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.
8 * This file contains a slow-but-accurate integer implementation of the
9 * forward DCT (Discrete Cosine Transform).
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.
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.
33 #define BITS_IN_JSAMPLE 8
35 #define RIGHT_SHIFT(x, n) ((x) >> (n))
36 #define MULTIPLY16C16(var,const) ((var)*(const))
38 #if 1 //def USE_ACCURATE_ROUNDING
39 #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
41 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
46 * This module is specialized to the case DCTSIZE = 8.
50 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
55 * The poop on this scaling stuff is as follows:
57 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
58 * larger than the true DCT outputs. The final outputs are therefore
59 * a factor of N larger than desired; since N=8 this can be cured by
60 * a simple right shift at the end of the algorithm. The advantage of
61 * this arrangement is that we save two multiplications per 1-D DCT,
62 * because the y0 and y4 outputs need not be divided by sqrt(N).
63 * In the IJG code, this factor of 8 is removed by the quantization step
64 * (in jcdctmgr.c), NOT in this module.
66 * We have to do addition and subtraction of the integer inputs, which
67 * is no problem, and multiplication by fractional constants, which is
68 * a problem to do in integer arithmetic. We multiply all the constants
69 * by CONST_SCALE and convert them to integer constants (thus retaining
70 * CONST_BITS bits of precision in the constants). After doing a
71 * multiplication we have to divide the product by CONST_SCALE, with proper
72 * rounding, to produce the correct output. This division can be done
73 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
74 * as long as possible so that partial sums can be added together with
75 * full fractional precision.
77 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
78 * they are represented to better-than-integral precision. These outputs
79 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
80 * with the recommended scaling. (For 12-bit sample data, the intermediate
81 * array is INT32 anyway.)
83 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
84 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
85 * shows that the values given below are the most effective.
88 #if BITS_IN_JSAMPLE == 8
90 #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
93 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
96 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
97 * causing a lot of useless floating-point operations at run time.
98 * To get around this we use the following pre-calculated constants.
99 * If you change CONST_BITS you may want to add appropriate values.
100 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
104 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
105 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
106 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
107 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
108 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
109 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
110 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
111 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
112 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
113 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
114 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
115 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
117 #define FIX_0_298631336 FIX(0.298631336)
118 #define FIX_0_390180644 FIX(0.390180644)
119 #define FIX_0_541196100 FIX(0.541196100)
120 #define FIX_0_765366865 FIX(0.765366865)
121 #define FIX_0_899976223 FIX(0.899976223)
122 #define FIX_1_175875602 FIX(1.175875602)
123 #define FIX_1_501321110 FIX(1.501321110)
124 #define FIX_1_847759065 FIX(1.847759065)
125 #define FIX_1_961570560 FIX(1.961570560)
126 #define FIX_2_053119869 FIX(2.053119869)
127 #define FIX_2_562915447 FIX(2.562915447)
128 #define FIX_3_072711026 FIX(3.072711026)
132 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
133 * For 8-bit samples with the recommended scaling, all the variable
134 * and constant values involved are no more than 16 bits wide, so a
135 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
136 * For 12-bit samples, a full 32-bit multiplication will be needed.
139 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
140 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
142 #define MULTIPLY(var,const) ((var) * (const))
147 * Perform the forward DCT on one block of samples.
151 ff_jpeg_fdct_islow (DCTELEM * data)
153 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
154 INT32 tmp10, tmp11, tmp12, tmp13;
155 INT32 z1, z2, z3, z4, z5;
160 /* Pass 1: process rows. */
161 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
162 /* furthermore, we scale the results by 2**PASS1_BITS. */
165 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
166 tmp0 = dataptr[0] + dataptr[7];
167 tmp7 = dataptr[0] - dataptr[7];
168 tmp1 = dataptr[1] + dataptr[6];
169 tmp6 = dataptr[1] - dataptr[6];
170 tmp2 = dataptr[2] + dataptr[5];
171 tmp5 = dataptr[2] - dataptr[5];
172 tmp3 = dataptr[3] + dataptr[4];
173 tmp4 = dataptr[3] - dataptr[4];
175 /* Even part per LL&M figure 1 --- note that published figure is faulty;
176 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
184 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
185 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
187 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
188 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
189 CONST_BITS-PASS1_BITS);
190 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
191 CONST_BITS-PASS1_BITS);
193 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
194 * cK represents cos(K*pi/16).
195 * i0..i3 in the paper are tmp4..tmp7 here.
202 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
204 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
205 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
206 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
207 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
208 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
209 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
210 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
211 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
216 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
217 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
218 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
219 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
221 dataptr += DCTSIZE; /* advance pointer to next row */
224 /* Pass 2: process columns.
225 * We remove the PASS1_BITS scaling, but leave the results scaled up
226 * by an overall factor of 8.
230 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
231 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
232 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
233 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
234 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
235 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
236 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
237 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
238 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
240 /* Even part per LL&M figure 1 --- note that published figure is faulty;
241 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
249 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
250 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
252 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
253 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
254 CONST_BITS+PASS1_BITS);
255 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
256 CONST_BITS+PASS1_BITS);
258 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
259 * cK represents cos(K*pi/16).
260 * i0..i3 in the paper are tmp4..tmp7 here.
267 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
269 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
270 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
271 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
272 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
273 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
274 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
275 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
276 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
281 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
282 CONST_BITS+PASS1_BITS);
283 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
284 CONST_BITS+PASS1_BITS);
285 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
286 CONST_BITS+PASS1_BITS);
287 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
288 CONST_BITS+PASS1_BITS);
290 dataptr++; /* advance pointer to next column */