/*

* jfdctint.c

*

* Copyright (C) 1991-1996, Thomas G. Lane.

* Modification developed 2003-2015 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);