1 /***************************************************************************/ |
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2 /* */ |
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3 /* ftcalc.c */ |
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4 /* */ |
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5 /* Arithmetic computations (body). */ |
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6 /* */ |
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7 /* Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006, 2008 by */ |
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8 /* David Turner, Robert Wilhelm, and Werner Lemberg. */ |
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9 /* */ |
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10 /* This file is part of the FreeType project, and may only be used, */ |
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11 /* modified, and distributed under the terms of the FreeType project */ |
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12 /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ |
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13 /* this file you indicate that you have read the license and */ |
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14 /* understand and accept it fully. */ |
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15 /* */ |
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16 /***************************************************************************/ |
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17 |
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18 /*************************************************************************/ |
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19 /* */ |
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20 /* Support for 1-complement arithmetic has been totally dropped in this */ |
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21 /* release. You can still write your own code if you need it. */ |
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22 /* */ |
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23 /*************************************************************************/ |
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24 |
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25 /*************************************************************************/ |
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26 /* */ |
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27 /* Implementing basic computation routines. */ |
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28 /* */ |
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29 /* FT_MulDiv(), FT_MulFix(), FT_DivFix(), FT_RoundFix(), FT_CeilFix(), */ |
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30 /* and FT_FloorFix() are declared in freetype.h. */ |
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31 /* */ |
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32 /*************************************************************************/ |
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33 |
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34 |
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35 #include <ft2build.h> |
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36 #include FT_GLYPH_H |
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37 #include FT_INTERNAL_CALC_H |
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38 #include FT_INTERNAL_DEBUG_H |
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39 #include FT_INTERNAL_OBJECTS_H |
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40 |
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41 #ifdef FT_MULFIX_INLINED |
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42 #undef FT_MulFix |
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43 #endif |
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44 |
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45 /* we need to define a 64-bits data type here */ |
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46 |
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47 #ifdef FT_LONG64 |
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48 |
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49 typedef FT_INT64 FT_Int64; |
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50 |
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51 #else |
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52 |
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53 typedef struct FT_Int64_ |
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54 { |
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55 FT_UInt32 lo; |
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56 FT_UInt32 hi; |
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57 |
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58 } FT_Int64; |
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59 |
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60 #endif /* FT_LONG64 */ |
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61 |
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62 |
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63 /*************************************************************************/ |
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64 /* */ |
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65 /* The macro FT_COMPONENT is used in trace mode. It is an implicit */ |
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66 /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log */ |
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67 /* messages during execution. */ |
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68 /* */ |
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69 #undef FT_COMPONENT |
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70 #define FT_COMPONENT trace_calc |
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71 |
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72 |
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73 /* The following three functions are available regardless of whether */ |
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74 /* FT_LONG64 is defined. */ |
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75 |
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76 /* documentation is in freetype.h */ |
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77 |
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78 FT_EXPORT_DEF( FT_Fixed ) |
