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/*
 * jfdctfst.c
 *
 * Copyright (C) 1994-1996, Thomas G. Lane.
 * Modified 2003-2009 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
 * forward DCT (Discrete Cosine Transform).
 *
 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
 * on each column.  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 DCTs. /* deliberate syntax err */
#endif


/* Scaling decisions are generally the same as in the LL&M algorithm;
 * see jfdctint.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.
 *
 * Again to save a few shifts, the intermediate results between pass 1 and
 * pass 2 are not upscaled, but are represented only to integral precision.
 *
 * 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).
 */

#define CONST_BITS  8


/* 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...)
 */