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/*
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* jidctflt.c
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*
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* This file was part of the Independent JPEG Group's software:
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* Copyright (C) 1994-1998, Thomas G. Lane.
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* Modified 2010 by Guido Vollbeding.
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* libjpeg-turbo Modifications:
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* Copyright (C) 2014, D. R. Commander.
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* For conditions of distribution and use, see the accompanying README.ijg
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* file.
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*
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* This file contains a floating-point implementation of the
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* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
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* must also perform dequantization of the input coefficients.
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*
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* This implementation should be more accurate than either of the integer
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* IDCT implementations. However, it may not give the same results on all
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* machines because of differences in roundoff behavior. Speed will depend
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* on the hardware's floating point capacity.
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*
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* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
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* on each row (or vice versa, but it's more convenient to emit a row at
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* a time). Direct algorithms are also available, but they are much more
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* 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 E-71(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.ijg). The following
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* code is based directly on figure 4-8 in P&M.
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* While an 8-point 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 a fixed-point
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* implementation, accuracy is lost due to imprecise representation of the
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* scaled quantization values. However, that problem does not arise if
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* we use floating point arithmetic.
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*/
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#define JPEG_INTERNALS
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#include "jinclude.h"
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#include "jpeglib.h"
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef DCT_FLOAT_SUPPORTED
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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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/* Dequantize a coefficient by multiplying it by the multiplier-table
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* entry; produce a float result.
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*/
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#define DEQUANTIZE(coef, quantval) (((FAST_FLOAT)(coef)) * (quantval))
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/*
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* Perform dequantization and inverse DCT on one block of coefficients.
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*/
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GLOBAL(void)
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jpeg_idct_float(j_decompress_ptr cinfo, jpeg_component_info *compptr,
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JCOEFPTR coef_block, JSAMPARRAY output_buf,
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JDIMENSION output_col)
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{
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FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
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FAST_FLOAT z5, z10, z11, z12, z13;
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JCOEFPTR inptr;
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FLOAT_MULT_TYPE *quantptr;
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FAST_FLOAT *wsptr;
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JSAMPROW outptr;
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JSAMPLE *range_limit = cinfo->sample_range_limit;
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int ctr;
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FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
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#define _0_125 ((FLOAT_MULT_TYPE)0.125)
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/* Pass 1: process columns from input, store into work array. */
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inptr = coef_block;
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quantptr = (FLOAT_MULT_TYPE *)compptr->dct_table;
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wsptr = workspace;
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for (ctr = DCTSIZE; ctr > 0; ctr--) {
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/* Due to quantization, we will usually find that many of the input
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* coefficients are zero, especially the AC terms. We can exploit this
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* by short-circuiting the IDCT calculation for any column in which all
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* the AC terms are zero. In that case each output is equal to the
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* DC coefficient (with scale factor as needed).
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* With typical images and quantization tables, half or more of the
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* column DCT calculations can be simplified this way.
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*/
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if (inptr[DCTSIZE * 1] == 0 && inptr[DCTSIZE * 2] == 0 &&
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inptr[DCTSIZE * 3] == 0 && inptr[DCTSIZE * 4] == 0 &&
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inptr[DCTSIZE * 5] == 0 && inptr[DCTSIZE * 6] == 0 &&
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inptr[DCTSIZE * 7] == 0) {
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/* AC terms all zero */
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FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE * 0],
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quantptr[DCTSIZE * 0] * _0_125);
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wsptr[DCTSIZE * 0] = dcval;
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wsptr[DCTSIZE * 1] = dcval;
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wsptr[DCTSIZE * 2] = dcval;
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wsptr[DCTSIZE * 3] = dcval;
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wsptr[DCTSIZE * 4] = dcval;
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wsptr[DCTSIZE * 5] = dcval;
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wsptr[DCTSIZE * 6] = dcval;
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wsptr[DCTSIZE * 7] = dcval;
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inptr++; /* advance pointers to next column */
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quantptr++;
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wsptr++;
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continue;