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79 FT_RoundFix( FT_Fixed a ) |
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80 { |
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81 return ( a >= 0 ) ? ( a + 0x8000L ) & ~0xFFFFL |
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82 : -((-a + 0x8000L ) & ~0xFFFFL ); |
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83 } |
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84 |
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85 |
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86 /* documentation is in freetype.h */ |
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87 |
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88 FT_EXPORT_DEF( FT_Fixed ) |
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89 FT_CeilFix( FT_Fixed a ) |
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90 { |
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91 return ( a >= 0 ) ? ( a + 0xFFFFL ) & ~0xFFFFL |
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92 : -((-a + 0xFFFFL ) & ~0xFFFFL ); |
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93 } |
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94 |
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95 |
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96 /* documentation is in freetype.h */ |
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97 |
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98 FT_EXPORT_DEF( FT_Fixed ) |
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99 FT_FloorFix( FT_Fixed a ) |
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100 { |
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101 return ( a >= 0 ) ? a & ~0xFFFFL |
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102 : -((-a) & ~0xFFFFL ); |
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103 } |
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104 |
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105 |
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106 #ifdef FT_CONFIG_OPTION_OLD_INTERNALS |
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107 |
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108 /* documentation is in ftcalc.h */ |
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109 |
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110 FT_EXPORT_DEF( FT_Int32 ) |
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111 FT_Sqrt32( FT_Int32 x ) |
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112 { |
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113 FT_UInt32 val, root, newroot, mask; |
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114 |
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115 |
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116 root = 0; |
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117 mask = (FT_UInt32)0x40000000UL; |
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118 val = (FT_UInt32)x; |
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119 |
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120 do |
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121 { |
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122 newroot = root + mask; |
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123 if ( newroot <= val ) |
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124 { |
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125 val -= newroot; |
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126 root = newroot + mask; |
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127 } |
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128 |
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129 root >>= 1; |
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130 mask >>= 2; |
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131 |
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132 } while ( mask != 0 ); |
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133 |
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134 return root; |
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135 } |
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136 |
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137 #endif /* FT_CONFIG_OPTION_OLD_INTERNALS */ |
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138 |
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139 |
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140 #ifdef FT_LONG64 |
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141 |
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142 |
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143 /* documentation is in freetype.h */ |
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144 |
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145 FT_EXPORT_DEF( FT_Long ) |
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146 FT_MulDiv( FT_Long a, |
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147 FT_Long b, |
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148 FT_Long c ) |
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149 { |
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150 FT_Int s; |
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151 FT_Long d; |
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152 |
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153 |
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154 s = 1; |
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155 if ( a < 0 ) { a = -a; s = -1; } |
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156 if ( b < 0 ) { b = -b; s = -s; } |
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157 if ( c < 0 ) { c = -c; s = -s; } |
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158 |
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159 d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c |
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160 : 0x7FFFFFFFL ); |
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161 |
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162 return ( s > 0 ) ? d : -d; |
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163 } |
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164 |
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165 |
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166 #ifdef TT_USE_BYTECODE_INTERPRETER |
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167 |
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168 /* documentation is in ftcalc.h */ |
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169 |
