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1 /*
2  * jfdctfst.c
3  *
4  * This file was part of the Independent JPEG Group's software:
5  * Copyright (C) 1994-1996, Thomas G. Lane.
6  * libjpeg-turbo Modifications:
7  * Copyright (C) 2015, D. R. Commander.
8  * For conditions of distribution and use, see the accompanying README.ijg
9  * file.
10  *
11  * This file contains a fast, not so accurate integer implementation of the
12  * forward DCT (Discrete Cosine Transform).
13  *
14  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
15  * on each column.  Direct algorithms are also available, but they are
16  * much more complex and seem not to be any faster when reduced to code.
17  *
18  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
19  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
20  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
21  * JPEG textbook (see REFERENCES section in file README.ijg).  The following
22  * code is based directly on figure 4-8 in P&M.
23  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
24  * possible to arrange the computation so that many of the multiplies are
25  * simple scalings of the final outputs.  These multiplies can then be
26  * folded into the multiplications or divisions by the JPEG quantization
27  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
28  * to be done in the DCT itself.
29  * The primary disadvantage of this method is that with fixed-point math,
30  * accuracy is lost due to imprecise representation of the scaled
31  * quantization values.  The smaller the quantization table entry, the less
32  * precise the scaled value, so this implementation does worse with high-
33  * quality-setting files than with low-quality ones.
34  */
35 
36 #define JPEG_INTERNALS
37 #include "jinclude.h"
38 #include "jpeglib.h"
39 #include "jdct.h"               /* Private declarations for DCT subsystem */
40 
41 #ifdef DCT_IFAST_SUPPORTED
42 
43 
44 /*
45  * This module is specialized to the case DCTSIZE = 8.
46  */
47 
48 #if DCTSIZE != 8
49   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
50 #endif
51 
52 
53 /* Scaling decisions are generally the same as in the LL&M algorithm;
54  * see jfdctint.c for more details.  However, we choose to descale
55  * (right shift) multiplication products as soon as they are formed,
56  * rather than carrying additional fractional bits into subsequent additions.
57  * This compromises accuracy slightly, but it lets us save a few shifts.
58  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
59  * everywhere except in the multiplications proper; this saves a good deal
60  * of work on 16-bit-int machines.
61  *
62  * Again to save a few shifts, the intermediate results between pass 1 and
63  * pass 2 are not upscaled, but are represented only to integral precision.
64  *
65  * A final compromise is to represent the multiplicative constants to only
66  * 8 fractional bits, rather than 13.  This saves some shifting work on some
67  * machines, and may also reduce the cost of multiplication (since there
68  * are fewer one-bits in the constants).
69  */
70 
71 #define CONST_BITS  8
72 
73 
74 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
75  * causing a lot of useless floating-point operations at run time.
76  * To get around this we use the following pre-calculated constants.
77  * If you change CONST_BITS you may want to add appropriate values.
78  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
79  */
80 
81 #if CONST_BITS == 8
82 #define FIX_0_382683433  ((JLONG)   98)         /* FIX(0.382683433) */
83 #define FIX_0_541196100  ((JLONG)  139)         /* FIX(0.541196100) */
84 #define FIX_0_707106781  ((JLONG)  181)         /* FIX(0.707106781) */
85 #define FIX_1_306562965  ((JLONG)  334)         /* FIX(1.306562965) */
86 #else
87 #define FIX_0_382683433  FIX(0.382683433)
88 #define FIX_0_541196100  FIX(0.541196100)
89 #define FIX_0_707106781  FIX(0.707106781)
90 #define FIX_1_306562965  FIX(1.306562965)
91 #endif
92 
93 
94 /* We can gain a little more speed, with a further compromise in accuracy,
95  * by omitting the addition in a descaling shift.  This yields an incorrectly
96  * rounded result half the time...
