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/*


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* jfdctfst.c

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*

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* Copyright (C) 19941996, 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 fast, not so accurate 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 Arai, Agui, and Nakajima's algorithm for

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* scaled DCT. Their original paper (Trans. IEICE E71(11):1095) is in

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* Japanese, but the algorithm is described in the Pennebaker & Mitchell

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* JPEG textbook (see REFERENCES section in file README). The following code

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* is based directly on figure 48 in P&M.

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* While an 8point DCT cannot be done in less than 11 multiplies, it is

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* possible to arrange the computation so that many of the multiplies are

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* simple scalings of the final outputs. These multiplies can then be

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* folded into the multiplications or divisions by the JPEG quantization

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* table entries. The AA&N method leaves only 5 multiplies and 29 adds

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* to be done in the DCT itself.

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* The primary disadvantage of this method is that with fixedpoint math,

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* accuracy is lost due to imprecise representation of the scaled

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* quantization values. The smaller the quantization table entry, the less

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* precise the scaled value, so this implementation does worse with high

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* qualitysetting files than with lowquality ones.

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*/

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/**

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* @file jfdctfst.c

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* Independent JPEG Group's fast AAN 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 DCTSIZE 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 SHIFT_TEMPS

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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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/* Scaling decisions are generally the same as in the LL&M algorithm;

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* see jfdctint.c for more details. However, we choose to descale

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* (right shift) multiplication products as soon as they are formed,

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* rather than carrying additional fractional bits into subsequent additions.

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* This compromises accuracy slightly, but it lets us save a few shifts.

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* More importantly, 16bit arithmetic is then adequate (for 8bit samples)

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* everywhere except in the multiplications proper; this saves a good deal

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* of work on 16bitint machines.

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*

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* Again to save a few shifts, the intermediate results between pass 1 and

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* pass 2 are not upscaled, but are represented only to integral precision.

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*

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* A final compromise is to represent the multiplicative constants to only

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* 8 fractional bits, rather than 13. This saves some shifting work on some

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* machines, and may also reduce the cost of multiplication (since there

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* are fewer onebits in the constants).

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*/

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#define CONST_BITS 8 
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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 == 8 
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#define FIX_0_382683433 ((int32_t) 98) /* FIX(0.382683433) */ 
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#define FIX_0_541196100 ((int32_t) 139) /* FIX(0.541196100) */ 
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#define FIX_0_707106781 ((int32_t) 181) /* FIX(0.707106781) */ 
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#define FIX_1_306562965 ((int32_t) 334) /* FIX(1.306562965) */ 
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#else

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#define FIX_0_382683433 FIX(0.382683433) 
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#define FIX_0_541196100 FIX(0.541196100) 
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#define FIX_0_707106781 FIX(0.707106781) 
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#define FIX_1_306562965 FIX(1.306562965) 
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#endif

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/* We can gain a little more speed, with a further compromise in accuracy,

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* by omitting the addition in a descaling shift. This yields an incorrectly

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* rounded result half the time...

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*/

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#ifndef USE_ACCURATE_ROUNDING

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#undef DESCALE

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

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#endif

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/* Multiply a DCTELEM variable by an int32_t constant, and immediately

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* descale to yield a DCTELEM result.

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*/

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#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 
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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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fdct_ifast (DCTELEM * data) 
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{ 
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DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
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DCTELEM tmp10, tmp11, tmp12, tmp13; 
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DCTELEM z1, z2, z3, z4, z5, z11, z13; 
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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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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 */

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tmp10 = tmp0 + tmp3; /* phase 2 */

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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] = tmp10 + tmp11; /* phase 3 */ 
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dataptr[4] = tmp10  tmp11;

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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

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dataptr[2] = tmp13 + z1; /* phase 5 */ 
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dataptr[6] = tmp13  z1;

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/* Odd part */

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tmp10 = tmp4 + tmp5; /* phase 2 */

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tmp11 = tmp5 + tmp6; 
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tmp12 = tmp6 + tmp7; 
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/* The rotator is modified from fig 48 to avoid extra negations. */

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z5 = MULTIPLY(tmp10  tmp12, FIX_0_382683433); /* c6 */

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z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2c6 */

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z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

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z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

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z11 = tmp7 + z3; /* phase 5 */

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z13 = tmp7  z3; 
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dataptr[5] = z13 + z2; /* phase 6 */ 
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dataptr[3] = z13  z2;

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dataptr[1] = z11 + z4;

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dataptr[7] = z11  z4;

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

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} 
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/* Pass 2: process columns. */

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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 */

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tmp10 = tmp0 + tmp3; /* phase 2 */

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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] = tmp10 + tmp11; /* phase 3 */ 
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dataptr[DCTSIZE*4] = tmp10  tmp11;

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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

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dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 
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dataptr[DCTSIZE*6] = tmp13  z1;

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/* Odd part */

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tmp10 = tmp4 + tmp5; /* phase 2 */

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tmp11 = tmp5 + tmp6; 
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tmp12 = tmp6 + tmp7; 
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/* The rotator is modified from fig 48 to avoid extra negations. */

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z5 = MULTIPLY(tmp10  tmp12, FIX_0_382683433); /* c6 */

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z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2c6 */

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z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

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z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

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z11 = tmp7 + z3; /* phase 5 */

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z13 = tmp7  z3; 
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dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 
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dataptr[DCTSIZE*3] = z13  z2;

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dataptr[DCTSIZE*1] = z11 + z4;

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dataptr[DCTSIZE*7] = z11  z4;

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

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} 
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} 
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#undef GLOBAL

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#undef CONST_BITS

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#undef DESCALE

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#undef FIX_0_541196100

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#undef FIX_1_306562965
