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jfdctint.c
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/*
* jfdctint.c
*
* Copyright (C) 1991-1996, Thomas G. Lane.
* Modification developed 2003-2018 by Guido Vollbeding.
* 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 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.
*
* We also provide FDCT routines with various input sample block sizes for
* direct resolution reduction or enlargement and for direct resolving the
* common 2x1 and 1x2 subsampling cases without additional resampling: NxN
* (N=1...16), 2NxN, and Nx2N (N=1...8) pixels for one 8x8 output DCT block.
*
* For N<8 we fill the remaining block coefficients with zero.
* For N>8 we apply a partial N-point FDCT on the input samples, computing
* just the lower 8 frequency coefficients and discarding the rest.
*
* We must scale the output coefficients of the N-point FDCT appropriately
* to the standard 8-point FDCT level by 8/N per 1-D pass. This scaling
* is folded into the constant multipliers (pass 2) and/or final/initial
* shifting.
*
* CAUTION: We rely on the FIX() macro except for the N=1,2,4,8 cases
* since there would be too many additional constants to pre-calculate.
*/
#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 DCT blocks. /* 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 INT32 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 ((INT32) 2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((INT32) 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 variable by an INT32 constant to yield an INT32 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, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2, tmp3;
INT32 tmp10, tmp11, tmp12, tmp13;
INT32 z1;
DCTELEM *dataptr;
JSAMPROW elemptr;
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.
* cK represents sqrt(2) * cos(K*pi/16).
*/
dataptr = data;
for (ctr = 0; ctr < DCTSIZE; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part per LL&M figure 1 --- note that published figure is faulty;
* rotator "c1" should be "c6".
*/
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);
tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);
tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);
tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);
tmp10 = tmp0 + tmp3;
tmp12 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp13 = tmp1 - tmp2;
tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);
tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);
tmp2 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);
tmp3 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM) ((tmp10 + tmp11 - 8 * CENTERJSAMPLE) << PASS1_BITS);
dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); /* c6 */
/* Add fudge factor here for final descale. */
z1 += ONE << (CONST_BITS-PASS1_BITS-1);
dataptr[2] = (DCTELEM)
RIGHT_SHIFT(z1 + MULTIPLY(tmp12, FIX_0_765366865), /* c2-c6 */
CONST_BITS-PASS1_BITS);
dataptr[6] = (DCTELEM)
RIGHT_SHIFT(z1 - MULTIPLY(tmp13, FIX_1_847759065), /* c2+c6 */
CONST_BITS-PASS1_BITS);
/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
* i0..i3 in the paper are tmp0..tmp3 here.
*/
tmp12 = tmp0 + tmp2;
tmp13 = tmp1 + tmp3;
z1 = MULTIPLY(tmp12 + tmp13, FIX_1_175875602); /* c3 */
/* Add fudge factor here for final descale. */
z1 += ONE << (CONST_BITS-PASS1_BITS-1);
tmp12 = MULTIPLY(tmp12, - FIX_0_390180644); /* -c3+c5 */
tmp13 = MULTIPLY(tmp13, - FIX_1_961570560); /* -c3-c5 */
tmp12 += z1;
tmp13 += z1;
z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223); /* -c3+c7 */
tmp0 = MULTIPLY(tmp0, FIX_1_501321110); /* c1+c3-c5-c7 */
tmp3 = MULTIPLY(tmp3, FIX_0_298631336); /* -c1+c3+c5-c7 */
tmp0 += z1 + tmp12;
tmp3 += z1 + tmp13;
z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447); /* -c1-c3 */
tmp1 = MULTIPLY(tmp1, FIX_3_072711026); /* c1+c3+c5-c7 */
tmp2 = MULTIPLY(tmp2, FIX_2_053119869); /* c1+c3-c5+c7 */
tmp1 += z1 + tmp13;
tmp2 += z1 + tmp12;
dataptr[1] = (DCTELEM) RIGHT_SHIFT(tmp0, CONST_BITS-PASS1_BITS);
dataptr[3] = (DCTELEM) RIGHT_SHIFT(tmp1, CONST_BITS-PASS1_BITS);
dataptr[5] = (DCTELEM) RIGHT_SHIFT(tmp2, CONST_BITS-PASS1_BITS);
dataptr[7] = (DCTELEM) RIGHT_SHIFT(tmp3, 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.
