    /*
     * jidctred.c
     *
     * Copyright (C) 1994-1998, 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 inverse-DCT routines that produce reduced-size output:
     * either 4x4, 2x2, or 1x1 pixels from an 8x8 DCT block.
     *
     * The implementation is based on the Loeffler, Ligtenberg and Moschytz (LL&M)
     * algorithm used in jidctint.c.  We simply replace each 8-to-8 1-D IDCT step
     * with an 8-to-4 step that produces the four averages of two adjacent outputs
     * (or an 8-to-2 step producing two averages of four outputs, for 2x2 output).
     * These steps were derived by computing the corresponding values at the end
     * of the normal LL&M code, then simplifying as much as possible.
     *
     * 1x1 is trivial: just take the DC coefficient divided by 8.
     *
     * See jidctint.c for additional comments.
     */

    #define JPEG_INTERNALS
    #include "jinclude.h"
    #include "jpeglib.h"
    #include "jdct.h"		/* Private declarations for DCT subsystem */

    #ifdef IDCT_SCALING_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

    /* Scaling is the same as in jidctint.c. */

    #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_211164243  ((long)  1730)	/* FIX(0.211164243) */
    #define FIX_0_509795579  ((long)  4176)	/* FIX(0.509795579) */
    #define FIX_0_601344887  ((long)  4926)	/* FIX(0.601344887) */
    #define FIX_0_720959822  ((long)  5906)	/* FIX(0.720959822) */
    #define FIX_0_765366865  ((long)  6270)	/* FIX(0.765366865) */
    #define FIX_0_850430095  ((long)  6967)	/* FIX(0.850430095) */
    #define FIX_0_899976223  ((long)  7373)	/* FIX(0.899976223) */
    #define FIX_1_061594337  ((long)  8697)	/* FIX(1.061594337) */
    #define FIX_1_272758580  ((long)  10426)	/* FIX(1.272758580) */
    #define FIX_1_451774981  ((long)  11893)	/* FIX(1.451774981) */
    #define FIX_1_847759065  ((long)  15137)	/* FIX(1.847759065) */
    #define FIX_2_172734803  ((long)  17799)	/* FIX(2.172734803) */
    #define FIX_2_562915447  ((long)  20995)	/* FIX(2.562915447) */
    #define FIX_3_624509785  ((long)  29692)	/* FIX(3.624509785) */
    #else
    #define FIX_0_211164243  FIX(0.211164243)
    #define FIX_0_509795579  FIX(0.509795579)
    #define FIX_0_601344887  FIX(0.601344887)
    #define FIX_0_720959822  FIX(0.720959822)
    #define FIX_0_765366865  FIX(0.765366865)
    #define FIX_0_850430095  FIX(0.850430095)
    #define FIX_0_899976223  FIX(0.899976223)
    #define FIX_1_061594337  FIX(1.061594337)
    #define FIX_1_272758580  FIX(1.272758580)
    #define FIX_1_451774981  FIX(1.451774981)
    #define FIX_1_847759065  FIX(1.847759065)
    #define FIX_2_172734803  FIX(2.172734803)
    #define FIX_2_562915447  FIX(2.562915447)
    #define FIX_3_624509785  FIX(3.624509785)
    #endif

    /* Multiply an long variable by an long constant to yield an long 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,
     * producing a reduced-size 4x4 output block.
     */

    GLOBAL(void)
    jpeg_idct_4x4 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
    	       JCOEFPTR coef_block,
    	       JSAMPARRAY output_buf, JDIMENSION output_col)
    {
      long tmp0, tmp2, tmp10, tmp12;
      long z1, z2, z3, z4;
      JCOEFPTR inptr;
      ISLOW_MULT_TYPE * quantptr;
      int * wsptr;
      JSAMPROW outptr;
      JSAMPLE *range_limit = IDCT_range_limit(cinfo);
      int ctr;
      int workspace[DCTSIZE*4];	/* buffers data between passes */
      SHIFT_TEMPS

