jdk
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1/*
2* reserved comment block
3* DO NOT REMOVE OR ALTER!
4*/
5/*
6* jidctint.c
7*
8* Copyright (C) 1991-1998, Thomas G. Lane.
9* This file is part of the Independent JPEG Group's software.
10* For conditions of distribution and use, see the accompanying README file.
11*
12* This file contains a slow-but-accurate integer implementation of the
13* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
14* must also perform dequantization of the input coefficients.
15*
16* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
17* on each row (or vice versa, but it's more convenient to emit a row at
18* a time). Direct algorithms are also available, but they are much more
19* complex and seem not to be any faster when reduced to code.
20*
21* This implementation is based on an algorithm described in
22* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
23* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
24* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
25* The primary algorithm described there uses 11 multiplies and 29 adds.
26* We use their alternate method with 12 multiplies and 32 adds.
27* The advantage of this method is that no data path contains more than one
28* multiplication; this allows a very simple and accurate implementation in
29* scaled fixed-point arithmetic, with a minimal number of shifts.
30*/
31
32#define JPEG_INTERNALS33#include "jinclude.h"34#include "jpeglib.h"35#include "jdct.h" /* Private declarations for DCT subsystem */36
37#ifdef DCT_ISLOW_SUPPORTED38
39
40/*
41* This module is specialized to the case DCTSIZE = 8.
42*/
43
44#if DCTSIZE != 845Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */46#endif47
48
49/*
50* The poop on this scaling stuff is as follows:
51*
52* Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
53* larger than the true IDCT outputs. The final outputs are therefore
54* a factor of N larger than desired; since N=8 this can be cured by
55* a simple right shift at the end of the algorithm. The advantage of
56* this arrangement is that we save two multiplications per 1-D IDCT,
57* because the y0 and y4 inputs need not be divided by sqrt(N).
58*
59* We have to do addition and subtraction of the integer inputs, which
60* is no problem, and multiplication by fractional constants, which is
61* a problem to do in integer arithmetic. We multiply all the constants
62* by CONST_SCALE and convert them to integer constants (thus retaining
63* CONST_BITS bits of precision in the constants). After doing a
64* multiplication we have to divide the product by CONST_SCALE, with proper
65* rounding, to produce the correct output. This division can be done
66* cheaply as a right shift of CONST_BITS bits. We postpone shifting
67* as long as possible so that partial sums can be added together with
68* full fractional precision.
69*
70* The outputs of the first pass are scaled up by PASS1_BITS bits so that
71* they are represented to better-than-integral precision. These outputs
72* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
73* with the recommended scaling. (To scale up 12-bit sample data further, an
74* intermediate INT32 array would be needed.)
75*
76* To avoid overflow of the 32-bit intermediate results in pass 2, we must
77* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
78* shows that the values given below are the most effective.
79*/
80
81#if BITS_IN_JSAMPLE == 882#define CONST_BITS 1383#define PASS1_BITS 284#else85#define CONST_BITS 1386#define PASS1_BITS 1 /* lose a little precision to avoid overflow */87#endif88
89/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
90* causing a lot of useless floating-point operations at run time.
91* To get around this we use the following pre-calculated constants.
92* If you change CONST_BITS you may want to add appropriate values.
93* (With a reasonable C compiler, you can just rely on the FIX() macro...)
94*/
95
96#if CONST_BITS == 1397#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */98#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */99#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */100#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */101#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */102#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */103#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */104#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */105#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */106#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */107#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */108#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */109#else110#define FIX_0_298631336 FIX(0.298631336)111#define FIX_0_390180644 FIX(0.390180644)112#define FIX_0_541196100 FIX(0.541196100)113#define FIX_0_765366865 FIX(0.765366865)114#define FIX_0_899976223 FIX(0.899976223)115#define FIX_1_175875602 FIX(1.175875602)116#define FIX_1_501321110 FIX(1.501321110)117#define FIX_1_847759065 FIX(1.847759065)118#define FIX_1_961570560 FIX(1.961570560)119#define FIX_2_053119869 FIX(2.053119869)120#define FIX_2_562915447 FIX(2.562915447)121#define FIX_3_072711026 FIX(3.072711026)122#endif123
124
125/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
126* For 8-bit samples with the recommended scaling, all the variable
127* and constant values involved are no more than 16 bits wide, so a
128* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
129* For 12-bit samples, a full 32-bit multiplication will be needed.
130*/
131
132#if BITS_IN_JSAMPLE == 8133#define MULTIPLY(var,const) MULTIPLY16C16(var,const)134#else135#define MULTIPLY(var,const) ((var) * (const))136#endif137
138
139/* Dequantize a coefficient by multiplying it by the multiplier-table
140* entry; produce an int result. In this module, both inputs and result
141* are 16 bits or less, so either int or short multiply will work.
142*/
143
144#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))145
146
147/*
148* Perform dequantization and inverse DCT on one block of coefficients.
149*/
150
151GLOBAL(void)152jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,153JCOEFPTR coef_block,154JSAMPARRAY output_buf, JDIMENSION output_col)155{
156INT32 tmp0, tmp1, tmp2, tmp3;157INT32 tmp10, tmp11, tmp12, tmp13;158INT32 z1, z2, z3, z4, z5;159JCOEFPTR inptr;160ISLOW_MULT_TYPE * quantptr;161int * wsptr;162JSAMPROW outptr;163JSAMPLE *range_limit = IDCT_range_limit(cinfo);164int ctr;165int workspace[DCTSIZE2]; /* buffers data between passes */166SHIFT_TEMPS
167
168/* Pass 1: process columns from input, store into work array. */169/* Note results are scaled up by sqrt(8) compared to a true IDCT; */170/* furthermore, we scale the results by 2**PASS1_BITS. */171
172inptr = coef_block;173quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;174wsptr = workspace;175for (ctr = DCTSIZE; ctr > 0; ctr--) {176/* Due to quantization, we will usually find that many of the input177* coefficients are zero, especially the AC terms. We can exploit this
178* by short-circuiting the IDCT calculation for any column in which all
179* the AC terms are zero. In that case each output is equal to the
180* DC coefficient (with scale factor as needed).
