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/*
* jfdctflt.c
*
* Copyright (C) 1994-1996, Thomas G. Lane.
* This file is part of the Independent JPEG Group's software.
* For conditions of distribution and use, see the accompanying README.ijg
* file.
*
* This file contains a floating-point implementation of the
* forward DCT (Discrete Cosine Transform).
*
* This implementation should be more accurate than either of the integer
* DCT implementations. However, it may not give the same results on all
* machines because of differences in roundoff behavior. Speed will depend
* on the hardware's floating point capacity.
*
* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
* on each column. Direct algorithms are also available, but they are
* much more complex and seem not to be any faster when reduced to code.
*
* This implementation is based on Arai, Agui, and Nakajima's algorithm for
* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
* Japanese, but the algorithm is described in the Pennebaker & Mitchell
* JPEG textbook (see REFERENCES section in file README.ijg). The following
* code is based directly on figure 4-8 in P&M.
* While an 8-point DCT cannot be done in less than 11 multiplies, it is
* possible to arrange the computation so that many of the multiplies are
* simple scalings of the final outputs. These multiplies can then be
* folded into the multiplications or divisions by the JPEG quantization
* table entries. The AA&N method leaves only 5 multiplies and 29 adds
* to be done in the DCT itself.
* The primary disadvantage of this method is that with a fixed-point
* implementation, accuracy is lost due to imprecise representation of the
* scaled quantization values. However, that problem does not arise if
* we use floating point arithmetic.
*/
#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
#ifdef DCT_FLOAT_SUPPORTED
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/*
* Perform the forward DCT on one block of samples.
*/
GLOBAL(void)
jpeg_fdct_float(FAST_FLOAT *data)
{
FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
FAST_FLOAT *dataptr;
int ctr;
/* Pass 1: process rows. */
dataptr = data;
for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
tmp0 = dataptr[0] + dataptr[7];
tmp7 = dataptr[0] - dataptr[7];
tmp1 = dataptr[1] + dataptr[6];
tmp6 = dataptr[1] - dataptr[6];
tmp2 = dataptr[2] + dataptr[5];
tmp5 = dataptr[2] - dataptr[5];
tmp3 = dataptr[3] + dataptr[4];
tmp4 = dataptr[3] - dataptr[4];
/* Even part */
tmp10 = tmp0 + tmp3; /* phase 2 */
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
dataptr[0] = tmp10 + tmp11; /* phase 3 */
dataptr[4] = tmp10 - tmp11;
z1 = (tmp12 + tmp13) * ((FAST_FLOAT)0.707106781); /* c4 */
dataptr[2] = tmp13 + z1; /* phase 5 */
dataptr[6] = tmp13 - z1;
/* Odd part */
tmp10 = tmp4 + tmp5; /* phase 2 */
tmp11 = tmp5 + tmp6;
tmp12 = tmp6 + tmp7;
/* The rotator is modified from fig 4-8 to avoid extra negations. */
z5 = (tmp10 - tmp12) * ((FAST_FLOAT)0.382683433); /* c6 */
z2 = ((FAST_FLOAT)0.541196100) * tmp10 + z5; /* c2-c6 */
z4 = ((FAST_FLOAT)1.306562965) * tmp12 + z5; /* c2+c6 */
z3 = tmp11 * ((FAST_FLOAT)0.707106781); /* c4 */
z11 = tmp7 + z3; /* phase 5 */
z13 = tmp7 - z3;
dataptr[5] = z13 + z2; /* phase 6 */
dataptr[3] = z13 - z2;
dataptr[1] = z11 + z4;
dataptr[7] = z11 - z4;
dataptr += DCTSIZE; /* advance pointer to next row */
}
/* Pass 2: process columns. */
dataptr = data;
for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
tmp0 = dataptr[DCTSIZE * 0] + dataptr[DCTSIZE * 7];
tmp7 = dataptr[DCTSIZE * 0] - dataptr[DCTSIZE * 7];
tmp1 = dataptr[DCTSIZE * 1] + dataptr[DCTSIZE * 6];
tmp6 = dataptr[DCTSIZE * 1] - dataptr[DCTSIZE * 6];
tmp2 = dataptr[DCTSIZE * 2] + dataptr[DCTSIZE * 5];
tmp5 = dataptr[DCTSIZE * 2] - dataptr[DCTSIZE * 5];
tmp3 = dataptr[DCTSIZE * 3] + dataptr[DCTSIZE * 4];
tmp4 = dataptr[DCTSIZE * 3] - dataptr[DCTSIZE * 4];
/* Even part */
tmp10 = tmp0 + tmp3; /* phase 2 */
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
dataptr[DCTSIZE * 0] = tmp10 + tmp11; /* phase 3 */
dataptr[DCTSIZE * 4] = tmp10 - tmp11;
z1 = (tmp12 + tmp13) * ((FAST_FLOAT)0.707106781); /* c4 */
dataptr[DCTSIZE * 2] = tmp13 + z1; /* phase 5 */
dataptr[DCTSIZE * 6] = tmp13 - z1;
/* Odd part */
tmp10 = tmp4 + tmp5; /* phase 2 */
tmp11 = tmp5 + tmp6;
tmp12 = tmp6 + tmp7;
/* The rotator is modified from fig 4-8 to avoid extra negations. */
z5 = (tmp10 - tmp12) * ((FAST_FLOAT)0.382683433); /* c6 */
z2 = ((FAST_FLOAT)0.541196100) * tmp10 + z5; /* c2-c6 */
z4 = ((FAST_FLOAT)1.306562965) * tmp12 + z5; /* c2+c6 */
z3 = tmp11 * ((FAST_FLOAT)0.707106781); /* c4 */
z11 = tmp7 + z3; /* phase 5 */
z13 = tmp7 - z3;
dataptr[DCTSIZE * 5] = z13 + z2; /* phase 6 */
dataptr[DCTSIZE * 3] = z13 - z2;
dataptr[DCTSIZE * 1] = z11 + z4;
dataptr[DCTSIZE * 7] = z11 - z4;
dataptr++; /* advance pointer to next column */
}
}
#endif /* DCT_FLOAT_SUPPORTED */
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