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

      inptr = coef_block;
      quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
      wsptr = workspace;
      for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
        /* Don't bother to process column 4, because second pass won't use it */
        if (ctr == DCTSIZE-4)
          continue;
        if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
    	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*5] == 0 &&
    	inptr[DCTSIZE*6] == 0 && inptr[DCTSIZE*7] == 0) {
          /* AC terms all zero; we need not examine term 4 for 4x4 output */
          int 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;

          continue;
        }

        /* Even part */

        tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
        tmp0 <<= (CONST_BITS+1);

        z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
        z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

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

        tmp10 = tmp0 + tmp2;
        tmp12 = tmp0 - tmp2;

        /* Odd part */

        z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
        z2 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
        z3 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
        z4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

        tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
    	 + MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
    	 + MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
    	 + MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */

        tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
    	 + MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
    	 + MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
    	 + MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */

        /* Final output stage */

        wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp2, CONST_BITS-PASS1_BITS+1);
        wsptr[DCTSIZE*3] = (int) DESCALE(tmp10 - tmp2, CONST_BITS-PASS1_BITS+1);
        wsptr[DCTSIZE*1] = (int) DESCALE(tmp12 + tmp0, CONST_BITS-PASS1_BITS+1);
        wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 - tmp0, CONST_BITS-PASS1_BITS+1);
      }

      /* Pass 2: process 4 rows from work array, store into output array. */

      wsptr = workspace;
      for (ctr = 0; ctr < 4; ctr++) {
        outptr = output_buf[ctr] + output_col;
        /* It's not clear whether a zero row test is worthwhile here ... */

    #ifndef NO_ZERO_ROW_TEST
        if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 &&
    	wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
          /* AC terms all zero */
          JSAMPLE dcval = range_limit[(int) DESCALE((long) wsptr[0], PASS1_BITS+3)
    				  & RANGE_MASK];

          outptr[0] = dcval;
          outptr[1] = dcval;
          outptr[2] = dcval;
          outptr[3] = dcval;

          wsptr += DCTSIZE;		/* advance pointer to next row */
          continue;
        }
    #endif

        /* Even part */

        tmp0 = ((long) wsptr[0]) << (CONST_BITS+1);

        tmp2 = MULTIPLY((long) wsptr[2], FIX_1_847759065)
    	 + MULTIPLY((long) wsptr[6], - FIX_0_765366865);

        tmp10 = tmp0 + tmp2;
        tmp12 = tmp0 - tmp2;

        /* Odd part */

        z1 = (long) wsptr[7];
        z2 = (long) wsptr[5];
        z3 = (long) wsptr[3];
        z4 = (long) wsptr[1];

        tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
    	 + MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
    	 + MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
    	 + MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */

        tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
    	 + MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
    	 + MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
    	 + MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */

        /* Final output stage */

        outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp2,
    					  CONST_BITS+PASS1_BITS+3+1)
    			    & RANGE_MASK];
        outptr[3] = range_limit[(int) DESCALE(tmp10 - tmp2,
    					  CONST_BITS+PASS1_BITS+3+1)
    			    & RANGE_MASK];
        outptr[1] = range_limit[(int) DESCALE(tmp12 + tmp0,
    					  CONST_BITS+PASS1_BITS+3+1)
    			    & RANGE_MASK];
        outptr[2] = range_limit[(int) DESCALE(tmp12 - tmp0,
    					  CONST_BITS+PASS1_BITS+3+1)
    			    & RANGE_MASK];

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

    /*
     * Perform dequantization and inverse DCT on one block of coefficients,
     * producing a reduced-size 2x2 output block.
     */

    GLOBAL(void)
    jpeg_idct_2x2 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
    	       JCOEFPTR coef_block,
    	       JSAMPARRAY output_buf, JDIMENSION output_col)
    {
      long tmp0, tmp10, z1;
      JCOEFPTR inptr;
      ISLOW_MULT_TYPE * quantptr;
      int * wsptr;
      JSAMPROW outptr;
      JSAMPLE *range_limit = IDCT_range_limit(cinfo);
      int ctr;
      int workspace[DCTSIZE*2];	/* buffers data between passes */
      SHIFT_TEMPS

