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1 /*
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2 * jfdctflt.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 floating-point implementation of the
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9 * forward DCT (Discrete Cosine Transform).
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10 *
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11 * This implementation should be more accurate than either of the integer
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12 * DCT implementations. However, it may not give the same results on all
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13 * machines because of differences in roundoff behavior. Speed will depend
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14 * on the hardware's floating point capacity.
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15 *
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16 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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17 * on each column. Direct algorithms are also available, but they are
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18 * much more complex and seem not to be any faster when reduced to code.
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19 *
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20 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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21 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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22 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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23 * JPEG textbook (see REFERENCES section in file README). The following code
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24 * is based directly on figure 4-8 in P&M.
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25 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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26 * possible to arrange the computation so that many of the multiplies are
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27 * simple scalings of the final outputs. These multiplies can then be
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28 * folded into the multiplications or divisions by the JPEG quantization
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29 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
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30 * to be done in the DCT itself.
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31 * The primary disadvantage of this method is that with a fixed-point
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32 * implementation, accuracy is lost due to imprecise representation of the
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33 * scaled quantization values. However, that problem does not arise if
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34 * we use floating point arithmetic.
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35 */
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36
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37 #define JPEG_INTERNALS
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38 #include "jinclude.h"
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39 #include "jpeglib.h"
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40 #include "jdct.h" /* Private declarations for DCT subsystem */
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41
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42 #ifdef DCT_FLOAT_SUPPORTED
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43
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44
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45 /*
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46 * This module is specialized to the case DCTSIZE = 8.
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47 */
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48
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49 #if DCTSIZE != 8
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50 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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51 #endif
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52
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53
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54 /*
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55 * Perform the forward DCT on one block of samples.
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56 */
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57
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58 GLOBAL(void)
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59 jpeg_fdct_float (FAST_FLOAT * data)
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60 {
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61 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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62 FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
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63 FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
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64 FAST_FLOAT *dataptr;
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65 int ctr;
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66
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67 /* Pass 1: process rows. */
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68
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69 dataptr = data;
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70 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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71 tmp0 = dataptr[0] + dataptr[7];
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72 tmp7 = dataptr[0] - dataptr[7];
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73 tmp1 = dataptr[1] + dataptr[6];
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74 tmp6 = dataptr[1] - dataptr[6];
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75 tmp2 = dataptr[2] + dataptr[5];
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76 tmp5 = dataptr[2] - dataptr[5];
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77 tmp3 = dataptr[3] + dataptr[4];
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78 tmp4 = dataptr[3] - dataptr[4];
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79
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80 /* Even part */
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81
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82 tmp10 = tmp0 + tmp3; /* phase 2 */
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83 tmp13 = tmp0 - tmp3;
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84 tmp11 = tmp1 + tmp2;
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85 tmp12 = tmp1 - tmp2;
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86
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87 dataptr[0] = tmp10 + tmp11; /* phase 3 */
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88 dataptr[4] = tmp10 - tmp11;
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89
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90 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
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91 dataptr[2] = tmp13 + z1; /* phase 5 */
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92 dataptr[6] = tmp13 - z1;
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93
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94 /* Odd part */
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95
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96 tmp10 = tmp4 + tmp5; /* phase 2 */
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97 tmp11 = tmp5 + tmp6;
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98 tmp12 = tmp6 + tmp7;
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99
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100 /* The rotator is modified from fig 4-8 to avoid extra negations. */
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101 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
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102 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
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103 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
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104 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
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105
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106 z11 = tmp7 + z3; /* phase 5 */
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107 z13 = tmp7 - z3;
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108
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109 dataptr[5] = z13 + z2; /* phase 6 */
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110 dataptr[3] = z13 - z2;
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111 dataptr[1] = z11 + z4;
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112 dataptr[7] = z11 - z4;
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113
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114 dataptr += DCTSIZE; /* advance pointer to next row */
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115 }
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116
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117 /* Pass 2: process columns. */
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118
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119 dataptr = data;
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120 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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121 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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122 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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123 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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124 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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125 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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126 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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127 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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128 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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129
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130 /* Even part */
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131
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132 tmp10 = tmp0 + tmp3; /* phase 2 */
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133 tmp13 = tmp0 - tmp3;
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134 tmp11 = tmp1 + tmp2;
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135 tmp12 = tmp1 - tmp2;
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136
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137 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
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138 dataptr[DCTSIZE*4] = tmp10 - tmp11;
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139
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140 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
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141 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
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142 dataptr[DCTSIZE*6] = tmp13 - z1;
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143
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144 /* Odd part */
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145
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146 tmp10 = tmp4 + tmp5; /* phase 2 */
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147 tmp11 = tmp5 + tmp6;
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148 tmp12 = tmp6 + tmp7;
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149
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150 /* The rotator is modified from fig 4-8 to avoid extra negations. */
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151 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
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152 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
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153 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
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154 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
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155
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156 z11 = tmp7 + z3; /* phase 5 */
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157 z13 = tmp7 - z3;
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158
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159 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
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160 dataptr[DCTSIZE*3] = z13 - z2;
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161 dataptr[DCTSIZE*1] = z11 + z4;
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162 dataptr[DCTSIZE*7] = z11 - z4;
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163
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164 dataptr++; /* advance pointer to next column */
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165 }
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166 }
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167
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168 #endif /* DCT_FLOAT_SUPPORTED */
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