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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.
*
* 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.
*/
#define DCTSIZE 8 /* The basic DCT block is 8x8 samples */
#define DCTSIZE2 64 /* DCTSIZE squared; # of elements in a block */
#define GLOBAL /* a function referenced thru EXTERNs */
#ifndef XMD_H /* X11/xmd.h correctly defines INT32 */
typedef int INT32;
#endif
typedef short DCTELEM;
typedef DCTELEM DCTBLOCK[DCTSIZE2];
/* We assume that right shift corresponds to signed division by 2 with
* rounding towards minus infinity. This is correct for typical "arithmetic
* shift" instructions that shift in copies of the sign bit. But some
* C compilers implement >> with an unsigned shift. For these machines you
* must define RIGHT_SHIFT_IS_UNSIGNED.
* RIGHT_SHIFT provides a proper signed right shift of an INT32 quantity.
* It is only applied with constant shift counts. SHIFT_TEMPS must be
* included in the variables of any routine using RIGHT_SHIFT.
*/
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define SHIFT_TEMPS INT32 shift_temp;
#define RIGHT_SHIFT(x,shft) \
((shift_temp = (x)) < 0 ? \
(shift_temp >> (shft)) | ((~((INT32) 0)) << (32-(shft))) : \
(shift_temp >> (shft)))
#else
#define SHIFT_TEMPS
#define RIGHT_SHIFT(x,shft) ((x) >> (shft))
#endif
/*
* 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.
* 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.
*/
#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
/* Precomputed idct value arrays. */
static DCTELEM PreIDCT[64][64];
/* Pre compute singleton coefficient IDCT values. */
void
init_pre_idct() {
int i;
void j_rev_dct();
for (i=0; i<64; i++) {
memset((char *) PreIDCT[i], 0, 64*sizeof(int));
PreIDCT[i][i] = 2047;
j_rev_dct(PreIDCT[i],0);
}
}
/*
* Perform the inverse DCT on one block of coefficients.
*/
void
j_rev_dct (data, sparseFlag)
DCTBLOCK data;
int sparseFlag;
{
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;
/* If sparseFlag != 0, do sparse idct instead. Reset sparseFlag. */
if (sparseFlag) {
short int val;
DCTELEM *ndataptr;
int scale, coeff, rr;
/* Restore position stored in sparse flag. */
sparseFlag--;
/* If DC Coefficient. */
if (sparseFlag == 0) {
register int v, *dp = (int *)dataptr;
if (*dataptr < 0) val = (*dataptr-3)>>3;
else val = (*dataptr+4)>>3;
/* Compute 32 bit value to assign. This speeds things up a bit */
v = (val & 0xffff) | ((val << 16) & 0xffff0000);
for (rr=0; rr<32; rr++) {
*dp++ = v;
}
}
/* Some other coefficient. */
else {
coeff = *(dataptr+sparseFlag);
scale = (coeff << CONST_BITS) / (2047 << CONST_BITS) ;
ndataptr = PreIDCT[sparseFlag];
for (rr =0; rr<64; rr++) {
*dataptr++ = (((*ndataptr++) * scale) >> CONST_BITS);
}
}
return;
}
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 */
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(0.509795578));
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(0.275899379));
z3 = MULTIPLY(d7, - FIX(1.961570560));
tmp0 = MULTIPLY(d7, - FIX(1.662939224));
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(0.275899379));
}
}
}
} 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(0.509795578));
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(0.275899379));
tmp3 = MULTIPLY(d3, FIX(1.175875602));
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(d1, FIX(0.275899379));
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.
*/
#ifndef NO_ZERO_COLUMN_TEST
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];
if ((d1 == 0) && (d2 == 0) && (d3 == 0) && (d4 == 0) &&
(d5 == 0) && (d6 == 0) && (d7 == 0)) {
/* AC terms all zero */
if (d0) {
DCTELEM dcval = (DCTELEM) DESCALE((INT32) d0, 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). */
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(0.509795578));
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(0.275899379));
z3 = MULTIPLY(d7, - FIX(1.961570560));
tmp0 = MULTIPLY(d7, - FIX(1.662939224));
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(0.275899379));
}
}
}
} 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(0.509795578));
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(0.275899379));
tmp3 = MULTIPLY(d3, FIX(1.175875602));
}
} else {
if (d1) {
/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
tmp0 = MULTIPLY(d1, FIX(0.275899379));
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 */
}
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.