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/*
* jfdctint.c
*
* This file was part of the Independent JPEG Group's software:
* Copyright (C) 1991-1996, Thomas G. Lane.
* libjpeg-turbo Modifications:
* Copyright (C) 2015, 2020, D. R. Commander.
* For conditions of distribution and use, see the accompanying README.ijg
* file.
*
* This file contains a slower but more 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.
*/
#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
#ifdef DCT_ISLOW_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
/*
* 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 JLONG 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.
*/
#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 13
#define PASS1_BITS 2
#else
#define CONST_BITS 13
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#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 ((JLONG)2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((JLONG)3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((JLONG)4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((JLONG)6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((JLONG)7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((JLONG)9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((JLONG)12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((JLONG)15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((JLONG)16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((JLONG)16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((JLONG)20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((JLONG)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 JLONG variable by an JLONG constant to yield an JLONG 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
#define MULTIPLY(var, const) MULTIPLY16C16(var, const)
#else
#define MULTIPLY(var, const) ((var) * (const))
#endif
/*
* Perform the forward DCT on one block of samples.
*/
GLOBAL(void)
jpeg_fdct_islow(DCTELEM *data)
{
JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
JLONG tmp10, tmp11, tmp12, tmp13;
JLONG z1, z2, z3, z4, z5;
DCTELEM *dataptr;
int ctr;
SHIFT_TEMPS
/* 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] = (DCTELEM)LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS);
dataptr[4] = (DCTELEM)LEFT_SHIFT(tmp10 - tmp11, PASS1_BITS);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[2] = (DCTELEM)DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS - PASS1_BITS);
dataptr[6] = (DCTELEM)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] = (DCTELEM)DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);
dataptr[5] = (DCTELEM)DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);
dataptr[3] = (DCTELEM)DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);
dataptr[1] = (DCTELEM)DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);
dataptr += DCTSIZE; /* advance pointer to next row */
}
/* 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] = (DCTELEM)DESCALE(tmp10 + tmp11, PASS1_BITS);
dataptr[DCTSIZE * 4] = (DCTELEM)DESCALE(tmp10 - tmp11, PASS1_BITS);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
dataptr[DCTSIZE * 2] =
(DCTELEM)DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
CONST_BITS + PASS1_BITS);
dataptr[DCTSIZE * 6] =
(DCTELEM)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[DCTSIZE * 7] = (DCTELEM)DESCALE(tmp4 + z1 + z3,
CONST_BITS + PASS1_BITS);
dataptr[DCTSIZE * 5] = (DCTELEM)DESCALE(tmp5 + z2 + z4,
CONST_BITS + PASS1_BITS);
dataptr[DCTSIZE * 3] = (DCTELEM)DESCALE(tmp6 + z2 + z3,
CONST_BITS + PASS1_BITS);
dataptr[DCTSIZE * 1] = (DCTELEM)DESCALE(tmp7 + z1 + z4,
CONST_BITS + PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
#endif /* DCT_ISLOW_SUPPORTED */
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