    /*
     * 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 */