jfdctint.c - third_party/libjpeg-turbo - Git at Google

 /*
  * jfdctint.c
  *
  * This file was part of the Independent JPEG Group's software.
  * Copyright (C) 1991-1996, Thomas G. Lane.
  * libjpeg-turbo Modifications:
  * Copyright (C) 2015, D. R. Commander.
  * For conditions of distribution and use, see the accompanying README.ijg
  * file.
  *
  * This file contains a slow-but-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 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 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).
  * In the IJG code, this factor of 8 is removed by the quantization step
  * (in jcdctmgr.c), NOT in this module.
  *
  * 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.  (For 12-bit sample data, the intermediate
  * array is JLONG anyway.)
  *
  * 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  ((JLONG)  2446)        /* FIX(0.298631336) */
 #define FIX_0_390180644  ((JLONG)  3196)        /* FIX(0.390180644) */
 #define FIX_0_541196100  ((JLONG)  4433)        /* FIX(0.541196100) */
 #define FIX_0_765366865  ((JLONG)  6270)        /* FIX(0.765366865) */
 #define FIX_0_899976223  ((JLONG)  7373)        /* FIX(0.899976223) */
 #define FIX_1_175875602  ((JLONG)  9633)        /* FIX(1.175875602) */
 #define FIX_1_501321110  ((JLONG)  12299)       /* FIX(1.501321110) */
 #define FIX_1_847759065  ((JLONG)  15137)       /* FIX(1.847759065) */
 #define FIX_1_961570560  ((JLONG)  16069)       /* FIX(1.961570560) */
 #define FIX_2_053119869  ((JLONG)  16819)       /* FIX(2.053119869) */
 #define FIX_2_562915447  ((JLONG)  20995)       /* FIX(2.562915447) */
 #define FIX_3_072711026  ((JLONG)  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 JLONG variable by an JLONG constant to yield an JLONG 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


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

 GLOBAL(void)
 jpeg_fdct_islow (DCTELEM *data)
 {
   JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
   JLONG tmp10, tmp11, tmp12, tmp13;
   JLONG z1, z2, z3, z4, z5;
   DCTELEM *dataptr;
   int ctr;
   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 (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
     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) LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS);
     dataptr[4] = (DCTELEM) LEFT_SHIFT(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.
    * We remove the PASS1_BITS scaling, but leave the results scaled up
    * by an overall factor of 8.
    */

   dataptr = data;
   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
     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);
     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);

     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
                                            CONST_BITS+PASS1_BITS);
     dataptr[DCTSIZE*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[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
                                            CONST_BITS+PASS1_BITS);
     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
                                            CONST_BITS+PASS1_BITS);
     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
                                            CONST_BITS+PASS1_BITS);
     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
                                            CONST_BITS+PASS1_BITS);

     dataptr++;                  /* advance pointer to next column */
   }
 }

 #endif /* DCT_ISLOW_SUPPORTED */
	/*
	* jfdctint.c
	*
	* This file was part of the Independent JPEG Group's software.
	* Copyright (C) 1991-1996, Thomas G. Lane.
	* libjpeg-turbo Modifications:
	* Copyright (C) 2015, D. R. Commander.
	* For conditions of distribution and use, see the accompanying README.ijg
	* file.
	*
	* This file contains a slow-but-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 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 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).
	* In the IJG code, this factor of 8 is removed by the quantization step
	* (in jcdctmgr.c), NOT in this module.
	*
	* 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. (For 12-bit sample data, the intermediate
	* array is JLONG anyway.)
	*
	* 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 ((JLONG) 2446) /* FIX(0.298631336) */
	#define FIX_0_390180644 ((JLONG) 3196) /* FIX(0.390180644) */
	#define FIX_0_541196100 ((JLONG) 4433) /* FIX(0.541196100) */
	#define FIX_0_765366865 ((JLONG) 6270) /* FIX(0.765366865) */
	#define FIX_0_899976223 ((JLONG) 7373) /* FIX(0.899976223) */
	#define FIX_1_175875602 ((JLONG) 9633) /* FIX(1.175875602) */
	#define FIX_1_501321110 ((JLONG) 12299) /* FIX(1.501321110) */
	#define FIX_1_847759065 ((JLONG) 15137) /* FIX(1.847759065) */
	#define FIX_1_961570560 ((JLONG) 16069) /* FIX(1.961570560) */
	#define FIX_2_053119869 ((JLONG) 16819) /* FIX(2.053119869) */
	#define FIX_2_562915447 ((JLONG) 20995) /* FIX(2.562915447) */
	#define FIX_3_072711026 ((JLONG) 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 JLONG variable by an JLONG constant to yield an JLONG 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


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

	GLOBAL(void)
	jpeg_fdct_islow (DCTELEM *data)
	{
	JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
	JLONG tmp10, tmp11, tmp12, tmp13;
	JLONG z1, z2, z3, z4, z5;
	DCTELEM *dataptr;
	int ctr;
	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 (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
	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) LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS);
	dataptr[4] = (DCTELEM) LEFT_SHIFT(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.
	* We remove the PASS1_BITS scaling, but leave the results scaled up
	* by an overall factor of 8.
	*/

	dataptr = data;
	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
	tmp0 = dataptr[DCTSIZE0] + dataptr[DCTSIZE7];
	tmp7 = dataptr[DCTSIZE0] - dataptr[DCTSIZE7];
	tmp1 = dataptr[DCTSIZE1] + dataptr[DCTSIZE6];
	tmp6 = dataptr[DCTSIZE1] - dataptr[DCTSIZE6];
	tmp2 = dataptr[DCTSIZE2] + dataptr[DCTSIZE5];
	tmp5 = dataptr[DCTSIZE2] - dataptr[DCTSIZE5];
	tmp3 = dataptr[DCTSIZE3] + dataptr[DCTSIZE4];
	tmp4 = dataptr[DCTSIZE3] - dataptr[DCTSIZE4];

	/* 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);
	dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);

	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
	dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
	CONST_BITS+PASS1_BITS);
	dataptr[DCTSIZE*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[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
	CONST_BITS+PASS1_BITS);
	dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
	CONST_BITS+PASS1_BITS);
	dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
	CONST_BITS+PASS1_BITS);
	dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
	CONST_BITS+PASS1_BITS);

	dataptr++; /* advance pointer to next column */
	}
	}

	#endif /* DCT_ISLOW_SUPPORTED */