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nuclear@2
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1 /*
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2 * jfdctint.c
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3 *
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4 * Copyright (C) 1991-1996, 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 slow-but-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 an algorithm described in
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16 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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17 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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18 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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19 * The primary algorithm described there uses 11 multiplies and 29 adds.
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20 * We use their alternate method with 12 multiplies and 32 adds.
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21 * The advantage of this method is that no data path contains more than one
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22 * multiplication; this allows a very simple and accurate implementation in
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23 * scaled fixed-point arithmetic, with a minimal number of shifts.
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24 */
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25
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26 #define JPEG_INTERNALS
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27 #include "jinclude.h"
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28 #include "jpeglib.h"
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29 #include "jdct.h" /* Private declarations for DCT subsystem */
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30
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31 #ifdef DCT_ISLOW_SUPPORTED
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32
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33
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34 /*
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35 * This module is specialized to the case DCTSIZE = 8.
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36 */
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37
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38 #if DCTSIZE != 8
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39 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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40 #endif
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41
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42
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43 /*
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44 * The poop on this scaling stuff is as follows:
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45 *
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46 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
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47 * larger than the true DCT outputs. The final outputs are therefore
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48 * a factor of N larger than desired; since N=8 this can be cured by
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49 * a simple right shift at the end of the algorithm. The advantage of
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50 * this arrangement is that we save two multiplications per 1-D DCT,
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51 * because the y0 and y4 outputs need not be divided by sqrt(N).
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52 * In the IJG code, this factor of 8 is removed by the quantization step
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53 * (in jcdctmgr.c), NOT in this module.
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54 *
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55 * We have to do addition and subtraction of the integer inputs, which
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56 * is no problem, and multiplication by fractional constants, which is
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57 * a problem to do in integer arithmetic. We multiply all the constants
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58 * by CONST_SCALE and convert them to integer constants (thus retaining
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59 * CONST_BITS bits of precision in the constants). After doing a
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60 * multiplication we have to divide the product by CONST_SCALE, with proper
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61 * rounding, to produce the correct output. This division can be done
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62 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
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63 * as long as possible so that partial sums can be added together with
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64 * full fractional precision.
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65 *
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66 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
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67 * they are represented to better-than-integral precision. These outputs
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68 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
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69 * with the recommended scaling. (For 12-bit sample data, the intermediate
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70 * array is INT32 anyway.)
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71 *
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72 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
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73 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
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74 * shows that the values given below are the most effective.
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75 */
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76
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77 #if BITS_IN_JSAMPLE == 8
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78 #define CONST_BITS 13
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79 #define PASS1_BITS 2
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80 #else
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81 #define CONST_BITS 13
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82 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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83 #endif
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84
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85 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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86 * causing a lot of useless floating-point operations at run time.
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87 * To get around this we use the following pre-calculated constants.
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88 * If you change CONST_BITS you may want to add appropriate values.
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89 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
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90 */
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91
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92 #if CONST_BITS == 13
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93 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
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94 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
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95 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
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96 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
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97 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
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98 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
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99 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
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100 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
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101 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
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102 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
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103 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
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104 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
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105 #else
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106 #define FIX_0_298631336 FIX(0.298631336)
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107 #define FIX_0_390180644 FIX(0.390180644)
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108 #define FIX_0_541196100 FIX(0.541196100)
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109 #define FIX_0_765366865 FIX(0.765366865)
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110 #define FIX_0_899976223 FIX(0.899976223)
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111 #define FIX_1_175875602 FIX(1.175875602)
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112 #define FIX_1_501321110 FIX(1.501321110)
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113 #define FIX_1_847759065 FIX(1.847759065)
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114 #define FIX_1_961570560 FIX(1.961570560)
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115 #define FIX_2_053119869 FIX(2.053119869)
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116 #define FIX_2_562915447 FIX(2.562915447)
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117 #define FIX_3_072711026 FIX(3.072711026)
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118 #endif
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119
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120
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121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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122 * For 8-bit samples with the recommended scaling, all the variable
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123 * and constant values involved are no more than 16 bits wide, so a
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124 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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125 * For 12-bit samples, a full 32-bit multiplication will be needed.
