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/*
* jfdctfst.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 file.
*
* This file contains a fast, not so accurate integer implementation of the
* forward DCT (Discrete Cosine Transform).
*
* 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). 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 fixed-point math,
* accuracy is lost due to imprecise representation of the scaled
* quantization values. The smaller the quantization table entry, the less
* precise the scaled value, so this implementation does worse with high-
* quality-setting files than with low-quality ones.
*/
#include <stdlib.h>
#include <stdio.h>
#include "common.h"
#include "dsputil.h"
#define DCTSIZE 8
#define GLOBAL(x) x
#define RIGHT_SHIFT(x, n) ((x) >> (n))
#define SHIFT_TEMPS
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/* Scaling decisions are generally the same as in the LL&M algorithm;
* see jfdctint.c for more details. However, we choose to descale
* (right shift) multiplication products as soon as they are formed,
* rather than carrying additional fractional bits into subsequent additions.
* This compromises accuracy slightly, but it lets us save a few shifts.
* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
* everywhere except in the multiplications proper; this saves a good deal
* of work on 16-bit-int machines.
*
* Again to save a few shifts, the intermediate results between pass 1 and
* pass 2 are not upscaled, but are represented only to integral precision.
*
* A final compromise is to represent the multiplicative constants to only
* 8 fractional bits, rather than 13. This saves some shifting work on some
* machines, and may also reduce the cost of multiplication (since there
* are fewer one-bits in the constants).
*/
#define CONST_BITS 8
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
* causing a lot of useless floating-point operations at run time.
* To get around this we use the following pre-calculated constants.
* If you change CONST_BITS you may want to add appropriate values.
* (With a reasonable C compiler, you can just rely on the FIX() macro...)
*/
#if CONST_BITS == 8
#define FIX_0_382683433 ((int32_t) 98) /* FIX(0.382683433) */
#define FIX_0_541196100 ((int32_t) 139) /* FIX(0.541196100) */
#define FIX_0_707106781 ((int32_t) 181) /* FIX(0.707106781) */
#define FIX_1_306562965 ((int32_t) 334) /* FIX(1.306562965) */
#else
#define FIX_0_382683433 FIX(0.382683433)
#define FIX_0_541196100 FIX(0.541196100)
#define FIX_0_707106781 FIX(0.707106781)
#define FIX_1_306562965 FIX(1.306562965)
#endif
/* We can gain a little more speed, with a further compromise in accuracy,
* by omitting the addition in a descaling shift. This yields an incorrectly
* rounded result half the time...
*/
#ifndef USE_ACCURATE_ROUNDING
#undef DESCALE
#define DESCALE(x,n) RIGHT_SHIFT(x, n)
#endif
/* Multiply a DCTELEM variable by an int32_t constant, and immediately
* descale to yield a DCTELEM result.
*/
#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
/*
* Perform the forward DCT on one block of samples.
*/
GLOBAL(void)
fdct_ifast (DCTELEM * data)
{
DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
DCTELEM tmp10, tmp11, tmp12, tmp13;
DCTELEM z1, z2, z3, z4, z5, z11, z13;
DCTELEM *dataptr;
int ctr;
SHIFT_TEMPS
/* 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 = MULTIPLY(tmp12 + tmp13, FIX_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 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
z3 = MULTIPLY(tmp11, FIX_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 = MULTIPLY(tmp12 + tmp13, FIX_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 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
z3 = MULTIPLY(tmp11, FIX_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 */
}
}
#undef GLOBAL
#undef CONST_BITS
#undef DESCALE
#undef FIX_0_541196100
#undef FIX_1_306562965
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