1 | /* |
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2 | * jidctfst.c |
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3 | * |
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4 | * Copyright (C) 1994-1998, Thomas G. Lane. |
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5 | * This file is part of the Independent JPEG Group's software. |
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6 | * For conditions of distribution and use, see the accompanying README file. |
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7 | * |
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8 | * This file contains a fast, not so accurate integer implementation of the |
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9 | * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine |
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10 | * must also perform dequantization of the input coefficients. |
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11 | * |
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12 | * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT |
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13 | * on each row (or vice versa, but it's more convenient to emit a row at |
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14 | * a time). Direct algorithms are also available, but they are much more |
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15 | * complex and seem not to be any faster when reduced to code. |
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16 | * |
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17 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for |
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18 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in |
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19 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell |
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20 | * JPEG textbook (see REFERENCES section in file README). The following code |
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21 | * is based directly on figure 4-8 in P&M. |
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22 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is |
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23 | * possible to arrange the computation so that many of the multiplies are |
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24 | * simple scalings of the final outputs. These multiplies can then be |
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25 | * folded into the multiplications or divisions by the JPEG quantization |
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26 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds |
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27 | * to be done in the DCT itself. |
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28 | * The primary disadvantage of this method is that with fixed-point math, |
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29 | * accuracy is lost due to imprecise representation of the scaled |
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30 | * quantization values. The smaller the quantization table entry, the less |
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31 | * precise the scaled value, so this implementation does worse with high- |
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32 | * quality-setting files than with low-quality ones. |
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33 | */ |
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34 | |
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35 | #define JPEG_INTERNALS |
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36 | #include "jinclude.h" |
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37 | #include "jpeglib.h" |
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38 | #include "jdct.h" /* Private declarations for DCT subsystem */ |
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39 | |
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40 | #ifdef DCT_IFAST_SUPPORTED |
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41 | |
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42 | |
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43 | /* |
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44 | * This module is specialized to the case DCTSIZE = 8. |
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45 | */ |
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46 | |
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47 | #if DCTSIZE != 8 |
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48 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
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49 | #endif |
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50 | |
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51 | |
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52 | /* Scaling decisions are generally the same as in the LL&M algorithm; |
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53 | * see jidctint.c for more details. However, we choose to descale |
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54 | * (right shift) multiplication products as soon as they are formed, |
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55 | * rather than carrying additional fractional bits into subsequent additions. |
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56 | * This compromises accuracy slightly, but it lets us save a few shifts. |
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57 | * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) |
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58 | * everywhere except in the multiplications proper; this saves a good deal |
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59 | * of work on 16-bit-int machines. |
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60 | * |
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61 | * The dequantized coefficients are not integers because the AA&N scaling |
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62 | * factors have been incorporated. We represent them scaled up by PASS1_BITS, |
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63 | * so that the first and second IDCT rounds have the same input scaling. |
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64 | * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to |
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65 | * avoid a descaling shift; this compromises accuracy rather drastically |
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66 | * for small quantization table entries, but it saves a lot of shifts. |
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67 | * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, |
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68 | * so we use a much larger scaling factor to preserve accuracy. |
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69 | * |
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70 | * A final compromise is to represent the multiplicative constants to only |
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71 | * 8 fractional bits, rather than 13. This saves some shifting work on some |
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72 | * machines, and may also reduce the cost of multiplication (since there |
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73 | * are fewer one-bits in the constants). |
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74 | */ |
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75 | |
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76 | #if BITS_IN_JSAMPLE == 8 |
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77 | #define CONST_BITS 8 |
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78 | #define PASS1_BITS 2 |
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79 | #else |
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80 | #define CONST_BITS 8 |
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81 | #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ |
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82 | #endif |
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83 | |
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84 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus |
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85 | * causing a lot of useless floating-point operations at run time. |
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86 | * To get around this we use the following pre-calculated constants. |
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87 | * If you change CONST_BITS you may want to add appropriate values. |
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88 | * (With a reasonable C compiler, you can just rely on the FIX() macro...) |
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89 | */ |
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90 | |
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91 | #if CONST_BITS == 8 |
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92 | #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */ |
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93 | #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ |
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94 | #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ |
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95 | #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */ |
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96 | #else |
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97 | #define FIX_1_082392200 FIX(1.082392200) |
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98 | #define FIX_1_414213562 FIX(1.414213562) |
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99 | #define FIX_1_847759065 FIX(1.847759065) |
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100 | #define FIX_2_613125930 FIX(2.613125930) |
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101 | #endif |
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102 | |
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103 | |
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104 | /* We can gain a little more speed, with a further compromise in accuracy, |
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105 | * by omitting the addition in a descaling shift. This yields an incorrectly |
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106 | * rounded result half the time... |
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107 | */ |
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108 | |
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109 | #ifndef USE_ACCURATE_ROUNDING |
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110 | #undef DESCALE |
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111 | #define DESCALE(x,n) RIGHT_SHIFT(x, n) |
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112 | #endif |
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113 | |
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114 | |
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115 | /* Multiply a DCTELEM variable by an INT32 constant, and immediately |
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116 | * descale to yield a DCTELEM result. |
