/*

* jidctint.c

*

* Copyright (C) 1991-1998, Thomas G. Lane.

* Modification developed 2002-2018 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

* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine

* must also perform dequantization of the input coefficients.

*

* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT

* on each row (or vice versa, but it's more convenient to emit a row at

* a time). 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 IDCT routines with various output 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 input DCT block.

*

* For N<8 we simply take the corresponding low-frequency coefficients of

* the 8x8 input DCT block and apply an NxN point IDCT on the sub-block

* to yield the downscaled outputs.

* This can be seen as direct low-pass downsampling from the DCT domain

* point of view rather than the usual spatial domain point of view,

* yielding significant computational savings and results at least

* as good as common bilinear (averaging) spatial downsampling.

*

* For N>8 we apply a partial NxN IDCT on the 8 input coefficients as

* lower frequencies and higher frequencies assumed to be zero.

* It turns out that the computational effort is similar to the 8x8 IDCT

* regarding the output size.

* Furthermore, the scaling and descaling is the same for all IDCT sizes.

*

* 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 IDCT step produces outputs which are a factor of sqrt(N)

* larger than the true IDCT 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 IDCT,

* because the y0 and y4 inputs need not be divided by sqrt(N).

*

* 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. (To scale up 12-bit sample data further, an

* intermediate INT32 array would be needed.)

*

* 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

/* Dequantize a coefficient by multiplying it by the multiplier-table

* entry; produce an int result. In this module, both inputs and result

* are 16 bits or less, so either int or short multiply will work.

*/

#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))

/*

* Perform dequantization and inverse DCT on one block of coefficients.

*

* Optimized algorithm with 12 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/16).

*/

GLOBAL(void)

jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp1, tmp2, tmp3;

INT32 tmp10, tmp11, tmp12, tmp13;

INT32 z1, z2, z3;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[DCTSIZE2]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array.

* Note results are scaled up by sqrt(8) compared to a true IDCT;

* furthermore, we scale the results by 2**PASS1_BITS.

*/

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = DCTSIZE; ctr > 0; ctr--) {

/* Due to quantization, we will usually find that many of the input

* coefficients are zero, especially the AC terms. We can exploit this

* by short-circuiting the IDCT calculation for any column in which all

* the AC terms are zero. In that case each output is equal to the

* DC coefficient (with scale factor as needed).

* With typical images and quantization tables, half or more of the

* column DCT calculations can be simplified this way.

*/

if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&

inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&

inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&

inptr[DCTSIZE*7] == 0) {

/* AC terms all zero */

int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;

wsptr[DCTSIZE*0] = dcval;

wsptr[DCTSIZE*1] = dcval;

wsptr[DCTSIZE*2] = dcval;

wsptr[DCTSIZE*3] = dcval;

wsptr[DCTSIZE*4] = dcval;

wsptr[DCTSIZE*5] = dcval;

wsptr[DCTSIZE*6] = dcval;

wsptr[DCTSIZE*7] = dcval;

inptr++; /* advance pointers to next column */

quantptr++;

wsptr++;

continue;

}

/* Even part: reverse the even part of the forward DCT.

* The rotator is c(-6).

*/

z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

z2 <<= CONST_BITS;

z3 <<= CONST_BITS;

/* Add fudge factor here for final descale. */

z2 += ONE << (CONST_BITS-PASS1_BITS-1);

tmp0 = z2 + z3;

tmp1 = z2 - z3;

z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

z1 = MULTIPLY(z2 + z3, FIX_0_541196100); /* c6 */

tmp2 = z1 + MULTIPLY(z2, FIX_0_765366865); /* c2-c6 */

tmp3 = z1 - MULTIPLY(z3, FIX_1_847759065); /* c2+c6 */

tmp10 = tmp0 + tmp2;

tmp13 = tmp0 - tmp2;

tmp11 = tmp1 + tmp3;

tmp12 = tmp1 - tmp3;

/* Odd part per figure 8; the matrix is unitary and hence its

* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.

