/*

 * jfdctfst.c

 *

 * Copyright (C) 1994-1996, 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 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...)

 */

#if CONST_BITS == 8

#define FIX_0_382683433  ((INT32)   98)   /* FIX(0.382683433) */

#define FIX_0_541196100  ((INT32)  139)   /* FIX(0.541196100) */

#define FIX_0_707106781  ((INT32)  181)   /* FIX(0.707106781) */

#define FIX_1_306562965  ((INT32)  334)   /* FIX(1.306562965) */

#else

#define FIX_0_382683433  FIX(0.382683433)

#define FIX_0_541196100  FIX(0.541196100)

#define FIX_0_707106781  FIX(0.707106781)

#define FIX_1_306562965  FIX(1.306562965)

#endif

/* We can gain a little more speed, with a further compromise in accuracy,

 * by omitting the addition in a descaling shift.  This yields an incorrectly

 * rounded result half the time...

 */

#ifndef USE_ACCURATE_ROUNDING

#undef DESCALE

#define DESCALE(x,n)  RIGHT_SHIFT(x, n)

#endif

/* Multiply a DCTELEM variable by an INT32 constant, and immediately

 * descale to yield a DCTELEM result.

 */

#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))

/*

 * Perform the forward DCT on one block of samples.

 */

GLOBAL(void)

jpeg_fdct_ifast (DCTELEM * data)

{

  DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  DCTELEM tmp10, tmp11, tmp12, tmp13;

  DCTELEM z1, z2, z3, z4, z5, z11, z13;

  DCTELEM *dataptr;

  int ctr;

  SHIFT_TEMPS

  /* Pass 1: process rows. */

  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 */

    tmp10 = tmp0 + tmp3;  /* phase 2 */

    tmp13 = tmp0 - tmp3;

    tmp11 = tmp1 + tmp2;

    tmp12 = tmp1 - tmp2;

    dataptr[0] = tmp10 + tmp11; /* phase 3 */

    dataptr[4] = tmp10 - tmp11;

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

    dataptr[2] = tmp13 + z1;  /* phase 5 */

    dataptr[6] = tmp13 - z1;

    /* Odd part */

    tmp10 = tmp4 + tmp5;  /* phase 2 */

    tmp11 = tmp5 + tmp6;

    tmp12 = tmp6 + tmp7;

    /* The rotator is modified from fig 4-8 to avoid extra negations. */

    z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */

    z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */

    z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

    z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

    z11 = tmp7 + z3;    /* phase 5 */

    z13 = tmp7 - z3;

    dataptr[5] = z13 + z2;  /* phase 6 */

    dataptr[3] = z13 - z2;

    dataptr[1] = z11 + z4;

    dataptr[7] = z11 - z4;

    dataptr += DCTSIZE;   /* advance pointer to next row */

  }

  /* Pass 2: process columns. */

  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 */

    tmp10 = tmp0 + tmp3;  /* phase 2 */

    tmp13 = tmp0 - tmp3;

    tmp11 = tmp1 + tmp2;

    tmp12 = tmp1 - tmp2;

    dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */

    dataptr[DCTSIZE*4] = tmp10 - tmp11;

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

    dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */

    dataptr[DCTSIZE*6] = tmp13 - z1;

    /* Odd part */

    tmp10 = tmp4 + tmp5;  /* phase 2 */

    tmp11 = tmp5 + tmp6;

    tmp12 = tmp6 + tmp7;

    /* The rotator is modified from fig 4-8 to avoid extra negations. */

    z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */

    z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */

    z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

    z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

    z11 = tmp7 + z3;    /* phase 5 */

    z13 = tmp7 - z3;

    dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */

    dataptr[DCTSIZE*3] = z13 - z2;

    dataptr[DCTSIZE*1] = z11 + z4;

    dataptr[DCTSIZE*7] = z11 - z4;

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

  }

}

#endif /* DCT_IFAST_SUPPORTED */