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117 | */ |
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118 | |
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119 | #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) |
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120 | |
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121 | |
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122 | /* Dequantize a coefficient by multiplying it by the multiplier-table |
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123 | * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 |
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124 | * multiplication will do. For 12-bit data, the multiplier table is |
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125 | * declared INT32, so a 32-bit multiply will be used. |
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126 | */ |
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127 | |
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128 | #if BITS_IN_JSAMPLE == 8 |
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129 | #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) |
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130 | #else |
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131 | #define DEQUANTIZE(coef,quantval) \ |
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132 | DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) |
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133 | #endif |
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134 | |
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135 | |
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136 | /* Like DESCALE, but applies to a DCTELEM and produces an int. |
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137 | * We assume that int right shift is unsigned if INT32 right shift is. |
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138 | */ |
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139 | |
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140 | #ifdef RIGHT_SHIFT_IS_UNSIGNED |
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141 | #define ISHIFT_TEMPS DCTELEM ishift_temp; |
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142 | #if BITS_IN_JSAMPLE == 8 |
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143 | #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ |
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144 | #else |
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145 | #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ |
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146 | #endif |
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147 | #define IRIGHT_SHIFT(x,shft) \ |
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148 | ((ishift_temp = (x)) < 0 ? \ |
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149 | (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ |
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150 | (ishift_temp >> (shft))) |
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151 | #else |
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152 | #define ISHIFT_TEMPS |
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153 | #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) |
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154 | #endif |
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155 | |
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156 | #ifdef USE_ACCURATE_ROUNDING |
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157 | #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) |
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158 | #else |
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159 | #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) |
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160 | #endif |
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161 | |
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162 | |
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163 | /* |
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164 | * Perform dequantization and inverse DCT on one block of coefficients. |
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165 | */ |
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166 | |
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167 | GLOBAL(void) |
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168 | jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, |
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169 | JCOEFPTR coef_block, |
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170 | JSAMPARRAY output_buf, JDIMENSION output_col) |
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171 | { |
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172 | DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
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173 | DCTELEM tmp10, tmp11, tmp12, tmp13; |
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174 | DCTELEM z5, z10, z11, z12, z13; |
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175 | JCOEFPTR inptr; |
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176 | IFAST_MULT_TYPE * quantptr; |
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177 | int * wsptr; |
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178 | JSAMPROW outptr; |
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179 | JSAMPLE *range_limit = IDCT_range_limit(cinfo); |
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180 | int ctr; |
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181 | int workspace[DCTSIZE2]; /* buffers data between passes */ |
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182 | SHIFT_TEMPS /* for DESCALE */ |
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183 | ISHIFT_TEMPS /* for IDESCALE */ |
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184 | |
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185 | /* Pass 1: process columns from input, store into work array. */ |
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186 | |
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187 | inptr = coef_block; |
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188 | quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; |
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189 | wsptr = workspace; |
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190 | for (ctr = DCTSIZE; ctr > 0; ctr--) { |
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191 | /* Due to quantization, we will usually find that many of the input |
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192 | * coefficients are zero, especially the AC terms. We can exploit this |
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193 | * by short-circuiting the IDCT calculation for any column in which all |
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194 | * the AC terms are zero. In that case each output is equal to the |
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195 | * DC coefficient (with scale factor as needed). |
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196 | * With typical images and quantization tables, half or more of the |
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197 | * column DCT calculations can be simplified this way. |
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198 | */ |
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199 | |
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200 | if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && |
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201 | inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && |
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202 | inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && |
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203 | inptr[DCTSIZE*7] == 0) { |
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204 | /* AC terms all zero */ |
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205 | int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); |
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206 | |
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207 | wsptr[DCTSIZE*0] = dcval; |
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208 | wsptr[DCTSIZE*1] = dcval; |
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209 | wsptr[DCTSIZE*2] = dcval; |
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210 | wsptr[DCTSIZE*3] = dcval; |
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211 | wsptr[DCTSIZE*4] = dcval; |
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212 | wsptr[DCTSIZE*5] = dcval; |
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213 | wsptr[DCTSIZE*6] = dcval; |
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214 | wsptr[DCTSIZE*7] = dcval; |
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215 | |
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216 | inptr++; /* advance pointers to next column */ |
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217 | quantptr++; |
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218 | wsptr++; |
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219 | continue; |
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220 | } |
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221 | |
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222 | /* Even part */ |
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223 | |
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224 | tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); |
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225 | tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); |
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226 | tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); |
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227 | tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); |
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228 | |
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229 | tmp10 = tmp0 + tmp2; /* phase 3 */ |
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230 | tmp11 = tmp0 - tmp2; |
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231 | |
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232 | tmp13 = tmp1 + tmp3; /* phases 5-3 */ |
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233 | tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ |
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234 | |
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235 | tmp0 = tmp10 + tmp13; /* phase 2 */ |
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236 | tmp3 = tmp10 - tmp13; |
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237 | tmp1 = tmp11 + tmp12; |
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238 | tmp2 = tmp11 - tmp12; |
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239 | |
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240 | /* Odd part */ |
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241 | |
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242 | tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); |
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243 | tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); |