* cK represents sqrt(2) * cos(K*pi/16).
*/
dataptr = data;
for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
/* Even part per LL&M figure 1 --- note that published figure is faulty;
* rotator "c1" should be "c6".
*/
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
/* Add fudge factor here for final descale. */
tmp10 = tmp0 + tmp3 + (ONE << (PASS1_BITS-1));
tmp12 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp13 = tmp1 - tmp2;
tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
tmp2 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
tmp3 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
dataptr[DCTSIZE*0] = (DCTELEM) RIGHT_SHIFT(tmp10 + tmp11, PASS1_BITS);
dataptr[DCTSIZE*4] = (DCTELEM) RIGHT_SHIFT(tmp10 - tmp11, PASS1_BITS);
z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); /* c6 */
/* Add fudge factor here for final descale. */
z1 += ONE << (CONST_BITS+PASS1_BITS-1);
dataptr[DCTSIZE*2] = (DCTELEM)
RIGHT_SHIFT(z1 + MULTIPLY(tmp12, FIX_0_765366865), /* c2-c6 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*6] = (DCTELEM)
RIGHT_SHIFT(z1 - MULTIPLY(tmp13, FIX_1_847759065), /* c2+c6 */
CONST_BITS+PASS1_BITS);
/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
* i0..i3 in the paper are tmp0..tmp3 here.
*/
tmp12 = tmp0 + tmp2;
tmp13 = tmp1 + tmp3;
z1 = MULTIPLY(tmp12 + tmp13, FIX_1_175875602); /* c3 */
/* Add fudge factor here for final descale. */
z1 += ONE << (CONST_BITS+PASS1_BITS-1);
tmp12 = MULTIPLY(tmp12, - FIX_0_390180644); /* -c3+c5 */
tmp13 = MULTIPLY(tmp13, - FIX_1_961570560); /* -c3-c5 */
tmp12 += z1;
tmp13 += z1;
z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223); /* -c3+c7 */
tmp0 = MULTIPLY(tmp0, FIX_1_501321110); /* c1+c3-c5-c7 */
tmp3 = MULTIPLY(tmp3, FIX_0_298631336); /* -c1+c3+c5-c7 */
tmp0 += z1 + tmp12;
tmp3 += z1 + tmp13;
z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447); /* -c1-c3 */
tmp1 = MULTIPLY(tmp1, FIX_3_072711026); /* c1+c3+c5-c7 */
tmp2 = MULTIPLY(tmp2, FIX_2_053119869); /* c1+c3-c5+c7 */
tmp1 += z1 + tmp13;
tmp2 += z1 + tmp12;
dataptr[DCTSIZE*1] = (DCTELEM) RIGHT_SHIFT(tmp0, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*3] = (DCTELEM) RIGHT_SHIFT(tmp1, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*5] = (DCTELEM) RIGHT_SHIFT(tmp2, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*7] = (DCTELEM) RIGHT_SHIFT(tmp3, CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
#ifdef DCT_SCALING_SUPPORTED
/*
* Perform the forward DCT on a 7x7 sample block.
*/
GLOBAL(void)
jpeg_fdct_7x7 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2, tmp3;
INT32 tmp10, tmp11, tmp12;
INT32 z1, z2, z3;
DCTELEM *dataptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* 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.
* cK represents sqrt(2) * cos(K*pi/14).