*/

tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);

tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);

tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

z2 = tmp0 + tmp2;

z3 = tmp1 + tmp3;

z1 = MULTIPLY(z2 + z3, FIX_1_175875602); /* c3 */

z2 = MULTIPLY(z2, - FIX_1_961570560); /* -c3-c5 */

z3 = MULTIPLY(z3, - FIX_0_390180644); /* -c3+c5 */

z2 += z1;

z3 += z1;

z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223); /* -c3+c7 */

tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* -c1+c3+c5-c7 */

tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* c1+c3-c5-c7 */

tmp0 += z1 + z2;

tmp3 += z1 + z3;

z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447); /* -c1-c3 */

tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* c1+c3-c5+c7 */

tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* c1+c3+c5-c7 */

tmp1 += z1 + z3;

tmp2 += z1 + z2;

/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

wsptr[DCTSIZE*0] = (int) RIGHT_SHIFT(tmp10 + tmp3, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*7] = (int) RIGHT_SHIFT(tmp10 - tmp3, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*1] = (int) RIGHT_SHIFT(tmp11 + tmp2, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*6] = (int) RIGHT_SHIFT(tmp11 - tmp2, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*2] = (int) RIGHT_SHIFT(tmp12 + tmp1, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*5] = (int) RIGHT_SHIFT(tmp12 - tmp1, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*3] = (int) RIGHT_SHIFT(tmp13 + tmp0, CONST_BITS-PASS1_BITS);

wsptr[DCTSIZE*4] = (int) RIGHT_SHIFT(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

inptr++; /* advance pointers to next column */

quantptr++;

wsptr++;

}

/* Pass 2: process rows from work array, store into output array.

* Note that we must descale the results by a factor of 8 == 2**3,

* and also undo the PASS1_BITS scaling.

*/

wsptr = workspace;

for (ctr = 0; ctr < DCTSIZE; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Add range center and fudge factor for final descale and range-limit. */

z2 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

/* Rows of zeroes can be exploited in the same way as we did with columns.

* However, the column calculation has created many nonzero AC terms, so

* the simplification applies less often (typically 5% to 10% of the time).

* On machines with very fast multiplication, it's possible that the

* test takes more time than it's worth. In that case this section

* may be commented out.

*/

#ifndef NO_ZERO_ROW_TEST

if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&

wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {

/* AC terms all zero */

JSAMPLE dcval = range_limit[(int) RIGHT_SHIFT(z2, PASS1_BITS+3)

& RANGE_MASK];

outptr[0] = dcval;

outptr[1] = dcval;

outptr[2] = dcval;

outptr[3] = dcval;

outptr[4] = dcval;

outptr[5] = dcval;

outptr[6] = dcval;

outptr[7] = dcval;

wsptr += DCTSIZE; /* advance pointer to next row */

continue;

}

#endif

/* Even part: reverse the even part of the forward DCT.

* The rotator is c(-6).

*/

z3 = (INT32) wsptr[4];

tmp0 = (z2 + z3) << CONST_BITS;

tmp1 = (z2 - z3) << CONST_BITS;

z2 = (INT32) wsptr[2];

z3 = (INT32) wsptr[6];

z1 = MULTIPLY(z2 + z3, FIX_0_541196100); /* c6 */

tmp2 = z1 + MULTIPLY(z2, FIX_0_765366865); /* c2-c6 */

tmp3 = z1 - MULTIPLY(z3, FIX_1_847759065); /* c2+c6 */

tmp10 = tmp0 + tmp2;

tmp13 = tmp0 - tmp2;

tmp11 = tmp1 + tmp3;

tmp12 = tmp1 - tmp3;

/* Odd part per figure 8; the matrix is unitary and hence its

* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.