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244 | tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); |
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245 | tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); |
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246 | |
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247 | z13 = tmp6 + tmp5; /* phase 6 */ |
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248 | z10 = tmp6 - tmp5; |
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249 | z11 = tmp4 + tmp7; |
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250 | z12 = tmp4 - tmp7; |
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251 | |
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252 | tmp7 = z11 + z13; /* phase 5 */ |
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253 | tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ |
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254 | |
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255 | z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ |
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256 | tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ |
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257 | tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ |
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258 | |
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259 | tmp6 = tmp12 - tmp7; /* phase 2 */ |
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260 | tmp5 = tmp11 - tmp6; |
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261 | tmp4 = tmp10 + tmp5; |
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262 | |
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263 | wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); |
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264 | wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); |
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265 | wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); |
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266 | wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); |
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267 | wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); |
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268 | wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); |
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269 | wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); |
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270 | wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); |
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271 | |
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272 | inptr++; /* advance pointers to next column */ |
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273 | quantptr++; |
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274 | wsptr++; |
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275 | } |
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276 | |
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277 | /* Pass 2: process rows from work array, store into output array. */ |
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278 | /* Note that we must descale the results by a factor of 8 == 2**3, */ |
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279 | /* and also undo the PASS1_BITS scaling. */ |
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280 | |
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281 | wsptr = workspace; |
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282 | for (ctr = 0; ctr < DCTSIZE; ctr++) { |
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283 | outptr = output_buf[ctr] + output_col; |
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284 | /* Rows of zeroes can be exploited in the same way as we did with columns. |
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285 | * However, the column calculation has created many nonzero AC terms, so |
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286 | * the simplification applies less often (typically 5% to 10% of the time). |
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287 | * On machines with very fast multiplication, it's possible that the |
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288 | * test takes more time than it's worth. In that case this section |
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289 | * may be commented out. |
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290 | */ |
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291 | |
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292 | #ifndef NO_ZERO_ROW_TEST |
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293 | if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && |
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294 | wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { |
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295 | /* AC terms all zero */ |
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296 | JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) |
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297 | & RANGE_MASK]; |
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298 | |
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299 | outptr[0] = dcval; |
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300 | outptr[1] = dcval; |
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301 | outptr[2] = dcval; |
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302 | outptr[3] = dcval; |
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303 | outptr[4] = dcval; |
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304 | outptr[5] = dcval; |
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305 | outptr[6] = dcval; |
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306 | outptr[7] = dcval; |
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307 | |
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308 | wsptr += DCTSIZE; /* advance pointer to next row */ |
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309 | continue; |
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310 | } |
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311 | #endif |
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312 | |
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313 | /* Even part */ |
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314 | |
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315 | tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); |
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316 | tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); |
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317 | |
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318 | tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); |
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319 | tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) |
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320 | - tmp13; |
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321 | |
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322 | tmp0 = tmp10 + tmp13; |
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323 | tmp3 = tmp10 - tmp13; |
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324 | tmp1 = tmp11 + tmp12; |
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325 | tmp2 = tmp11 - tmp12; |
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326 | |
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327 | /* Odd part */ |
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328 | |
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329 | z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; |
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330 | z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; |
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331 | z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; |
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332 | z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; |
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333 | |
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334 | tmp7 = z11 + z13; /* phase 5 */ |
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335 | tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ |
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336 | |
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337 | z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ |
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338 | tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ |
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339 | tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ |
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340 | |
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341 | tmp6 = tmp12 - tmp7; /* phase 2 */ |
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342 | tmp5 = tmp11 - tmp6; |
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343 | tmp4 = tmp10 + tmp5; |
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344 | |
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345 | /* Final output stage: scale down by a factor of 8 and range-limit */ |
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346 | |
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347 | outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) |
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348 | & RANGE_MASK]; |
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349 | outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) |
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350 | & RANGE_MASK]; |
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351 | outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) |
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352 | & RANGE_MASK]; |
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353 | outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) |
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354 | & RANGE_MASK]; |
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355 | outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) |
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356 | & RANGE_MASK]; |
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357 | outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) |
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358 | & RANGE_MASK]; |
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359 | outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) |
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360 | & RANGE_MASK]; |
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361 | outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) |
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362 | & RANGE_MASK]; |
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363 | |
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364 | wsptr += DCTSIZE; /* advance pointer to next row */ |
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365 | } |
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366 | } |
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367 | |
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368 | #endif /* DCT_IFAST_SUPPORTED */ |
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