define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */ 
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#define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */ 
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#define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */ 
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#define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */ 
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#define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */ 
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#define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */ 
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#define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */ 
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#define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */ 
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#define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */ 
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#define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */ 
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#else

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#define FIX_0_298631336 FIX(0.298631336) 
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#define FIX_0_390180644 FIX(0.390180644) 
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#define FIX_0_541196100 FIX(0.541196100) 
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#define FIX_0_765366865 FIX(0.765366865) 
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#define FIX_0_899976223 FIX(0.899976223) 
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#define FIX_1_175875602 FIX(1.175875602) 
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#define FIX_1_501321110 FIX(1.501321110) 
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#define FIX_1_847759065 FIX(1.847759065) 
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#define FIX_1_961570560 FIX(1.961570560) 
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#define FIX_2_053119869 FIX(2.053119869) 
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#define FIX_2_562915447 FIX(2.562915447) 
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#define FIX_3_072711026 FIX(3.072711026) 
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#endif

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/* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.

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* For 8bit samples with the recommended scaling, all the variable

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* and constant values involved are no more than 16 bits wide, so a

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* 16x16>32 bit multiply can be used instead of a full 32x32 multiply.

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* For 12bit samples, a full 32bit multiplication will be needed.

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*/

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#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2 
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#define MULTIPLY(var,const) MULTIPLY16C16(var,const) 
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#else

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#define MULTIPLY(var,const) ((var) * (const)) 
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#endif

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static always_inline void row_fdct(DCTELEM * data){ 
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int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
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int_fast32_t tmp10, tmp11, tmp12, tmp13; 
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int_fast32_t z1, z2, z3, z4, z5; 
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DCTELEM *dataptr; 
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int ctr;

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SHIFT_TEMPS 
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/* Pass 1: process rows. */

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/* Note results are scaled up by sqrt(8) compared to a true DCT; */

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/* furthermore, we scale the results by 2**PASS1_BITS. */

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dataptr = data; 
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for (ctr = DCTSIZE1; ctr >= 0; ctr) { 
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tmp0 = dataptr[0] + dataptr[7]; 
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tmp7 = dataptr[0]  dataptr[7]; 
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tmp1 = dataptr[1] + dataptr[6]; 
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tmp6 = dataptr[1]  dataptr[6]; 
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tmp2 = dataptr[2] + dataptr[5]; 
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tmp5 = dataptr[2]  dataptr[5]; 
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tmp3 = dataptr[3] + dataptr[4]; 
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tmp4 = dataptr[3]  dataptr[4]; 
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/* Even part per LL&M figure 1  note that published figure is faulty;

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* rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

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*/

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tmp10 = tmp0 + tmp3; 
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tmp13 = tmp0  tmp3; 
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tmp11 = tmp1 + tmp2; 
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tmp12 = tmp1  tmp2; 
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dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);

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dataptr[4] = (DCTELEM) ((tmp10  tmp11) << PASS1_BITS);

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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
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dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

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CONST_BITSPASS1_BITS); 
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dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12,  FIX_1_847759065),

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CONST_BITSPASS1_BITS); 
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/* Odd part per figure 8  note paper omits factor of sqrt(2).

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* cK represents cos(K*pi/16).

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* i0..i3 in the paper are tmp4..tmp7 here.

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*/

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z1 = tmp4 + tmp7; 
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z2 = tmp5 + tmp6; 
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z3 = tmp4 + tmp6; 
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z4 = tmp5 + tmp7; 
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z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

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tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (c1+c3+c5c7) */

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tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3c5+c7) */

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tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5c7) */

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tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3c5c7) */

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z1 = MULTIPLY(z1,  FIX_0_899976223); /* sqrt(2) * (c7c3) */

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z2 = MULTIPLY(z2,  FIX_2_562915447); /* sqrt(2) * (c1c3) */

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z3 = MULTIPLY(z3,  FIX_1_961570560); /* sqrt(2) * (c3c5) */

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z4 = MULTIPLY(z4,  FIX_0_390180644); /* sqrt(2) * (c5c3) */

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z3 += z5; 
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z4 += z5; 
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dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITSPASS1_BITS);

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dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITSPASS1_BITS);

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dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITSPASS1_BITS);

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dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITSPASS1_BITS);

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dataptr += DCTSIZE; /* advance pointer to next row */

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} 
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} 
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/*

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* Perform the forward DCT on one block of samples.