97  */
98 
99 #ifndef USE_ACCURATE_ROUNDING
100 #undef DESCALE
101 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
102 #endif
103 
104 
105 /* Multiply a DCTELEM variable by an JLONG constant, and immediately
106  * descale to yield a DCTELEM result.
107  */
108 
109 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
110 
111 
112 /*
113  * Perform the forward DCT on one block of samples.
114  */
115 
116 GLOBAL(void)
117 jpeg_fdct_ifast (DCTELEM *data)
118 {
119   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
120   DCTELEM tmp10, tmp11, tmp12, tmp13;
121   DCTELEM z1, z2, z3, z4, z5, z11, z13;
122   DCTELEM *dataptr;
123   int ctr;
124   SHIFT_TEMPS
125 
126   /* Pass 1: process rows. */
127 
128   dataptr = data;
129   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
130     tmp0 = dataptr[0] + dataptr[7];
131     tmp7 = dataptr[0] - dataptr[7];
132     tmp1 = dataptr[1] + dataptr[6];
133     tmp6 = dataptr[1] - dataptr[6];
134     tmp2 = dataptr[2] + dataptr[5];
135     tmp5 = dataptr[2] - dataptr[5];
136     tmp3 = dataptr[3] + dataptr[4];
137     tmp4 = dataptr[3] - dataptr[4];
138 
139     /* Even part */
140 
141     tmp10 = tmp0 + tmp3;        /* phase 2 */
142     tmp13 = tmp0 - tmp3;
143     tmp11 = tmp1 + tmp2;
144     tmp12 = tmp1 - tmp2;
145 
146     dataptr[0] = tmp10 + tmp11; /* phase 3 */
147     dataptr[4] = tmp10 - tmp11;
148 
149     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
150     dataptr[2] = tmp13 + z1;    /* phase 5 */
151     dataptr[6] = tmp13 - z1;
152 
153     /* Odd part */
154 
155     tmp10 = tmp4 + tmp5;        /* phase 2 */
156     tmp11 = tmp5 + tmp6;
157     tmp12 = tmp6 + tmp7;
158 
159     /* The rotator is modified from fig 4-8 to avoid extra negations. */
160     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
161     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
162     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
163     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
164 
165     z11 = tmp7 + z3;            /* phase 5 */
166     z13 = tmp7 - z3;
167 
168     dataptr[5] = z13 + z2;      /* phase 6 */
169     dataptr[3] = z13 - z2;
170     dataptr[1] = z11 + z4;
171     dataptr[7] = z11 - z4;
172 
173     dataptr += DCTSIZE;         /* advance pointer to next row */
174   }
175 
176   /* Pass 2: process columns. */
177 
178   dataptr = data;
179   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
180     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
181     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
182     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
183     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
184     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
185     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
186     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
187     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
188 
189     /* Even part */
190 
191     tmp10 = tmp0 + tmp3;        /* phase 2 */
192     tmp13 = tmp0 - tmp3;
193     tmp11 = tmp1 + tmp2;
194     tmp12 = tmp1 - tmp2;
195 
196     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
197     dataptr[DCTSIZE*4] = tmp10 - tmp11;
198 
199     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
200     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
201     dataptr[DCTSIZE*6] = tmp13 - z1;
202 
203     /* Odd part */
204 
205     tmp10 = tmp4 + tmp5;        /* phase 2 */
206     tmp11 = tmp5 + tmp6;
207     tmp12 = tmp6 + tmp7;
208 
209     /* The rotator is modified from fig 4-8 to avoid extra negations. */
210     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
211     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
212     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
213     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
214 
215     z11 = tmp7 + z3;            /* phase 5 */
216     z13 = tmp7 - z3;
217 
218     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
219     dataptr[DCTSIZE*3] = z13 - z2;
220     dataptr[DCTSIZE*1] = z11 + z4;
221     dataptr[DCTSIZE*7] = z11 - z4;
222 
223     dataptr++;                  /* advance pointer to next column */
224   }
225 }
226 
227 #endif /* DCT_IFAST_SUPPORTED */
228