*/
dataptr = data;
for (ctr = 0; ctr < 7; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[6]);
tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[5]);
tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[4]);
tmp3 = GETJSAMPLE(elemptr[3]);
tmp10 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[6]);
tmp11 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[5]);
tmp12 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[4]);
z1 = tmp0 + tmp2;
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM)
((z1 + tmp1 + tmp3 - 7 * CENTERJSAMPLE) << PASS1_BITS);
tmp3 += tmp3;
z1 -= tmp3;
z1 -= tmp3;
z1 = MULTIPLY(z1, FIX(0.353553391)); /* (c2+c6-c4)/2 */
z2 = MULTIPLY(tmp0 - tmp2, FIX(0.920609002)); /* (c2+c4-c6)/2 */
z3 = MULTIPLY(tmp1 - tmp2, FIX(0.314692123)); /* c6 */
dataptr[2] = (DCTELEM) DESCALE(z1 + z2 + z3, CONST_BITS-PASS1_BITS);
z1 -= z2;
z2 = MULTIPLY(tmp0 - tmp1, FIX(0.881747734)); /* c4 */
dataptr[4] = (DCTELEM)
DESCALE(z2 + z3 - MULTIPLY(tmp1 - tmp3, FIX(0.707106781)), /* c2+c6-c4 */
CONST_BITS-PASS1_BITS);
dataptr[6] = (DCTELEM) DESCALE(z1 + z2, CONST_BITS-PASS1_BITS);
/* Odd part */
tmp1 = MULTIPLY(tmp10 + tmp11, FIX(0.935414347)); /* (c3+c1-c5)/2 */
tmp2 = MULTIPLY(tmp10 - tmp11, FIX(0.170262339)); /* (c3+c5-c1)/2 */
tmp0 = tmp1 - tmp2;
tmp1 += tmp2;
tmp2 = MULTIPLY(tmp11 + tmp12, - FIX(1.378756276)); /* -c1 */
tmp1 += tmp2;
tmp3 = MULTIPLY(tmp10 + tmp12, FIX(0.613604268)); /* c5 */
tmp0 += tmp3;
tmp2 += tmp3 + MULTIPLY(tmp12, FIX(1.870828693)); /* c3+c1-c5 */
dataptr[1] = (DCTELEM) DESCALE(tmp0, CONST_BITS-PASS1_BITS);
dataptr[3] = (DCTELEM) DESCALE(tmp1, CONST_BITS-PASS1_BITS);
dataptr[5] = (DCTELEM) DESCALE(tmp2, 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.
* We must also scale the output by (8/7)**2 = 64/49, which we fold
* into the constant multipliers:
* cK now represents sqrt(2) * cos(K*pi/14) * 64/49.
*/
dataptr = data;
for (ctr = 0; ctr < 7; ctr++) {
/* Even part */
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*6];
tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*5];
tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*4];
tmp3 = dataptr[DCTSIZE*3];
tmp10 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*6];
tmp11 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*5];
tmp12 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*4];
z1 = tmp0 + tmp2;
dataptr[DCTSIZE*0] = (DCTELEM)
DESCALE(MULTIPLY(z1 + tmp1 + tmp3, FIX(1.306122449)), /* 64/49 */
CONST_BITS+PASS1_BITS);
tmp3 += tmp3;
z1 -= tmp3;
z1 -= tmp3;
z1 = MULTIPLY(z1, FIX(0.461784020)); /* (c2+c6-c4)/2 */
z2 = MULTIPLY(tmp0 - tmp2, FIX(1.202428084)); /* (c2+c4-c6)/2 */
z3 = MULTIPLY(tmp1 - tmp2, FIX(0.411026446)); /* c6 */
dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + z2 + z3, CONST_BITS+PASS1_BITS);
z1 -= z2;
z2 = MULTIPLY(tmp0 - tmp1, FIX(1.151670509)); /* c4 */
dataptr[DCTSIZE*4] = (DCTELEM)
DESCALE(z2 + z3 - MULTIPLY(tmp1 - tmp3, FIX(0.923568041)), /* c2+c6-c4 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + z2, CONST_BITS+PASS1_BITS);
/* Odd part */
tmp1 = MULTIPLY(tmp10 + tmp11, FIX(1.221765677)); /* (c3+c1-c5)/2 */
tmp2 = MULTIPLY(tmp10 - tmp11, FIX(0.222383464)); /* (c3+c5-c1)/2 */
tmp0 = tmp1 - tmp2;
tmp1 += tmp2;
tmp2 = MULTIPLY(tmp11 + tmp12, - FIX(1.800824523)); /* -c1 */
tmp1 += tmp2;
tmp3 = MULTIPLY(tmp10 + tmp12, FIX(0.801442310)); /* c5 */
tmp0 += tmp3;
tmp2 += tmp3 + MULTIPLY(tmp12, FIX(2.443531355)); /* c3+c1-c5 */
dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp0, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp1, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp2, CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
/*
* Perform the forward DCT on a 6x6 sample block.
