1 | <?xml version="1.0" standalone="no"?> |
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2 | <!DOCTYPE section PUBLIC "-//OASIS//DTD DocBook XML V4.2//EN" |
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3 | "http://www.oasis-open.org/docbook/xml/4.2/docbookx.dtd" [ |
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4 | |
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5 | ]> |
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6 | |
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7 | <section id="vorbis-spec-helper"> |
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8 | <sectioninfo> |
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9 | <releaseinfo> |
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10 | $Id: 09-helper.xml 7186 2004-07-20 07:19:25Z xiphmont $ |
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11 | </releaseinfo> |
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12 | </sectioninfo> |
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13 | <title>Helper equations</title> |
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14 | |
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15 | <section> |
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16 | <title>Overview</title> |
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17 | |
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18 | <para> |
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19 | The equations below are used in multiple places by the Vorbis codec |
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20 | specification. Rather than cluttering up the main specification |
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21 | documents, they are defined here and referenced where appropriate. |
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22 | </para> |
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23 | |
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24 | </section> |
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25 | |
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26 | <section> |
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27 | <title>Functions</title> |
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28 | |
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29 | <section id="vorbis-spec-ilog"> |
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30 | <title>ilog</title> |
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31 | |
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32 | <para> |
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33 | The "ilog(x)" function returns the position number (1 through n) of the highest set bit in the two's complement integer value |
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34 | <varname>[x]</varname>. Values of <varname>[x]</varname> less than zero are defined to return zero.</para> |
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35 | |
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36 | <programlisting> |
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37 | 1) [return_value] = 0; |
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38 | 2) if ( [x] is greater than zero ){ |
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39 | |
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40 | 3) increment [return_value]; |
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41 | 4) logical shift [x] one bit to the right, padding the MSb with zero |
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42 | 5) repeat at step 2) |
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43 | |
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44 | } |
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45 | |
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46 | 6) done |
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47 | </programlisting> |
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48 | |
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49 | <para> |
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50 | Examples: |
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51 | |
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52 | <itemizedlist> |
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53 | <listitem><simpara>ilog(0) = 0;</simpara></listitem> |
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54 | <listitem><simpara>ilog(1) = 1;</simpara></listitem> |
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55 | <listitem><simpara>ilog(2) = 2;</simpara></listitem> |
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56 | <listitem><simpara>ilog(3) = 2;</simpara></listitem> |
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57 | <listitem><simpara>ilog(4) = 3;</simpara></listitem> |
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58 | <listitem><simpara>ilog(7) = 3;</simpara></listitem> |
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59 | <listitem><simpara>ilog(negative number) = 0;</simpara></listitem> |
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60 | </itemizedlist> |
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61 | </para> |
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62 | |
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63 | </section> |
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64 | |
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65 | <section id="vorbis-spec-float32_unpack"> |
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66 | <title>float32_unpack</title> |
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67 | |
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68 | <para> |
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69 | "float32_unpack(x)" is intended to translate the packed binary |
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70 | representation of a Vorbis codebook float value into the |
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71 | representation used by the decoder for floating point numbers. For |
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72 | purposes of this example, we will unpack a Vorbis float32 into a |
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73 | host-native floating point number.</para> |
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74 | |
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75 | <programlisting> |
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76 | 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result) |
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77 | 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result) |
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78 | 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result) |
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79 | 4) if ( [sign] is nonzero ) then negate [mantissa] |
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80 | 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) ) |
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81 | </programlisting> |
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82 | |
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83 | </section> |
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84 | |
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85 | <section id="vorbis-spec-lookup1_values"> |
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86 | <title>lookup1_values</title> |
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87 | |
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88 | <para> |
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89 | "lookup1_values(codebook_entries,codebook_dimensions)" is used to |
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90 | compute the correct length of the value index for a codebook VQ lookup |
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91 | table of lookup type 1. The values on this list are permuted to |
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92 | construct the VQ vector lookup table of size |
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93 | <varname>[codebook_entries]</varname>.</para> |
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94 | |
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95 | <para> |
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96 | The return value for this function is defined to be 'the greatest |
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97 | integer value for which <varname>[return_value] to the power of |
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98 | [codebook_dimensions] is less than or equal to |
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99 | [codebook_entries]</varname>'.</para> |
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100 | |
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101 | </section> |
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102 | |
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103 | <section id="vorbis-spec-low_neighbor"> |