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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 MULTIPLY(var,const) MULTIPLY16C16(var,const)
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130 #else
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131 #define MULTIPLY(var,const) ((var) * (const))
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132 #endif
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133
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134
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135 /*
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136 * Perform the forward DCT on one block of samples.
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137 */
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138
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139 GLOBAL(void)
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140 jpeg_fdct_islow (DCTELEM * data)
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141 {
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142 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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143 INT32 tmp10, tmp11, tmp12, tmp13;
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144 INT32 z1, z2, z3, z4, z5;
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145 DCTELEM *dataptr;
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146 int ctr;
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147 SHIFT_TEMPS
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148
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149 /* Pass 1: process rows. */
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150 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
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151 /* furthermore, we scale the results by 2**PASS1_BITS. */
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152
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153 dataptr = data;
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154 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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155 tmp0 = dataptr[0] + dataptr[7];
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156 tmp7 = dataptr[0] - dataptr[7];
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157 tmp1 = dataptr[1] + dataptr[6];
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158 tmp6 = dataptr[1] - dataptr[6];
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159 tmp2 = dataptr[2] + dataptr[5];
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160 tmp5 = dataptr[2] - dataptr[5];
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161 tmp3 = dataptr[3] + dataptr[4];
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162 tmp4 = dataptr[3] - dataptr[4];
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163
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164 /* Even part per LL&M figure 1 --- note that published figure is faulty;
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165 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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166 */
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167
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168 tmp10 = tmp0 + tmp3;
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169 tmp13 = tmp0 - tmp3;
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170 tmp11 = tmp1 + tmp2;
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171 tmp12 = tmp1 - tmp2;
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172
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173 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
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174 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
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175
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176 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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177 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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178 CONST_BITS-PASS1_BITS);
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179 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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180 CONST_BITS-PASS1_BITS);
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181
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182 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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183 * cK represents cos(K*pi/16).
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184 * i0..i3 in the paper are tmp4..tmp7 here.
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185 */
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186
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187 z1 = tmp4 + tmp7;
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188 z2 = tmp5 + tmp6;
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189 z3 = tmp4 + tmp6;
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190 z4 = tmp5 + tmp7;
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191 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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192
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193 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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194 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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195 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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196 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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197 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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198 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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199 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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200 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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201
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202 z3 += z5;
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203 z4 += z5;
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204
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205 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
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206 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
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207 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
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208 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
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209
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210 dataptr += DCTSIZE; /* advance pointer to next row */
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211 }
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212
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213 /* Pass 2: process columns.
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214 * We remove the PASS1_BITS scaling, but leave the results scaled up
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215 * by an overall factor of 8.
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216 */
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217
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218 dataptr = data;
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219 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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220 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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221 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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222 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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223 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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224 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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225 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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226 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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227 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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228
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229 /* Even part per LL&M figure 1 --- note that published figure is faulty;
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230 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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231 */
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232
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233 tmp10 = tmp0 + tmp3;
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234 tmp13 = tmp0 - tmp3;
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235 tmp11 = tmp1 + tmp2;
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236 tmp12 = tmp1 - tmp2;
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237
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238 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
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239 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
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240
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241 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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242 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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243 CONST_BITS+PASS1_BITS);
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244 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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245 CONST_BITS+PASS1_BITS);
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246
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247 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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248 * cK represents cos(K*pi/16).
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249 * i0..i3 in the paper are tmp4..tmp7 here.
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250 */
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251
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252 z1 = tmp4 + tmp7;
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253 z2 = tmp5 + tmp6;
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254 z3 = tmp4 + tmp6;
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255 z4 = tmp5 + tmp7;
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256 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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257
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258 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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259 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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260 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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261 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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262 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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263 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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264 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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265 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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266
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267 z3 += z5;
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268 z4 += z5;
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269
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270 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
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271 CONST_BITS+PASS1_BITS);
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272 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
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273 CONST_BITS+PASS1_BITS);
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274 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
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275 CONST_BITS+PASS1_BITS);
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276 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
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277 CONST_BITS+PASS1_BITS);
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278
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279 dataptr++; /* advance pointer to next column */
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280 }
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281 }
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282
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283 #endif /* DCT_ISLOW_SUPPORTED */
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