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170 FT_BASE_DEF( FT_Long ) |
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171 FT_MulDiv_No_Round( FT_Long a, |
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172 FT_Long b, |
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173 FT_Long c ) |
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174 { |
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175 FT_Int s; |
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176 FT_Long d; |
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177 |
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178 |
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179 s = 1; |
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180 if ( a < 0 ) { a = -a; s = -1; } |
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181 if ( b < 0 ) { b = -b; s = -s; } |
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182 if ( c < 0 ) { c = -c; s = -s; } |
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183 |
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184 d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c |
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185 : 0x7FFFFFFFL ); |
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186 |
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187 return ( s > 0 ) ? d : -d; |
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188 } |
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189 |
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190 #endif /* TT_USE_BYTECODE_INTERPRETER */ |
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191 |
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192 |
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193 /* documentation is in freetype.h */ |
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194 |
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195 FT_EXPORT_DEF( FT_Long ) |
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196 FT_MulFix( FT_Long a, |
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197 FT_Long b ) |
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198 { |
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199 #ifdef FT_MULFIX_ASSEMBLER |
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200 |
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201 return FT_MULFIX_ASSEMBLER( a, b ); |
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202 |
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203 #else |
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204 |
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205 FT_Int s = 1; |
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206 FT_Long c; |
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207 |
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208 |
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209 if ( a < 0 ) |
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210 { |
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211 a = -a; |
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212 s = -1; |
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213 } |
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214 |
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215 if ( b < 0 ) |
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216 { |
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217 b = -b; |
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218 s = -s; |
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219 } |
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220 |
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221 c = (FT_Long)( ( (FT_Int64)a * b + 0x8000L ) >> 16 ); |
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222 |
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223 return ( s > 0 ) ? c : -c; |
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224 |
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225 #endif /* FT_MULFIX_ASSEMBLER */ |
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226 } |
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227 |
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228 |
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229 /* documentation is in freetype.h */ |
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230 |
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231 FT_EXPORT_DEF( FT_Long ) |
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232 FT_DivFix( FT_Long a, |
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233 FT_Long b ) |
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234 { |
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235 FT_Int32 s; |
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236 FT_UInt32 q; |
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237 |
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238 s = 1; |
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239 if ( a < 0 ) { a = -a; s = -1; } |
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240 if ( b < 0 ) { b = -b; s = -s; } |
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241 |
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242 if ( b == 0 ) |
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243 /* check for division by 0 */ |
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244 q = 0x7FFFFFFFL; |
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245 else |
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246 /* compute result directly */ |
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247 q = (FT_UInt32)( ( ( (FT_Int64)a << 16 ) + ( b >> 1 ) ) / b ); |
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248 |
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249 return ( s < 0 ? -(FT_Long)q : (FT_Long)q ); |
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250 } |
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251 |
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252 |
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253 #else /* !FT_LONG64 */ |
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254 |
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255 |
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256 static void |
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257 ft_multo64( FT_UInt32 x, |
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258 FT_UInt32 y, |
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259 FT_Int64 *z ) |
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260 { |
