| 1 | /*
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| 2 | * jfdctint.c
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| 3 | *
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| 4 | * Copyright (C) 1991-1996, 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 slow-but-accurate integer implementation of the
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| 9 | * forward DCT (Discrete Cosine Transform).
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| 10 | *
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| 11 | * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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| 12 | * on each column. Direct algorithms are also available, but they are
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| 13 | * much more complex and seem not to be any faster when reduced to code.
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| 14 | *
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| 15 | * This implementation is based on an algorithm described in
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| 16 | * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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| 17 | * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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| 18 | * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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| 19 | * The primary algorithm described there uses 11 multiplies and 29 adds.
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| 20 | * We use their alternate method with 12 multiplies and 32 adds.
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| 21 | * The advantage of this method is that no data path contains more than one
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| 22 | * multiplication; this allows a very simple and accurate implementation in
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| 23 | * scaled fixed-point arithmetic, with a minimal number of shifts.
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| 24 | */
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| 25 |
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| 26 | #define JPEG_INTERNALS
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| 27 | #include "jinclude.h"
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| 28 | #include "jpeglib.h"
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| 29 | #include "jdct.h" /* Private declarations for DCT subsystem */
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| 30 |
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| 31 | #ifdef DCT_ISLOW_SUPPORTED
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| 32 |
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| 33 |
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| 34 | /*
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| 35 | * This module is specialized to the case DCTSIZE = 8.
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| 36 | */
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| 37 |
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| 38 | #if DCTSIZE != 8
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| 39 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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| 40 | #endif
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| 41 |
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| 42 |
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| 43 | /*
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| 44 | * The poop on this scaling stuff is as follows:
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| 45 | *
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| 46 | * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
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| 47 | * larger than the true DCT outputs. The final outputs are therefore
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| 48 | * a factor of N larger than desired; since N=8 this can be cured by
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| 49 | * a simple right shift at the end of the algorithm. The advantage of
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| 50 | * this arrangement is that we save two multiplications per 1-D DCT,
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| 51 | * because the y0 and y4 outputs need not be divided by sqrt(N).
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| 52 | * In the IJG code, this factor of 8 is removed by the quantization step
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| 53 | * (in jcdctmgr.c), NOT in this module.
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| 54 | *
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| 55 | * We have to do addition and subtraction of the integer inputs, which
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| 56 | * is no problem, and multiplication by fractional constants, which is
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| 57 | * a problem to do in integer arithmetic. We multiply all the constants
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| 58 | * by CONST_SCALE and convert them to integer constants (thus retaining
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| 59 | * CONST_BITS bits of precision in the constants). After doing a
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| 60 | * multiplication we have to divide the product by CONST_SCALE, with proper
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| 61 | * rounding, to produce the correct output. This division can be done
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| 62 | * cheaply as a right shift of CONST_BITS bits. We postpone shifting
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| 63 | * as long as possible so that partial sums can be added together with
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| 64 | * full fractional precision.
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| 65 | *
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| 66 | * The outputs of the first pass are scaled up by PASS1_BITS bits so that
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| 67 | * they are represented to better-than-integral precision. These outputs
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| 68 | * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
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| 69 | * with the recommended scaling. (For 12-bit sample data, the intermediate
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| 70 | * array is INT32 anyway.)
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| 71 | *
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| 72 | * To avoid overflow of the 32-bit intermediate results in pass 2, we must
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| 73 | * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
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| 74 | * shows that the values given below are the most effective.
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| 75 | */
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| 76 |
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| 77 | #if BITS_IN_JSAMPLE == 8
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| 78 | #define CONST_BITS 13
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| 79 | #define PASS1_BITS 2
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| 80 | #else
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| 81 | #define CONST_BITS 13
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| 82 | #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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| 83 | #endif
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| 84 |
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| 85 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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| 86 | * causing a lot of useless floating-point operations at run time.
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| 87 | * To get around this we use the following pre-calculated constants.
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| 88 | * If you change CONST_BITS you may want to add appropriate values.
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| 89 | * (With a reasonable C compiler, you can just rely on the FIX() macro...)
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| 90 | */
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| 91 |
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| 92 | #if CONST_BITS == 13
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| 93 | #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
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| 94 | #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
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| 95 | #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
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| 96 | #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
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| 97 | #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
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| 98 | #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
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| 99 | #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
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| 100 | #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
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| 101 | #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
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| 102 | #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
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| 103 | #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
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| 104 | #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
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| 105 | #else
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| 106 | #define FIX_0_298631336 FIX(0.298631336)
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| 107 | #define FIX_0_390180644 FIX(0.390180644)
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| 108 | #define FIX_0_541196100 FIX(0.541196100)
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| 109 | #define FIX_0_765366865 FIX(0.765366865)
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| 110 | #define FIX_0_899976223 FIX(0.899976223)
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| 111 | #define FIX_1_175875602 FIX(1.175875602)
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| 112 | #define FIX_1_501321110 FIX(1.501321110)
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| 113 | #define FIX_1_847759065 FIX(1.847759065)
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| 114 | #define FIX_1_961570560 FIX(1.961570560)
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| 115 | #define FIX_2_053119869 FIX(2.053119869)
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| 116 | #define FIX_2_562915447 FIX(2.562915447)
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| 117 | #define FIX_3_072711026 FIX(3.072711026)
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| 118 | #endif
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| 119 |
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| 120 |
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| 121 | /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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| 122 | * For 8-bit samples with the recommended scaling, all the variable
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| 123 | * and constant values involved are no more than 16 bits wide, so a
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| 124 | * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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| 125 | * For 12-bit samples, a full 32-bit multiplication will be needed.
