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jidctint.c
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jidctint.c
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/*
* jidctint.c
*
* Copyright (C) 1991-1998, Thomas G. Lane.
* Modification developed 2002-2009 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 without additional resampling:
* NxN (N=1...16) 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.
*/
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, z4, z5;
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 sqrt(2)*c(-6). */
z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
tmp0 = (z2 + z3) << CONST_BITS;
tmp1 = (z2 - z3) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
/* 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]);
z1 = tmp0 + tmp3;
z2 = tmp1 + tmp2;
z3 = tmp0 + tmp2;
z4 = tmp1 + tmp3;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
wsptr[DCTSIZE*4] = (int) DESCALE(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;
/* 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) DESCALE((INT32) wsptr[0], 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 sqrt(2)*c(-6). */
z2 = (INT32) wsptr[2];
z3 = (INT32) wsptr[6];
z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
/* 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];
z1 = tmp0 + tmp3;
z2 = tmp1 + tmp2;
z3 = tmp0 + tmp2;
z4 = tmp1 + tmp3;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[4] = range_limit[(int) DESCALE(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 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 fudge factor here for final descale. */
tmp13 = (INT32) wsptr[0] + (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 fudge factor here for final descale. */
tmp0 = (INT32) wsptr[0] + (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 fudge factor here for final descale. */
tmp12 = (INT32) wsptr[0] + (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 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 fudge factor here for final descale. */
tmp0 = (INT32) wsptr[0] + (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];
tmp0 = MULTIPLY(tmp12, FIX(1.224744871)); /* c1 */
/* Final output stage */
outptr[0] = range_limit[(int) RIGHT_SHIFT(tmp10 + tmp0,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[2] = range_limit[(int) RIGHT_SHIFT(tmp10 - tmp0,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
outptr[1] = range_limit[(int) RIGHT_SHIFT(tmp2,
CONST_BITS+PASS1_BITS+3)
& RANGE_MASK];
wsptr += 3; /* advance pointer to next row */
}
}
/*
* Perform dequantization and inverse DCT on one block of coefficients,
* producing a 9x9 output block.
*
* Optimized algorithm with 10 multiplications in the 1-D kernel.
* cK represents sqrt(2) * cos(K*pi/18).
*/
GLOBAL(void)
jpeg_idct_9x9 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
JCOEFPTR coef_block,
JSAMPARRAY output_buf, JDIMENSION output_col)
{
INT32 tmp0, tmp1, tmp2, tmp3, tmp10, tmp11, tmp12, tmp13, tmp14;
INT32 z1, z2, z3, z4;
JCOEFPTR inptr;
ISLOW_MULT_TYPE * quantptr;
int * wsptr;
JSAMPROW outptr;
JSAMPLE *range_limit = IDCT_range_limit(cinfo);
int ctr;
int workspace[8*9]; /* 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 < 8; 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);
z1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
z2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
tmp3 = MULTIPLY(z3, FIX(0.707106781)); /* c6 */
tmp1 = tmp0 + tmp3;
tmp2 = tmp0 - tmp3 - tmp3;
tmp0 = MULTIPLY(z1 - z2, FIX(0.707106781)); /* c6 */
tmp11 = tmp2 + tmp0;
tmp14 = tmp2 - tmp0 - tmp0;
tmp0 = MULTIPLY(z1 + z2, FIX(1.328926049)); /* c2 */
tmp2 = MULTIPLY(z1, FIX(1.083350441)); /* c4 */
tmp3 = MULTIPLY(z2, FIX(0.245575608)); /* c8 */
tmp10 = tmp1 + tmp0 - tmp3;
tmp12 = tmp1 - tmp0 + tmp2;
tmp13 = tmp1 - tmp2 + tmp3;
/* 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]);
z4 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
z2 = MULTIPLY(z2, - FIX(1.224744871)); /* -c3 */
tmp2 = MULTIPLY(z1 + z3, FIX(0.909038955)); /* c5 */
tmp3 = MULTIPLY(z1 + z4, FIX(0.483689525)); /* c7 */
tmp0 = tmp2 + tmp3 - z2;
tmp1 = MULTIPLY(z3 - z4, FIX(1.392728481)); /* c1 */
tmp2 += z2 - tmp1;
tmp3 += z2 + tmp1;
tmp1 = MULTIPLY(z1 - z3 - z4, FIX(1.224744871)); /* c3 */
/* Final output stage */
wsptr[8*0] = (int) RIGHT_SHIFT(tmp10 + tmp0, CONST_BITS-PASS1_BITS);
wsptr[8*8] = (int) RIGHT_SHIFT(tmp10 - tmp0, CONST_BITS-PASS1_BITS);
wsptr[8*1] = (int) RIGHT_SHIFT(tmp11 + tmp1, CONST_BITS-PASS1_BITS);
wsptr[8*7] = (int) RIGHT_SHIFT(tmp11 - tmp1, CONST_BITS-PASS1_BITS);
wsptr[8*2] = (int) RIGHT_SHIFT(tmp12 + tmp2, CONST_BITS-PASS1_BITS);
wsptr[8*6] = (int) RIGHT_SHIFT(tmp12 - tmp2, CONST_BITS-PASS1_BITS);
wsptr[8*3] = (int) RIGHT_SHIFT(tmp13 + tmp3, CONST_BITS-PASS1_BITS);
wsptr[8*5] = (int) RIGHT_SHIFT(tmp13 - tmp3, CONST_BITS-PASS1_BITS);
wsptr[8*4] = (int) RIGHT_SHIFT(tmp14, CONST_BITS-PASS1_BITS);
}
/* Pass 2: process 9 rows from work array, store into output array. */
wsptr = workspace;
for (ctr = 0; ctr < 9; ctr++) {
outptr = output_buf[ctr] + output_col;
/* Even part */
/* Add fudge factor here for final descale. */
tmp0 = (INT32) wsptr[0] + (ONE << (PASS1_BITS+2));
tmp0 <<= CONST_BITS;
z1 = (INT32) wsptr[2];
z2 = (INT32) wsptr[4];
z3 = (INT32) wsptr[6];
tmp3 = MULTIPLY(z3, FIX(0.707106781)); /* c6 */
tmp1 = tmp0 + tmp3;
tmp2 = tmp0 - tmp3 - tmp3;
tmp0 = MULTIPLY(z1 - z2, FIX(0.707106781)); /* c6 */
tmp11 = tmp2 + tmp0;
tmp14 = tmp2 - tmp0 - tmp0;
tmp0 = MULTIPLY(z1 + z2, FIX(1.328926049)); /* c2 */