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261 FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2; |
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262 |
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263 |
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264 lo1 = x & 0x0000FFFFU; hi1 = x >> 16; |
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265 lo2 = y & 0x0000FFFFU; hi2 = y >> 16; |
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266 |
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267 lo = lo1 * lo2; |
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268 i1 = lo1 * hi2; |
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269 i2 = lo2 * hi1; |
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270 hi = hi1 * hi2; |
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271 |
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272 /* Check carry overflow of i1 + i2 */ |
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273 i1 += i2; |
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274 hi += (FT_UInt32)( i1 < i2 ) << 16; |
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275 |
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276 hi += i1 >> 16; |
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277 i1 = i1 << 16; |
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278 |
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279 /* Check carry overflow of i1 + lo */ |
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280 lo += i1; |
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281 hi += ( lo < i1 ); |
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282 |
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283 z->lo = lo; |
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284 z->hi = hi; |
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285 } |
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286 |
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287 |
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288 static FT_UInt32 |
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289 ft_div64by32( FT_UInt32 hi, |
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290 FT_UInt32 lo, |
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291 FT_UInt32 y ) |
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292 { |
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293 FT_UInt32 r, q; |
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294 FT_Int i; |
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295 |
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296 |
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297 q = 0; |
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298 r = hi; |
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299 |
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300 if ( r >= y ) |
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301 return (FT_UInt32)0x7FFFFFFFL; |
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302 |
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303 i = 32; |
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304 do |
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305 { |
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306 r <<= 1; |
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307 q <<= 1; |
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308 r |= lo >> 31; |
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309 |
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310 if ( r >= (FT_UInt32)y ) |
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311 { |
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312 r -= y; |
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313 q |= 1; |
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314 } |
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315 lo <<= 1; |
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316 } while ( --i ); |
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317 |
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318 return q; |
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319 } |
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320 |
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321 |
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322 static void |
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323 FT_Add64( FT_Int64* x, |
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324 FT_Int64* y, |
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325 FT_Int64 *z ) |
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326 { |
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327 register FT_UInt32 lo, hi; |
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328 |
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329 |
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330 lo = x->lo + y->lo; |
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331 hi = x->hi + y->hi + ( lo < x->lo ); |
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332 |
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333 z->lo = lo; |
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334 z->hi = hi; |
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335 } |
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336 |
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337 |
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338 /* documentation is in freetype.h */ |
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339 |
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340 /* The FT_MulDiv function has been optimized thanks to ideas from */ |
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341 /* Graham Asher. The trick is to optimize computation when everything */ |
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342 /* fits within 32-bits (a rather common case). */ |
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343 /* */ |
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344 /* we compute 'a*b+c/2', then divide it by 'c'. (positive values) */ |
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345 /* */ |
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346 /* 46340 is FLOOR(SQRT(2^31-1)). */ |
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347 /* */ |
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348 /* if ( a <= 46340 && b <= 46340 ) then ( a*b <= 0x7FFEA810 ) */ |
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349 /* */ |
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350 /* 0x7FFFFFFF - 0x7FFEA810 = 0x157F0 */ |
