/* * jidctflt.c * * Copyright (C) 1994-1998, 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 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).  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 = IDCT_range_limit(cinfo);  int ctr;  FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */  SHIFT_TEMPS  /* 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]);            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]);    tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);    tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);    tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);    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]);    tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);    tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);    tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);    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 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -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*4] = tmp3 + tmp4;    wsptr[DCTSIZE*3] = tmp3 - tmp4;    inptr++;			/* advance pointers to next column */    quantptr++;    wsptr++;  }    /* Pass 2: process rows from work array, store into output array. */  /* Note that we must descale the results by a factor of 8 == 2**3. */  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 */    tmp10 = wsptr[0] + wsptr[4];    tmp11 = wsptr[0] - 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 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */    tmp6 = tmp12 - tmp7;    tmp5 = tmp11 - tmp6;    tmp4 = tmp10 + tmp5;    /* Final output stage: scale down by a factor of 8 and range-limit */    outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)			    & RANGE_MASK];    outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)			    & RANGE_MASK];    outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)			    & RANGE_MASK];    outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)			    & RANGE_MASK];    outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)			    & RANGE_MASK];    outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)			    & RANGE_MASK];    outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)			    & RANGE_MASK];    outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)			    & RANGE_MASK];        wsptr += DCTSIZE;		/* advance pointer to next row */  }}#endif /* DCT_FLOAT_SUPPORTED */