389 lines
14 KiB
C++
389 lines
14 KiB
C++
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/*
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* jidctint.c
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*
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* Copyright (C) 1991-1994, Thomas G. Lane.
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* This file is part of the Independent JPEG Group's software.
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* For conditions of distribution and use, see the accompanying README file.
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*
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* This file contains a slow-but-accurate integer implementation of the
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* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
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* must also perform dequantization of the input coefficients.
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*
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* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
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* on each row (or vice versa, but it's more convenient to emit a row at
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* a time). Direct algorithms are also available, but they are much more
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* complex and seem not to be any faster when reduced to code.
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*
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* This implementation is based on an algorithm described in
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* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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* The primary algorithm described there uses 11 multiplies and 29 adds.
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* We use their alternate method with 12 multiplies and 32 adds.
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* The advantage of this method is that no data path contains more than one
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* multiplication; this allows a very simple and accurate implementation in
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* scaled fixed-point arithmetic, with a minimal number of shifts.
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*/
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#define JPEG_INTERNALS
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#include "jinclude.h"
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#include "jpeglib.h"
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef DCT_ISLOW_SUPPORTED
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/*
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* This module is specialized to the case DCTSIZE = 8.
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*/
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#if DCTSIZE != 8
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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#endif
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/*
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* The poop on this scaling stuff is as follows:
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*
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* Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
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* larger than the true IDCT outputs. The final outputs are therefore
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* a factor of N larger than desired; since N=8 this can be cured by
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* a simple right shift at the end of the algorithm. The advantage of
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* this arrangement is that we save two multiplications per 1-D IDCT,
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* because the y0 and y4 inputs need not be divided by sqrt(N).
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*
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* We have to do addition and subtraction of the integer inputs, which
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* is no problem, and multiplication by fractional constants, which is
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* a problem to do in integer arithmetic. We multiply all the constants
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* by CONST_SCALE and convert them to integer constants (thus retaining
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* CONST_BITS bits of precision in the constants). After doing a
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* multiplication we have to divide the product by CONST_SCALE, with proper
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* rounding, to produce the correct output. This division can be done
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* cheaply as a right shift of CONST_BITS bits. We postpone shifting
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* as long as possible so that partial sums can be added together with
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* full fractional precision.
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*
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* The outputs of the first pass are scaled up by PASS1_BITS bits so that
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* they are represented to better-than-integral precision. These outputs
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* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
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* with the recommended scaling. (To scale up 12-bit sample data further, an
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* intermediate INT32 array would be needed.)
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*
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* To avoid overflow of the 32-bit intermediate results in pass 2, we must
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* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
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* shows that the values given below are the most effective.
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*/
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#if BITS_IN_JSAMPLE == 8
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#define CONST_BITS 13
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#define PASS1_BITS 2
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#else
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#define CONST_BITS 13
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#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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#endif
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/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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* causing a lot of useless floating-point operations at run time.
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* To get around this we use the following pre-calculated constants.
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* If you change CONST_BITS you may want to add appropriate values.
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* (With a reasonable C compiler, you can just rely on the FIX() macro...)
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*/
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#if CONST_BITS == 13
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#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
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#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
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#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
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#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
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#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
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#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
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#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
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#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
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#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
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#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
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#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
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#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
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#else
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#define FIX_0_298631336 FIX(0.298631336)
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#define FIX_0_390180644 FIX(0.390180644)
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#define FIX_0_541196100 FIX(0.541196100)
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#define FIX_0_765366865 FIX(0.765366865)
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#define FIX_0_899976223 FIX(0.899976223)
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#define FIX_1_175875602 FIX(1.175875602)
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#define FIX_1_501321110 FIX(1.501321110)
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#define FIX_1_847759065 FIX(1.847759065)
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#define FIX_1_961570560 FIX(1.961570560)
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#define FIX_2_053119869 FIX(2.053119869)
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#define FIX_2_562915447 FIX(2.562915447)
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#define FIX_3_072711026 FIX(3.072711026)
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#endif
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/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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* For 8-bit samples with the recommended scaling, all the variable
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* and constant values involved are no more than 16 bits wide, so a
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* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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* For 12-bit samples, a full 32-bit multiplication will be needed.
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*/
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#if BITS_IN_JSAMPLE == 8
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#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
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#else
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#define MULTIPLY(var,const) ((var) * (const))
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#endif
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/* Dequantize a coefficient by multiplying it by the multiplier-table
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* entry; produce an int result. In this module, both inputs and result
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* are 16 bits or less, so either int or short multiply will work.
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*/
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#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
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/*
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* Perform dequantization and inverse DCT on one block of coefficients.
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*/
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GLOBAL void
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jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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JCOEFPTR coef_block,
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JSAMPARRAY output_buf, JDIMENSION output_col)
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{
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INT32 tmp0, tmp1, tmp2, tmp3;
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INT32 tmp10, tmp11, tmp12, tmp13;
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INT32 z1, z2, z3, z4, z5;
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JCOEFPTR inptr;
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ISLOW_MULT_TYPE * quantptr;
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int * wsptr;
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JSAMPROW outptr;
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JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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int ctr;
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int workspace[DCTSIZE2]; /* buffers data between passes */
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SHIFT_TEMPS
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/* Pass 1: process columns from input, store into work array. */
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/* Note results are scaled up by sqrt(8) compared to a true IDCT; */
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/* furthermore, we scale the results by 2**PASS1_BITS. */
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inptr = coef_block;
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quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
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wsptr = workspace;
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for (ctr = DCTSIZE; ctr > 0; ctr--) {
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/* Due to quantization, we will usually find that many of the input
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* coefficients are zero, especially the AC terms. We can exploit this
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* by short-circuiting the IDCT calculation for any column in which all
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* the AC terms are zero. In that case each output is equal to the
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* DC coefficient (with scale factor as needed).
