/*
* 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.
*
* I've made lots of modifications to attempt to take advantage of the
* sparse nature of the DCT matrices we're getting. Although the logic
* is cumbersome, it's straightforward and the resulting code is much
* faster.
*
* A better way to do this would be to pass in the DCT block as a sparse
* matrix, perhaps with the difference cases encoded.
*/
#include <memory.h>
#include "all.h"
#include "ansi.h"
#include "dct.h"
#define CONST_BITS 13
/*
* 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 PASS1_BITS 2
#else
#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.
* IMPORTANT: if your compiler doesn't do this arithmetic at compile time,
* you will pay a significant penalty in run time. In that case, figure
* the correct integer constant values and insert them by hand.
*/
/* Actually FIX is no longer used, we precomputed them all */
#define FIX(x) ((int32) ((x) * CONST_SCALE + 0.5))
/* 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
/*
Unlike our decoder where we approximate the FIXes, we need to use exact
ones here or successive P-frames will drift too much with Reference frame coding
*/
#define FIX_0_211164243 1730
#define FIX_0_275899380 2260
#define FIX_0_298631336 2446
#define FIX_0_390180644 3196
#define FIX_0_509795579 4176
#define FIX_0_541196100 4433
#define FIX_0_601344887 4926
#define FIX_0_765366865 6270
#define FIX_0_785694958 6436
#define FIX_0_899976223 7373
#define FIX_1_061594337 8697
#define FIX_1_111140466 9102
#define FIX_1_175875602 9633
#define FIX_1_306562965 10703
#define FIX_1_387039845 11363
#define FIX_1_451774981 11893
#define FIX_1_501321110 12299
#define FIX_1_662939225 13623
#define FIX_1_847759065 15137
#define FIX_1_961570560 16069
#define FIX_2_053119869 16819
#define FIX_2_172734803 17799
#define FIX_2_562915447 20995
#define FIX_3_072711026 25172
/*
Switch on reverse_dct choices
*/
void reference_rev_dct _ANSI_ARGS_((int16 *block));
void mpeg_jrevdct_quick _ANSI_ARGS_((int16 *block));
void init_idctref _ANSI_ARGS_((void));
extern boolean pureDCT;
void
mpeg_jrevdct(data)
DCTBLOCK data;
{
if (pureDCT) reference_rev_dct(data);
else mpeg_jrevdct_quick(data);
}
/*
* Perform the inverse DCT on one block of coefficients.
*/
void
mpeg_jrevdct_quick(data)
DCTBLOCK data;
{
int32 tmp0, tmp1, tmp2, tmp3;
int32 tmp10, tmp11, tmp12, tmp13;
int32 z1, z2, z3, z4, z5;
int32 d0, d1, d2, d3, d4, d5, d6, d7;
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.
*/
register int *idataptr = (int*)dataptr;
d0 = dataptr[0];
d1 = dataptr[1];
if ((d1 == 0) && (idataptr[1] | idataptr[2] | idataptr[3]) == 0) {
/* AC terms all zero */
if (d0) {
/* Compute a 32 bit value to assign. */
DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);
register int v = (dcval & 0xffff) | ((dcval << 16) & 0xffff0000);
idataptr[0] = v;
idataptr[1] = v;
idataptr[2] = v;
idataptr[3] = v;
}
dataptr += DCTSIZE; /* advance pointer to next row */
continue;
}
d2 = dataptr[2];
d3 = dataptr[3];
d4 = dataptr[4];
d5 = dataptr[5];
d6 = dataptr[6];
d7 = dataptr[7];
/* Even part: reverse the even part of the forward DCT. */
/* The rotator is sqrt(2)*c(-6). */
{
if (d6) {
if (d4) {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
}
} else {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
}
}
} else {
if (d4) {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
} else {
/* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
tmp10 = tmp13 = d4 << CONST_BITS;
tmp11 = tmp12 = -tmp10;
}
}
} else {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
} else {
/* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
tmp10 = tmp13 = tmp11 = tmp12 = 0;
}
}
}
}
/* Odd part per figure 8; the matrix is unitary and hence its
* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
*/
if (d7) {
if (d5) {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
z1 = d7 + d1;
z2 = d5 + d3;
z3 = d7 + d3;
z4 = d5 + d1;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
z2 = d5 + d3;
z3 = d7 + d3;
z5 = MULTIPLY(z3 + d5, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
