/* $Xorg: jfwddct.c,v 1.4 2001/02/09 02:04:29 xorgcvs Exp $ */
/* Module jfwddct.c */

/****************************************************************************

Copyright 1993, 1994, 1998  The Open Group

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in this Software without prior written authorization from The Open Group.


				NOTICE
                              
This software is being provided by AGE Logic, Inc. under the
following license.  By obtaining, using and/or copying this software,
you agree that you have read, understood, and will comply with these
terms and conditions:

     Permission to use, copy, modify, distribute and sell this
     software and its documentation for any purpose and without
     fee or royalty and to grant others any or all rights granted
     herein is hereby granted, provided that you agree to comply
     with the following copyright notice and statements, including
     the disclaimer, and that the same appears on all copies and
     derivative works of the software and documentation you make.
     
     "Copyright 1993, 1994 by AGE Logic, Inc."
     
     THIS SOFTWARE IS PROVIDED "AS IS".  AGE LOGIC MAKES NO
     REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED.  By way of
     example, but not limitation, AGE LOGIC MAKE NO
     REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS
     FOR ANY PARTICULAR PURPOSE OR THAT THE SOFTWARE DOES NOT
     INFRINGE THIRD-PARTY PROPRIETARY RIGHTS.  AGE LOGIC 
     SHALL BEAR NO LIABILITY FOR ANY USE OF THIS SOFTWARE.  IN NO
     EVENT SHALL EITHER PARTY BE LIABLE FOR ANY INDIRECT,
     INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES, INCLUDING LOSS
     OF PROFITS, REVENUE, DATA OR USE, INCURRED BY EITHER PARTY OR
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     HEREUNDER HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH
     DAMAGES.
    
     The name of AGE Logic, Inc. may not be used in
     advertising or publicity pertaining to this software without
     specific, written prior permission from AGE Logic.

     Title to this software shall at all times remain with AGE
     Logic, Inc.
*****************************************************************************

	Gary Rogers, AGE Logic, Inc., October 1993
	Gary Rogers, AGE Logic, Inc., January 1994

****************************************************************************/

/*
 * jfwddct.c
 *
 * Copyright (C) 1991, 1992, 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 the basic DCT (Discrete Cosine Transform)
 * transformation subroutine.
 *
 * 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.
 */

#include "jinclude.h"

/*
 * This routine is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif


/*
 * 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.
 *
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
 * larger than the true DCT 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 DCT,
 * because the y0 and y4 outputs 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, 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 <= 25.  Error analysis
 * shows that the values given below are the most effective.
 */

#ifdef EIGHT_BIT_SAMPLES
#define CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#define PASS1_BITS  0		/* lose a little precision to avoid overflow */
#endif

#define ONE	((INT32) 1)

#define CONST_SCALE (ONE << CONST_BITS)

/* Convert a positive real constant to an integer scaled by CONST_SCALE. */

#define FIX(x)	((INT32) ((x) * CONST_SCALE + 0.5))

/* 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


/* Descale and correctly round an INT32 value that's scaled by N bits.
 * We assume RIGHT_SHIFT rounds towards minus infinity, so adding
 * the fudge factor is correct for either sign of X.
 */

#define DESCALE(x,n)  RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)

/* 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;
 * this provides a useful speedup on many machines.
 * There is no way to specify a 16x16->32 multiply in portable C, but
 * some C compilers will do the right thing if you provide the correct
 * combination of casts.
 * NB: for 12-bit samples, a full 32-bit multiplication will be needed.
 */

#ifdef EIGHT_BIT_SAMPLES
#ifdef SHORTxSHORT_32		/* may work if 'int' is 32 bits */
#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT16) (const)))
#endif
#ifdef SHORTxLCONST_32		/* known to work with Microsoft C 6.0 */
#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT32) (const)))
#endif
#endif

#ifndef MULTIPLY				/* default definition */
#define MULTIPLY(var,const)  ((var) * (const))
#endif


/*
 * Perform the forward DCT on one block of samples.
 */

GLOBAL void
#ifdef XIE_SUPPORTED
#if NeedFunctionPrototypes
j_fwd_dct (DCTBLOCK data)
#else
j_fwd_dct (data)
	DCTBLOCK data;
#endif	/* NeedFunctionPrototypes */
#else
j_fwd_dct (DCTBLOCK data)
#endif	/* XIE_SUPPORTED */
{
  INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  register DCTELEM *dataptr;
  int rowctr;
  SHIFT_TEMPS

  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;
  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    tmp0 = dataptr[0] + dataptr[7];
    tmp7 = dataptr[0] - dataptr[7];
    tmp1 = dataptr[1] + dataptr[6];
    tmp6 = dataptr[1] - dataptr[6];
    tmp2 = dataptr[2] + dataptr[5];
    tmp5 = dataptr[2] - dataptr[5];
    tmp3 = dataptr[3] + dataptr[4];
    tmp4 = dataptr[3] - dataptr[4];
    
    /* Even part per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */
    
    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
    
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
				   CONST_BITS-PASS1_BITS);
    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
				   CONST_BITS-PASS1_BITS);
    
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */
    
    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, 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;
    
    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
    
    dataptr += DCTSIZE;		/* advance pointer to next row */
  }

  /* Pass 2: process columns. */
  /* Note that we must descale the results by a factor of 8 == 2**3, */
  /* and also undo the PASS1_BITS scaling. */

  dataptr = data;
  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
    
    /* Even part per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */
    
    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS+3);
    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS+3);
    
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
					   CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
					   CONST_BITS+PASS1_BITS+3);
    
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */
    
    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, 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;
    
    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
					   CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
					   CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
					   CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
					   CONST_BITS+PASS1_BITS+3);
    
    dataptr++;			/* advance pointer to next column */
  }
}