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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 MULTIPLY(var,const) MULTIPLY16C16(var,const)
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| 130 | #else
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| 131 | #define MULTIPLY(var,const) ((var) * (const))
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| 132 | #endif
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| 133 |
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| 134 |
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| 135 | /*
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| 136 | * Perform the forward DCT on one block of samples.
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| 137 | */
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| 138 |
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| 139 | GLOBAL(void)
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| 140 | jpeg_fdct_islow (DCTELEM * data)
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| 141 | {
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| 142 | INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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| 143 | INT32 tmp10, tmp11, tmp12, tmp13;
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| 144 | INT32 z1, z2, z3, z4, z5;
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| 145 | DCTELEM *dataptr;
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| 146 | int ctr;
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| 147 | SHIFT_TEMPS
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| 148 |
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| 149 | /* Pass 1: process rows. */
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| 150 | /* Note results are scaled up by sqrt(8) compared to a true DCT; */
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| 151 | /* furthermore, we scale the results by 2**PASS1_BITS. */
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| 152 |
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| 153 | dataptr = data;
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| 154 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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| 155 | tmp0 = dataptr[0] + dataptr[7];
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| 156 | tmp7 = dataptr[0] - dataptr[7];
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| 157 | tmp1 = dataptr[1] + dataptr[6];
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| 158 | tmp6 = dataptr[1] - dataptr[6];
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| 159 | tmp2 = dataptr[2] + dataptr[5];
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| 160 | tmp5 = dataptr[2] - dataptr[5];
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| 161 | tmp3 = dataptr[3] + dataptr[4];
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| 162 | tmp4 = dataptr[3] - dataptr[4];
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| 163 |
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| 164 | /* Even part per LL&M figure 1 --- note that published figure is faulty;
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| 165 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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| 166 | */
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| 167 |
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| 168 | tmp10 = tmp0 + tmp3;
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| 169 | tmp13 = tmp0 - tmp3;
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| 170 | tmp11 = tmp1 + tmp2;
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| 171 | tmp12 = tmp1 - tmp2;
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| 172 |
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| 173 | dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
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| 174 | dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
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| 175 |
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| 176 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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| 177 | dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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| 178 | CONST_BITS-PASS1_BITS);
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| 179 | dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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| 180 | CONST_BITS-PASS1_BITS);
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| 181 |
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| 182 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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| 183 | * cK represents cos(K*pi/16).
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| 184 | * i0..i3 in the paper are tmp4..tmp7 here.
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| 185 | */
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| 186 |
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| 187 | z1 = tmp4 + tmp7;
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| 188 | z2 = tmp5 + tmp6;
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| 189 | z3 = tmp4 + tmp6;
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| 190 | z4 = tmp5 + tmp7;
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| 191 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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| 192 |
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| 193 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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| 194 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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| 195 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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| 196 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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| 197 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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| 198 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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| 199 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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| 200 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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| 201 |
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| 202 | z3 += z5;
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| 203 | z4 += z5;
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| 204 |
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| 205 | dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
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| 206 | dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
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| 207 | dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
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| 208 | dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
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| 209 |
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| 210 | dataptr += DCTSIZE; /* advance pointer to next row */
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| 211 | }
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| 212 |
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| 213 | /* Pass 2: process columns.
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| 214 | * We remove the PASS1_BITS scaling, but leave the results scaled up
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| 215 | * by an overall factor of 8.
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| 216 | */
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| 217 |
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| 218 | dataptr = data;
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| 219 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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| 220 | tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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| 221 | tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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| 222 | tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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| 223 | tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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| 224 | tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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| 225 | tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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| 226 | tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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| 227 | tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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| 228 |
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| 229 | /* Even part per LL&M figure 1 --- note that published figure is faulty;
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| 230 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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| 231 | */
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| 232 |
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| 233 | tmp10 = tmp0 + tmp3;
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| 234 | tmp13 = tmp0 - tmp3;
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| 235 | tmp11 = tmp1 + tmp2;
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| 236 | tmp12 = tmp1 - tmp2;
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| 237 |
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| 238 | dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
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| 239 | dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
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| 240 |
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| 241 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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| 242 | dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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| 243 | CONST_BITS+PASS1_BITS);
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| 244 | dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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| 245 | CONST_BITS+PASS1_BITS);
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| 246 |
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| 247 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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| 248 | * cK represents cos(K*pi/16).
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| 249 | * i0..i3 in the paper are tmp4..tmp7 here.
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| 250 | */
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| 251 |
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| 252 | z1 = tmp4 + tmp7;
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| 253 | z2 = tmp5 + tmp6;
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| 254 | z3 = tmp4 + tmp6;
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| 255 | z4 = tmp5 + tmp7;
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| 256 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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| 257 |
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| 258 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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| 259 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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| 260 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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| 261 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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| 262 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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| 263 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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| 264 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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| 265 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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| 266 |
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| 267 | z3 += z5;
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| 268 | z4 += z5;
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| 269 |
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| 270 | dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
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| 271 | CONST_BITS+PASS1_BITS);
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| 272 | dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
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| 273 | CONST_BITS+PASS1_BITS);
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| 274 | dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
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| 275 | CONST_BITS+PASS1_BITS);
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| 276 | dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
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| 277 | CONST_BITS+PASS1_BITS);
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| 278 |
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| 279 | dataptr++; /* advance pointer to next column */
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| 280 | }
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| 281 | }
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| 282 |
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| 283 | #endif /* DCT_ISLOW_SUPPORTED */
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