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351 /* */ |
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352 /* if ( c < 0x157F0*2 ) then ( a*b+c/2 <= 0x7FFFFFFF ) */ |
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353 /* */ |
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354 /* and 2*0x157F0 = 176096 */ |
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355 /* */ |
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356 |
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357 FT_EXPORT_DEF( FT_Long ) |
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358 FT_MulDiv( FT_Long a, |
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359 FT_Long b, |
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360 FT_Long c ) |
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361 { |
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362 long s; |
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363 |
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364 |
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365 /* XXX: this function does not allow 64-bit arguments */ |
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366 if ( a == 0 || b == c ) |
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367 return a; |
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368 |
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369 s = a; a = FT_ABS( a ); |
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370 s ^= b; b = FT_ABS( b ); |
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371 s ^= c; c = FT_ABS( c ); |
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372 |
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373 if ( a <= 46340L && b <= 46340L && c <= 176095L && c > 0 ) |
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374 a = ( a * b + ( c >> 1 ) ) / c; |
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375 |
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376 else if ( c > 0 ) |
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377 { |
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378 FT_Int64 temp, temp2; |
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379 |
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380 |
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381 ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); |
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382 |
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383 temp2.hi = 0; |
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384 temp2.lo = (FT_UInt32)(c >> 1); |
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385 FT_Add64( &temp, &temp2, &temp ); |
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386 a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c ); |
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387 } |
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388 else |
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389 a = 0x7FFFFFFFL; |
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390 |
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391 return ( s < 0 ? -a : a ); |
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392 } |
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393 |
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394 |
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395 #ifdef TT_USE_BYTECODE_INTERPRETER |
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396 |
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397 FT_BASE_DEF( FT_Long ) |
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398 FT_MulDiv_No_Round( FT_Long a, |
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399 FT_Long b, |
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400 FT_Long c ) |
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401 { |
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402 long s; |
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403 |
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404 |
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405 if ( a == 0 || b == c ) |
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406 return a; |
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407 |
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408 s = a; a = FT_ABS( a ); |
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409 s ^= b; b = FT_ABS( b ); |
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410 s ^= c; c = FT_ABS( c ); |
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411 |
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412 if ( a <= 46340L && b <= 46340L && c > 0 ) |
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413 a = a * b / c; |
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414 |
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415 else if ( c > 0 ) |
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416 { |
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417 FT_Int64 temp; |
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418 |
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419 |
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420 ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); |
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421 a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c ); |
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422 } |
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423 else |
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424 a = 0x7FFFFFFFL; |
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425 |
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426 return ( s < 0 ? -a : a ); |
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427 } |
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428 |
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429 #endif /* TT_USE_BYTECODE_INTERPRETER */ |
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430 |
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431 |
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432 /* documentation is in freetype.h */ |
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433 |
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434 FT_EXPORT_DEF( FT_Long ) |
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435 FT_MulFix( FT_Long a, |
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436 FT_Long b ) |
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437 { |
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438 #ifdef FT_MULFIX_ASSEMBLER |
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439 |
