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1 /* |
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2 * jidctflt.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 floating-point 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 * This implementation should be more accurate than either of the integer |
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13 * IDCT implementations. However, it may not give the same results on all |
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14 * machines because of differences in roundoff behavior. Speed will depend |
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15 * on the hardware's floating point capacity. |
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16 * |
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17 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT |
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18 * on each row (or vice versa, but it's more convenient to emit a row at |
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19 * a time). Direct algorithms are also available, but they are much more |
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20 * complex and seem not to be any faster when reduced to code. |
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21 * |
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22 * This implementation is based on Arai, Agui, and Nakajima's algorithm for |
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23 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in |
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24 * Japanese, but the algorithm is described in the Pennebaker & Mitchell |
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25 * JPEG textbook (see REFERENCES section in file README). The following code |
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26 * is based directly on figure 4-8 in P&M. |
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27 * While an 8-point DCT cannot be done in less than 11 multiplies, it is |
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28 * possible to arrange the computation so that many of the multiplies are |
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29 * simple scalings of the final outputs. These multiplies can then be |
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30 * folded into the multiplications or divisions by the JPEG quantization |
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31 * table entries. The AA&N method leaves only 5 multiplies and 29 adds |
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32 * to be done in the DCT itself. |
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33 * The primary disadvantage of this method is that with a fixed-point |
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34 * implementation, accuracy is lost due to imprecise representation of the |
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35 * scaled quantization values. However, that problem does not arise if |
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36 * we use floating point arithmetic. |
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37 */ |
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38 |
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39 #define JPEG_INTERNALS |
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40 #include "jinclude.h" |
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41 #include "jpeglib.h" |
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42 #include "jdct.h" /* Private declarations for DCT subsystem */ |
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43 |
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44 #ifdef DCT_FLOAT_SUPPORTED |
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45 |
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46 |
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47 /* |
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48 * This module is specialized to the case DCTSIZE = 8. |
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49 */ |
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50 |
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51 #if DCTSIZE != 8 |
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52 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
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53 #endif |
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54 |
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55 |
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56 /* Dequantize a coefficient by multiplying it by the multiplier-table |
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57 * entry; produce a float result. |
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58 */ |
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59 |
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60 #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval)) |
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61 |
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62 |
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63 /* |
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64 * Perform dequantization and inverse DCT on one block of coefficients. |
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65 */ |
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66 |
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67 GLOBAL(void) |
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68 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, |
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69 JCOEFPTR coef_block, |
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70 JSAMPARRAY output_buf, JDIMENSION output_col) |
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71 { |
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72 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
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73 FAST_FLOAT tmp10, tmp11, tmp12, tmp13; |
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74 FAST_FLOAT z5, z10, z11, z12, z13; |
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75 JCOEFPTR inptr; |
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76 FLOAT_MULT_TYPE * quantptr; |
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77 FAST_FLOAT * wsptr; |
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78 JSAMPROW outptr; |
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79 JSAMPLE *range_limit = IDCT_range_limit(cinfo); |
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80 int ctr; |
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81 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ |
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82 SHIFT_TEMPS |
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83 |
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84 /* Pass 1: process columns from input, store into work array. */ |
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85 |
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86 inptr = coef_block; |
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87 quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table; |
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88 wsptr = workspace; |
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89 for (ctr = DCTSIZE; ctr > 0; ctr--) { |
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90 /* Due to quantization, we will usually find that many of the input |
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91 * coefficients are zero, especially the AC terms. We can exploit this |
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92 * by short-circuiting the IDCT calculation for any column in which all |
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93 * the AC terms are zero. In that case each output is equal to the |
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94 * DC coefficient (with scale factor as needed). |
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95 * With typical images and quantization tables, half or more of the |
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96 * column DCT calculations can be simplified this way. |
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97 */ |
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98 |
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99 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && |
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100 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && |
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101 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && |
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102 inptr[DCTSIZE*7] == 0) { |
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103 /* AC terms all zero */ |
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104 FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); |
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105 |
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106 wsptr[DCTSIZE*0] = dcval; |
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107 wsptr[DCTSIZE*1] = dcval; |
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108 wsptr[DCTSIZE*2] = dcval; |
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109 wsptr[DCTSIZE*3] = dcval; |
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110 wsptr[DCTSIZE*4] = dcval; |
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111 wsptr[DCTSIZE*5] = dcval; |
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112 wsptr[DCTSIZE*6] = dcval; |
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113 wsptr[DCTSIZE*7] = dcval; |
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114 |
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115 inptr++; /* advance pointers to next column */ |
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116 quantptr++; |
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117 wsptr++; |
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118 continue; |
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119 } |
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120 |
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121 /* Even part */ |
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122 |