*/

tmp0 = (INT32) wsptr[7];

tmp1 = (INT32) wsptr[5];

tmp2 = (INT32) wsptr[3];

tmp3 = (INT32) wsptr[1];

z2 = tmp0 + tmp2;

z3 = tmp1 + tmp3;

z1 = MULTIPLY(z2 + z3, FIX_1_175875602); /* c3 */

z2 = MULTIPLY(z2, - FIX_1_961570560); /* -c3-c5 */

z3 = MULTIPLY(z3, - FIX_0_390180644); /* -c3+c5 */

z2 += z1;

z3 += z1;

z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223); /* -c3+c7 */

tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* -c1+c3+c5-c7 */

tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* c1+c3-c5-c7 */

tmp0 += z1 + z2;

tmp3 += z1 + z3;

z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447); /* -c1-c3 */

tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* c1+c3-c5+c7 */

tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* c1+c3+c5-c7 */

tmp1 += z1 + z3;

tmp2 += z1 + z2;

/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp3,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[7] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp3,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp11 + tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[6] = range_limit[(int) RIGHT_SHIFT(tmp11 - tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp12 + tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[5] = range_limit[(int) RIGHT_SHIFT(tmp12 - tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[3] = range_limit[(int) RIGHT_SHIFT(tmp13 + tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[4] = range_limit[(int) RIGHT_SHIFT(tmp13 - tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

wsptr += DCTSIZE; /* advance pointer to next row */

}

}

#ifdef IDCT_SCALING_SUPPORTED

/*

* Perform dequantization and inverse DCT on one block of coefficients,

* producing a reduced-size 7x7 output block.

*

* Optimized algorithm with 12 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/14).

*/

GLOBAL(void)

jpeg_idct_7x7 (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp1, tmp2, tmp10, tmp11, tmp12, tmp13;

INT32 z1, z2, z3;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[7*7]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array. */

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = 0; ctr < 7; ctr++, inptr++, quantptr++, wsptr++) {

/* Even part */

tmp13 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

tmp13 <<= CONST_BITS;

/* Add fudge factor here for final descale. */

tmp13 += ONE << (CONST_BITS-PASS1_BITS-1);

z1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

z2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

tmp10 = MULTIPLY(z2 - z3, FIX(0.881747734)); /* c4 */

tmp12 = MULTIPLY(z1 - z2, FIX(0.314692123)); /* c6 */

tmp11 = tmp10 + tmp12 + tmp13 - MULTIPLY(z2, FIX(1.841218003)); /* c2+c4-c6 */

tmp0 = z1 + z3;

z2 -= tmp0;

tmp0 = MULTIPLY(tmp0, FIX(1.274162392)) + tmp13; /* c2 */

tmp10 += tmp0 - MULTIPLY(z3, FIX(0.077722536)); /* c2-c4-c6 */

tmp12 += tmp0 - MULTIPLY(z1, FIX(2.470602249)); /* c2+c4+c6 */

tmp13 += MULTIPLY(z2, FIX(1.414213562)); /* c0 */

/* Odd part */

z1 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

z2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

z3 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);

tmp1 = MULTIPLY(z1 + z2, FIX(0.935414347)); /* (c3+c1-c5)/2 */

tmp2 = MULTIPLY(z1 - z2, FIX(0.170262339)); /* (c3+c5-c1)/2 */

tmp0 = tmp1 - tmp2;

tmp1 += tmp2;

tmp2 = MULTIPLY(z2 + z3, - FIX(1.378756276)); /* -c1 */

tmp1 += tmp2;

z2 = MULTIPLY(z1 + z3, FIX(0.613604268)); /* c5 */

tmp0 += z2;

tmp2 += z2 + MULTIPLY(z3, FIX(1.870828693)); /* c3+c1-c5 */

/* Final output stage */

wsptr[7*0] = (int) RIGHT_SHIFT(tmp10 + tmp0, CONST_BITS-PASS1_BITS);

wsptr[7*6] = (int) RIGHT_SHIFT(tmp10 - tmp0, CONST_BITS-PASS1_BITS);

wsptr[7*1] = (int) RIGHT_SHIFT(tmp11 + tmp1, CONST_BITS-PASS1_BITS);

wsptr[7*5] = (int) RIGHT_SHIFT(tmp11 - tmp1, CONST_BITS-PASS1_BITS);

wsptr[7*2] = (int) RIGHT_SHIFT(tmp12 + tmp2, CONST_BITS-PASS1_BITS);

wsptr[7*4] = (int) RIGHT_SHIFT(tmp12 - tmp2, CONST_BITS-PASS1_BITS);

wsptr[7*3] = (int) RIGHT_SHIFT(tmp13, CONST_BITS-PASS1_BITS);