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440 return FT_MULFIX_ASSEMBLER( a, b ); |
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441 |
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442 #elif 0 |
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443 |
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444 /* |
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445 * This code is nonportable. See comment below. |
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446 * |
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447 * However, on a platform where right-shift of a signed quantity fills |
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448 * the leftmost bits by copying the sign bit, it might be faster. |
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449 */ |
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450 |
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451 FT_Long sa, sb; |
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452 FT_ULong ua, ub; |
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453 |
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454 |
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455 if ( a == 0 || b == 0x10000L ) |
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456 return a; |
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457 |
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458 /* |
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459 * This is a clever way of converting a signed number `a' into its |
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460 * absolute value (stored back into `a') and its sign. The sign is |
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461 * stored in `sa'; 0 means `a' was positive or zero, and -1 means `a' |
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462 * was negative. (Similarly for `b' and `sb'). |
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463 * |
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464 * Unfortunately, it doesn't work (at least not portably). |
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465 * |
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466 * It makes the assumption that right-shift on a negative signed value |
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467 * fills the leftmost bits by copying the sign bit. This is wrong. |
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468 * According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206, |
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469 * the result of right-shift of a negative signed value is |
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470 * implementation-defined. At least one implementation fills the |
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471 * leftmost bits with 0s (i.e., it is exactly the same as an unsigned |
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472 * right shift). This means that when `a' is negative, `sa' ends up |
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473 * with the value 1 rather than -1. After that, everything else goes |
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474 * wrong. |
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475 */ |
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476 sa = ( a >> ( sizeof ( a ) * 8 - 1 ) ); |
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477 a = ( a ^ sa ) - sa; |
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478 sb = ( b >> ( sizeof ( b ) * 8 - 1 ) ); |
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479 b = ( b ^ sb ) - sb; |
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480 |
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481 ua = (FT_ULong)a; |
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482 ub = (FT_ULong)b; |
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483 |
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484 if ( ua <= 2048 && ub <= 1048576L ) |
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485 ua = ( ua * ub + 0x8000U ) >> 16; |
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486 else |
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487 { |
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488 FT_ULong al = ua & 0xFFFFU; |
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489 |
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490 |
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491 ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) + |
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492 ( ( al * ( ub & 0xFFFFU ) + 0x8000U ) >> 16 ); |
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493 } |
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494 |
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495 sa ^= sb, |
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496 ua = (FT_ULong)(( ua ^ sa ) - sa); |
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497 |
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498 return (FT_Long)ua; |
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499 |
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500 #else /* 0 */ |
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501 |
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502 FT_Long s; |
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503 FT_ULong ua, ub; |
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504 |
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505 |
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506 if ( a == 0 || b == 0x10000L ) |
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507 return a; |
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508 |
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509 s = a; a = FT_ABS( a ); |
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510 s ^= b; b = FT_ABS( b ); |
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511 |
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512 ua = (FT_ULong)a; |
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513 ub = (FT_ULong)b; |
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514 |
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515 if ( ua <= 2048 && ub <= 1048576L ) |
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516 ua = ( ua * ub + 0x8000UL ) >> 16; |
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517 else |
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518 { |
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519 FT_ULong al = ua & 0xFFFFUL; |
