1 /*
2  * jfdctfst.c
3  *
4  * Copyright (C) 1994-1996, Thomas G. Lane.
5  * Modified 2003-2015 by Guido Vollbeding.
6  * This file is part of the Independent JPEG Group's software.
7  * For conditions of distribution and use, see the accompanying README file.
8  *
9  * This file contains a fast, not so accurate integer implementation of the
10  * forward DCT (Discrete Cosine Transform).
11  *
12  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
13  * on each column.  Direct algorithms are also available, but they are
14  * much more complex and seem not to be any faster when reduced to code.
15  *
16  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
17  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
18  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
19  * JPEG textbook (see REFERENCES section in file README).  The following code
20  * is based directly on figure 4-8 in P&M.
21  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
22  * possible to arrange the computation so that many of the multiplies are
23  * simple scalings of the final outputs.  These multiplies can then be
24  * folded into the multiplications or divisions by the JPEG quantization
25  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
26  * to be done in the DCT itself.
27  * The primary disadvantage of this method is that with fixed-point math,
28  * accuracy is lost due to imprecise representation of the scaled
29  * quantization values.  The smaller the quantization table entry, the less
30  * precise the scaled value, so this implementation does worse with high-
31  * quality-setting files than with low-quality ones.
32  */
33 
34 #define JPEG_INTERNALS
35 #include "jinclude.h"
36 #include "jpeglib.h"
37 #include "jdct.h"		/* Private declarations for DCT subsystem */
38 
39 #ifdef DCT_IFAST_SUPPORTED
40 
41 
42 /*
43  * This module is specialized to the case DCTSIZE = 8.
44  */
45 
46 #if DCTSIZE != 8
47   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
48 #endif
49 
50 
51 /* Scaling decisions are generally the same as in the LL&M algorithm;
52  * see jfdctint.c for more details.  However, we choose to descale
53  * (right shift) multiplication products as soon as they are formed,
54  * rather than carrying additional fractional bits into subsequent additions.
55  * This compromises accuracy slightly, but it lets us save a few shifts.
56  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
57  * everywhere except in the multiplications proper; this saves a good deal
58  * of work on 16-bit-int machines.
59  *
60  * Again to save a few shifts, the intermediate results between pass 1 and
61  * pass 2 are not upscaled, but are represented only to integral precision.
62  *
63  * A final compromise is to represent the multiplicative constants to only
64  * 8 fractional bits, rather than 13.  This saves some shifting work on some
65  * machines, and may also reduce the cost of multiplication (since there
66  * are fewer one-bits in the constants).
67  */
68 
69 #define CONST_BITS  8
70 
71 
72 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
73  * causing a lot of useless floating-point operations at run time.
74  * To get around this we use the following pre-calculated constants.
75  * If you change CONST_BITS you may want to add appropriate values.
76  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
77  */
78 
79 #if CONST_BITS == 8
80 #define FIX_0_382683433  ((INT32)   98)		/* FIX(0.382683433) */
81 #define FIX_0_541196100  ((INT32)  139)		/* FIX(0.541196100) */
82 #define FIX_0_707106781  ((INT32)  181)		/* FIX(0.707106781) */
83 #define FIX_1_306562965  ((INT32)  334)		/* FIX(1.306562965) */
84 #else
85 #define FIX_0_382683433  FIX(0.382683433)
86 #define FIX_0_541196100  FIX(0.541196100)
87 #define FIX_0_707106781  FIX(0.707106781)
88 #define FIX_1_306562965  FIX(1.306562965)
89 #endif
90 
91 
92 /* We can gain a little more speed, with a further compromise in accuracy,
93  * by omitting the addition in a descaling shift.  This yields an incorrectly
94  * rounded result half the time...
95  */
96 
97 #ifndef USE_ACCURATE_ROUNDING
98 #undef DESCALE
99 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
100 #endif
101 
102 
103 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
104  * descale to yield a DCTELEM result.
105  */
106 
107 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
108 
109 
110 /*
111  * Perform the forward DCT on one block of samples.
112  *
113  * cK represents cos(K*pi/16).
114  */
115 
116 GLOBAL(void)
117 jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
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   JSAMPROW elemptr;
124   int ctr;
125   SHIFT_TEMPS
126 
127   /* Pass 1: process rows. */
128 
129   dataptr = data;
130   for (ctr = 0; ctr < DCTSIZE; ctr++) {
131     elemptr = sample_data[ctr] + start_col;
132 
133     /* Load data into workspace */
134     tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);
135     tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);
136     tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);
137     tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);
138     tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);
139     tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);
140     tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);
141     tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);
142 
143     /* Even part */
144 
145     tmp10 = tmp0 + tmp3;	/* phase 2 */
146     tmp13 = tmp0 - tmp3;
147     tmp11 = tmp1 + tmp2;
148     tmp12 = tmp1 - tmp2;
149 
150     /* Apply unsigned->signed conversion. */
151     dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */
152     dataptr[4] = tmp10 - tmp11;
153 
154     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
155     dataptr[2] = tmp13 + z1;	/* phase 5 */
156     dataptr[6] = tmp13 - z1;
157 
158     /* Odd part */
159 
160     tmp10 = tmp4 + tmp5;	/* phase 2 */
161     tmp11 = tmp5 + tmp6;
162     tmp12 = tmp6 + tmp7;
163 
164     /* The rotator is modified from fig 4-8 to avoid extra negations. */
165     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
166     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
167     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
168     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
169 
170     z11 = tmp7 + z3;		/* phase 5 */
171     z13 = tmp7 - z3;
172 
173     dataptr[5] = z13 + z2;	/* phase 6 */
174     dataptr[3] = z13 - z2;
175     dataptr[1] = z11 + z4;
176     dataptr[7] = z11 - z4;
177 
178     dataptr += DCTSIZE;		/* advance pointer to next row */
179   }
180 
181   /* Pass 2: process columns. */
182 
183   dataptr = data;
184   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
185     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
186     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
187     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
188     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
189     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
190     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
191     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
192     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
193 
194     /* Even part */
195 
196     tmp10 = tmp0 + tmp3;	/* phase 2 */
197     tmp13 = tmp0 - tmp3;
198     tmp11 = tmp1 + tmp2;
199     tmp12 = tmp1 - tmp2;
200 
201     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
202     dataptr[DCTSIZE*4] = tmp10 - tmp11;
203 
204     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
205     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
206     dataptr[DCTSIZE*6] = tmp13 - z1;
207 
208     /* Odd part */
209 
210     tmp10 = tmp4 + tmp5;	/* phase 2 */
211     tmp11 = tmp5 + tmp6;
212     tmp12 = tmp6 + tmp7;
213 
214     /* The rotator is modified from fig 4-8 to avoid extra negations. */
215     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
216     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
217     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
218     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
219 
220     z11 = tmp7 + z3;		/* phase 5 */
221     z13 = tmp7 - z3;
222 
223     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
224     dataptr[DCTSIZE*3] = z13 - z2;
225     dataptr[DCTSIZE*1] = z11 + z4;
226     dataptr[DCTSIZE*7] = z11 - z4;
227 
228     dataptr++;			/* advance pointer to next column */
229   }
230 }
231 
232 #endif /* DCT_IFAST_SUPPORTED */
233