/*
 * jidctflt.c
 *
 * This file was part of the Independent JPEG Group's software:
 * Copyright (C) 1994-1998, Thomas G. Lane.
 * Modified 2010 by Guido Vollbeding.
 * libjpeg-turbo Modifications:
 * Copyright (C) 2014, D. R. Commander.
 * For conditions of distribution and use, see the accompanying README.ijg
 * file.
 *
 * This file contains a floating-point implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * This implementation should be more accurate than either of the integer
 * IDCT implementations.  However, it may not give the same results on all
 * machines because of differences in roundoff behavior.  Speed will depend
 * on the hardware's floating point capacity.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
 * on each row (or vice versa, but it's more convenient to emit a row at
 * a time).  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.ijg).  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 a fixed-point
 * implementation, accuracy is lost due to imprecise representation of the
 * scaled quantization values.  However, that problem does not arise if
 * we use floating point arithmetic.
 */

#define JPEG_INTERNALS

#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"               /* Private declarations for DCT subsystem */

#ifdef DCT_FLOAT_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


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce a float result.
 */

#define DEQUANTIZE(coef, quantval)  (((FAST_FLOAT) (coef)) * (quantval))


/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */

GLOBAL(void)
jpeg_idct_float(j_decompress_ptr cinfo, jpeg_component_info *compptr,
                JCOEFPTR coef_block,
                JSAMPARRAY output_buf, JDIMENSION output_col) {
	FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
	FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
	FAST_FLOAT z5, z10, z11, z12, z13;
	JCOEFPTR inptr;
	FLOAT_MULT_TYPE *quantptr;
	FAST_FLOAT *wsptr;
	JSAMPROW outptr;
	JSAMPLE *range_limit = cinfo->sample_range_limit;
	int ctr;
	FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
#define _0_125 ((FLOAT_MULT_TYPE)0.125)

	/* Pass 1: process columns from input, store into work array. */

	inptr = coef_block;
	quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
	wsptr = workspace;
	for (ctr = DCTSIZE; ctr > 0; ctr--) {
		/* Due to quantization, we will usually find that many of the input
		 * coefficients are zero, especially the AC terms.  We can exploit this
		 * by short-circuiting the IDCT calculation for any column in which all
		 * the AC terms are zero.  In that case each output is equal to the
		 * DC coefficient (with scale factor as needed).
		 * With typical images and quantization tables, half or more of the
		 * column DCT calculations can be simplified this way.
		 */

		if (inptr[DCTSIZE * 1] == 0 && inptr[DCTSIZE * 2] == 0 &&
		    inptr[DCTSIZE * 3] == 0 && inptr[DCTSIZE * 4] == 0 &&
		    inptr[DCTSIZE * 5] == 0 && inptr[DCTSIZE * 6] == 0 &&
		    inptr[DCTSIZE * 7] == 0) {
			/* AC terms all zero */
			FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE * 0],
			                              quantptr[DCTSIZE * 0] * _0_125);

			wsptr[DCTSIZE * 0] = dcval;
			wsptr[DCTSIZE * 1] = dcval;
			wsptr[DCTSIZE * 2] = dcval;
			wsptr[DCTSIZE * 3] = dcval;
			wsptr[DCTSIZE * 4] = dcval;
			wsptr[DCTSIZE * 5] = dcval;
			wsptr[DCTSIZE * 6] = dcval;
			wsptr[DCTSIZE * 7] = dcval;

			inptr++;                  /* advance pointers to next column */
			quantptr++;
			wsptr++;
			continue;
		}

		/* Even part */

		tmp0 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] * _0_125);
		tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] * _0_125);
		tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] * _0_125);
		tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] * _0_125);

		tmp10 = tmp0 + tmp2;        /* phase 3 */
		tmp11 = tmp0 - tmp2;

		tmp13 = tmp1 + tmp3;        /* phases 5-3 */
		tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */

		tmp0 = tmp10 + tmp13;       /* phase 2 */
		tmp3 = tmp10 - tmp13;
		tmp1 = tmp11 + tmp12;
		tmp2 = tmp11 - tmp12;