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

      inptr = coef_block;
      quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
      wsptr = workspace;
      for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
        /* Don't bother to process columns 2,4,6 */
        if (ctr == DCTSIZE-2 || ctr == DCTSIZE-4 || ctr == DCTSIZE-6)
          continue;
        if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*3] == 0 &&
    	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*7] == 0) {
          /* AC terms all zero; we need not examine terms 2,4,6 for 2x2 output */
          int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;

          wsptr[DCTSIZE*0] = dcval;
          wsptr[DCTSIZE*1] = dcval;

          continue;
        }

        /* Even part */

        z1 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
        tmp10 = z1 << (CONST_BITS+2);

        /* Odd part */

        z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
        tmp0 = MULTIPLY(z1, - FIX_0_720959822); /* sqrt(2) * (c7-c5+c3-c1) */
        z1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
        tmp0 += MULTIPLY(z1, FIX_0_850430095); /* sqrt(2) * (-c1+c3+c5+c7) */
        z1 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
        tmp0 += MULTIPLY(z1, - FIX_1_272758580); /* sqrt(2) * (-c1+c3-c5-c7) */
        z1 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
        tmp0 += MULTIPLY(z1, FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */

        /* Final output stage */

        wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp0, CONST_BITS-PASS1_BITS+2);
        wsptr[DCTSIZE*1] = (int) DESCALE(tmp10 - tmp0, CONST_BITS-PASS1_BITS+2);
      }

      /* Pass 2: process 2 rows from work array, store into output array. */

      wsptr = workspace;
      for (ctr = 0; ctr < 2; ctr++) {
        outptr = output_buf[ctr] + output_col;
        /* It's not clear whether a zero row test is worthwhile here ... */

    #ifndef NO_ZERO_ROW_TEST
        if (wsptr[1] == 0 && wsptr[3] == 0 && wsptr[5] == 0 && wsptr[7] == 0) {
          /* AC terms all zero */
          JSAMPLE dcval = range_limit[(int) DESCALE((long) wsptr[0], PASS1_BITS+3)
    				  & RANGE_MASK];

          outptr[0] = dcval;
          outptr[1] = dcval;

          wsptr += DCTSIZE;		/* advance pointer to next row */
          continue;
        }
    #endif

        /* Even part */

        tmp10 = ((long) wsptr[0]) << (CONST_BITS+2);

        /* Odd part */

        tmp0 = MULTIPLY((long) wsptr[7], - FIX_0_720959822) /* sqrt(2) * (c7-c5+c3-c1) */
    	 + MULTIPLY((long) wsptr[5], FIX_0_850430095) /* sqrt(2) * (-c1+c3+c5+c7) */
    	 + MULTIPLY((long) wsptr[3], - FIX_1_272758580) /* sqrt(2) * (-c1+c3-c5-c7) */
    	 + MULTIPLY((long) wsptr[1], FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */

        /* Final output stage */

        outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp0,
    					  CONST_BITS+PASS1_BITS+3+2)
    			    & RANGE_MASK];
        outptr[1] = range_limit[(int) DESCALE(tmp10 - tmp0,
    					  CONST_BITS+PASS1_BITS+3+2)
    			    & RANGE_MASK];

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

    /*
     * Perform dequantization and inverse DCT on one block of coefficients,
     * producing a reduced-size 1x1 output block.
     */

    GLOBAL(void)
    jpeg_idct_1x1 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
    	       JCOEFPTR coef_block,
    	       JSAMPARRAY output_buf, JDIMENSION output_col)
    {
      int dcval;
      ISLOW_MULT_TYPE * quantptr;
      JSAMPLE *range_limit = IDCT_range_limit(cinfo);
      SHIFT_TEMPS

      /* We hardly need an inverse DCT routine for this: just take the
       * average pixel value, which is one-eighth of the DC coefficient.
       */
      quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
      dcval = DEQUANTIZE(coef_block[0], quantptr[0]);
      dcval = (int) DESCALE((long) dcval, 3);

      output_buf[0][output_col] = range_limit[dcval & RANGE_MASK];
    }

    #endif /* IDCT_SCALING_SUPPORTED */