| 1 | /*
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| 2 | * jidctfst.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 fast, not so accurate integer 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 | * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
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| 13 | * on each row (or vice versa, but it's more convenient to emit a row at
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| 14 | * a time). Direct algorithms are also available, but they are much more
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| 15 | * complex and seem not to be any faster when reduced to code.
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| 16 | *
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| 17 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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| 18 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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| 19 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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| 20 | * JPEG textbook (see REFERENCES section in file README). The following code
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| 21 | * is based directly on figure 4-8 in P&M.
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| 22 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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| 23 | * possible to arrange the computation so that many of the multiplies are
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| 24 | * simple scalings of the final outputs. These multiplies can then be
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| 25 | * folded into the multiplications or divisions by the JPEG quantization
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| 26 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds
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| 27 | * to be done in the DCT itself.
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| 28 | * The primary disadvantage of this method is that with fixed-point math,
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| 29 | * accuracy is lost due to imprecise representation of the scaled
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| 30 | * quantization values. The smaller the quantization table entry, the less
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| 31 | * precise the scaled value, so this implementation does worse with high-
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| 32 | * quality-setting files than with low-quality ones.
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| 33 | */
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| 34 |
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| 35 | #define JPEG_INTERNALS
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| 36 | #include "jinclude.h"
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| 37 | #include "jpeglib.h"
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| 38 | #include "jdct.h" /* Private declarations for DCT subsystem */
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| 39 |
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| 40 | #ifdef DCT_IFAST_SUPPORTED
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| 41 |
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| 42 |
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| 43 | /*
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| 44 | * This module is specialized to the case DCTSIZE = 8.
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| 45 | */
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| 46 |
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| 47 | #if DCTSIZE != 8
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| 48 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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| 49 | #endif
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| 50 |
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| 51 |
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| 52 | /* Scaling decisions are generally the same as in the LL&M algorithm;
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| 53 | * see jidctint.c for more details. However, we choose to descale
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| 54 | * (right shift) multiplication products as soon as they are formed,
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| 55 | * rather than carrying additional fractional bits into subsequent additions.
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| 56 | * This compromises accuracy slightly, but it lets us save a few shifts.
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| 57 | * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
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| 58 | * everywhere except in the multiplications proper; this saves a good deal
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| 59 | * of work on 16-bit-int machines.
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| 60 | *
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| 61 | * The dequantized coefficients are not integers because the AA&N scaling
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| 62 | * factors have been incorporated. We represent them scaled up by PASS1_BITS,
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| 63 | * so that the first and second IDCT rounds have the same input scaling.
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| 64 | * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
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| 65 | * avoid a descaling shift; this compromises accuracy rather drastically
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| 66 | * for small quantization table entries, but it saves a lot of shifts.
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| 67 | * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
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| 68 | * so we use a much larger scaling factor to preserve accuracy.
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| 69 | *
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| 70 | * A final compromise is to represent the multiplicative constants to only
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| 71 | * 8 fractional bits, rather than 13. This saves some shifting work on some
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| 72 | * machines, and may also reduce the cost of multiplication (since there
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| 73 | * are fewer one-bits in the constants).
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| 74 | */
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| 75 |
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| 76 | #if BITS_IN_JSAMPLE == 8
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| 77 | #define CONST_BITS 8
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| 78 | #define PASS1_BITS 2
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| 79 | #else
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| 80 | #define CONST_BITS 8
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| 81 | #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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| 82 | #endif
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| 83 |
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| 84 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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| 85 | * causing a lot of useless floating-point operations at run time.
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| 86 | * To get around this we use the following pre-calculated constants.
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| 87 | * If you change CONST_BITS you may want to add appropriate values.
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| 88 | * (With a reasonable C compiler, you can just rely on the FIX() macro...)
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| 89 | */
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| 90 |
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| 91 | #if CONST_BITS == 8
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| 92 | #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
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| 93 | #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
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| 94 | #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
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| 95 | #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
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| 96 | #else
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| 97 | #define FIX_1_082392200 FIX(1.082392200)
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| 98 | #define FIX_1_414213562 FIX(1.414213562)
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| 99 | #define FIX_1_847759065 FIX(1.847759065)
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| 100 | #define FIX_2_613125930 FIX(2.613125930)
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| 101 | #endif
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| 102 |
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| 103 |
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| 104 | /* We can gain a little more speed, with a further compromise in accuracy,
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| 105 | * by omitting the addition in a descaling shift. This yields an incorrectly
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| 106 | * rounded result half the time...
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| 107 | */
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| 108 |
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| 109 | #ifndef USE_ACCURATE_ROUNDING
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| 110 | #undef DESCALE
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| 111 | #define DESCALE(x,n) RIGHT_SHIFT(x, n)
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| 112 | #endif
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| 113 |
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| 114 |
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| 115 | /* Multiply a DCTELEM variable by an INT32 constant, and immediately
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| 116 | * descale to yield a DCTELEM result.