}

/* Pass 2: process 7 rows from work array, store into output array. */

wsptr = workspace;

for (ctr = 0; ctr < 7; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Even part */

/* Add range center and fudge factor for final descale and range-limit. */

tmp13 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

tmp13 <<= CONST_BITS;

z1 = (INT32) wsptr[2];

z2 = (INT32) wsptr[4];

z3 = (INT32) wsptr[6];

tmp10 = MULTIPLY(z2 - z3, FIX(0.881747734)); /* c4 */

tmp12 = MULTIPLY(z1 - z2, FIX(0.314692123)); /* c6 */

tmp11 = tmp10 + tmp12 + tmp13 - MULTIPLY(z2, FIX(1.841218003)); /* c2+c4-c6 */

tmp0 = z1 + z3;

z2 -= tmp0;

tmp0 = MULTIPLY(tmp0, FIX(1.274162392)) + tmp13; /* c2 */

tmp10 += tmp0 - MULTIPLY(z3, FIX(0.077722536)); /* c2-c4-c6 */

tmp12 += tmp0 - MULTIPLY(z1, FIX(2.470602249)); /* c2+c4+c6 */

tmp13 += MULTIPLY(z2, FIX(1.414213562)); /* c0 */

/* Odd part */

z1 = (INT32) wsptr[1];

z2 = (INT32) wsptr[3];

z3 = (INT32) wsptr[5];

tmp1 = MULTIPLY(z1 + z2, FIX(0.935414347)); /* (c3+c1-c5)/2 */

tmp2 = MULTIPLY(z1 - z2, FIX(0.170262339)); /* (c3+c5-c1)/2 */

tmp0 = tmp1 - tmp2;

tmp1 += tmp2;

tmp2 = MULTIPLY(z2 + z3, - FIX(1.378756276)); /* -c1 */

tmp1 += tmp2;

z2 = MULTIPLY(z1 + z3, FIX(0.613604268)); /* c5 */

tmp0 += z2;

tmp2 += z2 + MULTIPLY(z3, FIX(1.870828693)); /* c3+c1-c5 */

/* Final output stage */

outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[6] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp11 + tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[5] = range_limit[(int) RIGHT_SHIFT(tmp11 - tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp12 + tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[4] = range_limit[(int) RIGHT_SHIFT(tmp12 - tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[3] = range_limit[(int) RIGHT_SHIFT(tmp13,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

wsptr += 7; /* advance pointer to next row */

}

}

/*

* Perform dequantization and inverse DCT on one block of coefficients,

* producing a reduced-size 6x6 output block.

*

* Optimized algorithm with 3 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/12).

*/

GLOBAL(void)

jpeg_idct_6x6 (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp1, tmp2, tmp10, tmp11, tmp12;

INT32 z1, z2, z3;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[6*6]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array. */

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = 0; ctr < 6; ctr++, inptr++, quantptr++, wsptr++) {

/* Even part */

tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

tmp0 <<= CONST_BITS;

/* Add fudge factor here for final descale. */

tmp0 += ONE << (CONST_BITS-PASS1_BITS-1);

tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

tmp10 = MULTIPLY(tmp2, FIX(0.707106781)); /* c4 */

tmp1 = tmp0 + tmp10;

tmp11 = RIGHT_SHIFT(tmp0 - tmp10 - tmp10, CONST_BITS-PASS1_BITS);

tmp10 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

tmp0 = MULTIPLY(tmp10, FIX(1.224744871)); /* c2 */

tmp10 = tmp1 + tmp0;

tmp12 = tmp1 - tmp0;