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*/

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GLOBAL(void)

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ff_jpeg_fdct_islow (DCTELEM * data) 
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{ 
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int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
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int_fast32_t tmp10, tmp11, tmp12, tmp13; 
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int_fast32_t z1, z2, z3, z4, z5; 
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DCTELEM *dataptr; 
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int ctr;

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SHIFT_TEMPS 
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row_fdct(data); 
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/* Pass 2: process columns.

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* We remove the PASS1_BITS scaling, but leave the results scaled up

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* by an overall factor of 8.

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*/

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dataptr = data; 
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for (ctr = DCTSIZE1; ctr >= 0; ctr) { 
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tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 
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tmp7 = dataptr[DCTSIZE*0]  dataptr[DCTSIZE*7]; 
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tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 
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tmp6 = dataptr[DCTSIZE*1]  dataptr[DCTSIZE*6]; 
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tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 
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tmp5 = dataptr[DCTSIZE*2]  dataptr[DCTSIZE*5]; 
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tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 
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tmp4 = dataptr[DCTSIZE*3]  dataptr[DCTSIZE*4]; 
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/* Even part per LL&M figure 1  note that published figure is faulty;

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* rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

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*/

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tmp10 = tmp0 + tmp3; 
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tmp13 = tmp0  tmp3; 
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tmp11 = tmp1 + tmp2; 
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tmp12 = tmp1  tmp2; 
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dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

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dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10  tmp11, PASS1_BITS);

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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
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dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12,  FIX_1_847759065),

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CONST_BITS+PASS1_BITS); 
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/* Odd part per figure 8  note paper omits factor of sqrt(2).

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* cK represents cos(K*pi/16).

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* i0..i3 in the paper are tmp4..tmp7 here.

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*/

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z1 = tmp4 + tmp7; 
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z2 = tmp5 + tmp6; 
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z3 = tmp4 + tmp6; 
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z4 = tmp5 + tmp7; 
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z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

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tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (c1+c3+c5c7) */

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tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3c5+c7) */

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tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5c7) */

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tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3c5c7) */

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z1 = MULTIPLY(z1,  FIX_0_899976223); /* sqrt(2) * (c7c3) */

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z2 = MULTIPLY(z2,  FIX_2_562915447); /* sqrt(2) * (c1c3) */

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z3 = MULTIPLY(z3,  FIX_1_961570560); /* sqrt(2) * (c3c5) */

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z4 = MULTIPLY(z4,  FIX_0_390180644); /* sqrt(2) * (c5c3) */

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z3 += z5; 
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z4 += z5; 
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dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,

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CONST_BITS+PASS1_BITS); 
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dataptr++; /* advance pointer to next column */

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} 
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} 
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/*

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* The secret of DCT248 is really simple  you do the usual 1DCT

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* on the rows and then, instead of doing even and odd, part on the colums

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* you do even part two times.

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*/

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GLOBAL(void)

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ff_fdct248_islow (DCTELEM * data) 
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{ 
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int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
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int_fast32_t tmp10, tmp11, tmp12, tmp13; 
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int_fast32_t z1; 
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DCTELEM *dataptr; 
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int ctr;

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SHIFT_TEMPS 
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row_fdct(data); 
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/* Pass 2: process columns.

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* We remove the PASS1_BITS scaling, but leave the results scaled up

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* by an overall factor of 8.

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*/

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dataptr = data; 
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for (ctr = DCTSIZE1; ctr >= 0; ctr) { 
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tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1]; 
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tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3]; 
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tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5]; 
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tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7]; 
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tmp4 = dataptr[DCTSIZE*0]  dataptr[DCTSIZE*1]; 
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tmp5 = dataptr[DCTSIZE*2]  dataptr[DCTSIZE*3]; 
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tmp6 = dataptr[DCTSIZE*4]  dataptr[DCTSIZE*5]; 
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tmp7 = dataptr[DCTSIZE*6]  dataptr[DCTSIZE*7]; 
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tmp10 = tmp0 + tmp3; 
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tmp11 = tmp1 + tmp2; 
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tmp12 = tmp1  tmp2; 
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tmp13 = tmp0  tmp3; 
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dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

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dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10  tmp11, PASS1_BITS);

350 

351 
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
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dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12,  FIX_1_847759065),

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CONST_BITS+PASS1_BITS); 
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tmp10 = tmp4 + tmp7; 
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tmp11 = tmp5 + tmp6; 
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tmp12 = tmp5  tmp6; 
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tmp13 = tmp4  tmp7; 
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dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

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dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10  tmp11, PASS1_BITS);

364 

365 
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
366 
dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

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CONST_BITS+PASS1_BITS); 
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dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12,  FIX_1_847759065),

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CONST_BITS+PASS1_BITS); 
370 

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dataptr++; /* advance pointer to next column */

372 
} 
373 
} 