/src/dcmtk/dcmjpeg/libijg16/jfdctint.c

Source
/*
 * jfdctint.c
 *
 * Copyright (C) 1991-1996, 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 a slow-but-accurate integer implementation of the
 * forward DCT (Discrete Cosine Transform).
 *
 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
 * 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.
 *
 * 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.
 */

#define JPEG_INTERNALS
#include "jinclude16.h"
#include "jpeglib16.h"
#include "jdct16.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 DCTs. /* deliberate syntax err */
#endif


/*
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
 * larger than the true DCT 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 DCT,
 * because the y0 and y4 outputs need not be divided by sqrt(N).
 * In the IJG code, this factor of 8 is removed by the quantization step
 * (in jcdctmgr.c), NOT in this module.
 *
 * 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.  (For 12-bit sample data, the intermediate
 * array is IJG_INT32 anyway.)
 *
 * 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  ((IJG_INT32)  2446)  /* FIX(0.298631336) */
#define FIX_0_390180644  ((IJG_INT32)  3196)  /* FIX(0.390180644) */
#define FIX_0_541196100  ((IJG_INT32)  4433)  /* FIX(0.541196100) */
#define FIX_0_765366865  ((IJG_INT32)  6270)  /* FIX(0.765366865) */
#define FIX_0_899976223  ((IJG_INT32)  7373)  /* FIX(0.899976223) */
#define FIX_1_175875602  ((IJG_INT32)  9633)  /* FIX(1.175875602) */
#define FIX_1_501321110  ((IJG_INT32)  12299) /* FIX(1.501321110) */
#define FIX_1_847759065  ((IJG_INT32)  15137) /* FIX(1.847759065) */
#define FIX_1_961570560  ((IJG_INT32)  16069) /* FIX(1.961570560) */
#define FIX_2_053119869  ((IJG_INT32)  16819) /* FIX(2.053119869) */
#define FIX_2_562915447  ((IJG_INT32)  20995) /* FIX(2.562915447) */
#define FIX_3_072711026  ((IJG_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 IJG_INT32 variable by an IJG_INT32 constant to yield an IJG_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


/*
 * Perform the forward DCT on one block of samples.
 */

GLOBAL(void)
jpeg_fdct_islow (DCTELEM * data)
{
  IJG_INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  IJG_INT32 tmp10, tmp11, tmp12, tmp13;
  IJG_INT32 z1, z2, z3, z4, z5;
  DCTELEM *dataptr;
  int ctr;
  SHIFT_TEMPS

  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
    tmp0 = dataptr[0] + dataptr[7];
    tmp7 = dataptr[0] - dataptr[7];
    tmp1 = dataptr[1] + dataptr[6];
    tmp6 = dataptr[1] - dataptr[6];
    tmp2 = dataptr[2] + dataptr[5];
    tmp5 = dataptr[2] - dataptr[5];
    tmp3 = dataptr[3] + dataptr[4];
    tmp4 = dataptr[3] - dataptr[4];
    
    /* Even part per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */
    
    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
    
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
           CONST_BITS-PASS1_BITS);
    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
           CONST_BITS-PASS1_BITS);
    
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */
    
    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, 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;
    
    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
    
    dataptr += DCTSIZE;   /* advance pointer to next row */
  }

  /* Pass 2: process columns.
   * We remove the PASS1_BITS scaling, but leave the results scaled up
   * by an overall factor of 8.
   */

  dataptr = data;
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
    
    /* Even part per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */
    
    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
    
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
             CONST_BITS+PASS1_BITS);
    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
             CONST_BITS+PASS1_BITS);
    
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */
    
    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, 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;
    
    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
             CONST_BITS+PASS1_BITS);
    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
             CONST_BITS+PASS1_BITS);
    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
             CONST_BITS+PASS1_BITS);
    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
             CONST_BITS+PASS1_BITS);
    