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104 | <title>low_neighbor</title> |
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105 | |
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106 | <para> |
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107 | "low_neighbor(v,x)" finds the position <varname>n</varname> in vector <varname>[v]</varname> of |
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108 | the greatest value scalar element for which <varname>n</varname> is less than |
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109 | <varname>[x]</varname> and vector <varname>[v]</varname> element <varname>n</varname> is less |
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110 | than vector <varname>[v]</varname> element <varname>[x]</varname>.</para> |
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111 | |
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112 | <section id="vorbis-spec-high_neighbor"> |
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113 | <title>high_neighbor</title> |
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114 | |
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115 | <para> |
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116 | "high_neighbor(v,x)" finds the position <varname>n</varname> in vector [v] of |
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117 | the lowest value scalar element for which <varname>n</varname> is less than |
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118 | <varname>[x]</varname> and vector <varname>[v]</varname> element <varname>n</varname> is greater |
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119 | than vector <varname>[v]</varname> element <varname>[x]</varname>.</para> |
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120 | |
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121 | </section> |
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122 | |
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123 | <section id="vorbis-spec-render_point"> |
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124 | <title>render_point</title> |
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125 | |
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126 | <para> |
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127 | "render_point(x0,y0,x1,y1,X)" is used to find the Y value at point X |
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128 | along the line specified by x0, x1, y0 and y1. This function uses an |
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129 | integer algorithm to solve for the point directly without calculating |
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130 | intervening values along the line.</para> |
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131 | |
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132 | <programlisting> |
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133 | 1) [dy] = [y1] - [y0] |
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134 | 2) [adx] = [x1] - [x0] |
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135 | 3) [ady] = absolute value of [dy] |
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136 | 4) [err] = [ady] * ([X] - [x0]) |
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137 | 5) [off] = [err] / [adx] using integer division |
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138 | 6) if ( [dy] is less than zero ) { |
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139 | |
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140 | 7) [Y] = [y0] - [off] |
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141 | |
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142 | } else { |
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143 | |
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144 | 8) [Y] = [y0] + [off] |
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145 | |
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146 | } |
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147 | |
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148 | 9) done |
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149 | </programlisting> |
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150 | |
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151 | </section> |
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152 | |
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153 | <section id="vorbis-spec-render_line"> |
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154 | <title>render_line</title> |
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155 | |
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156 | <para> |
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157 | Floor decode type one uses the integer line drawing algorithm of |
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158 | "render_line(x0, y0, x1, y1, v)" to construct an integer floor |
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159 | curve for contiguous piecewise line segments. Note that it has not |
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160 | been relevant elsewhere, but here we must define integer division as |
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161 | rounding division of both positive and negative numbers toward zero. |
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162 | </para> |
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163 | |
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164 | <programlisting> |
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165 | 1) [dy] = [y1] - [y0] |
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166 | 2) [adx] = [x1] - [x0] |
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167 | 3) [ady] = absolute value of [dy] |
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168 | 4) [base] = [dy] / [adx] using integer division |
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169 | 5) [x] = [x0] |
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170 | 6) [y] = [y0] |
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171 | 7) [err] = 0 |
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172 | |
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173 | 8) if ( [dy] is less than 0 ) { |
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174 | |
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175 | 9) [sy] = [base] - 1 |
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176 | |
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177 | } else { |
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178 | |
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179 | 10) [sy] = [base] + 1 |
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180 | |
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181 | } |
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182 | |
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183 | 11) [ady] = [ady] - (absolute value of [base]) * [adx] |
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184 | 12) vector [v] element [x] = [y] |
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185 | |
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186 | 13) iterate [x] over the range [x0]+1 ... [x1]-1 { |
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187 | |
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188 | 14) [err] = [err] + [ady]; |
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189 | 15) if ( [err] >= [adx] ) { |
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190 | |
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191 | 16) [err] = [err] - [adx] |
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192 | 17) [y] = [y] + [sy] |
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193 | |
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194 | } else { |
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195 | |
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196 | 18) [y] = [y] + [base] |
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197 | |
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198 | } |
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199 | |
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200 | 19) vector [v] element [x] = [y] |
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201 | |
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202 | } |
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203 | </programlisting> |
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204 | |
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205 | </section> |
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206 | |
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207 | </section> |
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208 | |
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209 | </section> |
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210 | |
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211 | </section> |
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