////////////////////////////////////////////////////////////////////////
//
//	Note : this file is included as part of the Smaller Animals Software
//	JpegFile package. Though this file has not been modified from it's 
//	original IJG 6a form, it is not the responsibility on the Independent
//	JPEG Group to answer questions regarding this code.
//	
//	Any questions you have about this code should be addressed to :
//
//	CHRISDL@PAGESZ.NET	- the distributor of this package.
//
//	Remember, by including this code in the JpegFile package, Smaller 
//	Animals Software assumes all responsibilities for answering questions
//	about it. If we (SA Software) can't answer your questions ourselves, we 
//	will direct you to people who can.
//
//	Thanks, CDL.
//
////////////////////////////////////////////////////////////////////////

/*
 * jidctint.c
 *
 * Copyright (C) 1991-1996, 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 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] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] |
	 inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] |
	 inptr[DCTSIZE*7]) == 0) {
      /* AC terms all zero */
      int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;