| 1 | /*
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| 2 | * jidctflt.c
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| 3 | *
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| 4 | * Copyright (C) 1994-1998, Thomas G. Lane.
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| 5 | * This file is part of the Independent JPEG Group's software.
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| 6 | * For conditions of distribution and use, see the accompanying README file.
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| 7 | *
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| 8 | * This file contains a floating-point implementation of the
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| 9 | * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
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| 10 | * must also perform dequantization of the input coefficients.
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| 11 | *
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| 12 | * This implementation should be more accurate than either of the integer
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| 13 | * IDCT implementations. However, it may not give the same results on all
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| 14 | * machines because of differences in roundoff behavior. Speed will depend
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| 15 | * on the hardware's floating point capacity.
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| 16 | *
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| 17 | * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
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| 18 | * on each row (or vice versa, but it's more convenient to emit a row at
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| 19 | * a time). Direct algorithms are also available, but they are much more
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| 20 | * complex and seem not to be any faster when reduced to code.
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| 21 | *
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| 22 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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| 23 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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| 24 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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| 25 | * JPEG textbook (see REFERENCES section in file README). The following code
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| 26 | * is based directly on figure 4-8 in P&M.
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| 27 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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| 28 | * possible to arrange the computation so that many of the multiplies are
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| 29 | * simple scalings of the final outputs. These multiplies can then be
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| 30 | * folded into the multiplications or divisions by the JPEG quantization
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| 31 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds
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| 32 | * to be done in the DCT itself.
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| 33 | * The primary disadvantage of this method is that with a fixed-point
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| 34 | * implementation, accuracy is lost due to imprecise representation of the
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| 35 | * scaled quantization values. However, that problem does not arise if
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| 36 | * we use floating point arithmetic.
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| 37 | */
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| 38 |
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| 39 | #define JPEG_INTERNALS
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| 40 | #include "jinclude.h"
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| 41 | #include "jpeglib.h"
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| 42 | #include "jdct.h" /* Private declarations for DCT subsystem */
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| 43 |
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| 44 | #ifdef DCT_FLOAT_SUPPORTED
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| 45 |
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| 46 |
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| 47 | /*
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| 48 | * This module is specialized to the case DCTSIZE = 8.
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| 49 | */
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| 50 |
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| 51 | #if DCTSIZE != 8
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| 52 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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| 53 | #endif
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| 54 |
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| 55 |
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| 56 | /* Dequantize a coefficient by multiplying it by the multiplier-table
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| 57 | * entry; produce a float result.
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| 58 | */
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| 59 |
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| 60 | #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
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| 61 |
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| 62 |
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| 63 | /*
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| 64 | * Perform dequantization and inverse DCT on one block of coefficients.
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| 65 | */
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| 66 |
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| 67 | GLOBAL(void)
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| 68 | jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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| 69 | JCOEFPTR coef_block,
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| 70 | JSAMPARRAY output_buf, JDIMENSION output_col)
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| 71 | {
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| 72 | FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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| 73 | FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
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| 74 | FAST_FLOAT z5, z10, z11, z12, z13;
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| 75 | JCOEFPTR inptr;
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| 76 | FLOAT_MULT_TYPE * quantptr;
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| 77 | FAST_FLOAT * wsptr;
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| 78 | JSAMPROW outptr;
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| 79 | JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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| 80 | int ctr;
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| 81 | FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
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| 82 | SHIFT_TEMPS
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| 83 |
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| 84 | /* Pass 1: process columns from input, store into work array. */
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| 85 |
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| 86 | inptr = coef_block;
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| 87 | quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
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| 88 | wsptr = workspace;
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| 89 | for (ctr = DCTSIZE; ctr > 0; ctr--) {
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| 90 | /* Due to quantization, we will usually find that many of the input
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| 91 | * coefficients are zero, especially the AC terms. We can exploit this
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| 92 | * by short-circuiting the IDCT calculation for any column in which all
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| 93 | * the AC terms are zero. In that case each output is equal to the
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| 94 | * DC coefficient (with scale factor as needed).
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| 95 | * With typical images and quantization tables, half or more of the
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| 96 | * column DCT calculations can be simplified this way.
