/*
* jidctfst.c
*
* Copyright (C) 1994-1996, Thomas G. Lane.
* 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.
*/
/*
* This module is specialized to the case DCTSIZE = 8.
*/
/* 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).
*/
#define BITS_IN_JSAMPLE 8
#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 (277) /* FIX(1.082392200) */
#define FIX_1_414213562 (362) /* FIX(1.414213562) */
#define FIX_1_847759065 (473) /* FIX(1.847759065) */
#define FIX_2_613125930 (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...
*/
/* Multiply a DCTELEM variable by an INT32 constant, and immediately
* descale to yield a DCTELEM result.
*/
#define MULTIPLY(var,const) (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) (coef)
#else
#define DEQUANTIZE(coef,quantval) \
DESCALE((coef), IFAST_SCALE_BITS-PASS1_BITS)
#endif
/* Like DESCALE, but applies to a DCTELEM and produces an int.
* We assume that int right shift is unsigned if INT32 right shift is.
*/
#define DESCALE(x,n) ((x)>>(n))
#define RANGE(n) (n)
#define BLOCK int
/*
* Perform dequantization and inverse DCT on one block of coefficients.
*/
#define DCTSIZE 8
#define DCTSIZE2 64
static void IDCT1(BLOCK *block)
{
int val = RANGE(DESCALE(block[0], PASS1_BITS+3));
int i;
for(i=0;i<DCTSIZE2;i++) block[i]=val;
}
void IDCT(BLOCK *block,int k)
{
int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int z5, z10, z11, z12, z13;
BLOCK *ptr;
int i;
/* Pass 1: process columns from input, store into work array. */
switch(k){
case 1:IDCT1(block); return;
}
ptr = block;
for (i = 0; i< DCTSIZE; i++,ptr++) {
/* 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 ((ptr[DCTSIZE*1] | ptr[DCTSIZE*2] | ptr[DCTSIZE*3] |
ptr[DCTSIZE*4] | ptr[DCTSIZE*5] | ptr[DCTSIZE*6] |
ptr[DCTSIZE*7]) == 0) {
/* AC terms all zero */
ptr[DCTSIZE*0] =
ptr[DCTSIZE*1] =
ptr[DCTSIZE*2] =
ptr[DCTSIZE*3] =
ptr[DCTSIZE*4] =
ptr[DCTSIZE*5] =
ptr[DCTSIZE*6] =
ptr[DCTSIZE*7] =
ptr[DCTSIZE*0];
continue;
}
/* Even part */
z10 = ptr[DCTSIZE*0] + ptr[DCTSIZE*4]; /* phase 3 */
z11 = ptr[DCTSIZE*0] - ptr[DCTSIZE*4];
z13 = ptr[DCTSIZE*2] + ptr[DCTSIZE*6]; /* phases 5-3 */
z12 = MULTIPLY(ptr[DCTSIZE*2] - ptr[DCTSIZE*6], FIX_1_414213562) - z13; /* 2*c4 */
tmp0 = z10 + z13; /* phase 2 */
tmp3 = z10 - z13;
tmp1 = z11 + z12;
tmp2 = z11 - z12;
/* Odd part */
z13 = ptr[DCTSIZE*3] + ptr[DCTSIZE*5]; /* phase 6 */
z10 = ptr[DCTSIZE*3] - ptr[DCTSIZE*5];
z11 = ptr[DCTSIZE*1] + ptr[DCTSIZE*7];
z12 = ptr[DCTSIZE*1] - ptr[DCTSIZE*7];
z5 = MULTIPLY(z12 - z10, FIX_1_847759065);
tmp7 = z11 + z13; /* phase 5 */
tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */
tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6;
tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5;
ptr[DCTSIZE*0] = (tmp0 + tmp7);
ptr[DCTSIZE*7] = (tmp0 - tmp7);
ptr[DCTSIZE*1] = (tmp1 + tmp6);
ptr[DCTSIZE*6] = (tmp1 - tmp6);
ptr[DCTSIZE*2] = (tmp2 + tmp5);
ptr[DCTSIZE*5] = (tmp2 - tmp5);
ptr[DCTSIZE*4] = (tmp3 + tmp4);
ptr[DCTSIZE*3] = (tmp3 - tmp4);
}
/* 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. */
ptr = block;
for (i = 0; i < DCTSIZE; i++ ,ptr+=DCTSIZE) {
/* 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 ((ptr[1] | ptr[2] | ptr[3] | ptr[4] | ptr[5] | ptr[6] |
ptr[7]) == 0) {
/* AC terms all zero */
ptr[0] =
ptr[1] =
ptr[2] =
ptr[3] =
ptr[4] =
ptr[5] =
ptr[6] =
ptr[7] =
RANGE(DESCALE(ptr[0], PASS1_BITS+3));;
continue;
}
#endif
/* Even part */
z10 = ptr[0] + ptr[4];
z11 = ptr[0] - ptr[4];
z13 = ptr[2] + ptr[6];
z12 = MULTIPLY(ptr[2] - ptr[6], FIX_1_414213562) - z13;
tmp0 = z10 + z13;
tmp3 = z10 - z13;
tmp1 = z11 + z12;
tmp2 = z11 - z12;
/* Odd part */
z13 = ptr[3] + ptr[5];
z10 = ptr[3] - ptr[5];
z11 = ptr[1] + ptr[7];
z12 = ptr[1] - ptr[7];
z5 = MULTIPLY(z12 - z10, FIX_1_847759065);
tmp7 = z11 + z13; /* phase 5 */
tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */
tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6;
tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5;
/* Final output stage: scale down by a factor of 8 and range-limit */
ptr[0] = RANGE(DESCALE(tmp0 + tmp7, PASS1_BITS+3));;
ptr[7] = RANGE(DESCALE(tmp0 - tmp7, PASS1_BITS+3));;
ptr[1] = RANGE(DESCALE(tmp1 + tmp6, PASS1_BITS+3));;
ptr[6] = RANGE(DESCALE(tmp1 - tmp6, PASS1_BITS+3));;
ptr[2] = RANGE(DESCALE(tmp2 + tmp5, PASS1_BITS+3));;
ptr[5] = RANGE(DESCALE(tmp2 - tmp5, PASS1_BITS+3));;
ptr[4] = RANGE(DESCALE(tmp3 + tmp4, PASS1_BITS+3));;
ptr[3] = RANGE(DESCALE(tmp3 - tmp4, PASS1_BITS+3));;
}
}