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520 |
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521 |
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522 ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) + |
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523 ( ( al * ( ub & 0xFFFFUL ) + 0x8000UL ) >> 16 ); |
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524 } |
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525 |
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526 return ( s < 0 ? -(FT_Long)ua : (FT_Long)ua ); |
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527 |
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528 #endif /* 0 */ |
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529 |
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530 } |
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531 |
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532 |
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533 /* documentation is in freetype.h */ |
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534 |
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535 FT_EXPORT_DEF( FT_Long ) |
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536 FT_DivFix( FT_Long a, |
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537 FT_Long b ) |
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538 { |
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539 FT_Int32 s; |
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540 FT_UInt32 q; |
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541 |
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542 |
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543 /* XXX: this function does not allow 64-bit arguments */ |
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544 s = (FT_Int32)a; a = FT_ABS( a ); |
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545 s ^= (FT_Int32)b; b = FT_ABS( b ); |
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546 |
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547 if ( b == 0 ) |
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548 { |
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549 /* check for division by 0 */ |
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550 q = (FT_UInt32)0x7FFFFFFFL; |
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551 } |
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552 else if ( ( a >> 16 ) == 0 ) |
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553 { |
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554 /* compute result directly */ |
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555 q = (FT_UInt32)( (a << 16) + (b >> 1) ) / (FT_UInt32)b; |
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556 } |
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557 else |
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558 { |
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559 /* we need more bits; we have to do it by hand */ |
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560 FT_Int64 temp, temp2; |
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561 |
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562 temp.hi = (FT_Int32) (a >> 16); |
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563 temp.lo = (FT_UInt32)(a << 16); |
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564 temp2.hi = 0; |
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565 temp2.lo = (FT_UInt32)( b >> 1 ); |
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566 FT_Add64( &temp, &temp2, &temp ); |
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567 q = ft_div64by32( temp.hi, temp.lo, (FT_Int32)b ); |
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568 } |
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569 |
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570 return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
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571 } |
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572 |
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573 |
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574 #if 0 |
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575 |
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576 /* documentation is in ftcalc.h */ |
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577 |
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578 FT_EXPORT_DEF( void ) |
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579 FT_MulTo64( FT_Int32 x, |
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580 FT_Int32 y, |
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581 FT_Int64 *z ) |
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582 { |
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583 FT_Int32 s; |
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584 |
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585 |
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586 s = x; x = FT_ABS( x ); |
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587 s ^= y; y = FT_ABS( y ); |
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588 |
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589 ft_multo64( x, y, z ); |
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590 |
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591 if ( s < 0 ) |
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592 { |
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593 z->lo = (FT_UInt32)-(FT_Int32)z->lo; |
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594 z->hi = ~z->hi + !( z->lo ); |
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595 } |
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596 } |
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597 |
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598 |
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599 /* apparently, the second version of this code is not compiled correctly */ |
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600 /* on Mac machines with the MPW C compiler.. tsk, tsk, tsk... */ |
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601 |
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602 #if 1 |
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603 |
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604 FT_EXPORT_DEF( FT_Int32 ) |
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605 FT_Div64by32( FT_Int64* x, |
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606 FT_Int32 y ) |
|
607 { |
|
608 FT_Int32 s; |
|
609 FT_UInt32 q, r, i, lo; |
|
610 |