*/
GLOBAL(void)
jpeg_fdct_6x6 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2;
INT32 tmp10, tmp11, tmp12;
DCTELEM *dataptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* 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.
* cK represents sqrt(2) * cos(K*pi/12).
*/
dataptr = data;
for (ctr = 0; ctr < 6; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[5]);
tmp11 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[4]);
tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[3]);
tmp10 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[5]);
tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[4]);
tmp2 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[3]);
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM)
((tmp10 + tmp11 - 6 * CENTERJSAMPLE) << PASS1_BITS);
dataptr[2] = (DCTELEM)
DESCALE(MULTIPLY(tmp12, FIX(1.224744871)), /* c2 */
CONST_BITS-PASS1_BITS);
dataptr[4] = (DCTELEM)
DESCALE(MULTIPLY(tmp10 - tmp11 - tmp11, FIX(0.707106781)), /* c4 */
CONST_BITS-PASS1_BITS);
/* Odd part */
tmp10 = DESCALE(MULTIPLY(tmp0 + tmp2, FIX(0.366025404)), /* c5 */
CONST_BITS-PASS1_BITS);
dataptr[1] = (DCTELEM) (tmp10 + ((tmp0 + tmp1) << PASS1_BITS));
dataptr[3] = (DCTELEM) ((tmp0 - tmp1 - tmp2) << PASS1_BITS);
dataptr[5] = (DCTELEM) (tmp10 + ((tmp2 - tmp1) << 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.
* We must also scale the output by (8/6)**2 = 16/9, which we fold
* into the constant multipliers:
* cK now represents sqrt(2) * cos(K*pi/12) * 16/9.
*/
dataptr = data;
for (ctr = 0; ctr < 6; ctr++) {
/* Even part */
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*5];
tmp11 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*4];
tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
tmp10 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*5];
tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*4];
tmp2 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
dataptr[DCTSIZE*0] = (DCTELEM)
DESCALE(MULTIPLY(tmp10 + tmp11, FIX(1.777777778)), /* 16/9 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*2] = (DCTELEM)
DESCALE(MULTIPLY(tmp12, FIX(2.177324216)), /* c2 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*4] = (DCTELEM)
DESCALE(MULTIPLY(tmp10 - tmp11 - tmp11, FIX(1.257078722)), /* c4 */
CONST_BITS+PASS1_BITS);
/* Odd part */
tmp10 = MULTIPLY(tmp0 + tmp2, FIX(0.650711829)); /* c5 */
dataptr[DCTSIZE*1] = (DCTELEM)
DESCALE(tmp10 + MULTIPLY(tmp0 + tmp1, FIX(1.777777778)), /* 16/9 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*3] = (DCTELEM)
DESCALE(MULTIPLY(tmp0 - tmp1 - tmp2, FIX(1.777777778)), /* 16/9 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*5] = (DCTELEM)
DESCALE(tmp10 + MULTIPLY(tmp2 - tmp1, FIX(1.777777778)), /* 16/9 */
CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
/*
* Perform the forward DCT on a 5x5 sample block.
*/
GLOBAL(void)
jpeg_fdct_5x5 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2;
INT32 tmp10, tmp11;
DCTELEM *dataptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* 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.
* We scale the results further by 2 as part of output adaption
* scaling for different DCT size.
* cK represents sqrt(2) * cos(K*pi/10).
