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1 /* |
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2 * jfdctfst.c |
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3 * |
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4 * Copyright (C) 1994-1996, Thomas G. Lane. |
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5 * This file is part of the Independent JPEG Group's software. |
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6 * For conditions of distribution and use, see the accompanying README file. |
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7 * |
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8 * This file contains a fast, not so accurate integer implementation of the |
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9 * forward DCT (Discrete Cosine Transform). |
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10 * |
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11 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT |
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12 * on each column. Direct algorithms are also available, but they are |
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13 * much more complex and seem not to be any faster when reduced to code. |
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14 * |
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15 * This implementation is based on Arai, Agui, and Nakajima's algorithm for |
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16 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in |
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17 * Japanese, but the algorithm is described in the Pennebaker & Mitchell |
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18 * JPEG textbook (see REFERENCES section in file README). The following code |
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19 * is based directly on figure 4-8 in P&M. |
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20 * While an 8-point DCT cannot be done in less than 11 multiplies, it is |
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21 * possible to arrange the computation so that many of the multiplies are |
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22 * simple scalings of the final outputs. These multiplies can then be |
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23 * folded into the multiplications or divisions by the JPEG quantization |
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24 * table entries. The AA&N method leaves only 5 multiplies and 29 adds |
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25 * to be done in the DCT itself. |
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26 * The primary disadvantage of this method is that with fixed-point math, |
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27 * accuracy is lost due to imprecise representation of the scaled |
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28 * quantization values. The smaller the quantization table entry, the less |
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29 * precise the scaled value, so this implementation does worse with high- |
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30 * quality-setting files than with low-quality ones. |
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31 */ |
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32 |
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33 #define JPEG_INTERNALS |
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34 #include "jinclude.h" |
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35 #include "jpeglib.h" |
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36 #include "jdct.h" /* Private declarations for DCT subsystem */ |
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37 |
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38 #ifdef DCT_IFAST_SUPPORTED |
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39 |
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40 |
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41 /* |
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42 * This module is specialized to the case DCTSIZE = 8. |
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43 */ |
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44 |
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45 #if DCTSIZE != 8 |
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46 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
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47 #endif |
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48 |
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49 |
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50 /* Scaling decisions are generally the same as in the LL&M algorithm; |
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51 * see jfdctint.c for more details. However, we choose to descale |
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52 * (right shift) multiplication products as soon as they are formed, |
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53 * rather than carrying additional fractional bits into subsequent additions. |
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54 * This compromises accuracy slightly, but it lets us save a few shifts. |
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55 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) |
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56 * everywhere except in the multiplications proper; this saves a good deal |
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57 * of work on 16-bit-int machines. |
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58 * |
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59 * Again to save a few shifts, the intermediate results between pass 1 and |
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60 * pass 2 are not upscaled, but are represented only to integral precision. |
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61 * |
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62 * A final compromise is to represent the multiplicative constants to only |
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63 * 8 fractional bits, rather than 13. This saves some shifting work on some |
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64 * machines, and may also reduce the cost of multiplication (since there |
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65 * are fewer one-bits in the constants). |
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66 */ |
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67 |
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68 #define CONST_BITS 8 |
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69 |
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70 |
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71 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus |
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72 * causing a lot of useless floating-point operations at run time. |
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73 * To get around this we use the following pre-calculated constants. |
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74 * If you change CONST_BITS you may want to add appropriate values. |
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75 * (With a reasonable C compiler, you can just rely on the FIX() macro...) |
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76 */ |
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77 |
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78 #if CONST_BITS == 8 |
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79 #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ |
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80 #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ |
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81 #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ |
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82 #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ |
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83 #else |
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84 #define FIX_0_382683433 FIX(0.382683433) |
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85 #define FIX_0_541196100 FIX(0.541196100) |
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86 #define FIX_0_707106781 FIX(0.707106781) |
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87 #define FIX_1_306562965 FIX(1.306562965) |
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88 #endif |
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89 |
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90 |
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91 /* We can gain a little more speed, with a further compromise in accuracy, |
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92 * by omitting the addition in a descaling shift. This yields an incorrectly |
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93 * rounded result half the time... |
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94 */ |
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95 |
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96 #ifndef USE_ACCURATE_ROUNDING |
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97 #undef DESCALE |
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98 #define DESCALE(x,n) RIGHT_SHIFT(x, n) |
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99 #endif |
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100 |
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101 |
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102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately |
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103 * descale to yield a DCTELEM result. |
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104 */ |
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105 |