/* Odd part */

z1 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

z2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

z3 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);

tmp1 = MULTIPLY(z1 + z3, FIX(0.366025404)); /* c5 */

tmp0 = tmp1 + ((z1 + z2) << CONST_BITS);

tmp2 = tmp1 + ((z3 - z2) << CONST_BITS);

tmp1 = (z1 - z2 - z3) << PASS1_BITS;

/* Final output stage */

wsptr[6*0] = (int) RIGHT_SHIFT(tmp10 + tmp0, CONST_BITS-PASS1_BITS);

wsptr[6*5] = (int) RIGHT_SHIFT(tmp10 - tmp0, CONST_BITS-PASS1_BITS);

wsptr[6*1] = (int) (tmp11 + tmp1);

wsptr[6*4] = (int) (tmp11 - tmp1);

wsptr[6*2] = (int) RIGHT_SHIFT(tmp12 + tmp2, CONST_BITS-PASS1_BITS);

wsptr[6*3] = (int) RIGHT_SHIFT(tmp12 - tmp2, CONST_BITS-PASS1_BITS);

}

/* Pass 2: process 6 rows from work array, store into output array. */

wsptr = workspace;

for (ctr = 0; ctr < 6; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Even part */

/* Add range center and fudge factor for final descale and range-limit. */

tmp0 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

tmp0 <<= CONST_BITS;

tmp2 = (INT32) wsptr[4];

tmp10 = MULTIPLY(tmp2, FIX(0.707106781)); /* c4 */

tmp1 = tmp0 + tmp10;

tmp11 = tmp0 - tmp10 - tmp10;

tmp10 = (INT32) wsptr[2];

tmp0 = MULTIPLY(tmp10, FIX(1.224744871)); /* c2 */

tmp10 = tmp1 + tmp0;

tmp12 = tmp1 - tmp0;

/* Odd part */

z1 = (INT32) wsptr[1];

z2 = (INT32) wsptr[3];

z3 = (INT32) wsptr[5];

tmp1 = MULTIPLY(z1 + z3, FIX(0.366025404)); /* c5 */

tmp0 = tmp1 + ((z1 + z2) << CONST_BITS);

tmp2 = tmp1 + ((z3 - z2) << CONST_BITS);

tmp1 = (z1 - z2 - z3) << CONST_BITS;

/* Final output stage */

outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[5] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp11 + tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[4] = range_limit[(int) RIGHT_SHIFT(tmp11 - tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp12 + tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[3] = range_limit[(int) RIGHT_SHIFT(tmp12 - tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

wsptr += 6; /* advance pointer to next row */

}

}

/*

* Perform dequantization and inverse DCT on one block of coefficients,

* producing a reduced-size 5x5 output block.

*

* Optimized algorithm with 5 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/10).

*/

GLOBAL(void)

jpeg_idct_5x5 (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp1, tmp10, tmp11, tmp12;

INT32 z1, z2, z3;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[5*5]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array. */

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = 0; ctr < 5; ctr++, inptr++, quantptr++, wsptr++) {

/* Even part */

tmp12 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

tmp12 <<= CONST_BITS;

/* Add fudge factor here for final descale. */

tmp12 += ONE << (CONST_BITS-PASS1_BITS-1);

tmp0 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

tmp1 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

z1 = MULTIPLY(tmp0 + tmp1, FIX(0.790569415)); /* (c2+c4)/2 */

z2 = MULTIPLY(tmp0 - tmp1, FIX(0.353553391)); /* (c2-c4)/2 */

z3 = tmp12 + z2;

tmp10 = z3 + z1;

tmp11 = z3 - z1;

tmp12 -= z2 << 2;

