/*
* jidctfst.c
*
* Copyright (C) 1994-1998, Thomas G. Lane.
* Modified 2015-2017 by Guido Vollbeding.
* This file is part of the Independent JPEG Group's software.
* For conditions of distribution and use, see the accompanying README file.
*
* This file contains a fast, not so accurate integer implementation of the
* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
* must also perform dequantization of the input coefficients.
*
* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
* on each row (or vice versa, but it's more convenient to emit a row at
* a time). Direct algorithms are also available, but they are much more
* complex and seem not to be any faster when reduced to code.
*
* This implementation is based on Arai, Agui, and Nakajima's algorithm for
* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
* Japanese, but the algorithm is described in the Pennebaker & Mitchell
* JPEG textbook (see REFERENCES section in file README). The following code
* is based directly on figure 4-8 in P&M.
* While an 8-point DCT cannot be done in less than 11 multiplies, it is
* possible to arrange the computation so that many of the multiplies are
* simple scalings of the final outputs. These multiplies can then be
* folded into the multiplications or divisions by the JPEG quantization
* table entries. The AA&N method leaves only 5 multiplies and 29 adds
* to be done in the DCT itself.
* The primary disadvantage of this method is that with fixed-point math,
* accuracy is lost due to imprecise representation of the scaled
* quantization values. The smaller the quantization table entry, the less
* precise the scaled value, so this implementation does worse with high-
* quality-setting files than with low-quality ones.
*/
#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
#ifdef DCT_IFAST_SUPPORTED
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */
#endif
/* Scaling decisions are generally the same as in the LL&M algorithm;
* see jidctint.c for more details. However, we choose to descale
* (right shift) multiplication products as soon as they are formed,
* rather than carrying additional fractional bits into subsequent additions.
* This compromises accuracy slightly, but it lets us save a few shifts.
* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
* everywhere except in the multiplications proper; this saves a good deal
* of work on 16-bit-int machines.
*
* The dequantized coefficients are not integers because the AA&N scaling
* factors have been incorporated. We represent them scaled up by PASS1_BITS,
* so that the first and second IDCT rounds have the same input scaling.
* For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
* avoid a descaling shift; this compromises accuracy rather drastically
* for small quantization table entries, but it saves a lot of shifts.
* For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
* so we use a much larger scaling factor to preserve accuracy.
*
* A final compromise is to represent the multiplicative constants to only
* 8 fractional bits, rather than 13. This saves some shifting work on some
* machines, and may also reduce the cost of multiplication (since there
* are fewer one-bits in the constants).
*/
#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 8
#define PASS1_BITS 2
#else
#define CONST_BITS 8
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#endif
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
* causing a lot of useless floating-point operations at run time.
* To get around this we use the following pre-calculated constants.
* If you change CONST_BITS you may want to add appropriate values.
* (With a reasonable C compiler, you can just rely on the FIX() macro...)
*/
#if CONST_BITS == 8
#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
#else
#define FIX_1_082392200 FIX(1.082392200)
#define FIX_1_414213562 FIX(1.414213562)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_2_613125930 FIX(2.613125930)
#endif
/* We can gain a little more speed, with a further compromise in accuracy,
* by omitting the addition in a descaling shift. This yields an incorrectly
* rounded result half the time...
*/
#ifndef USE_ACCURATE_ROUNDING
#undef DESCALE
#define DESCALE(x,n) RIGHT_SHIFT(x, n)
#endif
/* Multiply a DCTELEM variable by an INT32 constant, and immediately
* descale to yield a DCTELEM result.
*/
#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
/* Dequantize a coefficient by multiplying it by the multiplier-table
* entry; produce a DCTELEM result. For 8-bit data a 16x16->16
* multiplication will do. For 12-bit data, the multiplier table is
* declared INT32, so a 32-bit multiply will be used.
*/
#if BITS_IN_JSAMPLE == 8
#define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
#else
#define DEQUANTIZE(coef,quantval) \
DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
#endif
/*
* Perform dequantization and inverse DCT on one block of coefficients.
*
* cK represents cos(K*pi/16).
*/
GLOBAL(void)
jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
JCOEFPTR coef_block,
JSAMPARRAY output_buf, JDIMENSION output_col)
{
DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
DCTELEM tmp10, tmp11, tmp12, tmp13;
DCTELEM z5, z10, z11, z12, z13;
JCOEFPTR inptr;
IFAST_MULT_TYPE * quantptr;
int * wsptr;
JSAMPROW outptr;
JSAMPLE *range_limit = IDCT_range_limit(cinfo);
int ctr;
int workspace[DCTSIZE2]; /* buffers data between passes */
SHIFT_TEMPS /* for DESCALE */
ISHIFT_TEMPS /* for IRIGHT_SHIFT */
/* Pass 1: process columns from input, store into work array. */
inptr = coef_block;
quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
wsptr = workspace;
for (ctr = DCTSIZE; ctr > 0; ctr--) {
/* Due to quantization, we will usually find that many of the input
* coefficients are zero, especially the AC terms. We can exploit this
* by short-circuiting the IDCT calculation for any column in which all
* the AC terms are zero. In that case each output is equal to the
* DC coefficient (with scale factor as needed).
* With typical images and quantization tables, half or more of the
* column DCT calculations can be simplified this way.