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* With typical images and quantization tables, half or more of the
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* column DCT calculations can be simplified this way.
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*/
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if ((inptr[DCTSIZE*1] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] |
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inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] |
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inptr[DCTSIZE*7]) == 0) {
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/* AC terms all zero */
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int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
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wsptr[DCTSIZE*0] = dcval;
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wsptr[DCTSIZE*1] = dcval;
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wsptr[DCTSIZE*2] = dcval;
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wsptr[DCTSIZE*3] = dcval;
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wsptr[DCTSIZE*4] = dcval;
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wsptr[DCTSIZE*5] = dcval;
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wsptr[DCTSIZE*6] = dcval;
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wsptr[DCTSIZE*7] = dcval;
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inptr++; /* advance pointers to next column */
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quantptr++;
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wsptr++;
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continue;
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}
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/* Even part: reverse the even part of the forward DCT. */
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/* The rotator is sqrt(2)*c(-6). */
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z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
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tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
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tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
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z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
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tmp0 = (z2 + z3) << CONST_BITS;
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tmp1 = (z2 - z3) << CONST_BITS;
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tmp10 = tmp0 + tmp3;
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tmp13 = tmp0 - tmp3;
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tmp11 = tmp1 + tmp2;
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tmp12 = tmp1 - tmp2;
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/* Odd part per figure 8; the matrix is unitary and hence its
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* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
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*/
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tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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z1 = tmp0 + tmp3;
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z2 = tmp1 + tmp2;
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z3 = tmp0 + tmp2;
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z4 = tmp1 + tmp3;
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z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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z3 += z5;
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z4 += z5;
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tmp0 += z1 + z3;
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tmp1 += z2 + z4;
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tmp2 += z2 + z3;
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tmp3 += z1 + z4;
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/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
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wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
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wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
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inptr++; /* advance pointers to next column */
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quantptr++;
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wsptr++;
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}
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/* Pass 2: process rows from work array, store into output array. */
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/* Note that we must descale the results by a factor of 8 == 2**3, */
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/* and also undo the PASS1_BITS scaling. */
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wsptr = workspace;
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for (ctr = 0; ctr < DCTSIZE; ctr++) {
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outptr = output_buf[ctr] + output_col;
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/* Rows of zeroes can be exploited in the same way as we did with columns.
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* However, the column calculation has created many nonzero AC terms, so
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* the simplification applies less often (typically 5% to 10% of the time).
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* On machines with very fast multiplication, it's possible that the
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* test takes more time than it's worth. In that case this section
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* may be commented out.
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*/
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#ifndef NO_ZERO_ROW_TEST
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if ((wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] |
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wsptr[7]) == 0) {
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/* AC terms all zero */
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JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
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& RANGE_MASK];
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outptr[0] = dcval;
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outptr[1] = dcval;
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outptr[2] = dcval;
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outptr[3] = dcval;
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outptr[4] = dcval;
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outptr[5] = dcval;
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outptr[6] = dcval;
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outptr[7] = dcval;
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wsptr += DCTSIZE; /* advance pointer to next row */
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continue;
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}
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#endif
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/* Even part: reverse the even part of the forward DCT. */
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/* The rotator is sqrt(2)*c(-6). */
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z2 = (INT32) wsptr[2];
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|
|
z3 = (INT32) wsptr[6];
|
||
|
|
|
||
|
|
z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
|
||
|
|
tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
|
||
|
|
tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
|
||
|
|
|
||
|
|
tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
|
||
|
|
tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
|
||
|
|
|
||
|
|
tmp10 = tmp0 + tmp3;
|
||
|
|
tmp13 = tmp0 - tmp3;
|
||
|
|
tmp11 = tmp1 + tmp2;
|
||
|
|
tmp12 = tmp1 - tmp2;
|
||
|
|
|
||
|
|
/* Odd part per figure 8; the matrix is unitary and hence its
|
||
|
|
* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
|
||
|
|
*/
|
||
|
|
|
||
|
|
tmp0 = (INT32) wsptr[7];
|
||
|
|
tmp1 = (INT32) wsptr[5];
|
||
|
|
tmp2 = (INT32) wsptr[3];
|
||
|
|
tmp3 = (INT32) wsptr[1];
|
||
|
|
|
||
|
|
z1 = tmp0 + tmp3;
|
||
|
|
z2 = tmp1 + tmp2;
|
||
|
|
z3 = tmp0 + tmp2;
|
||
|
|
z4 = tmp1 + tmp3;
|
||
|
|
z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
|
||
|
|
|
||
|
|
tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
|
||
|
|
tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
|
||
|
|
tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
|
||
|
|
tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
|
||
|
|
z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
|
||
|
|
z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
|
||
|
|
z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
|
||
|
|
z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
|
||
|
|
|
||
|
|
z3 += z5;
|
||
|
|
z4 += z5;
|
||
|
|
|
||
|
|
tmp0 += z1 + z3;
|
||
|
|
tmp1 += z2 + z4;
|
||
|
|
tmp2 += z2 + z3;
|
||
|
|
tmp3 += z1 + z4;
|
||
|
|
|
||
|
|
/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
|
||
|
|
|
||
|
|
outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
|
||
|
|
CONST_BITS+PASS1_BITS+3)
|
||
|
|
& RANGE_MASK];
|
||
|
|
|
||
|
|
wsptr += DCTSIZE; /* advance pointer to next row */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif /* DCT_ISLOW_SUPPORTED */
|