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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 */ |