z1 = MULTIPLY(-d7, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 = z1 + z4;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
z1 = d7 + d1;
z4 = d5 + d1;
z5 = MULTIPLY(d7 + z4, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z3 = MULTIPLY(-d7, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 = z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
tmp0 = MULTIPLY(-d7, FIX_0_601344887);
z1 = MULTIPLY(-d7, FIX_0_899976223);
z3 = MULTIPLY(-d7, FIX_1_961570560);
tmp1 = MULTIPLY(-d5, FIX_0_509795579);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
z3 += z5;
z4 += z5;
tmp0 += z3;
tmp1 += z4;
tmp2 = z2 + z3;
tmp3 = z1 + z4;
}
}
} else {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
z1 = d7 + d1;
z3 = d7 + d3;
z5 = MULTIPLY(z3 + d1, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-d3, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-d1, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 = z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
z3 = d7 + d3;
tmp0 = MULTIPLY(-d7, FIX_0_601344887);
z1 = MULTIPLY(-d7, FIX_0_899976223);
tmp2 = MULTIPLY(d3, FIX_0_509795579);
z2 = MULTIPLY(-d3, FIX_2_562915447);
z5 = MULTIPLY(z3, FIX_1_175875602);
z3 = MULTIPLY(-z3, FIX_0_785694958);
tmp0 += z3;
tmp1 = z2 + z5;
tmp2 += z3;
tmp3 = z1 + z5;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
z1 = d7 + d1;
z5 = MULTIPLY(z1, FIX_1_175875602);
z1 = MULTIPLY(z1, FIX_0_275899380);
z3 = MULTIPLY(-d7, FIX_1_961570560);
tmp0 = MULTIPLY(-d7, FIX_1_662939225);
z4 = MULTIPLY(-d1, FIX_0_390180644);
tmp3 = MULTIPLY(d1, FIX_1_111140466);
tmp0 += z1;
tmp1 = z4 + z5;
tmp2 = z3 + z5;
tmp3 += z1;
} else {
/* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
tmp0 = MULTIPLY(-d7, FIX_1_387039845);
tmp1 = MULTIPLY(d7, FIX_1_175875602);
tmp2 = MULTIPLY(-d7, FIX_0_785694958);
tmp3 = MULTIPLY(d7, FIX_0_275899380);
}
}
}
} else {
if (d5) {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
z2 = d5 + d3;
z4 = d5 + d1;
z5 = MULTIPLY(d3 + z4, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-d1, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-d3, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 = z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
z2 = d5 + d3;
z5 = MULTIPLY(z2, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_1_662939225);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z2 = MULTIPLY(-z2, FIX_1_387039845);
tmp2 = MULTIPLY(d3, FIX_1_111140466);
z3 = MULTIPLY(-d3, FIX_1_961570560);
tmp0 = z3 + z5;
tmp1 += z2;
tmp2 += z2;
tmp3 = z4 + z5;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
z4 = d5 + d1;
z5 = MULTIPLY(z4, FIX_1_175875602);
z1 = MULTIPLY(-d1, FIX_0_899976223);
tmp3 = MULTIPLY(d1, FIX_0_601344887);
tmp1 = MULTIPLY(-d5, FIX_0_509795579);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z4 = MULTIPLY(z4, FIX_0_785694958);
tmp0 = z1 + z5;
tmp1 += z4;
tmp2 = z2 + z5;
tmp3 += z4;
} else {
/* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
tmp0 = MULTIPLY(d5, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_0_275899380);
tmp2 = MULTIPLY(-d5, FIX_1_387039845);
tmp3 = MULTIPLY(d5, FIX_0_785694958);
}
}
} else {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
z5 = d1 + d3;
tmp3 = MULTIPLY(d1, FIX_0_211164243);
tmp2 = MULTIPLY(-d3, FIX_1_451774981);
z1 = MULTIPLY(d1, FIX_1_061594337);
z2 = MULTIPLY(-d3, FIX_2_172734803);
z4 = MULTIPLY(z5, FIX_0_785694958);
z5 = MULTIPLY(z5, FIX_1_175875602);
tmp0 = z1 - z4;
tmp1 = z2 + z4;
tmp2 += z5;
tmp3 += z5;
} else {
/* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(-d3, FIX_0_785694958);
tmp1 = MULTIPLY(-d3, FIX_1_387039845);
tmp2 = MULTIPLY(-d3, FIX_0_275899380);
tmp3 = MULTIPLY(d3, FIX_1_175875602);
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(d1, FIX_0_275899380);
tmp1 = MULTIPLY(d1, FIX_0_785694958);
tmp2 = MULTIPLY(d1, FIX_1_175875602);
tmp3 = MULTIPLY(d1, FIX_1_387039845);
} else {
/* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = tmp1 = tmp2 = tmp3 = 0;
}
}
}
}
}
/* 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.
