/*
* This file is part of the Independent JPEG Group's software.
*
* The authors make NO WARRANTY or representation, either express or implied,
* with respect to this software, its quality, accuracy, merchantability, or
* fitness for a particular purpose. This software is provided "AS IS", and
* you, its user, assume the entire risk as to its quality and accuracy.
*
* This software is copyright (C) 1991-1996, Thomas G. Lane.
* All Rights Reserved except as specified below.
*
* Permission is hereby granted to use, copy, modify, and distribute this
* software (or portions thereof) for any purpose, without fee, subject to
* these conditions:
* (1) If any part of the source code for this software is distributed, then
* this README file must be included, with this copyright and no-warranty
* notice unaltered; and any additions, deletions, or changes to the original
* files must be clearly indicated in accompanying documentation.
* (2) If only executable code is distributed, then the accompanying
* documentation must state that "this software is based in part on the work
* of the Independent JPEG Group".
* (3) Permission for use of this software is granted only if the user accepts
* full responsibility for any undesirable consequences; the authors accept
* NO LIABILITY for damages of any kind.
*
* These conditions apply to any software derived from or based on the IJG
* code, not just to the unmodified library. If you use our work, you ought
* to acknowledge us.
*
* Permission is NOT granted for the use of any IJG author's name or company
* name in advertising or publicity relating to this software or products
* derived from it. This software may be referred to only as "the Independent
* JPEG Group's software".
*
* We specifically permit and encourage the use of this software as the basis
* of commercial products, provided that all warranty or liability claims are
* assumed by the product vendor.
*
* This file contains a slow-but-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 an algorithm described in
* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
* The primary algorithm described there uses 11 multiplies and 29 adds.
* We use their alternate method with 12 multiplies and 32 adds.
* The advantage of this method is that no data path contains more than one
* multiplication; this allows a very simple and accurate implementation in
* scaled fixed-point arithmetic, with a minimal number of shifts.
*/
/**
* @file
* Independent JPEG Group's slow & accurate dct.
*/
#include "libavutil/common.h"
#include "dct.h"
#include "bit_depth_template.c"
#define DCTSIZE 8
#define BITS_IN_JSAMPLE BIT_DEPTH
#define GLOBAL(x) x
#define RIGHT_SHIFT(x, n) ((x) >> (n))
#define MULTIPLY16C16(var,const) ((var)*(const))
#define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
#error "Sorry, this code only copes with 8x8 DCTs."
#endif
/*
* The poop on this scaling stuff is as follows:
*
* Each 1-D DCT step produces outputs which are a factor of sqrt(N)
* larger than the true DCT outputs. The final outputs are therefore
* a factor of N larger than desired; since N=8 this can be cured by
* a simple right shift at the end of the algorithm. The advantage of
* this arrangement is that we save two multiplications per 1-D DCT,
* because the y0 and y4 outputs need not be divided by sqrt(N).
* In the IJG code, this factor of 8 is removed by the quantization step
* (in jcdctmgr.c), NOT in this module.
*
* We have to do addition and subtraction of the integer inputs, which
* is no problem, and multiplication by fractional constants, which is
* a problem to do in integer arithmetic. We multiply all the constants
* by CONST_SCALE and convert them to integer constants (thus retaining
* CONST_BITS bits of precision in the constants). After doing a
* multiplication we have to divide the product by CONST_SCALE, with proper
* rounding, to produce the correct output. This division can be done
* cheaply as a right shift of CONST_BITS bits. We postpone shifting
* as long as possible so that partial sums can be added together with
* full fractional precision.
*
* The outputs of the first pass are scaled up by PASS1_BITS bits so that
* they are represented to better-than-integral precision. These outputs
* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
* with the recommended scaling. (For 12-bit sample data, the intermediate
* array is int32_t anyway.)
*
* To avoid overflow of the 32-bit intermediate results in pass 2, we must
* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
* shows that the values given below are the most effective.
*/
#undef CONST_BITS
#undef PASS1_BITS
#undef OUT_SHIFT
#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 13
#define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
#define OUT_SHIFT PASS1_BITS
#else
#define CONST_BITS 13
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#define OUT_SHIFT (PASS1_BITS + 1)
#endif
/* 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 == 13
#define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
#else
#define FIX_0_298631336 FIX(0.298631336)
#define FIX_0_390180644 FIX(0.390180644)
#define FIX_0_541196100 FIX(0.541196100)
#define FIX_0_765366865 FIX(0.765366865)
#define FIX_0_899976223 FIX(0.899976223)
#define FIX_1_175875602 FIX(1.175875602)
#define FIX_1_501321110 FIX(1.501321110)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_1_961570560 FIX(1.961570560)
#define FIX_2_053119869 FIX(2.053119869)
#define FIX_2_562915447 FIX(2.562915447)
#define FIX_3_072711026 FIX(3.072711026)
#endif
/* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
* For 8-bit samples with the recommended scaling, all the variable
* and constant values involved are no more than 16 bits wide, so a
* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
* For 12-bit samples, a full 32-bit multiplication will be needed.