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}
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/* Even part */
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tmp0 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] * _0_125);
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tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] * _0_125);
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tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] * _0_125);
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tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] * _0_125);
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tmp10 = tmp0 + tmp2; /* phase 3 */
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tmp11 = tmp0 - tmp2;
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tmp13 = tmp1 + tmp3; /* phases 5-3 */
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tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT)1.414213562) - tmp13; /* 2*c4 */
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tmp0 = tmp10 + tmp13; /* phase 2 */
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tmp3 = tmp10 - tmp13;
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tmp1 = tmp11 + tmp12;
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tmp2 = tmp11 - tmp12;
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/* Odd part */
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tmp4 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] * _0_125);
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tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] * _0_125);
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tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] * _0_125);
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tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] * _0_125);
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z13 = tmp6 + tmp5; /* phase 6 */
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z10 = tmp6 - tmp5;
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z11 = tmp4 + tmp7;
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z12 = tmp4 - tmp7;
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tmp7 = z11 + z13; /* phase 5 */
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tmp11 = (z11 - z13) * ((FAST_FLOAT)1.414213562); /* 2*c4 */
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z5 = (z10 + z12) * ((FAST_FLOAT)1.847759065); /* 2*c2 */
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tmp10 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */
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tmp12 = z5 - z10 * ((FAST_FLOAT)2.613125930); /* 2*(c2+c6) */
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tmp6 = tmp12 - tmp7; /* phase 2 */
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tmp5 = tmp11 - tmp6;
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tmp4 = tmp10 - tmp5;
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wsptr[DCTSIZE * 0] = tmp0 + tmp7;
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wsptr[DCTSIZE * 7] = tmp0 - tmp7;
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wsptr[DCTSIZE * 1] = tmp1 + tmp6;
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wsptr[DCTSIZE * 6] = tmp1 - tmp6;
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wsptr[DCTSIZE * 2] = tmp2 + tmp5;
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wsptr[DCTSIZE * 5] = tmp2 - tmp5;
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wsptr[DCTSIZE * 3] = tmp3 + tmp4;
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wsptr[DCTSIZE * 4] = tmp3 - tmp4;
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inptr++; /* advance pointers to next column */
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quantptr++;
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wsptr++;
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}
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/* Pass 2: process rows from work array, store into output array. */
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wsptr = workspace;
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for (ctr = 0; ctr < DCTSIZE; ctr++) {
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outptr = output_buf[ctr] + output_col;
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/* Rows of zeroes can be exploited in the same way as we did with columns.
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* However, the column calculation has created many nonzero AC terms, so
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* the simplification applies less often (typically 5% to 10% of the time).
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* And testing floats for zero is relatively expensive, so we don't bother.
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*/
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/* Even part */
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/* Apply signed->unsigned and prepare float->int conversion */
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z5 = wsptr[0] + ((FAST_FLOAT)CENTERJSAMPLE + (FAST_FLOAT)0.5);
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tmp10 = z5 + wsptr[4];
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tmp11 = z5 - wsptr[4];
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tmp13 = wsptr[2] + wsptr[6];
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tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT)1.414213562) - tmp13;
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tmp0 = tmp10 + tmp13;
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tmp3 = tmp10 - tmp13;
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tmp1 = tmp11 + tmp12;
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tmp2 = tmp11 - tmp12;
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/* Odd part */
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z13 = wsptr[5] + wsptr[3];
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z10 = wsptr[5] - wsptr[3];
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z11 = wsptr[1] + wsptr[7];
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z12 = wsptr[1] - wsptr[7];
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tmp7 = z11 + z13;
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tmp11 = (z11 - z13) * ((FAST_FLOAT)1.414213562);
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z5 = (z10 + z12) * ((FAST_FLOAT)1.847759065); /* 2*c2 */
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tmp10 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */
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tmp12 = z5 - z10 * ((FAST_FLOAT)2.613125930); /* 2*(c2+c6) */
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tmp6 = tmp12 - tmp7;
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tmp5 = tmp11 - tmp6;
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tmp4 = tmp10 - tmp5;
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/* Final output stage: float->int conversion and range-limit */
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outptr[0] = range_limit[((int)(tmp0 + tmp7)) & RANGE_MASK];
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outptr[7] = range_limit[((int)(tmp0 - tmp7)) & RANGE_MASK];
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outptr[1] = range_limit[((int)(tmp1 + tmp6)) & RANGE_MASK];
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outptr[6] = range_limit[((int)(tmp1 - tmp6)) & RANGE_MASK];
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outptr[2] = range_limit[((int)(tmp2 + tmp5)) & RANGE_MASK];
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outptr[5] = range_limit[((int)(tmp2 - tmp5)) & RANGE_MASK];
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outptr[3] = range_limit[((int)(tmp3 + tmp4)) & RANGE_MASK];
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outptr[4] = range_limit[((int)(tmp3 - tmp4)) & RANGE_MASK];
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wsptr += DCTSIZE; /* advance pointer to next row */
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}
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}
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```
#endif /* DCT_FLOAT_SUPPORTED */
```