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1 /*
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2 * jidctint.c
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3 *
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4 * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in
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18 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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19 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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20 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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21 * The primary algorithm described there uses 11 multiplies and 29 adds.
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22 * We use their alternate method with 12 multiplies and 32 adds.
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23 * The advantage of this method is that no data path contains more than one
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24 * multiplication; this allows a very simple and accurate implementation in
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25 * scaled fixed-point arithmetic, with a minimal number of shifts.
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26 */
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27
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28 #define JPEG_INTERNALS
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29 #include "jinclude.h"
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30 #include "jpeglib.h"
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31 #include "jdct.h" /* Private declarations for DCT subsystem */
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32
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33 #ifdef DCT_ISLOW_SUPPORTED
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34
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35
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36 /*
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37 * This module is specialized to the case DCTSIZE = 8.
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38 */
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39
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40 #if DCTSIZE != 8
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41 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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42 #endif
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43
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44
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45 /*
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46 * The poop on this scaling stuff is as follows:
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47 *
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48 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
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49 * larger than the true IDCT outputs. The final outputs are therefore
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50 * a factor of N larger than desired; since N=8 this can be cured by
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51 * a simple right shift at the end of the algorithm. The advantage of
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52 * this arrangement is that we save two multiplications per 1-D IDCT,
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53 * because the y0 and y4 inputs need not be divided by sqrt(N).
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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. (To scale up 12-bit sample data further, an
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70 * intermediate INT32 array would be needed.)
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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 /* Dequantize a coefficient by multiplying it by the multiplier-table
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136 * entry; produce an int result. In this module, both inputs and result
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137 * are 16 bits or less, so either int or short multiply will work.
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138 */
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139
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140 #define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
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141
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142
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143 /*
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144 * Perform dequantization and inverse DCT on one block of coefficients.
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145 */
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146
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147 GLOBAL(void)
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148 jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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149 JCOEFPTR coef_block,
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150 JSAMPARRAY output_buf, JDIMENSION output_col)
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151 {
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152 INT32 tmp0, tmp1, tmp2, tmp3;
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153 INT32 tmp10, tmp11, tmp12, tmp13;
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154 INT32 z1, z2, z3, z4, z5;
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155 JCOEFPTR inptr;
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156 ISLOW_MULT_TYPE * quantptr;
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157 int * wsptr;
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158 JSAMPROW outptr;
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159 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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160 int ctr;
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161 int workspace[DCTSIZE2]; /* buffers data between passes */
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162 SHIFT_TEMPS
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163
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164 /* Pass 1: process columns from input, store into work array. */
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165 /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
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166 /* furthermore, we scale the results by 2**PASS1_BITS. */
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167
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168 inptr = coef_block;
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169 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
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170 wsptr = workspace;
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171 for (ctr = DCTSIZE; ctr > 0; ctr--) {
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172 /* Due to quantization, we will usually find that many of the input
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173 * coefficients are zero, especially the AC terms. We can exploit this
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174 * by short-circuiting the IDCT calculation for any column in which all
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175 * the AC terms are zero. In that case each output is equal to the
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176 * DC coefficient (with scale factor as needed).
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177 * With typical images and quantization tables, half or more of the
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178 * column DCT calculations can be simplified this way.
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179 */
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180
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181 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
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182 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
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183 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
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184 inptr[DCTSIZE*7] == 0) {
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185 /* AC terms all zero */
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186 int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
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187
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188 wsptr[DCTSIZE*0] = dcval;
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189 wsptr[DCTSIZE*1] = dcval;
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190 wsptr[DCTSIZE*2] = dcval;
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191 wsptr[DCTSIZE*3] = dcval;
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192 wsptr[DCTSIZE*4] = dcval;
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193 wsptr[DCTSIZE*5] = dcval;
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194 wsptr[DCTSIZE*6] = dcval;
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195 wsptr[DCTSIZE*7] = dcval;
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196
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197 inptr++; /* advance pointers to next column */
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198 quantptr++;
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199 wsptr++;
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200 continue;
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201 }
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202
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203 /* Even part: reverse the even part of the forward DCT. */
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204 /* The rotator is sqrt(2)*c(-6). */
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205
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206 z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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207 z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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208
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209 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
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210 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
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211 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
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212
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213 z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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214 z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
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215
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216 tmp0 = (z2 + z3) << CONST_BITS;
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217 tmp1 = (z2 - z3) << CONST_BITS;
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218
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219 tmp10 = tmp0 + tmp3;
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220 tmp13 = tmp0 - tmp3;
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221 tmp11 = tmp1 + tmp2;
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222 tmp12 = tmp1 - tmp2;
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223
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224 /* Odd part per figure 8; the matrix is unitary and hence its
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225 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
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226 */
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227
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228 tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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229 tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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230 tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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231 tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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232
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233 z1 = tmp0 + tmp3;
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234 z2 = tmp1 + tmp2;
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235 z3 = tmp0 + tmp2;
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236 z4 = tmp1 + tmp3;
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237 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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238
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239 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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240 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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241 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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242 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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243 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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244 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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245 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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246 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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247
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248 z3 += z5;
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249 z4 += z5;
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250
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251 tmp0 += z1 + z3;
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252 tmp1 += z2 + z4;
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253 tmp2 += z2 + z3;
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254 tmp3 += z1 + z4;
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255
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256 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
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257
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258 wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
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259 wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
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260 wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
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261 wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
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262 wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
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263 wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
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264 wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
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265 wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
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266
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267 inptr++; /* advance pointers to next column */
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268 quantptr++;
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269 wsptr++;
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270 }
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271
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272 /* Pass 2: process rows from work array, store into output array. */
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273 /* Note that we must descale the results by a factor of 8 == 2**3, */
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274 /* and also undo the PASS1_BITS scaling. */
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275
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276 wsptr = workspace;
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277 for (ctr = 0; ctr < DCTSIZE; ctr++) {
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278 outptr = output_buf[ctr] + output_col;
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279 /* Rows of zeroes can be exploited in the same way as we did with columns.