		/* Odd part */

		tmp4 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] * _0_125);
		tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] * _0_125);
		tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] * _0_125);
		tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] * _0_125);

		z13 = tmp6 + tmp5;          /* phase 6 */
		z10 = tmp6 - tmp5;
		z11 = tmp4 + tmp7;
		z12 = tmp4 - tmp7;

		tmp7 = z11 + z13;           /* phase 5 */
		tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */

		z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
		tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
		tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */

		tmp6 = tmp12 - tmp7;        /* phase 2 */
		tmp5 = tmp11 - tmp6;
		tmp4 = tmp10 - tmp5;

		wsptr[DCTSIZE * 0] = tmp0 + tmp7;
		wsptr[DCTSIZE * 7] = tmp0 - tmp7;
		wsptr[DCTSIZE * 1] = tmp1 + tmp6;
		wsptr[DCTSIZE * 6] = tmp1 - tmp6;
		wsptr[DCTSIZE * 2] = tmp2 + tmp5;
		wsptr[DCTSIZE * 5] = tmp2 - tmp5;
		wsptr[DCTSIZE * 3] = tmp3 + tmp4;
		wsptr[DCTSIZE * 4] = tmp3 - tmp4;

		inptr++;                    /* advance pointers to next column */
		quantptr++;
		wsptr++;
	}

	/* Pass 2: process rows from work array, store into output array. */

	wsptr = workspace;
	for (ctr = 0; ctr < DCTSIZE; ctr++) {
		outptr = output_buf[ctr] + output_col;
		/* Rows of zeroes can be exploited in the same way as we did with columns.
		 * However, the column calculation has created many nonzero AC terms, so
		 * the simplification applies less often (typically 5% to 10% of the time).
		 * And testing floats for zero is relatively expensive, so we don't bother.
		 */

		/* Even part */

		/* Apply signed->unsigned and prepare float->int conversion */
		z5 = wsptr[0] + ((FAST_FLOAT) CENTERJSAMPLE + (FAST_FLOAT) 0.5);
		tmp10 = z5 + wsptr[4];
		tmp11 = z5 - wsptr[4];

		tmp13 = wsptr[2] + wsptr[6];
		tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;

		tmp0 = tmp10 + tmp13;
		tmp3 = tmp10 - tmp13;
		tmp1 = tmp11 + tmp12;
		tmp2 = tmp11 - tmp12;

		/* Odd part */

		z13 = wsptr[5] + wsptr[3];
		z10 = wsptr[5] - wsptr[3];
		z11 = wsptr[1] + wsptr[7];
		z12 = wsptr[1] - wsptr[7];

		tmp7 = z11 + z13;
		tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);

		z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
		tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
		tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */

		tmp6 = tmp12 - tmp7;
		tmp5 = tmp11 - tmp6;
		tmp4 = tmp10 - tmp5;

		/* Final output stage: float->int conversion and range-limit */

		outptr[0] = range_limit[((int) (tmp0 + tmp7)) & RANGE_MASK];
		outptr[7] = range_limit[((int) (tmp0 - tmp7)) & RANGE_MASK];
		outptr[1] = range_limit[((int) (tmp1 + tmp6)) & RANGE_MASK];
		outptr[6] = range_limit[((int) (tmp1 - tmp6)) & RANGE_MASK];
		outptr[2] = range_limit[((int) (tmp2 + tmp5)) & RANGE_MASK];
		outptr[5] = range_limit[((int) (tmp2 - tmp5)) & RANGE_MASK];
		outptr[3] = range_limit[((int) (tmp3 + tmp4)) & RANGE_MASK];
		outptr[4] = range_limit[((int) (tmp3 - tmp4)) & RANGE_MASK];

		wsptr += DCTSIZE;           /* advance pointer to next row */
	}
}

#endif /* DCT_FLOAT_SUPPORTED */