/* Odd part */

z2 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

z3 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

z1 = MULTIPLY(z2 + z3, FIX(0.831253876)); /* c3 */

tmp0 = z1 + MULTIPLY(z2, FIX(0.513743148)); /* c1-c3 */

tmp1 = z1 - MULTIPLY(z3, FIX(2.176250899)); /* c1+c3 */

/* Final output stage */

wsptr[5*0] = (int) RIGHT_SHIFT(tmp10 + tmp0, CONST_BITS-PASS1_BITS);

wsptr[5*4] = (int) RIGHT_SHIFT(tmp10 - tmp0, CONST_BITS-PASS1_BITS);

wsptr[5*1] = (int) RIGHT_SHIFT(tmp11 + tmp1, CONST_BITS-PASS1_BITS);

wsptr[5*3] = (int) RIGHT_SHIFT(tmp11 - tmp1, CONST_BITS-PASS1_BITS);

wsptr[5*2] = (int) RIGHT_SHIFT(tmp12, CONST_BITS-PASS1_BITS);

}

/* Pass 2: process 5 rows from work array, store into output array. */

wsptr = workspace;

for (ctr = 0; ctr < 5; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Even part */

/* Add range center and fudge factor for final descale and range-limit. */

tmp12 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

tmp12 <<= CONST_BITS;

tmp0 = (INT32) wsptr[2];

tmp1 = (INT32) wsptr[4];

z1 = MULTIPLY(tmp0 + tmp1, FIX(0.790569415)); /* (c2+c4)/2 */

z2 = MULTIPLY(tmp0 - tmp1, FIX(0.353553391)); /* (c2-c4)/2 */

z3 = tmp12 + z2;

tmp10 = z3 + z1;

tmp11 = z3 - z1;

tmp12 -= z2 << 2;

/* Odd part */

z2 = (INT32) wsptr[1];

z3 = (INT32) wsptr[3];

z1 = MULTIPLY(z2 + z3, FIX(0.831253876)); /* c3 */

tmp0 = z1 + MULTIPLY(z2, FIX(0.513743148)); /* c1-c3 */

tmp1 = z1 - MULTIPLY(z3, FIX(2.176250899)); /* c1+c3 */

/* Final output stage */

outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[4] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp11 + tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[3] = range_limit[(int) RIGHT_SHIFT(tmp11 - tmp1,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp12,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

wsptr += 5; /* advance pointer to next row */

}

}

/*

* Perform dequantization and inverse DCT on one block of coefficients,

* producing a reduced-size 4x4 output block.

*

* Optimized algorithm with 3 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/16) [refers to 8-point IDCT].

*/

GLOBAL(void)

jpeg_idct_4x4 (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp2, tmp10, tmp12;

INT32 z1, z2, z3;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[4*4]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array. */

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = 0; ctr < 4; ctr++, inptr++, quantptr++, wsptr++) {

/* Even part */

tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

tmp2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

tmp10 = (tmp0 + tmp2) << PASS1_BITS;

tmp12 = (tmp0 - tmp2) << PASS1_BITS;

/* Odd part */

/* Same rotation as in the even part of the 8x8 LL&M IDCT */

z2 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

z3 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

z1 = MULTIPLY(z2 + z3, FIX_0_541196100); /* c6 */

/* Add fudge factor here for final descale. */

z1 += ONE << (CONST_BITS-PASS1_BITS-1);

tmp0 = RIGHT_SHIFT(z1 + MULTIPLY(z2, FIX_0_765366865), /* c2-c6 */

CONST_BITS-PASS1_BITS);

tmp2 = RIGHT_SHIFT(z1 - MULTIPLY(z3, FIX_1_847759065), /* c2+c6 */

CONST_BITS-PASS1_BITS);

/* Final output stage */

wsptr[4*0] = (int) (tmp10 + tmp0);

wsptr[4*3] = (int) (tmp10 - tmp0);

wsptr[4*1] = (int) (tmp12 + tmp2);

wsptr[4*2] = (int) (tmp12 - tmp2);