    dataptr++;      /* advance pointer to next column */
  }
}

#endif /* DCT_ISLOW_SUPPORTED */

Coverage Report

Created: 2026-08-14 06:52

Line	Count	Source
1		/*
2		* jfdctint.c
3		*
4		* Copyright (C) 1991-1996, Thomas G. Lane.
5		* This file is part of the Independent JPEG Group's software.
6		* For conditions of distribution and use, see the accompanying README file.
7		*
8		* This file contains a slow-but-accurate integer implementation of the
9		* forward DCT (Discrete Cosine Transform).
10		*
11		* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
12		* on each column. Direct algorithms are also available, but they are
13		* much more complex and seem not to be any faster when reduced to code.
14		*
15		* This implementation is based on an algorithm described in
16		* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
17		* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
18		* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
19		* The primary algorithm described there uses 11 multiplies and 29 adds.
20		* We use their alternate method with 12 multiplies and 32 adds.
21		* The advantage of this method is that no data path contains more than one
22		* multiplication; this allows a very simple and accurate implementation in
23		* scaled fixed-point arithmetic, with a minimal number of shifts.
24		*/
25
26		#define JPEG_INTERNALS
27		#include "jinclude16.h"
28		#include "jpeglib16.h"
29		#include "jdct16.h" /* Private declarations for DCT subsystem */
30
31		#ifdef DCT_ISLOW_SUPPORTED
32
33
34		/*
35		* This module is specialized to the case DCTSIZE = 8.
36		*/
37
38		#if DCTSIZE != 8
39		Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
40		#endif
41
42
43		/*
44		* The poop on this scaling stuff is as follows:
45		*
46		* Each 1-D DCT step produces outputs which are a factor of sqrt(N)
47		* larger than the true DCT outputs. The final outputs are therefore
48		* a factor of N larger than desired; since N=8 this can be cured by
49		* a simple right shift at the end of the algorithm. The advantage of
50		* this arrangement is that we save two multiplications per 1-D DCT,
51		* because the y0 and y4 outputs need not be divided by sqrt(N).
52		* In the IJG code, this factor of 8 is removed by the quantization step
53		* (in jcdctmgr.c), NOT in this module.
54		*
55		* We have to do addition and subtraction of the integer inputs, which
56		* is no problem, and multiplication by fractional constants, which is
57		* a problem to do in integer arithmetic. We multiply all the constants
58		* by CONST_SCALE and convert them to integer constants (thus retaining
59		* CONST_BITS bits of precision in the constants). After doing a
60		* multiplication we have to divide the product by CONST_SCALE, with proper
61		* rounding, to produce the correct output. This division can be done
62		* cheaply as a right shift of CONST_BITS bits. We postpone shifting
63		* as long as possible so that partial sums can be added together with
64		* full fractional precision.
65		*
66		* The outputs of the first pass are scaled up by PASS1_BITS bits so that
67		* they are represented to better-than-integral precision. These outputs
68		* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
69		* with the recommended scaling. (For 12-bit sample data, the intermediate
70		* array is IJG_INT32 anyway.)
71		*
72		* To avoid overflow of the 32-bit intermediate results in pass 2, we must
73		* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
74		* shows that the values given below are the most effective.
75		*/
76
77		#if BITS_IN_JSAMPLE == 8
78		#define CONST_BITS 13
79		#define PASS1_BITS 2
80		#else
81		#define CONST_BITS 13
82	0	#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
83		#endif
84
85		/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
86		* causing a lot of useless floating-point operations at run time.
87		* To get around this we use the following pre-calculated constants.
88		* If you change CONST_BITS you may want to add appropriate values.
89		* (With a reasonable C compiler, you can just rely on the FIX() macro...)
90		*/
91
92		#if CONST_BITS == 13
93		#define FIX_0_298631336 ((IJG_INT32) 2446) /* FIX(0.298631336) */
94		#define FIX_0_390180644 ((IJG_INT32) 3196) /* FIX(0.390180644) */
95		#define FIX_0_541196100 ((IJG_INT32) 4433) /* FIX(0.541196100) */
96		#define FIX_0_765366865 ((IJG_INT32) 6270) /* FIX(0.765366865) */
97		#define FIX_0_899976223 ((IJG_INT32) 7373) /* FIX(0.899976223) */
98		#define FIX_1_175875602 ((IJG_INT32) 9633) /* FIX(1.175875602) */
99		#define FIX_1_501321110 ((IJG_INT32) 12299) /* FIX(1.501321110) */
100		#define FIX_1_847759065 ((IJG_INT32) 15137) /* FIX(1.847759065) */
101		#define FIX_1_961570560 ((IJG_INT32) 16069) /* FIX(1.961570560) */
102		#define FIX_2_053119869 ((IJG_INT32) 16819) /* FIX(2.053119869) */
103		#define FIX_2_562915447 ((IJG_INT32) 20995) /* FIX(2.562915447) */
104		#define FIX_3_072711026 ((IJG_INT32) 25172) /* FIX(3.072711026) */
105		#else
106		#define FIX_0_298631336 FIX(0.298631336)
107		#define FIX_0_390180644 FIX(0.390180644)
108		#define FIX_0_541196100 FIX(0.541196100)
109		#define FIX_0_765366865 FIX(0.765366865)
110		#define FIX_0_899976223 FIX(0.899976223)
111		#define FIX_1_175875602 FIX(1.175875602)
112		#define FIX_1_501321110 FIX(1.501321110)
113		#define FIX_1_847759065 FIX(1.847759065)
114		#define FIX_1_961570560 FIX(1.961570560)
115		#define FIX_2_053119869 FIX(2.053119869)
116		#define FIX_2_562915447 FIX(2.562915447)
117		#define FIX_3_072711026 FIX(3.072711026)
118		#endif
119
120
121		/* Multiply an IJG_INT32 variable by an IJG_INT32 constant to yield an IJG_INT32 result.
122		* For 8-bit samples with the recommended scaling, all the variable
