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/*
* jrevdct.c
*
* Copyright (C) 1991, 1992, Thomas G. Lane.
* 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 the basic inverse-DCT transformation subroutine.
*
* 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.
*/
#include "jinclude.h"
/*
* This routine is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/*
* A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT
* 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.
*
* 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.
*/
#ifdef EIGHT_BIT_SAMPLES
#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
#define ONE ((INT32) 1)
#define CONST_SCALE (ONE << CONST_BITS)
/* Convert a positive real constant to an integer scaled by CONST_SCALE. */
#define FIX(x) ((INT32) ((x) * CONST_SCALE + 0.5))
/* 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
/* Descale and correctly round an INT32 value that's scaled by N bits.
* We assume RIGHT_SHIFT rounds towards minus infinity, so adding
* the fudge factor is correct for either sign of X.
*/
#define DESCALE(x,n) RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)
/* 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;
* this provides a useful speedup on many machines.
* There is no way to specify a 16x16->32 multiply in portable C, but
* some C compilers will do the right thing if you provide the correct
* combination of casts.
* NB: for 12-bit samples, a full 32-bit multiplication will be needed.
*/
#ifdef EIGHT_BIT_SAMPLES
#ifdef SHORTxSHORT_32 /* may work if 'int' is 32 bits */
#define MULTIPLY(var,const) (((INT16) (var)) * ((INT16) (const)))
#endif
#ifdef SHORTxLCONST_32 /* known to work with Microsoft C 6.0 */
#define MULTIPLY(var,const) (((INT16) (var)) * ((INT32) (const)))
#endif
#endif
#ifndef MULTIPLY /* default definition */
#define MULTIPLY(var,const) ((var) * (const))
#endif
/*
* Perform the inverse DCT on one block of coefficients.
*/
GLOBAL void
j_rev_dct (DCTBLOCK data)
{
INT32 tmp0, tmp1, tmp2, tmp3;
INT32 tmp10, tmp11, tmp12, tmp13;
INT32 z1, z2, z3, z4, z5;
register DCTELEM *dataptr;
int rowctr;
SHIFT_TEMPS
/* Pass 1: process rows. */
/* Note results are scaled up by sqrt(8) compared to a true IDCT; */
/* furthermore, we scale the results by 2**PASS1_BITS. */
dataptr = data;
for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
/* 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 row 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
* row DCT calculations can be simplified this way.
*/
if ((dataptr[1] | dataptr[2] | dataptr[3] | dataptr[4] |
dataptr[5] | dataptr[6] | dataptr[7]) == 0) {
/* AC terms all zero */
DCTELEM dcval = (DCTELEM) (dataptr[0] << PASS1_BITS);
dataptr[0] = dcval;
dataptr[1] = dcval;
dataptr[2] = dcval;
dataptr[3] = dcval;
dataptr[4] = dcval;
dataptr[5] = dcval;
dataptr[6] = dcval;
dataptr[7] = dcval;
dataptr += DCTSIZE; /* advance pointer to next row */
continue;
}
/* Even part: reverse the even part of the forward DCT. */
/* The rotator is sqrt(2)*c(-6). */
z2 = (INT32) dataptr[2];
z3 = (INT32) dataptr[6];
z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
tmp0 = ((INT32) dataptr[0] + (INT32) dataptr[4]) << CONST_BITS;
tmp1 = ((INT32) dataptr[0] - (INT32) dataptr[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) dataptr[7];
tmp1 = (INT32) dataptr[5];
tmp2 = (INT32) dataptr[3];
tmp3 = (INT32) dataptr[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 */
dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
dataptr += DCTSIZE; /* advance pointer to next row */
}
/* Pass 2: process columns. */
/* Note that we must descale the results by a factor of 8 == 2**3, */
/* and also undo the PASS1_BITS scaling. */
dataptr = data;
for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
/* Columns of zeroes can be exploited in the same way as we did with rows.
* However, the row 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_COLUMN_TEST
if ((dataptr[DCTSIZE*1] | dataptr[DCTSIZE*2] | dataptr[DCTSIZE*3] |
dataptr[DCTSIZE*4] | dataptr[DCTSIZE*5] | dataptr[DCTSIZE*6] |
dataptr[DCTSIZE*7]) == 0) {
/* AC terms all zero */
DCTELEM dcval = (DCTELEM) DESCALE((INT32) dataptr[0], PASS1_BITS+3);
dataptr[DCTSIZE*0] = dcval;
dataptr[DCTSIZE*1] = dcval;
dataptr[DCTSIZE*2] = dcval;
dataptr[DCTSIZE*3] = dcval;
dataptr[DCTSIZE*4] = dcval;
dataptr[DCTSIZE*5] = dcval;
dataptr[DCTSIZE*6] = dcval;
dataptr[DCTSIZE*7] = dcval;
dataptr++; /* advance pointer to next column */
continue;
}
#endif
/* Even part: reverse the even part of the forward DCT. */
/* The rotator is sqrt(2)*c(-6). */
z2 = (INT32) dataptr[DCTSIZE*2];
z3 = (INT32) dataptr[DCTSIZE*6];
z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
tmp0 = ((INT32) dataptr[DCTSIZE*0] + (INT32) dataptr[DCTSIZE*4]) << CONST_BITS;
tmp1 = ((INT32) dataptr[DCTSIZE*0] - (INT32) dataptr[DCTSIZE*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) dataptr[DCTSIZE*7];
tmp1 = (INT32) dataptr[DCTSIZE*5];
tmp2 = (INT32) dataptr[DCTSIZE*3];
tmp3 = (INT32) dataptr[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 */
dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,
CONST_BITS+PASS1_BITS+3);
dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,
CONST_BITS+PASS1_BITS+3);
dataptr++; /* advance pointer to next column */
}
}
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