}

/* Pass 2: process 4 rows from work array, store into output array. */

wsptr = workspace;

for (ctr = 0; ctr < 4; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Even part */

/* Add range center and fudge factor for final descale and range-limit. */

tmp0 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

tmp2 = (INT32) wsptr[2];

tmp10 = (tmp0 + tmp2) << CONST_BITS;

tmp12 = (tmp0 - tmp2) << CONST_BITS;

/* Odd part */

/* Same rotation as in the even part of the 8x8 LL&M IDCT */

z2 = (INT32) wsptr[1];

z3 = (INT32) wsptr[3];

z1 = MULTIPLY(z2 + z3, FIX_0_541196100); /* c6 */

tmp0 = z1 + MULTIPLY(z2, FIX_0_765366865); /* c2-c6 */

tmp2 = z1 - MULTIPLY(z3, FIX_1_847759065); /* c2+c6 */

/* Final output stage */

outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[3] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp0,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp12 + tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp12 - tmp2,

CONST_BITS+PASS1_BITS+3)

& RANGE_MASK];

wsptr += 4; /* advance pointer to next row */

}

}

/*

* Perform dequantization and inverse DCT on one block of coefficients,

* producing a reduced-size 3x3 output block.

*

* Optimized algorithm with 2 multiplications in the 1-D kernel.

* cK represents sqrt(2) * cos(K*pi/6).

*/

GLOBAL(void)

jpeg_idct_3x3 (j_decompress_ptr cinfo, jpeg_component_info * compptr,

JCOEFPTR coef_block,

JSAMPARRAY output_buf, JDIMENSION output_col)

{

INT32 tmp0, tmp2, tmp10, tmp12;

JCOEFPTR inptr;

ISLOW_MULT_TYPE * quantptr;

int * wsptr;

JSAMPROW outptr;

JSAMPLE *range_limit = IDCT_range_limit(cinfo);

int ctr;

int workspace[3*3]; /* buffers data between passes */

SHIFT_TEMPS

/* Pass 1: process columns from input, store into work array. */

inptr = coef_block;

quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;

wsptr = workspace;

for (ctr = 0; ctr < 3; ctr++, inptr++, quantptr++, wsptr++) {

/* Even part */

tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

tmp0 <<= CONST_BITS;

/* Add fudge factor here for final descale. */

tmp0 += ONE << (CONST_BITS-PASS1_BITS-1);

tmp2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

tmp12 = MULTIPLY(tmp2, FIX(0.707106781)); /* c2 */

tmp10 = tmp0 + tmp12;

tmp2 = tmp0 - tmp12 - tmp12;

/* Odd part */

tmp12 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

tmp0 = MULTIPLY(tmp12, FIX(1.224744871)); /* c1 */

/* Final output stage */

wsptr[3*0] = (int) RIGHT_SHIFT(tmp10 + tmp0, CONST_BITS-PASS1_BITS);

wsptr[3*2] = (int) RIGHT_SHIFT(tmp10 - tmp0, CONST_BITS-PASS1_BITS);

wsptr[3*1] = (int) RIGHT_SHIFT(tmp2, CONST_BITS-PASS1_BITS);

}

/* Pass 2: process 3 rows from work array, store into output array. */

wsptr = workspace;

for (ctr = 0; ctr < 3; ctr++) {

outptr = output_buf[ctr] + output_col;

/* Even part */

/* Add range center and fudge factor for final descale and range-limit. */

tmp0 = (INT32) wsptr[0] +

((((INT32) RANGE_CENTER) << (PASS1_BITS+3)) +

(ONE << (PASS1_BITS+2)));

tmp0 <<= CONST_BITS;

tmp2 = (INT32) wsptr[2];

tmp12 = MULTIPLY(tmp2, FIX(0.707106781)); /* c2 */

tmp10 = tmp0 + tmp12;

tmp2 = tmp0 - tmp12 - tmp12;

/* Odd part */

tmp12 = (INT32) wsptr[1];