*/
d0 = dataptr[DCTSIZE*0];
d1 = dataptr[DCTSIZE*1];
d2 = dataptr[DCTSIZE*2];
d3 = dataptr[DCTSIZE*3];
d4 = dataptr[DCTSIZE*4];
d5 = dataptr[DCTSIZE*5];
d6 = dataptr[DCTSIZE*6];
d7 = dataptr[DCTSIZE*7];
/* Even part: reverse the even part of the forward DCT. */
/* The rotator is sqrt(2)*c(-6). */
if (d6) {
if (d4) {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
}
} else {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
tmp2 = MULTIPLY(-d6, FIX_1_306562965);
tmp3 = MULTIPLY(d6, FIX_0_541196100);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
}
}
} else {
if (d4) {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = (d0 + d4) << CONST_BITS;
tmp1 = (d0 - d4) << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp1 + tmp2;
tmp12 = tmp1 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = d4 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp2 - tmp0;
tmp12 = -(tmp0 + tmp2);
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
} else {
/* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
tmp10 = tmp13 = d4 << CONST_BITS;
tmp11 = tmp12 = -tmp10;
}
}
} else {
if (d2) {
if (d0) {
/* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp0 = d0 << CONST_BITS;
tmp10 = tmp0 + tmp3;
tmp13 = tmp0 - tmp3;
tmp11 = tmp0 + tmp2;
tmp12 = tmp0 - tmp2;
} else {
/* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
tmp2 = MULTIPLY(d2, FIX_0_541196100);
tmp3 = MULTIPLY(d2, FIX_1_306562965);
tmp10 = tmp3;
tmp13 = -tmp3;
tmp11 = tmp2;
tmp12 = -tmp2;
}
} else {
if (d0) {
/* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
} else {
/* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
tmp10 = tmp13 = tmp11 = tmp12 = 0;
}
}
}
}
/* Odd part per figure 8; the matrix is unitary and hence its
* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
*/
if (d7) {
if (d5) {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
z1 = d7 + d1;
z2 = d5 + d3;
z3 = d7 + d3;
z4 = d5 + d1;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
z1 = d7;
z2 = d5 + d3;
z3 = d7 + d3;
z5 = MULTIPLY(z3 + d5, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
z1 = MULTIPLY(-d7, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 = z1 + z4;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
z1 = d7 + d1;
z2 = d5;
z3 = d7;
z4 = d5 + d1;
z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z3 = MULTIPLY(-d7, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 += z2 + z4;
tmp2 = z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
tmp0 = MULTIPLY(-d7, FIX_0_601344887);
z1 = MULTIPLY(-d7, FIX_0_899976223);
z3 = MULTIPLY(-d7, FIX_1_961570560);
tmp1 = MULTIPLY(-d5, FIX_0_509795579);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
z3 += z5;
z4 += z5;
tmp0 += z3;
tmp1 += z4;
tmp2 = z2 + z3;
tmp3 = z1 + z4;
}
}
} else {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
z1 = d7 + d1;
z3 = d7 + d3;
z5 = MULTIPLY(z3 + d1, FIX_1_175875602);
tmp0 = MULTIPLY(d7, FIX_0_298631336);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-z1, FIX_0_899976223);