*/
#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
#else
#define MULTIPLY(var,const) ((var) * (const))
#endif
static av_always_inline void FUNC(row_fdct)(int16_t *data)
{
int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int tmp10, tmp11, tmp12, tmp13;
int z1, z2, z3, z4, z5;
int16_t *dataptr;
int ctr;
/* Pass 1: process rows. */
/* Note results are scaled up by sqrt(8) compared to a true DCT; */
/* furthermore, we scale the results by 2**PASS1_BITS. */
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 per LL&M figure 1 --- note that published figure is faulty;
* rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
*/
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
dataptr[0] = (int16_t) ((tmp10 + tmp11) * (1 << PASS1_BITS));
dataptr[4] = (int16_t) ((tmp10 - tmp11) * (1 << PASS1_BITS));
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[2] = (int16_t) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS-PASS1_BITS);
dataptr[6] = (int16_t) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
CONST_BITS-PASS1_BITS);
/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
* cK represents cos(K*pi/16).
* i0..i3 in the paper are tmp4..tmp7 here.
*/
z1 = tmp4 + tmp7;
z2 = tmp5 + tmp6;
z3 = tmp4 + tmp6;
z4 = tmp5 + tmp7;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
dataptr[7] = (int16_t) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
dataptr[5] = (int16_t) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
dataptr[3] = (int16_t) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
dataptr[1] = (int16_t) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
dataptr += DCTSIZE; /* advance pointer to next row */
}
}
/*
* Perform the forward DCT on one block of samples.
*/
GLOBAL(void)
FUNC(ff_jpeg_fdct_islow)(int16_t *data)
{
int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int tmp10, tmp11, tmp12, tmp13;
int z1, z2, z3, z4, z5;
int16_t *dataptr;
int ctr;
FUNC(row_fdct)(data);
/* Pass 2: process columns.
* We remove the PASS1_BITS scaling, but leave the results scaled up
* by an overall factor of 8.
*/
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 per LL&M figure 1 --- note that published figure is faulty;
* rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
*/
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS + OUT_SHIFT);
dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
CONST_BITS + OUT_SHIFT);
/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
* cK represents cos(K*pi/16).
* i0..i3 in the paper are tmp4..tmp7 here.
*/
z1 = tmp4 + tmp7;
z2 = tmp5 + tmp6;
z3 = tmp4 + tmp6;
z4 = tmp5 + tmp7;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
dataptr[DCTSIZE*7] = DESCALE(tmp4 + z1 + z3, CONST_BITS + OUT_SHIFT);
dataptr[DCTSIZE*5] = DESCALE(tmp5 + z2 + z4, CONST_BITS + OUT_SHIFT);
dataptr[DCTSIZE*3] = DESCALE(tmp6 + z2 + z3, CONST_BITS + OUT_SHIFT);
dataptr[DCTSIZE*1] = DESCALE(tmp7 + z1 + z4, CONST_BITS + OUT_SHIFT);
dataptr++; /* advance pointer to next column */
}
}
/*
* The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
* on the rows and then, instead of doing even and odd, part on the columns
* you do even part two times.
*/
GLOBAL(void)
FUNC(ff_fdct248_islow)(int16_t *data)
{
int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int tmp10, tmp11, tmp12, tmp13;
int z1;
int16_t *dataptr;
int ctr;
FUNC(row_fdct)(data);
/* Pass 2: process columns.
* We remove the PASS1_BITS scaling, but leave the results scaled up
* by an overall factor of 8.
*/
dataptr = data;
for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
tmp10 = tmp0 + tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
tmp13 = tmp0 - tmp3;
dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS+OUT_SHIFT);
dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
CONST_BITS+OUT_SHIFT);
tmp10 = tmp4 + tmp7;
tmp11 = tmp5 + tmp6;
tmp12 = tmp5 - tmp6;
tmp13 = tmp4 - tmp7;
dataptr[DCTSIZE*1] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
dataptr[DCTSIZE*5] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[DCTSIZE*3] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS + OUT_SHIFT);
dataptr[DCTSIZE*7] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
CONST_BITS + OUT_SHIFT);
dataptr++; /* advance pointer to next column */
}
}