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* Copyright (C) 1994-1998, 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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* This file contains a fast, not so 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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* 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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* This implementation is based on Arai, Agui, and Nakajima's algorithm for
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* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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* Japanese, but the algorithm is described in the Pennebaker & Mitchell
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* JPEG textbook (see REFERENCES section in file README). The following code
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* is based directly on figure 4-8 in P&M.
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* While an 8-point DCT cannot be done in less than 11 multiplies, it is
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* possible to arrange the computation so that many of the multiplies are
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* simple scalings of the final outputs. These multiplies can then be
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* folded into the multiplications or divisions by the JPEG quantization
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* table entries. The AA&N method leaves only 5 multiplies and 29 adds
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* to be done in the DCT itself.
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* The primary disadvantage of this method is that with fixed-point math,
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* accuracy is lost due to imprecise representation of the scaled
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* quantization values. The smaller the quantization table entry, the less
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* precise the scaled value, so this implementation does worse with high-
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* quality-setting files than with low-quality ones.
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#define JPEG_INTERNALS
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef DCT_IFAST_SUPPORTED
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* This module is specialized to the case DCTSIZE = 8.
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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/* Scaling decisions are generally the same as in the LL&M algorithm;
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* see jidctint.c for more details. However, we choose to descale
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* (right shift) multiplication products as soon as they are formed,
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* rather than carrying additional fractional bits into subsequent additions.
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* This compromises accuracy slightly, but it lets us save a few shifts.
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* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
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* everywhere except in the multiplications proper; this saves a good deal
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* of work on 16-bit-int machines.
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* The dequantized coefficients are not integers because the AA&N scaling
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* factors have been incorporated. We represent them scaled up by PASS1_BITS,
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* so that the first and second IDCT rounds have the same input scaling.
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* For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
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* avoid a descaling shift; this compromises accuracy rather drastically
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* for small quantization table entries, but it saves a lot of shifts.
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* For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
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* so we use a much larger scaling factor to preserve accuracy.
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* A final compromise is to represent the multiplicative constants to only
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* 8 fractional bits, rather than 13. This saves some shifting work on some
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* machines, and may also reduce the cost of multiplication (since there
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* are fewer one-bits in the constants).
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#if BITS_IN_JSAMPLE == 8
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#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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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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#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
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#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
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#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
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#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
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#define FIX_1_082392200 FIX(1.082392200)
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#define FIX_1_414213562 FIX(1.414213562)
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#define FIX_1_847759065 FIX(1.847759065)
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#define FIX_2_613125930 FIX(2.613125930)
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/* We can gain a little more speed, with a further compromise in accuracy,
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* by omitting the addition in a descaling shift. This yields an incorrectly
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* rounded result half the time...
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#ifndef USE_ACCURATE_ROUNDING
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#define DESCALE(x,n) RIGHT_SHIFT(x, n)
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/* Multiply a DCTELEM variable by an INT32 constant, and immediately
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* descale to yield a DCTELEM result.
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#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
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/* Dequantize a coefficient by multiplying it by the multiplier-table
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* entry; produce a DCTELEM result. For 8-bit data a 16x16->16
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* multiplication will do. For 12-bit data, the multiplier table is
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* declared INT32, so a 32-bit multiply will be used.
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#if BITS_IN_JSAMPLE == 8
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#define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
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#define DEQUANTIZE(coef,quantval) \
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DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
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/* Like DESCALE, but applies to a DCTELEM and produces an int.
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* We assume that int right shift is unsigned if INT32 right shift is.
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#ifdef RIGHT_SHIFT_IS_UNSIGNED
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#define ISHIFT_TEMPS DCTELEM ishift_temp;
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#if BITS_IN_JSAMPLE == 8
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#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
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#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
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#define IRIGHT_SHIFT(x,shft) \
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((ishift_temp = (x)) < 0 ? \
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(ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
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(ishift_temp >> (shft)))
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#define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
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#ifdef USE_ACCURATE_ROUNDING
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#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
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#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
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* Perform dequantization and inverse DCT on one block of coefficients.
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jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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JSAMPARRAY output_buf, JDIMENSION output_col)
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DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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DCTELEM tmp10, tmp11, tmp12, tmp13;
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DCTELEM z5, z10, z11, z12, z13;
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IFAST_MULT_TYPE * quantptr;
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JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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int workspace[DCTSIZE2]; /* buffers data between passes */
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SHIFT_TEMPS /* for DESCALE */
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ISHIFT_TEMPS /* for IDESCALE */
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/* Pass 1: process columns from input, store into work array. */
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quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
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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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if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
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inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
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inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
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inptr[DCTSIZE*7] == 0) {
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/* AC terms all zero */
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int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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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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tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
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tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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tmp10 = tmp0 + tmp2; /* phase 3 */
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tmp13 = tmp1 + tmp3; /* phases 5-3 */
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tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
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tmp0 = tmp10 + tmp13; /* phase 2 */
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tmp3 = tmp10 - tmp13;
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tmp1 = tmp11 + tmp12;
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tmp2 = tmp11 - tmp12;
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tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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z13 = tmp6 + tmp5; /* phase 6 */
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tmp7 = z11 + z13; /* phase 5 */
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tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
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z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
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tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
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tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
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tmp6 = tmp12 - tmp7; /* phase 2 */
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wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
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wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
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wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
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wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
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wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
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wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
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wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
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wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
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inptr++; /* advance pointers to next column */
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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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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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#ifndef NO_ZERO_ROW_TEST
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if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
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wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
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/* AC terms all zero */
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JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
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wsptr += DCTSIZE; /* advance pointer to next row */
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tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
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tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
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tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
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tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
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tmp0 = tmp10 + tmp13;
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tmp3 = tmp10 - tmp13;
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tmp1 = tmp11 + tmp12;
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tmp2 = tmp11 - tmp12;
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z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
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z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
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z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
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z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
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tmp7 = z11 + z13; /* phase 5 */
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tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
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z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
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tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
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tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
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tmp6 = tmp12 - tmp7; /* phase 2 */
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/* Final output stage: scale down by a factor of 8 and range-limit */
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outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
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outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
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outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
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outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
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outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
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outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
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outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
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outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
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wsptr += DCTSIZE; /* advance pointer to next row */
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#endif /* DCT_IFAST_SUPPORTED */
added
removed
source/Irrlicht/jpeglib/jidctfst.c