z2 = MULTIPLY(-d3, FIX_2_562915447);
z3 = MULTIPLY(-z3, FIX_1_961570560);
z4 = MULTIPLY(-d1, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 += z1 + z3;
tmp1 = z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
z3 = d7 + d3;
tmp0 = MULTIPLY(-d7, FIX_0_601344887);
z1 = MULTIPLY(-d7, FIX_0_899976223);
tmp2 = MULTIPLY(d3, FIX_0_509795579);
z2 = MULTIPLY(-d3, FIX_2_562915447);
z5 = MULTIPLY(z3, FIX_1_175875602);
z3 = MULTIPLY(-z3, FIX_0_785694958);
tmp0 += z3;
tmp1 = z2 + z5;
tmp2 += z3;
tmp3 = z1 + z5;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
z1 = d7 + d1;
z5 = MULTIPLY(z1, FIX_1_175875602);
z1 = MULTIPLY(z1, FIX_0_275899380);
z3 = MULTIPLY(-d7, FIX_1_961570560);
tmp0 = MULTIPLY(-d7, FIX_1_662939225);
z4 = MULTIPLY(-d1, FIX_0_390180644);
tmp3 = MULTIPLY(d1, FIX_1_111140466);
tmp0 += z1;
tmp1 = z4 + z5;
tmp2 = z3 + z5;
tmp3 += z1;
} else {
/* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
tmp0 = MULTIPLY(-d7, FIX_1_387039845);
tmp1 = MULTIPLY(d7, FIX_1_175875602);
tmp2 = MULTIPLY(-d7, FIX_0_785694958);
tmp3 = MULTIPLY(d7, FIX_0_275899380);
}
}
}
} else {
if (d5) {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
z2 = d5 + d3;
z4 = d5 + d1;
z5 = MULTIPLY(d3 + z4, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_2_053119869);
tmp2 = MULTIPLY(d3, FIX_3_072711026);
tmp3 = MULTIPLY(d1, FIX_1_501321110);
z1 = MULTIPLY(-d1, FIX_0_899976223);
z2 = MULTIPLY(-z2, FIX_2_562915447);
z3 = MULTIPLY(-d3, FIX_1_961570560);
z4 = MULTIPLY(-z4, FIX_0_390180644);
z3 += z5;
z4 += z5;
tmp0 = z1 + z3;
tmp1 += z2 + z4;
tmp2 += z2 + z3;
tmp3 += z1 + z4;
} else {
/* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
z2 = d5 + d3;
z5 = MULTIPLY(z2, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_1_662939225);
z4 = MULTIPLY(-d5, FIX_0_390180644);
z2 = MULTIPLY(-z2, FIX_1_387039845);
tmp2 = MULTIPLY(d3, FIX_1_111140466);
z3 = MULTIPLY(-d3, FIX_1_961570560);
tmp0 = z3 + z5;
tmp1 += z2;
tmp2 += z2;
tmp3 = z4 + z5;
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
z4 = d5 + d1;
z5 = MULTIPLY(z4, FIX_1_175875602);
z1 = MULTIPLY(-d1, FIX_0_899976223);
tmp3 = MULTIPLY(d1, FIX_0_601344887);
tmp1 = MULTIPLY(-d5, FIX_0_509795579);
z2 = MULTIPLY(-d5, FIX_2_562915447);
z4 = MULTIPLY(z4, FIX_0_785694958);
tmp0 = z1 + z5;
tmp1 += z4;
tmp2 = z2 + z5;
tmp3 += z4;
} else {
/* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
tmp0 = MULTIPLY(d5, FIX_1_175875602);
tmp1 = MULTIPLY(d5, FIX_0_275899380);
tmp2 = MULTIPLY(-d5, FIX_1_387039845);
tmp3 = MULTIPLY(d5, FIX_0_785694958);
}
}
} else {
if (d3) {
if (d1) {
/* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
z5 = d1 + d3;
tmp3 = MULTIPLY(d1, FIX_0_211164243);
tmp2 = MULTIPLY(-d3, FIX_1_451774981);
z1 = MULTIPLY(d1, FIX_1_061594337);
z2 = MULTIPLY(-d3, FIX_2_172734803);
z4 = MULTIPLY(z5, FIX_0_785694958);
z5 = MULTIPLY(z5, FIX_1_175875602);
tmp0 = z1 - z4;
tmp1 = z2 + z4;
tmp2 += z5;
tmp3 += z5;
} else {
/* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(-d3, FIX_0_785694958);
tmp1 = MULTIPLY(-d3, FIX_1_387039845);