*/
dataptr = data;
for (ctr = 0; ctr < 5; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[4]);
tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[3]);
tmp2 = GETJSAMPLE(elemptr[2]);
tmp10 = tmp0 + tmp1;
tmp11 = tmp0 - tmp1;
tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[4]);
tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[3]);
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM)
((tmp10 + tmp2 - 5 * CENTERJSAMPLE) << (PASS1_BITS+1));
tmp11 = MULTIPLY(tmp11, FIX(0.790569415)); /* (c2+c4)/2 */
tmp10 -= tmp2 << 2;
tmp10 = MULTIPLY(tmp10, FIX(0.353553391)); /* (c2-c4)/2 */
dataptr[2] = (DCTELEM) DESCALE(tmp11 + tmp10, CONST_BITS-PASS1_BITS-1);
dataptr[4] = (DCTELEM) DESCALE(tmp11 - tmp10, CONST_BITS-PASS1_BITS-1);
/* Odd part */
tmp10 = MULTIPLY(tmp0 + tmp1, FIX(0.831253876)); /* c3 */
dataptr[1] = (DCTELEM)
DESCALE(tmp10 + MULTIPLY(tmp0, FIX(0.513743148)), /* c1-c3 */
CONST_BITS-PASS1_BITS-1);
dataptr[3] = (DCTELEM)
DESCALE(tmp10 - MULTIPLY(tmp1, FIX(2.176250899)), /* c1+c3 */
CONST_BITS-PASS1_BITS-1);
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.
* We must also scale the output by (8/5)**2 = 64/25, which we partially
* fold into the constant multipliers (other part was done in pass 1):
* cK now represents sqrt(2) * cos(K*pi/10) * 32/25.
*/
dataptr = data;
for (ctr = 0; ctr < 5; ctr++) {
/* Even part */
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*4];
tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*3];
tmp2 = dataptr[DCTSIZE*2];
tmp10 = tmp0 + tmp1;
tmp11 = tmp0 - tmp1;
tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*4];
tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*3];
dataptr[DCTSIZE*0] = (DCTELEM)
DESCALE(MULTIPLY(tmp10 + tmp2, FIX(1.28)), /* 32/25 */
CONST_BITS+PASS1_BITS);
tmp11 = MULTIPLY(tmp11, FIX(1.011928851)); /* (c2+c4)/2 */
tmp10 -= tmp2 << 2;
tmp10 = MULTIPLY(tmp10, FIX(0.452548340)); /* (c2-c4)/2 */
dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp11 + tmp10, CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp11 - tmp10, CONST_BITS+PASS1_BITS);
/* Odd part */
tmp10 = MULTIPLY(tmp0 + tmp1, FIX(1.064004961)); /* c3 */
dataptr[DCTSIZE*1] = (DCTELEM)
DESCALE(tmp10 + MULTIPLY(tmp0, FIX(0.657591230)), /* c1-c3 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*3] = (DCTELEM)
DESCALE(tmp10 - MULTIPLY(tmp1, FIX(2.785601151)), /* c1+c3 */
CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
/*
* Perform the forward DCT on a 4x4 sample block.
*/
GLOBAL(void)
jpeg_fdct_4x4 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1;
INT32 tmp10, tmp11;
DCTELEM *dataptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* 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.
* We must also scale the output by (8/4)**2 = 2**2, which we add here.
* cK represents sqrt(2) * cos(K*pi/16) [refers to 8-point FDCT].
*/
dataptr = data;
for (ctr = 0; ctr < 4; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[3]);
tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[2]);
tmp10 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[3]);
tmp11 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[2]);
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM)
((tmp0 + tmp1 - 4 * CENTERJSAMPLE) << (PASS1_BITS+2));
dataptr[2] = (DCTELEM) ((tmp0 - tmp1) << (PASS1_BITS+2));
/* Odd part */
tmp0 = MULTIPLY(tmp10 + tmp11, FIX_0_541196100); /* c6 */
/* Add fudge factor here for final descale. */
tmp0 += ONE << (CONST_BITS-PASS1_BITS-3);
dataptr[1] = (DCTELEM)
RIGHT_SHIFT(tmp0 + MULTIPLY(tmp10, FIX_0_765366865), /* c2-c6 */
CONST_BITS-PASS1_BITS-2);
dataptr[3] = (DCTELEM)
RIGHT_SHIFT(tmp0 - MULTIPLY(tmp11, FIX_1_847759065), /* c2+c6 */
CONST_BITS-PASS1_BITS-2);
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.