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| 97 | */
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| 98 |
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| 99 | if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
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| 100 | inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
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| 101 | inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
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| 102 | inptr[DCTSIZE*7] == 0) {
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| 103 | /* AC terms all zero */
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| 104 | FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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| 105 |
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| 106 | wsptr[DCTSIZE*0] = dcval;
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| 107 | wsptr[DCTSIZE*1] = dcval;
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| 108 | wsptr[DCTSIZE*2] = dcval;
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| 109 | wsptr[DCTSIZE*3] = dcval;
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| 110 | wsptr[DCTSIZE*4] = dcval;
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| 111 | wsptr[DCTSIZE*5] = dcval;
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| 112 | wsptr[DCTSIZE*6] = dcval;
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| 113 | wsptr[DCTSIZE*7] = dcval;
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| 114 |
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| 115 | inptr++; /* advance pointers to next column */
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| 116 | quantptr++;
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| 117 | wsptr++;
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| 118 | continue;
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| 119 | }
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| 120 |
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| 121 | /* Even part */
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| 122 |
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| 123 | tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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| 124 | tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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| 125 | tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
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| 126 | tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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| 127 |
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| 128 | tmp10 = tmp0 + tmp2; /* phase 3 */
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| 129 | tmp11 = tmp0 - tmp2;
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| 130 |
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| 131 | tmp13 = tmp1 + tmp3; /* phases 5-3 */
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| 132 | tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
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| 133 |
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| 134 | tmp0 = tmp10 + tmp13; /* phase 2 */
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| 135 | tmp3 = tmp10 - tmp13;
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| 136 | tmp1 = tmp11 + tmp12;
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| 137 | tmp2 = tmp11 - tmp12;
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| 138 |
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| 139 | /* Odd part */
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| 140 |
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| 141 | tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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| 142 | tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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| 143 | tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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| 144 | tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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| 145 |
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| 146 | z13 = tmp6 + tmp5; /* phase 6 */
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| 147 | z10 = tmp6 - tmp5;
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| 148 | z11 = tmp4 + tmp7;
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| 149 | z12 = tmp4 - tmp7;
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| 150 |
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| 151 | tmp7 = z11 + z13; /* phase 5 */
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| 152 | tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
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| 153 |
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| 154 | z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
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| 155 | tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
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| 156 | tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
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| 157 |
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| 158 | tmp6 = tmp12 - tmp7; /* phase 2 */
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| 159 | tmp5 = tmp11 - tmp6;
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| 160 | tmp4 = tmp10 + tmp5;
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| 161 |
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| 162 | wsptr[DCTSIZE*0] = tmp0 + tmp7;
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| 163 | wsptr[DCTSIZE*7] = tmp0 - tmp7;
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| 164 | wsptr[DCTSIZE*1] = tmp1 + tmp6;
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| 165 | wsptr[DCTSIZE*6] = tmp1 - tmp6;
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| 166 | wsptr[DCTSIZE*2] = tmp2 + tmp5;
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| 167 | wsptr[DCTSIZE*5] = tmp2 - tmp5;
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| 168 | wsptr[DCTSIZE*4] = tmp3 + tmp4;
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| 169 | wsptr[DCTSIZE*3] = tmp3 - tmp4;
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| 170 |
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| 171 | inptr++; /* advance pointers to next column */
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| 172 | quantptr++;
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| 173 | wsptr++;
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| 174 | }
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| 175 |
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| 176 | /* Pass 2: process rows from work array, store into output array. */
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| 177 | /* Note that we must descale the results by a factor of 8 == 2**3. */
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| 178 |
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| 179 | wsptr = workspace;
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| 180 | for (ctr = 0; ctr < DCTSIZE; ctr++) {
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| 181 | outptr = output_buf[ctr] + output_col;
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| 182 | /* Rows of zeroes can be exploited in the same way as we did with columns.
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| 183 | * However, the column calculation has created many nonzero AC terms, so
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| 184 | * the simplification applies less often (typically 5% to 10% of the time).
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| 185 | * And testing floats for zero is relatively expensive, so we don't bother.
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| 186 | */
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| 187 |
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| 188 | /* Even part */
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| 189 |
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| 190 | tmp10 = wsptr[0] + wsptr[4];
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| 191 | tmp11 = wsptr[0] - wsptr[4];
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| 192 |
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| 193 | tmp13 = wsptr[2] + wsptr[6];
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| 194 | tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
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| 195 |
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| 196 | tmp0 = tmp10 + tmp13;
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| 197 | tmp3 = tmp10 - tmp13;
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| 198 | tmp1 = tmp11 + tmp12;
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| 199 | tmp2 = tmp11 - tmp12;
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| 200 |
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| 201 | /* Odd part */
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| 202 |
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| 203 | z13 = wsptr[5] + wsptr[3];
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| 204 | z10 = wsptr[5] - wsptr[3];
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| 205 | z11 = wsptr[1] + wsptr[7];
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| 206 | z12 = wsptr[1] - wsptr[7];
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| 207 |
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| 208 | tmp7 = z11 + z13;
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| 209 | tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
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| 210 |
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| 211 | z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
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| 212 | tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
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| 213 | tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
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| 214 |
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| 215 | tmp6 = tmp12 - tmp7;
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| 216 | tmp5 = tmp11 - tmp6;
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| 217 | tmp4 = tmp10 + tmp5;
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| 218 |
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| 219 | /* Final output stage: scale down by a factor of 8 and range-limit */
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| 220 |
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| 221 | outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
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| 222 | & RANGE_MASK];
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| 223 | outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
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| 224 | & RANGE_MASK];
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| 225 | outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
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| 226 | & RANGE_MASK];
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| 227 | outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
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| 228 | & RANGE_MASK];
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| 229 | outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
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| 230 | & RANGE_MASK];
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| 231 | outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
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| 232 | & RANGE_MASK];
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| 233 | outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
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| 234 | & RANGE_MASK];
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| 235 | outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
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| 236 | & RANGE_MASK];
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| 237 |
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| 238 | wsptr += DCTSIZE; /* advance pointer to next row */
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| 239 | }
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| 240 | }
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| 241 |
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| 242 | #endif /* DCT_FLOAT_SUPPORTED */
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