/*
 * jidctint.c
 *
 * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
 * The primary algorithm described there uses 11 multiplies and 29 adds.
 * We use their alternate method with 12 multiplies and 32 adds.
 * The advantage of this method is that no data path contains more than one
 * multiplication; this allows a very simple and accurate implementation in
 * scaled fixed-point arithmetic, with a minimal number of shifts.
 */
#include "GenericTypeDefs.h"

/*
 * This module is specialized to the case DCTSIZE = 8.
 */

/*
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
 * larger than the true IDCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D IDCT,
 * because the y0 and y4 inputs need not be divided by sqrt(N).
 *
 * We have to do addition and subtraction of the integer inputs, which
 * is no problem, and multiplication by fractional constants, which is
 * a problem to do in integer arithmetic.  We multiply all the constants
 * by CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (To scale up 12-bit sample data further, an
 * intermediate INT32 array would be needed.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */
#define DCTSIZE         8               /* The basic DCT block is 8x8 samples */
#define DCTSIZE2        64              /* DCTSIZE squared; # of elements in a block */
#define BITS_IN_JSAMPLE 8
#define NO_ZERO_ROW_TEST
#define DCTELEM     LONG

#define CONST_BITS  13
#define PASS1_BITS  2

#define INT32       LONG

/* 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...)
 */
#define FIX_0_298631336 ((INT32) 2446)  /* FIX(0.298631336) */
#define FIX_0_390180644 ((INT32) 3196)  /* FIX(0.390180644) */
#define FIX_0_541196100 ((INT32) 4433)  /* FIX(0.541196100) */
#define FIX_0_765366865 ((INT32) 6270)  /* FIX(0.765366865) */
#define FIX_0_899976223 ((INT32) 7373)  /* FIX(0.899976223) */
#define FIX_1_175875602 ((INT32) 9633)  /* FIX(1.175875602) */
#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */

/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 * For 12-bit samples, a full 32-bit multiplication will be needed.
 */
#define DESCALE(x, n)           ((x) + ((LONG) 0x01 << ((n) - 1))) >> (n)
#define MULTIPLY(var, constant) ((LONG) (var) * (constant));
#define range_limit(x)          ((x) < -128) ? -128 : ((x) > 127) ? 127 : (x)

/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce an int result.  In this module, both inputs and result
 * are 16 bits or less, so either int or short multiply will work.
 */
#define DEQUANTIZE(coef, quantval)  ((LONG) (coef) * (quantval))

/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */
void jpeg_idct_islow(SHORT *inbuf, WORD *quantptr)
{
    LONG    tmp0, tmp1, tmp2, tmp3;
    LONG    tmp10, tmp11, tmp12, tmp13;
    LONG    z1, z2, z3, z4, z5;

    BYTE    ctr;
    SHORT   *inptr = inbuf, *outptr;
    DCTELEM *wsptr;
    DCTELEM workspace[DCTSIZE2];                    /* buffers data between passes */

    wsptr = workspace;

    /* Pass 1: process columns from input, store into work array. */

    /* Note results are scaled up by sqrt(8) compared to a true IDCT; */

    /* furthermore, we scale the results by 2**PASS1_BITS. */
    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 */
            LONG    dcval = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]) << PASS1_BITS;

            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: reverse the even part of the forward DCT. */

        /* The rotator is sqrt(2)*c(-6). */
        z2 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2]);
        z3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6]);

        z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
        tmp2 = z1 + MULTIPLY(z3, -FIX_1_847759065);
        tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

        z2 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]);
        z3 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4]);

        tmp0 = (z2 + z3) << CONST_BITS;
        tmp1 = (z2 - z3) << 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 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7]);
        tmp1 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5]);
        tmp2 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3]);
        tmp3 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 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 */
        wsptr[DCTSIZE * 0] = (LONG) DESCALE((tmp10 + tmp3), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 7] = (LONG) DESCALE((tmp10 - tmp3), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 1] = (LONG) DESCALE((tmp11 + tmp2), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 6] = (LONG) DESCALE((tmp11 - tmp2), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 2] = (LONG) DESCALE((tmp12 + tmp1), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 5] = (LONG) DESCALE((tmp12 - tmp1), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 3] = (LONG) DESCALE((tmp13 + tmp0), (CONST_BITS - PASS1_BITS));
        wsptr[DCTSIZE * 4] = (LONG) DESCALE((tmp13 - tmp0), (CONST_BITS - PASS1_BITS));

        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;
    outptr = &inbuf[0];
    for(ctr = 0; ctr < DCTSIZE; ctr++)
    {

        /* 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[(LONG) DESCALE((INT32) wsptr[0], 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: reverse the even part of the forward DCT. */

        /* The rotator is sqrt(2)*c(-6). */
        z2 = (INT32) wsptr[2];
        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] = (SHORT) range_limit((LONG) DESCALE(tmp10 + tmp3, CONST_BITS + PASS1_BITS + 3));
        outptr[7] = (SHORT) range_limit((LONG) DESCALE(tmp10 - tmp3, CONST_BITS + PASS1_BITS + 3));
        outptr[1] = (SHORT) range_limit((LONG) DESCALE(tmp11 + tmp2, CONST_BITS + PASS1_BITS + 3));
        outptr[6] = (SHORT) range_limit((LONG) DESCALE(tmp11 - tmp2, CONST_BITS + PASS1_BITS + 3));
        outptr[2] = (SHORT) range_limit((LONG) DESCALE(tmp12 + tmp1, CONST_BITS + PASS1_BITS + 3));
        outptr[5] = (SHORT) range_limit((LONG) DESCALE(tmp12 - tmp1, CONST_BITS + PASS1_BITS + 3));
        outptr[3] = (SHORT) range_limit((LONG) DESCALE(tmp13 + tmp0, CONST_BITS + PASS1_BITS + 3));
        outptr[4] = (SHORT) range_limit((LONG) DESCALE(tmp13 - tmp0, CONST_BITS + PASS1_BITS + 3));

        outptr += DCTSIZE;                          /* advance pointer to next row */
        wsptr += DCTSIZE;                           /* advance pointer to next row */
    }
}