* cK represents sqrt(2) * cos(K*pi/16) [refers to 8-point FDCT].
*/
dataptr = data;
for (ctr = 0; ctr < 4; ctr++) {
/* Even part */
/* Add fudge factor here for final descale. */
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*3] + (ONE << (PASS1_BITS-1));
tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*2];
tmp10 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*3];
tmp11 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*2];
dataptr[DCTSIZE*0] = (DCTELEM) RIGHT_SHIFT(tmp0 + tmp1, PASS1_BITS);
dataptr[DCTSIZE*2] = (DCTELEM) RIGHT_SHIFT(tmp0 - tmp1, PASS1_BITS);
/* Odd part */
tmp0 = MULTIPLY(tmp10 + tmp11, FIX_0_541196100); /* c6 */
/* Add fudge factor here for final descale. */
tmp0 += ONE << (CONST_BITS+PASS1_BITS-1);
dataptr[DCTSIZE*1] = (DCTELEM)
RIGHT_SHIFT(tmp0 + MULTIPLY(tmp10, FIX_0_765366865), /* c2-c6 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*3] = (DCTELEM)
RIGHT_SHIFT(tmp0 - MULTIPLY(tmp11, FIX_1_847759065), /* c2+c6 */
CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
/*
* Perform the forward DCT on a 3x3 sample block.
*/
GLOBAL(void)
jpeg_fdct_3x3 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2;
DCTELEM *dataptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* 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.
* We scale the results further by 2**2 as part of output adaption
* scaling for different DCT size.
* cK represents sqrt(2) * cos(K*pi/6).
*/
dataptr = data;
for (ctr = 0; ctr < 3; ctr++) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[2]);
tmp1 = GETJSAMPLE(elemptr[1]);
tmp2 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[2]);
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM)
((tmp0 + tmp1 - 3 * CENTERJSAMPLE) << (PASS1_BITS+2));
dataptr[2] = (DCTELEM)
DESCALE(MULTIPLY(tmp0 - tmp1 - tmp1, FIX(0.707106781)), /* c2 */
CONST_BITS-PASS1_BITS-2);
/* Odd part */
dataptr[1] = (DCTELEM)
DESCALE(MULTIPLY(tmp2, FIX(1.224744871)), /* c1 */
CONST_BITS-PASS1_BITS-2);
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.
* We must also scale the output by (8/3)**2 = 64/9, which we partially
* fold into the constant multipliers (other part was done in pass 1):
* cK now represents sqrt(2) * cos(K*pi/6) * 16/9.
*/
dataptr = data;
for (ctr = 0; ctr < 3; ctr++) {
/* Even part */
tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*2];
tmp1 = dataptr[DCTSIZE*1];
tmp2 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*2];
dataptr[DCTSIZE*0] = (DCTELEM)
DESCALE(MULTIPLY(tmp0 + tmp1, FIX(1.777777778)), /* 16/9 */
CONST_BITS+PASS1_BITS);
dataptr[DCTSIZE*2] = (DCTELEM)
DESCALE(MULTIPLY(tmp0 - tmp1 - tmp1, FIX(1.257078722)), /* c2 */
CONST_BITS+PASS1_BITS);
/* Odd part */
dataptr[DCTSIZE*1] = (DCTELEM)
DESCALE(MULTIPLY(tmp2, FIX(2.177324216)), /* c1 */
CONST_BITS+PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
}
/*
* Perform the forward DCT on a 2x2 sample block.