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106 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) |
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107 |
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108 |
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109 /* |
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110 * Perform the forward DCT on one block of samples. |
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111 */ |
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112 |
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113 GLOBAL(void) |
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114 jpeg_fdct_ifast (DCTELEM * data) |
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115 { |
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116 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
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117 DCTELEM tmp10, tmp11, tmp12, tmp13; |
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118 DCTELEM z1, z2, z3, z4, z5, z11, z13; |
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119 DCTELEM *dataptr; |
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120 int ctr; |
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121 SHIFT_TEMPS |
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122 |
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123 /* Pass 1: process rows. */ |
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124 |
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125 dataptr = data; |
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126 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
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127 tmp0 = dataptr[0] + dataptr[7]; |
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128 tmp7 = dataptr[0] - dataptr[7]; |
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129 tmp1 = dataptr[1] + dataptr[6]; |
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130 tmp6 = dataptr[1] - dataptr[6]; |
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131 tmp2 = dataptr[2] + dataptr[5]; |
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132 tmp5 = dataptr[2] - dataptr[5]; |
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133 tmp3 = dataptr[3] + dataptr[4]; |
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134 tmp4 = dataptr[3] - dataptr[4]; |
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135 |
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136 /* Even part */ |
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137 |
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138 tmp10 = tmp0 + tmp3; /* phase 2 */ |
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139 tmp13 = tmp0 - tmp3; |
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140 tmp11 = tmp1 + tmp2; |
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141 tmp12 = tmp1 - tmp2; |
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142 |
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143 dataptr[0] = tmp10 + tmp11; /* phase 3 */ |
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144 dataptr[4] = tmp10 - tmp11; |
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145 |
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146 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ |
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147 dataptr[2] = tmp13 + z1; /* phase 5 */ |
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148 dataptr[6] = tmp13 - z1; |
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149 |
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150 /* Odd part */ |
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151 |
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152 tmp10 = tmp4 + tmp5; /* phase 2 */ |
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153 tmp11 = tmp5 + tmp6; |
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154 tmp12 = tmp6 + tmp7; |
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155 |
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156 /* The rotator is modified from fig 4-8 to avoid extra negations. */ |
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157 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ |
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158 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ |
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159 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ |
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160 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ |
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161 |
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162 z11 = tmp7 + z3; /* phase 5 */ |
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163 z13 = tmp7 - z3; |
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164 |
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165 dataptr[5] = z13 + z2; /* phase 6 */ |
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166 dataptr[3] = z13 - z2; |
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167 dataptr[1] = z11 + z4; |
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168 dataptr[7] = z11 - z4; |
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169 |
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170 dataptr += DCTSIZE; /* advance pointer to next row */ |
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171 } |
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172 |
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173 /* Pass 2: process columns. */ |
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174 |
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175 dataptr = data; |
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176 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
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177 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; |
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178 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; |
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179 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; |
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180 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; |
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181 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; |
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182 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; |
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183 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; |
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184 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; |
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185 |
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186 /* Even part */ |
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187 |
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188 tmp10 = tmp0 + tmp3; /* phase 2 */ |
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189 tmp13 = tmp0 - tmp3; |
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190 tmp11 = tmp1 + tmp2; |
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191 tmp12 = tmp1 - tmp2; |
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192 |
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193 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ |
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194 dataptr[DCTSIZE*4] = tmp10 - tmp11; |
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195 |
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196 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ |
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197 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ |
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198 dataptr[DCTSIZE*6] = tmp13 - z1; |
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199 |
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200 /* Odd part */ |
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201 |
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202 tmp10 = tmp4 + tmp5; /* phase 2 */ |
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203 tmp11 = tmp5 + tmp6; |
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204 tmp12 = tmp6 + tmp7; |
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205 |
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206 /* The rotator is modified from fig 4-8 to avoid extra negations. */ |
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207 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ |
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208 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ |
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209 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ |
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210 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ |
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211 |
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212 z11 = tmp7 + z3; /* phase 5 */ |
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213 z13 = tmp7 - z3; |
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214 |
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215 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ |
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216 dataptr[DCTSIZE*3] = z13 - z2; |
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217 dataptr[DCTSIZE*1] = z11 + z4; |
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218 dataptr[DCTSIZE*7] = z11 - z4; |
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219 |
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220 dataptr++; /* advance pointer to next column */ |
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221 } |
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222 } |
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223 |
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224 #endif /* DCT_IFAST_SUPPORTED */ |