*/
if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
inptr[DCTSIZE*7] == 0) {
/* AC terms all zero */
int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
wsptr[DCTSIZE*0] = dcval;
wsptr[DCTSIZE*1] = dcval;
wsptr[DCTSIZE*2] = dcval;
wsptr[DCTSIZE*3] = dcval;
wsptr[DCTSIZE*4] = dcval;
wsptr[DCTSIZE*5] = dcval;
wsptr[DCTSIZE*6] = dcval;
wsptr[DCTSIZE*7] = dcval;
inptr++; /* advance pointers to next column */
quantptr++;
wsptr++;
continue;
}
/* Even part */
tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
tmp10 = tmp0 + tmp2; /* phase 3 */
tmp11 = tmp0 - tmp2;
tmp13 = tmp1 + tmp3; /* phases 5-3 */
tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
tmp0 = tmp10 + tmp13; /* phase 2 */
tmp3 = tmp10 - tmp13;
tmp1 = tmp11 + tmp12;
tmp2 = tmp11 - tmp12;
/* Odd part */
tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
z13 = tmp6 + tmp5; /* phase 6 */
z10 = tmp6 - tmp5;
z11 = tmp4 + tmp7;
z12 = tmp4 - tmp7;
tmp7 = z11 + z13; /* phase 5 */
tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */
tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */
tmp6 = tmp12 - tmp7; /* phase 2 */
tmp5 = tmp11 - tmp6;
tmp4 = tmp10 - tmp5;
wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
wsptr[DCTSIZE*3] = (int) (tmp3 + tmp4);
wsptr[DCTSIZE*4] = (int) (tmp3 - tmp4);
inptr++; /* advance pointers to next column */
quantptr++;
wsptr++;
}
/* Pass 2: process rows from work array, store into output array.
* Note that we must descale the results by a factor of 8 == 2**3,
* and also undo the PASS1_BITS scaling.
*/
wsptr = workspace;
for (ctr = 0; ctr < DCTSIZE; ctr++) {
outptr = output_buf[ctr] + output_col;
/* Add range center and fudge factor for final descale and range-limit. */
z5 = (DCTELEM) wsptr[0] +
((((DCTELEM) RANGE_CENTER) << (PASS1_BITS+3)) +
(1 << (PASS1_BITS+2)));
/* Rows of zeroes can be exploited in the same way as we did with columns.
* However, the column calculation has created many nonzero AC terms, so
* the simplification applies less often (typically 5% to 10% of the time).
* On machines with very fast multiplication, it's possible that the
* test takes more time than it's worth. In that case this section
* may be commented out.
*/
#ifndef NO_ZERO_ROW_TEST
if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
/* AC terms all zero */
JSAMPLE dcval = range_limit[(int) IRIGHT_SHIFT(z5, PASS1_BITS+3)
& RANGE_MASK];
outptr[0] = dcval;
outptr[1] = dcval;
outptr[2] = dcval;
outptr[3] = dcval;
outptr[4] = dcval;
outptr[5] = dcval;
outptr[6] = dcval;
outptr[7] = dcval;
wsptr += DCTSIZE; /* advance pointer to next row */
continue;
}
#endif
/* Even part */
tmp10 = z5 + (DCTELEM) wsptr[4];
tmp11 = z5 - (DCTELEM) wsptr[4];
tmp13 = (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6];
tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6],
FIX_1_414213562) - tmp13; /* 2*c4 */
tmp0 = tmp10 + tmp13;
tmp3 = tmp10 - tmp13;
tmp1 = tmp11 + tmp12;
tmp2 = tmp11 - tmp12;
/* Odd part */
z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
tmp7 = z11 + z13; /* phase 5 */
tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */
tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */
tmp6 = tmp12 - tmp7; /* phase 2 */
tmp5 = tmp11 - tmp6;
tmp4 = tmp10 - tmp5;
/* Final output stage: scale down by a factor of 8 and range-limit */
outptr[0] = range_limit[(int) IRIGHT_SHIFT(tmp0 + tmp7, PASS1_BITS+3)
& RANGE_MASK];
outptr[7] = range_limit[(int) IRIGHT_SHIFT(tmp0 - tmp7, PASS1_BITS+3)
& RANGE_MASK];
outptr[1] = range_limit[(int) IRIGHT_SHIFT(tmp1 + tmp6, PASS1_BITS+3)
& RANGE_MASK];
outptr[6] = range_limit[(int) IRIGHT_SHIFT(tmp1 - tmp6, PASS1_BITS+3)
& RANGE_MASK];
outptr[2] = range_limit[(int) IRIGHT_SHIFT(tmp2 + tmp5, PASS1_BITS+3)
& RANGE_MASK];
outptr[5] = range_limit[(int) IRIGHT_SHIFT(tmp2 - tmp5, PASS1_BITS+3)
& RANGE_MASK];
outptr[3] = range_limit[(int) IRIGHT_SHIFT(tmp3 + tmp4, PASS1_BITS+3)
& RANGE_MASK];
outptr[4] = range_limit[(int) IRIGHT_SHIFT(tmp3 - tmp4, PASS1_BITS+3)
& RANGE_MASK];
wsptr += DCTSIZE; /* advance pointer to next row */
}
}
#endif /* DCT_IFAST_SUPPORTED */