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| 117 | */
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| 118 |
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| 119 | #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
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| 120 |
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| 121 |
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| 122 | /* Dequantize a coefficient by multiplying it by the multiplier-table
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| 123 | * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
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| 124 | * multiplication will do. For 12-bit data, the multiplier table is
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| 125 | * declared INT32, so a 32-bit multiply will be used.
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| 126 | */
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| 127 |
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| 128 | #if BITS_IN_JSAMPLE == 8
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| 129 | #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
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| 130 | #else
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| 131 | #define DEQUANTIZE(coef,quantval) \
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| 132 | DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
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| 133 | #endif
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| 134 |
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| 135 |
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| 136 | /* Like DESCALE, but applies to a DCTELEM and produces an int.
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| 137 | * We assume that int right shift is unsigned if INT32 right shift is.
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| 138 | */
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| 139 |
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| 140 | #ifdef RIGHT_SHIFT_IS_UNSIGNED
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| 141 | #define ISHIFT_TEMPS DCTELEM ishift_temp;
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| 142 | #if BITS_IN_JSAMPLE == 8
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| 143 | #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
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| 144 | #else
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| 145 | #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
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| 146 | #endif
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| 147 | #define IRIGHT_SHIFT(x,shft) \
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| 148 | ((ishift_temp = (x)) < 0 ? \
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| 149 | (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
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| 150 | (ishift_temp >> (shft)))
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| 151 | #else
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| 152 | #define ISHIFT_TEMPS
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| 153 | #define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
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| 154 | #endif
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| 155 |
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| 156 | #ifdef USE_ACCURATE_ROUNDING
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| 157 | #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
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| 158 | #else
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| 159 | #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
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| 160 | #endif
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| 161 |
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| 162 |
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| 163 | /*
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| 164 | * Perform dequantization and inverse DCT on one block of coefficients.
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| 165 | */
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| 166 |
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| 167 | GLOBAL(void)
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| 168 | jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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| 169 | JCOEFPTR coef_block,
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| 170 | JSAMPARRAY output_buf, JDIMENSION output_col)
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| 171 | {
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| 172 | DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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| 173 | DCTELEM tmp10, tmp11, tmp12, tmp13;
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| 174 | DCTELEM z5, z10, z11, z12, z13;
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| 175 | JCOEFPTR inptr;
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| 176 | IFAST_MULT_TYPE * quantptr;
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| 177 | int * wsptr;
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| 178 | JSAMPROW outptr;
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| 179 | JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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| 180 | int ctr;
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| 181 | int workspace[DCTSIZE2]; /* buffers data between passes */
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| 182 | SHIFT_TEMPS /* for DESCALE */
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| 183 | ISHIFT_TEMPS /* for IDESCALE */
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| 184 |
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| 185 | /* Pass 1: process columns from input, store into work array. */
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| 186 |
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| 187 | inptr = coef_block;
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| 188 | quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
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| 189 | wsptr = workspace;
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| 190 | for (ctr = DCTSIZE; ctr > 0; ctr--) {
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| 191 | /* Due to quantization, we will usually find that many of the input
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| 192 | * coefficients are zero, especially the AC terms. We can exploit this
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| 193 | * by short-circuiting the IDCT calculation for any column in which all
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| 194 | * the AC terms are zero. In that case each output is equal to the
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| 195 | * DC coefficient (with scale factor as needed).
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| 196 | * With typical images and quantization tables, half or more of the
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| 197 | * column DCT calculations can be simplified this way.
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| 198 | */
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| 199 |
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| 200 | if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
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| 201 | inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
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| 202 | inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
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| 203 | inptr[DCTSIZE*7] == 0) {
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| 204 | /* AC terms all zero */
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| 205 | int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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| 206 |
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| 207 | wsptr[DCTSIZE*0] = dcval;
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| 208 | wsptr[DCTSIZE*1] = dcval;
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| 209 | wsptr[DCTSIZE*2] = dcval;
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| 210 | wsptr[DCTSIZE*3] = dcval;
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| 211 | wsptr[DCTSIZE*4] = dcval;
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| 212 | wsptr[DCTSIZE*5] = dcval;
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| 213 | wsptr[DCTSIZE*6] = dcval;
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| 214 | wsptr[DCTSIZE*7] = dcval;
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| 215 |
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| 216 | inptr++; /* advance pointers to next column */
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| 217 | quantptr++;
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| 218 | wsptr++;
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| 219 | continue;
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| 220 | }
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| 221 |
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| 222 | /* Even part */
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| 223 |
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| 224 | tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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| 225 | tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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| 226 | tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
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| 227 | tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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| 228 |
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| 229 | tmp10 = tmp0 + tmp2; /* phase 3 */
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| 230 | tmp11 = tmp0 - tmp2;
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| 231 |
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| 232 | tmp13 = tmp1 + tmp3; /* phases 5-3 */
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| 233 | tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
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| 234 |
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| 235 | tmp0 = tmp10 + tmp13; /* phase 2 */
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| 236 | tmp3 = tmp10 - tmp13;
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| 237 | tmp1 = tmp11 + tmp12;
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| 238 | tmp2 = tmp11 - tmp12;
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| 239 |
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| 240 | /* Odd part */
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| 241 |
