/*

* jfdctfst.c

*

* Copyright (C) 1994-1996, Thomas G. Lane.

* Modified 2003-2015 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...)

*/

#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.

*

* cK represents cos(K*pi/16).

*/

GLOBAL(void)

jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

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

DCTELEM tmp10, tmp11, tmp12, tmp13;

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

DCTELEM *dataptr;

JSAMPROW elemptr;

int ctr;

SHIFT_TEMPS

/* Pass 1: process rows. */

dataptr = data;

for (ctr = 0; ctr < DCTSIZE; ctr++) {

elemptr = sample_data[ctr] + start_col;

/* Load data into workspace */

tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);

tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);

tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);

tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);

tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);

tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);

tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);

tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);

/* Even part */

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

tmp13 = tmp0 - tmp3;

tmp11 = tmp1 + tmp2;

tmp12 = tmp1 - tmp2;

/* Apply unsigned->signed conversion. */

dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* 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 */