123		* and constant values involved are no more than 16 bits wide, so a
124		* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
125		* For 12-bit samples, a full 32-bit multiplication will be needed.
126		*/
127
128		#if BITS_IN_JSAMPLE == 8
129		#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
130		#else
131	0	#define MULTIPLY(var,const) ((var) * (const))
132		#endif
133
134
135		/*
136		* Perform the forward DCT on one block of samples.
137		*/
138
139		GLOBAL(void)
140		jpeg_fdct_islow (DCTELEM * data)
141	0	{
142	0	IJG_INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
143	0	IJG_INT32 tmp10, tmp11, tmp12, tmp13;
144	0	IJG_INT32 z1, z2, z3, z4, z5;
145	0	DCTELEM *dataptr;
146	0	int ctr;
147	0	SHIFT_TEMPS
148
149		/* Pass 1: process rows. */
150		/* Note results are scaled up by sqrt(8) compared to a true DCT; */
151		/* furthermore, we scale the results by 2*PASS1_BITS. /
152
153	0	dataptr = data;
154	0	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
155	0	tmp0 = dataptr[0] + dataptr[7];
156	0	tmp7 = dataptr[0] - dataptr[7];
157	0	tmp1 = dataptr[1] + dataptr[6];
158	0	tmp6 = dataptr[1] - dataptr[6];
159	0	tmp2 = dataptr[2] + dataptr[5];
160	0	tmp5 = dataptr[2] - dataptr[5];
161	0	tmp3 = dataptr[3] + dataptr[4];
162	0	tmp4 = dataptr[3] - dataptr[4];
163
164		/* Even part per LL&M figure 1 --- note that published figure is faulty;
165		* rotator "sqrt(2)c1" should be "sqrt(2)c6".
166		*/
167
168	0	tmp10 = tmp0 + tmp3;
169	0	tmp13 = tmp0 - tmp3;
170	0	tmp11 = tmp1 + tmp2;
171	0	tmp12 = tmp1 - tmp2;
172
173	0	dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
174	0	dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
175
176	0	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
177	0	dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
178	0	CONST_BITS-PASS1_BITS);
179	0	dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
180	0	CONST_BITS-PASS1_BITS);
181
182		/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
183		* cK represents cos(K*pi/16).
184		* i0..i3 in the paper are tmp4..tmp7 here.
185		*/
186
187	0	z1 = tmp4 + tmp7;
188	0	z2 = tmp5 + tmp6;
189	0	z3 = tmp4 + tmp6;
190	0	z4 = tmp5 + tmp7;
191	0	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
192
193	0	tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
194	0	tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
195	0	tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
196	0	tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
197	0	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
198	0	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
199	0	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
200	0	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
201
202	0	z3 += z5;
203	0	z4 += z5;
204
205	0	dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
206	0	dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
207	0	dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
208	0	dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
209
210	0	dataptr += DCTSIZE; /* advance pointer to next row */
211	0	}
212
213		/* Pass 2: process columns.
214		* We remove the PASS1_BITS scaling, but leave the results scaled up
215		* by an overall factor of 8.
216		*/
217
218	0	dataptr = data;
219	0	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
220	0	tmp0 = dataptr[DCTSIZE0] + dataptr[DCTSIZE7];
221	0	tmp7 = dataptr[DCTSIZE0] - dataptr[DCTSIZE7];
222	0	tmp1 = dataptr[DCTSIZE1] + dataptr[DCTSIZE6];
223	0	tmp6 = dataptr[DCTSIZE1] - dataptr[DCTSIZE6];
224	0	tmp2 = dataptr[DCTSIZE2] + dataptr[DCTSIZE5];
225	0	tmp5 = dataptr[DCTSIZE2] - dataptr[DCTSIZE5];
226	0	tmp3 = dataptr[DCTSIZE3] + dataptr[DCTSIZE4];
227	0	tmp4 = dataptr[DCTSIZE3] - dataptr[DCTSIZE4];
228
229		/* Even part per LL&M figure 1 --- note that published figure is faulty;
230		* rotator "sqrt(2)c1" should be "sqrt(2)c6".
231		*/
232
233	0	tmp10 = tmp0 + tmp3;
234	0	tmp13 = tmp0 - tmp3;
235	0	tmp11 = tmp1 + tmp2;
236	0	tmp12 = tmp1 - tmp2;
237
238	0	dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
239	0	dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
240
241	0	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
242	0	dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
243	0	CONST_BITS+PASS1_BITS);
244	0	dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
245	0	CONST_BITS+PASS1_BITS);
246
247		/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
248		* cK represents cos(K*pi/16).
249		* i0..i3 in the paper are tmp4..tmp7 here.
250		*/
251
252	0	z1 = tmp4 + tmp7;
253	0	z2 = tmp5 + tmp6;
254	0	z3 = tmp4 + tmp6;
255	0	z4 = tmp5 + tmp7;
256	0	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
257
258	0	tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
259	0	tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
260	0	tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
261	0	tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
262	0	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
263	0	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
264	0	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
265	0	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
266
267	0	z3 += z5;
268	0	z4 += z5;
269
270	0	dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
271	0	CONST_BITS+PASS1_BITS);
272	0	dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
273	0	CONST_BITS+PASS1_BITS);
274	0	dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
275	0	CONST_BITS+PASS1_BITS);
276	0	dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
277	0	CONST_BITS+PASS1_BITS);
278
279	0	dataptr++; /* advance pointer to next column */
280	0	}
281	0	}
282
283		#endif /* DCT_ISLOW_SUPPORTED */