181* With typical images and quantization tables, half or more of the
182* column DCT calculations can be simplified this way.
183*/
184
185if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&186inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&187inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&188inptr[DCTSIZE*7] == 0) {189/* AC terms all zero */190int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;191
192wsptr[DCTSIZE*0] = dcval;193wsptr[DCTSIZE*1] = dcval;194wsptr[DCTSIZE*2] = dcval;195wsptr[DCTSIZE*3] = dcval;196wsptr[DCTSIZE*4] = dcval;197wsptr[DCTSIZE*5] = dcval;198wsptr[DCTSIZE*6] = dcval;199wsptr[DCTSIZE*7] = dcval;200
201inptr++; /* advance pointers to next column */202quantptr++;203wsptr++;204continue;205}206
207/* Even part: reverse the even part of the forward DCT. */208/* The rotator is sqrt(2)*c(-6). */209
210z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);211z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);212
213z1 = MULTIPLY(z2 + z3, FIX_0_541196100);214tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);215tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);216
217z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);218z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);219
220tmp0 = (z2 + z3) << CONST_BITS;221tmp1 = (z2 - z3) << CONST_BITS;222
223tmp10 = tmp0 + tmp3;224tmp13 = tmp0 - tmp3;225tmp11 = tmp1 + tmp2;226tmp12 = tmp1 - tmp2;227
228/* Odd part per figure 8; the matrix is unitary and hence its229* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
230*/
231
232tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);233tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);234tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);235tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);236
237z1 = tmp0 + tmp3;238z2 = tmp1 + tmp2;239z3 = tmp0 + tmp2;240z4 = tmp1 + tmp3;241z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */242
243tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */244tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */245tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */246tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */247z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */248z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */249z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */250z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */251
252z3 += z5;253z4 += z5;254
255tmp0 += z1 + z3;256tmp1 += z2 + z4;257tmp2 += z2 + z3;258tmp3 += z1 + z4;259
260/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */261
262wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);263wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);264wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);265wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);266wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);267wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);268wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);269wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);270
271inptr++; /* advance pointers to next column */272quantptr++;273wsptr++;274}275
276/* Pass 2: process rows from work array, store into output array. */277/* Note that we must descale the results by a factor of 8 == 2**3, */278/* and also undo the PASS1_BITS scaling. */279
280wsptr = workspace;281for (ctr = 0; ctr < DCTSIZE; ctr++) {282outptr = output_buf[ctr] + output_col;283/* Rows of zeroes can be exploited in the same way as we did with columns.284* However, the column calculation has created many nonzero AC terms, so
285* the simplification applies less often (typically 5% to 10% of the time).
286* On machines with very fast multiplication, it's possible that the
287* test takes more time than it's worth. In that case this section
288* may be commented out.
289*/
290
291#ifndef NO_ZERO_ROW_TEST292if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&293wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {294/* AC terms all zero */295JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)296& RANGE_MASK];297
298outptr[0] = dcval;299outptr[1] = dcval;300outptr[2] = dcval;301outptr[3] = dcval;302outptr[4] = dcval;303outptr[5] = dcval;304outptr[6] = dcval;305outptr[7] = dcval;306
307wsptr += DCTSIZE; /* advance pointer to next row */308continue;309}310#endif311
312/* Even part: reverse the even part of the forward DCT. */313/* The rotator is sqrt(2)*c(-6). */314
315z2 = (INT32) wsptr[2];316z3 = (INT32) wsptr[6];317
318z1 = MULTIPLY(z2 + z3, FIX_0_541196100);319tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);320tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);321
322tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;323tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;324
325tmp10 = tmp0 + tmp3;326tmp13 = tmp0 - tmp3;327tmp11 = tmp1 + tmp2;328tmp12 = tmp1 - tmp2;329
330/* Odd part per figure 8; the matrix is unitary and hence its331* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
332*/
333
334tmp0 = (INT32) wsptr[7];335tmp1 = (INT32) wsptr[5];336tmp2 = (INT32) wsptr[3];337tmp3 = (INT32) wsptr[1];338
339z1 = tmp0 + tmp3;340z2 = tmp1 + tmp2;341z3 = tmp0 + tmp2;342z4 = tmp1 + tmp3;343z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */344
345tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */346tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */347tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */348tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */349z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */350z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */351z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */352z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */353
354z3 += z5;355z4 += z5;356
357tmp0 += z1 + z3;358tmp1 += z2 + z4;359tmp2 += z2 + z3;360tmp3 += z1 + z4;361
362/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */363
364outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,365CONST_BITS+PASS1_BITS+3)366& RANGE_MASK];367outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,368CONST_BITS+PASS1_BITS+3)369& RANGE_MASK];370outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,371CONST_BITS+PASS1_BITS+3)372& RANGE_MASK];373outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,374CONST_BITS+PASS1_BITS+3)375& RANGE_MASK];376outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,377CONST_BITS+PASS1_BITS+3)378& RANGE_MASK];379outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,380CONST_BITS+PASS1_BITS+3)381& RANGE_MASK];382outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,383CONST_BITS+PASS1_BITS+3)384& RANGE_MASK];385outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,386CONST_BITS+PASS1_BITS+3)387& RANGE_MASK];388
389wsptr += DCTSIZE; /* advance pointer to next row */390}391}
392
393#endif /* DCT_ISLOW_SUPPORTED */394