*/
GLOBAL(void)
jpeg_fdct_2x2 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
DCTELEM tmp0, tmp1, tmp2, tmp3;
JSAMPROW elemptr;
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
/* Pass 1: process rows.
* Note results are scaled up by sqrt(8) compared to a true DCT.
*/
/* Row 0 */
elemptr = sample_data[0] + start_col;
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[1]);
tmp1 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[1]);
/* Row 1 */
elemptr = sample_data[1] + start_col;
tmp2 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[1]);
tmp3 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[1]);
/* Pass 2: process columns.
* We leave the results scaled up by an overall factor of 8.
* We must also scale the output by (8/2)**2 = 2**4.
*/
/* Column 0 */
/* Apply unsigned->signed conversion. */
data[DCTSIZE*0] = (tmp0 + tmp2 - 4 * CENTERJSAMPLE) << 4;
data[DCTSIZE*1] = (tmp0 - tmp2) << 4;
/* Column 1 */
data[DCTSIZE*0+1] = (tmp1 + tmp3) << 4;
data[DCTSIZE*1+1] = (tmp1 - tmp3) << 4;
}
/*
* Perform the forward DCT on a 1x1 sample block.
*/
GLOBAL(void)
jpeg_fdct_1x1 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
DCTELEM dcval;
/* Pre-zero output coefficient block. */
MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);
dcval = GETJSAMPLE(sample_data[0][start_col]);
/* We leave the result scaled up by an overall factor of 8. */
/* We must also scale the output by (8/1)**2 = 2**6. */
/* Apply unsigned->signed conversion. */
data[0] = (dcval - CENTERJSAMPLE) << 6;
}
/*
* Perform the forward DCT on a 9x9 sample block.
*/
GLOBAL(void)
jpeg_fdct_9x9 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
{
INT32 tmp0, tmp1, tmp2, tmp3, tmp4;
INT32 tmp10, tmp11, tmp12, tmp13;
INT32 z1, z2;
DCTELEM workspace[8];
DCTELEM *dataptr;
DCTELEM *wsptr;
JSAMPROW elemptr;
int ctr;
SHIFT_TEMPS
/* Pass 1: process rows.
* Note results are scaled up by sqrt(8) compared to a true DCT;
* we scale the results further by 2 as part of output adaption
* scaling for different DCT size.
* cK represents sqrt(2) * cos(K*pi/18).
*/
dataptr = data;
ctr = 0;
for (;;) {
elemptr = sample_data[ctr] + start_col;
/* Even part */
tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[8]);
tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[7]);
tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[6]);
tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[5]);
tmp4 = GETJSAMPLE(elemptr[4]);
tmp10 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[8]);
tmp11 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[7]);
tmp12 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[6]);
tmp13 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[5]);
z1 = tmp0 + tmp2 + tmp3;
z2 = tmp1 + tmp4;
/* Apply unsigned->signed conversion. */
dataptr[0] = (DCTELEM) ((z1 + z2 - 9 * CENTERJSAMPLE) << 1);
dataptr[6] = (DCTELEM)
DESCALE(MULTIPLY(z1 - z2 - z2, FIX(0.707106781)), /* c6 */
CONST_BITS-1);
z1 = MULTIPLY(tmp0 - tmp2, FIX(1.328926049)); /* c2 */
z2 = MULTIPLY(tmp1 - tmp4 - tmp4, FIX(0.707106781)); /* c6 */
dataptr[2] = (DCTELEM)
DESCALE(MULTIPLY(tmp2 - tmp3, FIX(1.083350441)) /* c4 */
+ z1 + z2, CONST_BITS-1);
dataptr[4] = (DCTELEM)
DESCALE(MULTIPLY(tmp3 - tmp0, FIX(0.245575608)) /* c8 */
+ z1 - z2, CONST_BITS-1);
/* Odd part */
dataptr[3] = (DCTELEM)
DESCALE(MULTIPLY(tmp10 - tmp12 - tmp13, FIX(1.224744871)), /* c3 */
CONST_BITS-1);