tmp2 = MULTIPLY(-d3, FIX_0_275899380);
tmp3 = MULTIPLY(d3, FIX_1_175875602);
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(d1, FIX_0_275899380);
tmp1 = MULTIPLY(d1, FIX_0_785694958);
tmp2 = MULTIPLY(d1, FIX_1_175875602);
tmp3 = MULTIPLY(d1, FIX_1_387039845);
} else {
/* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = tmp1 = tmp2 = tmp3 = 0;
}
}
}
}
/* 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 */
}
}
/* here is the reference one, in case of problems with the normal one */
/* idctref.c, Inverse Discrete Fourier Transform, double precision */
/* Copyright (C) 1994, MPEG Software Simulation Group. All Rights Reserved. */
/*
* Disclaimer of Warranty
*
* These software programs are available to the user without any license fee or
* royalty on an "as is" basis. The MPEG Software Simulation Group disclaims
* any and all warranties, whether express, implied, or statuary, including any
* implied warranties or merchantability or of fitness for a particular
* purpose. In no event shall the copyright-holder be liable for any
* incidental, punitive, or consequential damages of any kind whatsoever
* arising from the use of these programs.
*
* This disclaimer of warranty extends to the user of these programs and user's
* customers, employees, agents, transferees, successors, and assigns.
*
* The MPEG Software Simulation Group does not represent or warrant that the
* programs furnished hereunder are free of infringement of any third-party
* patents.
*
* Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
* are subject to royalty fees to patent holders. Many of these patents are
* general enough such that they are unavoidable regardless of implementation
* design.
*
*/
/* Perform IEEE 1180 reference (64-bit floating point, separable 8x1
* direct matrix multiply) Inverse Discrete Cosine Transform
*/
/* Here we use math.h to generate constants. Compiler results may
vary a little */
#ifndef PI
#ifdef M_PI
#define PI M_PI
#else
#define PI 3.14159265358979323846
#endif
#endif
/* cosine transform matrix for 8x1 IDCT */
static double itrans_coef[8][8];
/* initialize DCT coefficient matrix */
void init_idctref()
{
int freq, time;
double scale;
for (freq=0; freq < 8; freq++)
{
scale = (freq == 0) ? sqrt(0.125) : 0.5;
for (time=0; time<8; time++)
itrans_coef[freq][time] = scale*cos((PI/8.0)*freq*(time + 0.5));
}
}
/* perform IDCT matrix multiply for 8x8 coefficient block */
void reference_rev_dct(block)
int16 *block;
{
int i, j, k, v;
double partial_product;
double tmp[64];
for (i=0; i<8; i++)
for (j=0; j<8; j++)
{
partial_product = 0.0;
for (k=0; k<8; k++)
partial_product+= itrans_coef[k][j]*block[8*i+k];
tmp[8*i+j] = partial_product;
}
/* Transpose operation is integrated into address mapping by switching
loop order of i and j */
for (j=0; j<8; j++)
for (i=0; i<8; i++)
{
partial_product = 0.0;
for (k=0; k<8; k++)
partial_product+= itrans_coef[k][i]*tmp[8*k+j];
v = floor(partial_product+0.5);
block[8*i+j] = (v<-256) ? -256 : ((v>255) ? 255 : v);
}
}