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280 * However, the column calculation has created many nonzero AC terms, so
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281 * the simplification applies less often (typically 5% to 10% of the time).
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282 * On machines with very fast multiplication, it's possible that the
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283 * test takes more time than it's worth. In that case this section
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284 * may be commented out.
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285 */
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286
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287 #ifndef NO_ZERO_ROW_TEST
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288 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
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289 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
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290 /* AC terms all zero */
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291 JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
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292 & RANGE_MASK];
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293
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294 outptr[0] = dcval;
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295 outptr[1] = dcval;
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296 outptr[2] = dcval;
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297 outptr[3] = dcval;
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298 outptr[4] = dcval;
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299 outptr[5] = dcval;
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300 outptr[6] = dcval;
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301 outptr[7] = dcval;
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302
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303 wsptr += DCTSIZE; /* advance pointer to next row */
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304 continue;
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305 }
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306 #endif
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nuclear@0
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307
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nuclear@0
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308 /* Even part: reverse the even part of the forward DCT. */
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nuclear@0
|
309 /* The rotator is sqrt(2)*c(-6). */
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nuclear@0
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310
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nuclear@0
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311 z2 = (INT32) wsptr[2];
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nuclear@0
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312 z3 = (INT32) wsptr[6];
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nuclear@0
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313
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nuclear@0
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314 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
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nuclear@0
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315 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
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nuclear@0
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316 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
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nuclear@0
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317
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nuclear@0
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318 tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
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nuclear@0
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319 tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
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nuclear@0
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320
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nuclear@0
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321 tmp10 = tmp0 + tmp3;
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nuclear@0
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322 tmp13 = tmp0 - tmp3;
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nuclear@0
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323 tmp11 = tmp1 + tmp2;
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nuclear@0
|
324 tmp12 = tmp1 - tmp2;
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nuclear@0
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325
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nuclear@0
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326 /* Odd part per figure 8; the matrix is unitary and hence its
|
nuclear@0
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327 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
|
nuclear@0
|
328 */
|
nuclear@0
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329
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nuclear@0
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330 tmp0 = (INT32) wsptr[7];
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nuclear@0
|
331 tmp1 = (INT32) wsptr[5];
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nuclear@0
|
332 tmp2 = (INT32) wsptr[3];
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nuclear@0
|
333 tmp3 = (INT32) wsptr[1];
|
nuclear@0
|
334
|
nuclear@0
|
335 z1 = tmp0 + tmp3;
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nuclear@0
|
336 z2 = tmp1 + tmp2;
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nuclear@0
|
337 z3 = tmp0 + tmp2;
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nuclear@0
|
338 z4 = tmp1 + tmp3;
|
nuclear@0
|
339 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
|
nuclear@0
|
340
|
nuclear@0
|
341 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
|
nuclear@0
|
342 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
|
nuclear@0
|
343 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
|
nuclear@0
|
344 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
|
nuclear@0
|
345 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
|
nuclear@0
|
346 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
|
nuclear@0
|
347 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
|
nuclear@0
|
348 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
|
nuclear@0
|
349
|
nuclear@0
|
350 z3 += z5;
|
nuclear@0
|
351 z4 += z5;
|
nuclear@0
|
352
|
nuclear@0
|
353 tmp0 += z1 + z3;
|
nuclear@0
|
354 tmp1 += z2 + z4;
|
nuclear@0
|
355 tmp2 += z2 + z3;
|
nuclear@0
|
356 tmp3 += z1 + z4;
|
nuclear@0
|
357
|
nuclear@0
|
358 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
|
nuclear@0
|
359
|
nuclear@0
|
360 outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
|
nuclear@0
|
361 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
362 & RANGE_MASK];
|
nuclear@0
|
363 outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
|
nuclear@0
|
364 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
365 & RANGE_MASK];
|
nuclear@0
|
366 outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
|
nuclear@0
|
367 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
368 & RANGE_MASK];
|
nuclear@0
|
369 outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
|
nuclear@0
|
370 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
371 & RANGE_MASK];
|
nuclear@0
|
372 outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
|
nuclear@0
|
373 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
374 & RANGE_MASK];
|
nuclear@0
|
375 outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
|
nuclear@0
|
376 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
377 & RANGE_MASK];
|
nuclear@0
|
378 outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
|
nuclear@0
|
379 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
380 & RANGE_MASK];
|
nuclear@0
|
381 outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
|
nuclear@0
|
382 CONST_BITS+PASS1_BITS+3)
|
nuclear@0
|
383 & RANGE_MASK];
|
nuclear@0
|
384
|
nuclear@0
|
385 wsptr += DCTSIZE; /* advance pointer to next row */
|
nuclear@0
|
386 }
|
nuclear@0
|
387 }
|
nuclear@0
|
388
|
nuclear@0
|
389 #endif /* DCT_ISLOW_SUPPORTED */
|