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+/*
+ * 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 */
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