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| 242 | tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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| 243 | tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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| 244 | tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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| 245 | tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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| 246 |
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| 247 | z13 = tmp6 + tmp5; /* phase 6 */
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| 248 | z10 = tmp6 - tmp5;
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| 249 | z11 = tmp4 + tmp7;
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| 250 | z12 = tmp4 - tmp7;
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| 251 |
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| 252 | tmp7 = z11 + z13; /* phase 5 */
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| 253 | tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
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| 254 |
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| 255 | z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
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| 256 | tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
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| 257 | tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
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| 258 |
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| 259 | tmp6 = tmp12 - tmp7; /* phase 2 */
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| 260 | tmp5 = tmp11 - tmp6;
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| 261 | tmp4 = tmp10 + tmp5;
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| 262 |
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| 263 | wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
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| 264 | wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
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| 265 | wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
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| 266 | wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
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| 267 | wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
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| 268 | wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
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| 269 | wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
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| 270 | wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
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| 271 |
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| 272 | inptr++; /* advance pointers to next column */
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| 273 | quantptr++;
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| 274 | wsptr++;
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| 275 | }
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| 276 |
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| 277 | /* Pass 2: process rows from work array, store into output array. */
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| 278 | /* Note that we must descale the results by a factor of 8 == 2**3, */
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| 279 | /* and also undo the PASS1_BITS scaling. */
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| 280 |
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| 281 | wsptr = workspace;
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| 282 | for (ctr = 0; ctr < DCTSIZE; ctr++) {
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| 283 | outptr = output_buf[ctr] + output_col;
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| 284 | /* Rows of zeroes can be exploited in the same way as we did with columns.
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| 285 | * However, the column calculation has created many nonzero AC terms, so
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| 286 | * the simplification applies less often (typically 5% to 10% of the time).
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| 287 | * On machines with very fast multiplication, it's possible that the
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| 288 | * test takes more time than it's worth. In that case this section
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| 289 | * may be commented out.
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| 290 | */
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| 291 |
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| 292 | #ifndef NO_ZERO_ROW_TEST
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| 293 | if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
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| 294 | wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
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| 295 | /* AC terms all zero */
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| 296 | JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
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| 297 | & RANGE_MASK];
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| 298 |
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| 299 | outptr[0] = dcval;
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| 300 | outptr[1] = dcval;
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| 301 | outptr[2] = dcval;
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| 302 | outptr[3] = dcval;
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| 303 | outptr[4] = dcval;
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| 304 | outptr[5] = dcval;
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| 305 | outptr[6] = dcval;
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| 306 | outptr[7] = dcval;
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| 307 |
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| 308 | wsptr += DCTSIZE; /* advance pointer to next row */
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| 309 | continue;
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| 310 | }
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| 311 | #endif
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| 312 |
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| 313 | /* Even part */
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| 314 |
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| 315 | tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
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| 316 | tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
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| 317 |
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| 318 | tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
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| 319 | tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
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| 320 | - tmp13;
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| 321 |
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| 322 | tmp0 = tmp10 + tmp13;
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| 323 | tmp3 = tmp10 - tmp13;
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| 324 | tmp1 = tmp11 + tmp12;
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| 325 | tmp2 = tmp11 - tmp12;
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| 326 |
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| 327 | /* Odd part */
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| 328 |
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| 329 | z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
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| 330 | z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
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| 331 | z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
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| 332 | z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
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| 333 |
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| 334 | tmp7 = z11 + z13; /* phase 5 */
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| 335 | tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
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| 336 |
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| 337 | z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
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| 338 | tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
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| 339 | tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
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| 340 |
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| 341 | tmp6 = tmp12 - tmp7; /* phase 2 */
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| 342 | tmp5 = tmp11 - tmp6;
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| 343 | tmp4 = tmp10 + tmp5;
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| 344 |
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| 345 | /* Final output stage: scale down by a factor of 8 and range-limit */
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| 346 |
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| 347 | outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
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| 348 | & RANGE_MASK];
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| 349 | outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
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| 350 | & RANGE_MASK];
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| 351 | outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
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| 352 | & RANGE_MASK];
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| 353 | outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
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| 354 | & RANGE_MASK];
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| 355 | outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
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| 356 | & RANGE_MASK];
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| 357 | outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
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| 358 | & RANGE_MASK];
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| 359 | outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
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|---|
| 360 | & RANGE_MASK];
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|---|
| 361 | outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
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|---|
| 362 | & RANGE_MASK];
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| 363 |
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| 364 | wsptr += DCTSIZE; /* advance pointer to next row */
|
|---|
| 365 | }
|
|---|
| 366 | }
|
|---|
| 367 |
|
|---|
| 368 | #endif /* DCT_IFAST_SUPPORTED */
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|---|
