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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307 | |
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308 | /* Even part: reverse the even part of the forward DCT. */ |
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309 | /* The rotator is sqrt(2)*c(-6). */ |
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310 | |
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311 | z2 = (INT32) wsptr[2]; |
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312 | z3 = (INT32) wsptr[6]; |
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313 | |
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314 | z1 = MULTIPLY(z2 + z3, FIX_0_541196100); |
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315 | tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); |
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316 | tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); |
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317 | |
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318 | tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS; |
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319 | tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS; |
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320 | |
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321 | tmp10 = tmp0 + tmp3; |
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322 | tmp13 = tmp0 - tmp3; |
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323 | tmp11 = tmp1 + tmp2; |
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324 | tmp12 = tmp1 - tmp2; |
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325 | |
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326 | /* Odd part per figure 8; the matrix is unitary and hence its |
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327 | * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. |
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328 | */ |
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329 | |
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330 | tmp0 = (INT32) wsptr[7]; |
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331 | tmp1 = (INT32) wsptr[5]; |
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332 | tmp2 = (INT32) wsptr[3]; |
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333 | tmp3 = (INT32) wsptr[1]; |
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334 | |
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335 | z1 = tmp0 + tmp3; |
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336 | z2 = tmp1 + tmp2; |
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337 | z3 = tmp0 + tmp2; |
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338 | z4 = tmp1 + tmp3; |
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339 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ |
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340 | |
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341 | tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ |
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342 | tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ |
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343 | tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ |
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344 | tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ |
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345 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ |
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346 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ |
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347 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ |
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348 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ |
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349 | |
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350 | z3 += z5; |
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351 | z4 += z5; |
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352 | |
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353 | tmp0 += z1 + z3; |
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354 | tmp1 += z2 + z4; |
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355 | tmp2 += z2 + z3; |
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356 | tmp3 += z1 + z4; |
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357 | |
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358 | /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ |
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359 | |
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360 | outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3, |
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361 | CONST_BITS+PASS1_BITS+3) |
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362 | & RANGE_MASK]; |
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363 | outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3, |
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364 | CONST_BITS+PASS1_BITS+3) |
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365 | & RANGE_MASK]; |
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366 | outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2, |
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367 | CONST_BITS+PASS1_BITS+3) |
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368 | & RANGE_MASK]; |
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369 | outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2, |
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370 | CONST_BITS+PASS1_BITS+3) |
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371 | & RANGE_MASK]; |
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372 | outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1, |
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373 | CONST_BITS+PASS1_BITS+3) |
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374 | & RANGE_MASK]; |
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375 | outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1, |
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376 | CONST_BITS+PASS1_BITS+3) |
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377 | & RANGE_MASK]; |
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378 | outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0, |
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379 | CONST_BITS+PASS1_BITS+3) |
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380 | & RANGE_MASK]; |
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381 | outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0, |
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382 | CONST_BITS+PASS1_BITS+3) |
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383 | & RANGE_MASK]; |
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384 | |
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385 | wsptr += DCTSIZE; /* advance pointer to next row */ |
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386 | } |
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387 | } |
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388 | |
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389 | #endif /* DCT_ISLOW_SUPPORTED */ |
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