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+/*
+ * jfdctflt.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 floating-point implementation of the
+ * forward DCT (Discrete Cosine Transform).
+ *
+ * This implementation should be more accurate than either of the integer
+ * DCT 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 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 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
+
+
+/*
+ * Perform the forward DCT on one block of samples.
+ */
+
+GLOBAL(void)
+jpeg_fdct_float (FAST_FLOAT * data)
+{
+ FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
+ FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
+ FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
+ FAST_FLOAT *dataptr;
+ int ctr;
+
+ /* 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 = (tmp12 + tmp13) * ((FAST_FLOAT) 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 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
+ z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
+ z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
+ z3 = tmp11 * ((FAST_FLOAT) 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 = (tmp12 + tmp13) * ((FAST_FLOAT) 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 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
+ z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
+ z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
+ z3 = tmp11 * ((FAST_FLOAT) 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_FLOAT_SUPPORTED */