/*

 * 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.

 */

#define JPEG_INTERNALS

#include "jinclude.h"

#include "jpeglib.h"

#include "jdct.h"   /* Private declarations for DCT subsystem */

#ifdef DCT_ISLOW_SUPPORTED

/*

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

 */

#if DCTSIZE != 8

  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */

#endif

/*

 * 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.

 */

#if BITS_IN_JSAMPLE == 8

#define CONST_BITS  13

#define PASS1_BITS  2

#else

#define CONST_BITS  13

#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 == 13

#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) */

#else

#define FIX_0_298631336  FIX(0.298631336)

#define FIX_0_390180644  FIX(0.390180644)

#define FIX_0_541196100  FIX(0.541196100)

#define FIX_0_765366865  FIX(0.765366865)

#define FIX_0_899976223  FIX(0.899976223)

#define FIX_1_175875602  FIX(1.175875602)

#define FIX_1_501321110  FIX(1.501321110)

#define FIX_1_847759065  FIX(1.847759065)

#define FIX_1_961570560  FIX(1.961570560)

#define FIX_2_053119869  FIX(2.053119869)

#define FIX_2_562915447  FIX(2.562915447)

#define FIX_3_072711026  FIX(3.072711026)

#endif

/* 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.

 */

#if BITS_IN_JSAMPLE == 8

#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)

#else

#define MULTIPLY(var,const)  ((var) * (const))

#endif

/* 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)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))

/*

 * Perform dequantization and inverse DCT on one block of coefficients.

 */

GLOBAL(void)

jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,

     JCOEFPTR coef_block,

     JSAMPARRAY output_buf, JDIMENSION output_col)

{

  INT32 tmp0, tmp1, tmp2, tmp3;

  INT32 tmp10, tmp11, tmp12, tmp13;

  INT32 z1, z2, z3, z4, z5;

  JCOEFPTR inptr;

  ISLOW_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

  /* 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. */

  inptr = coef_block;

  quantptr = (ISLOW_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)LEFT_SHIFT(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 = LEFT_SHIFT(z2 + z3, CONST_BITS);

    tmp1 = LEFT_SHIFT(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] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);

    wsptr[DCTSIZE*4] = (int) 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;

  for (ctr = 0; ctr < DCTSIZE; ctr++) {

    outptr = output_buf[ctr] + output_col;

    /* 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) 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 = LEFT_SHIFT((INT32) wsptr[0] + (INT32) wsptr[4], CONST_BITS);

    tmp1 = LEFT_SHIFT((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 */