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123 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); |
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124 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); |
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125 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); |
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126 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); |
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127 |
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128 tmp10 = tmp0 + tmp2; /* phase 3 */ |
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129 tmp11 = tmp0 - tmp2; |
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130 |
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131 tmp13 = tmp1 + tmp3; /* phases 5-3 */ |
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132 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ |
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133 |
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134 tmp0 = tmp10 + tmp13; /* phase 2 */ |
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135 tmp3 = tmp10 - tmp13; |
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136 tmp1 = tmp11 + tmp12; |
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137 tmp2 = tmp11 - tmp12; |
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138 |
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139 /* Odd part */ |
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140 |
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141 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); |
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142 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); |
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143 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); |
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144 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); |
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145 |
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146 z13 = tmp6 + tmp5; /* phase 6 */ |
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147 z10 = tmp6 - tmp5; |
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148 z11 = tmp4 + tmp7; |
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149 z12 = tmp4 - tmp7; |
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150 |
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151 tmp7 = z11 + z13; /* phase 5 */ |
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152 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ |
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153 |
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154 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ |
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155 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ |
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156 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ |
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157 |
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158 tmp6 = tmp12 - tmp7; /* phase 2 */ |
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159 tmp5 = tmp11 - tmp6; |
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160 tmp4 = tmp10 + tmp5; |
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161 |
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162 wsptr[DCTSIZE*0] = tmp0 + tmp7; |
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163 wsptr[DCTSIZE*7] = tmp0 - tmp7; |
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164 wsptr[DCTSIZE*1] = tmp1 + tmp6; |
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165 wsptr[DCTSIZE*6] = tmp1 - tmp6; |
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166 wsptr[DCTSIZE*2] = tmp2 + tmp5; |
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167 wsptr[DCTSIZE*5] = tmp2 - tmp5; |
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168 wsptr[DCTSIZE*4] = tmp3 + tmp4; |
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169 wsptr[DCTSIZE*3] = tmp3 - tmp4; |
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170 |
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171 inptr++; /* advance pointers to next column */ |
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172 quantptr++; |
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173 wsptr++; |
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174 } |
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175 |
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176 /* Pass 2: process rows from work array, store into output array. */ |
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177 /* Note that we must descale the results by a factor of 8 == 2**3. */ |
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178 |
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179 wsptr = workspace; |
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180 for (ctr = 0; ctr < DCTSIZE; ctr++) { |
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181 outptr = output_buf[ctr] + output_col; |
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182 /* Rows of zeroes can be exploited in the same way as we did with columns. |
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183 * However, the column calculation has created many nonzero AC terms, so |
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184 * the simplification applies less often (typically 5% to 10% of the time). |
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185 * And testing floats for zero is relatively expensive, so we don't bother. |
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186 */ |
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187 |
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188 /* Even part */ |
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189 |
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190 tmp10 = wsptr[0] + wsptr[4]; |
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191 tmp11 = wsptr[0] - wsptr[4]; |
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192 |
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193 tmp13 = wsptr[2] + wsptr[6]; |
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194 tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; |
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195 |
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196 tmp0 = tmp10 + tmp13; |
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197 tmp3 = tmp10 - tmp13; |
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198 tmp1 = tmp11 + tmp12; |
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199 tmp2 = tmp11 - tmp12; |
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200 |
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201 /* Odd part */ |
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202 |
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203 z13 = wsptr[5] + wsptr[3]; |
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204 z10 = wsptr[5] - wsptr[3]; |
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205 z11 = wsptr[1] + wsptr[7]; |
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206 z12 = wsptr[1] - wsptr[7]; |
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207 |
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208 tmp7 = z11 + z13; |
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209 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); |
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210 |
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211 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ |
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212 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ |
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213 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ |
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214 |
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215 tmp6 = tmp12 - tmp7; |
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216 tmp5 = tmp11 - tmp6; |
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217 tmp4 = tmp10 + tmp5; |
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218 |
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219 /* Final output stage: scale down by a factor of 8 and range-limit */ |
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220 |
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221 outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) |
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222 & RANGE_MASK]; |
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223 outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) |
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224 & RANGE_MASK]; |
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225 outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) |
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226 & RANGE_MASK]; |
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227 outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) |
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228 & RANGE_MASK]; |
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229 outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) |
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230 & RANGE_MASK]; |
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231 outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) |
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232 & RANGE_MASK]; |
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233 outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) |
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234 & RANGE_MASK]; |
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235 outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) |
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236 & RANGE_MASK]; |
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237 |
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238 wsptr += DCTSIZE; /* advance pointer to next row */ |
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239 } |
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240 } |
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241 |
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242 #endif /* DCT_FLOAT_SUPPORTED */ |