1 /*
2  * jfdctfst.c
3  *
4  * Copyright (C) 1994-1996, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for
16  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
17  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
18  * JPEG textbook (see REFERENCES section in file README).  The following code
19  * is based directly on figure 4-8 in P&M.
20  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
21  * possible to arrange the computation so that many of the multiplies are
22  * simple scalings of the final outputs.  These multiplies can then be
23  * folded into the multiplications or divisions by the JPEG quantization
24  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
25  * to be done in the DCT itself.
26  * The primary disadvantage of this method is that with fixed-point math,
27  * accuracy is lost due to imprecise representation of the scaled
28  * quantization values.  The smaller the quantization table entry, the less
29  * precise the scaled value, so this implementation does worse with high-
30  * quality-setting files than with low-quality ones.
31  */
32 
33 #define JPEG_INTERNALS
34 #include "jinclude.h"
35 #include "jpeglib.h"
36 #include "jdct.h"		/* Private declarations for DCT subsystem */
37 
38 #ifdef DCT_IFAST_SUPPORTED
39 
40 
41 /*
42  * This module is specialized to the case DCTSIZE = 8.
43  */
44 
45 #if DCTSIZE != 8
46   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
47 #endif
48 
49 
50 /* Scaling decisions are generally the same as in the LL&M algorithm;
51  * see jfdctint.c for more details.  However, we choose to descale
52  * (right shift) multiplication products as soon as they are formed,
53  * rather than carrying additional fractional bits into subsequent additions.
54  * This compromises accuracy slightly, but it lets us save a few shifts.
55  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
56  * everywhere except in the multiplications proper; this saves a good deal
57  * of work on 16-bit-int machines.
58  *
59  * Again to save a few shifts, the intermediate results between pass 1 and
60  * pass 2 are not upscaled, but are represented only to integral precision.
61  *
62  * A final compromise is to represent the multiplicative constants to only
63  * 8 fractional bits, rather than 13.  This saves some shifting work on some
64  * machines, and may also reduce the cost of multiplication (since there
65  * are fewer one-bits in the constants).
66  */
67 
68 #define CONST_BITS  8
69 
70 
71 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
72  * causing a lot of useless floating-point operations at run time.
73  * To get around this we use the following pre-calculated constants.
74  * If you change CONST_BITS you may want to add appropriate values.
75  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
76  */
77 
78 #if CONST_BITS == 8
79 #define FIX_0_382683433  ((INT32)   98)		/* FIX(0.382683433) */
80 #define FIX_0_541196100  ((INT32)  139)		/* FIX(0.541196100) */
81 #define FIX_0_707106781  ((INT32)  181)		/* FIX(0.707106781) */
82 #define FIX_1_306562965  ((INT32)  334)		/* FIX(1.306562965) */
83 #else
84 #define FIX_0_382683433  FIX(0.382683433)
85 #define FIX_0_541196100  FIX(0.541196100)
86 #define FIX_0_707106781  FIX(0.707106781)
87 #define FIX_1_306562965  FIX(1.306562965)
88 #endif
89 
90 
91 /* We can gain a little more speed, with a further compromise in accuracy,
92  * by omitting the addition in a descaling shift.  This yields an incorrectly
93  * rounded result half the time...
94  */
95 
96 #ifndef USE_ACCURATE_ROUNDING
97 #undef DESCALE
98 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
99 #endif
100 
101 
102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
103  * descale to yield a DCTELEM result.
104  */
105 
106 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
107 
108 
109 /*
110  * Perform the forward DCT on one block of samples.
111  */
112 
113 GLOBAL(void)
114 jpeg_fdct_ifast (DCTELEM * data)
115 {
116   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
117   DCTELEM tmp10, tmp11, tmp12, tmp13;
118   DCTELEM z1, z2, z3, z4, z5, z11, z13;
119   DCTELEM *dataptr;
120   int ctr;
121   SHIFT_TEMPS
122 
123   /* Pass 1: process rows. */
124 
125   dataptr = data;
126   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
127     tmp0 = dataptr[0] + dataptr[7];
128     tmp7 = dataptr[0] - dataptr[7];
129     tmp1 = dataptr[1] + dataptr[6];
130     tmp6 = dataptr[1] - dataptr[6];
131     tmp2 = dataptr[2] + dataptr[5];
132     tmp5 = dataptr[2] - dataptr[5];
133     tmp3 = dataptr[3] + dataptr[4];
134     tmp4 = dataptr[3] - dataptr[4];
135 
136     /* Even part */
137 
138     tmp10 = tmp0 + tmp3;	/* phase 2 */
139     tmp13 = tmp0 - tmp3;
140     tmp11 = tmp1 + tmp2;
141     tmp12 = tmp1 - tmp2;
142 
143     dataptr[0] = tmp10 + tmp11; /* phase 3 */
144     dataptr[4] = tmp10 - tmp11;
145 
146     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
147     dataptr[2] = tmp13 + z1;	/* phase 5 */
148     dataptr[6] = tmp13 - z1;
149 
150     /* Odd part */
151 
152     tmp10 = tmp4 + tmp5;	/* phase 2 */
153     tmp11 = tmp5 + tmp6;
154     tmp12 = tmp6 + tmp7;
155 
156     /* The rotator is modified from fig 4-8 to avoid extra negations. */
157     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
158     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
159     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
160     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
161 
162     z11 = tmp7 + z3;		/* phase 5 */
163     z13 = tmp7 - z3;
164 
165     dataptr[5] = z13 + z2;	/* phase 6 */
166     dataptr[3] = z13 - z2;
167     dataptr[1] = z11 + z4;
168     dataptr[7] = z11 - z4;
169 
170     dataptr += DCTSIZE;		/* advance pointer to next row */
171   }
172 
173   /* Pass 2: process columns. */
174 
175   dataptr = data;
176   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
177     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
178     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
179     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
180     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
181     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
182     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
183     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
184     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
185 
186     /* Even part */
187 
188     tmp10 = tmp0 + tmp3;	/* phase 2 */
189     tmp13 = tmp0 - tmp3;
190     tmp11 = tmp1 + tmp2;
191     tmp12 = tmp1 - tmp2;
192 
193     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
194     dataptr[DCTSIZE*4] = tmp10 - tmp11;
195 
196     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
197     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
198     dataptr[DCTSIZE*6] = tmp13 - z1;
199 
200     /* Odd part */
201 
202     tmp10 = tmp4 + tmp5;	/* phase 2 */
203     tmp11 = tmp5 + tmp6;
204     tmp12 = tmp6 + tmp7;
205 
206     /* The rotator is modified from fig 4-8 to avoid extra negations. */
207     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
208     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
209     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
210     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
211 
212     z11 = tmp7 + z3;		/* phase 5 */
213     z13 = tmp7 - z3;
214 
215     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
216     dataptr[DCTSIZE*3] = z13 - z2;
217     dataptr[DCTSIZE*1] = z11 + z4;
218     dataptr[DCTSIZE*7] = z11 - z4;
219 
220     dataptr++;			/* advance pointer to next column */
221   }
222 }
223 
224 #endif /* DCT_IFAST_SUPPORTED */
225