|
611 |
|
612 s = x->hi; |
|
613 if ( s < 0 ) |
|
614 { |
|
615 x->lo = (FT_UInt32)-(FT_Int32)x->lo; |
|
616 x->hi = ~x->hi + !x->lo; |
|
617 } |
|
618 s ^= y; y = FT_ABS( y ); |
|
619 |
|
620 /* Shortcut */ |
|
621 if ( x->hi == 0 ) |
|
622 { |
|
623 if ( y > 0 ) |
|
624 q = x->lo / y; |
|
625 else |
|
626 q = 0x7FFFFFFFL; |
|
627 |
|
628 return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
|
629 } |
|
630 |
|
631 r = x->hi; |
|
632 lo = x->lo; |
|
633 |
|
634 if ( r >= (FT_UInt32)y ) /* we know y is to be treated as unsigned here */ |
|
635 return ( s < 0 ? 0x80000001UL : 0x7FFFFFFFUL ); |
|
636 /* Return Max/Min Int32 if division overflow. */ |
|
637 /* This includes division by zero! */ |
|
638 q = 0; |
|
639 for ( i = 0; i < 32; i++ ) |
|
640 { |
|
641 r <<= 1; |
|
642 q <<= 1; |
|
643 r |= lo >> 31; |
|
644 |
|
645 if ( r >= (FT_UInt32)y ) |
|
646 { |
|
647 r -= y; |
|
648 q |= 1; |
|
649 } |
|
650 lo <<= 1; |
|
651 } |
|
652 |
|
653 return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
|
654 } |
|
655 |
|
656 #else /* 0 */ |
|
657 |
|
658 FT_EXPORT_DEF( FT_Int32 ) |
|
659 FT_Div64by32( FT_Int64* x, |
|
660 FT_Int32 y ) |
|
661 { |
|
662 FT_Int32 s; |
|
663 FT_UInt32 q; |
|
664 |
|
665 |
|
666 s = x->hi; |
|
667 if ( s < 0 ) |
|
668 { |
|
669 x->lo = (FT_UInt32)-(FT_Int32)x->lo; |
|
670 x->hi = ~x->hi + !x->lo; |
|
671 } |
|
672 s ^= y; y = FT_ABS( y ); |
|
673 |
|
674 /* Shortcut */ |
|
675 if ( x->hi == 0 ) |
|
676 { |
|
677 if ( y > 0 ) |
|
678 q = ( x->lo + ( y >> 1 ) ) / y; |
|
679 else |
|
680 q = 0x7FFFFFFFL; |
|
681 |
|
682 return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
|
683 } |
|
684 |
|
685 q = ft_div64by32( x->hi, x->lo, y ); |
|
686 |
|
687 return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
|
688 } |
|
689 |
|
690 #endif /* 0 */ |
|
691 |
|
692 #endif /* 0 */ |
|
693 |
|
694 |
|
695 #endif /* FT_LONG64 */ |
|
696 |
|
697 |
|
698 /* documentation is in ftglyph.h */ |
|
699 |
|
700 FT_EXPORT_DEF( void ) |
|
701 FT_Matrix_Multiply( const FT_Matrix* a, |
|
702 FT_Matrix *b ) |
|
703 { |
|
704 FT_Fixed xx, xy, yx, yy; |
|
705 |
|
706 |
|
707 if ( !a || !b ) |
|
708 return; |
|
709 |
|
710 xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx ); |
|
711 xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy ); |
|
712 yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx ); |
|
713 yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy ); |
|
714 |
|
715 b->xx = xx; b->xy = xy; |
|
716 b->yx = yx; b->yy = yy; |
|
717 } |
|
718 |
|
719 |
|
720 /* documentation is in ftglyph.h */ |
|
721 |
|
722 FT_EXPORT_DEF( FT_Error ) |
|
723 FT_Matrix_Invert( FT_Matrix* matrix ) |
|
724 { |
|
725 FT_Pos delta, xx, yy; |
|
726 |
|
727 |
|
728 if ( !matrix ) |
|
729 return FT_Err_Invalid_Argument; |
|
730 |
|
731 /* compute discriminant */ |
|
732 delta = FT_MulFix( matrix->xx, matrix->yy ) - |
|
733 FT_MulFix( matrix->xy, matrix->yx ); |
|
734 |
|
735 if ( !delta ) |
|
736 return FT_Err_Invalid_Argument; /* matrix can't be inverted */ |
|
737 |
|
738 matrix->xy = - FT_DivFix( matrix->xy, delta ); |
|
739 matrix->yx = - FT_DivFix( matrix->yx, delta ); |
|
740 |
|
741 xx = matrix->xx; |
|
742 yy = matrix->yy; |
|
743 |
|
744 matrix->xx = FT_DivFix( yy, delta ); |
|
745 matrix->yy = FT_DivFix( xx, delta ); |
|
746 |
|
747 return FT_Err_Ok; |
|
748 } |
|
749 |
|
750 |
|
751 /* documentation is in ftcalc.h */ |
|
752 |
|
753 FT_BASE_DEF( void ) |
|
754 FT_Matrix_Multiply_Scaled( const FT_Matrix* a, |
|
755 FT_Matrix *b, |
|
756 FT_Long scaling ) |
|
757 { |
|
758 FT_Fixed xx, xy, yx, yy; |
|
759 |
|
760 FT_Long val = 0x10000L * scaling; |
|
761 |
|
762 |
|
763 if ( !a || !b ) |
|
764 return; |
|
765 |
|
766 xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val ); |
|
767 xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val ); |
|
768 yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val ); |
|
769 yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val ); |
|
770 |
|
771 b->xx = xx; b->xy = xy; |
|
772 b->yx = yx; b->yy = yy; |
|
773 } |
|
774 |
|
775 |
|
776 /* documentation is in ftcalc.h */ |
|
777 |
|
778 FT_BASE_DEF( void ) |
|
779 FT_Vector_Transform_Scaled( FT_Vector* vector, |
|
780 const FT_Matrix* matrix, |
|
781 FT_Long scaling ) |
|
782 { |
|
783 FT_Pos xz, yz; |
|
784 |
|
785 FT_Long val = 0x10000L * scaling; |
|
786 |
|
787 |
|
788 if ( !vector || !matrix ) |
|
789 return; |
|
790 |
|
791 xz = FT_MulDiv( vector->x, matrix->xx, val ) + |
|
792 FT_MulDiv( vector->y, matrix->xy, val ); |
|
793 |
|
794 yz = FT_MulDiv( vector->x, matrix->yx, val ) + |
|
795 FT_MulDiv( vector->y, matrix->yy, val ); |
|
796 |
|
797 vector->x = xz; |
|
798 vector->y = yz; |
|
799 } |
|
800 |
|
801 |
|
802 /* documentation is in ftcalc.h */ |
|
803 |
|
804 FT_BASE_DEF( FT_Int32 ) |
|
805 FT_SqrtFixed( FT_Int32 x ) |
|
806 { |
|
807 FT_UInt32 root, rem_hi, rem_lo, test_div; |
|
808 FT_Int count; |
|
809 |
|
810 |
|
811 root = 0; |
|
812 |
|
813 if ( x > 0 ) |
|
814 { |
|
815 rem_hi = 0; |
|
816 rem_lo = x; |
|
817 count = 24; |
|
818 do |
|
819 { |
|
820 rem_hi = ( rem_hi << 2 ) | ( rem_lo >> 30 ); |
|
821 rem_lo <<= 2; |
|
822 root <<= 1; |
|
823 test_div = ( root << 1 ) + 1; |
|
824 |
|
825 if ( rem_hi >= test_div ) |
|
826 { |
|
827 rem_hi -= test_div; |
|
828 root += 1; |
|
829 } |
|
830 } while ( --count ); |
|
831 } |
|
832 |
|
833 return (FT_Int32)root; |
|
834 } |
|
835 |
|
836 |
|
837 /* documentation is in ftcalc.h */ |
|
838 |
|
839 FT_BASE_DEF( FT_Int ) |
|
840 ft_corner_orientation( FT_Pos in_x, |
|
841 FT_Pos in_y, |
|
842 FT_Pos out_x, |
|
843 FT_Pos out_y ) |
|
844 { |
|
845 FT_Long result; /* avoid overflow on 16-bit system */ |
|
846 |
|
847 |
|
848 /* deal with the trivial cases quickly */ |
|
849 if ( in_y == 0 ) |
|
850 { |
|
851 if ( in_x >= 0 ) |
|
852 result = out_y; |
|
853 else |
|
854 result = -out_y; |
|
855 } |
|
856 else if ( in_x == 0 ) |
|
857 { |
|
858 if ( in_y >= 0 ) |
|
859 result = -out_x; |
|
860 else |
|
861 result = out_x; |
|
862 } |
|
863 else if ( out_y == 0 ) |
|
864 { |
|
865 if ( out_x >= 0 ) |
|
866 result = in_y; |
|
867 else |
|
868 result = -in_y; |
|
869 } |
|
870 else if ( out_x == 0 ) |
|
871 { |
|
872 if ( out_y >= 0 ) |
|
873 result = -in_x; |
|
874 else |
|
875 result = in_x; |
|
876 } |
|
877 else /* general case */ |
|
878 { |
|
879 #ifdef FT_LONG64 |
|
880 |
|
881 FT_Int64 delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x; |
|
882 |
|
883 |
|
884 if ( delta == 0 ) |
|
885 result = 0; |
|
886 else |
|
887 result = 1 - 2 * ( delta < 0 ); |
|
888 |
|
889 #else |
|
890 |
|
891 FT_Int64 z1, z2; |
|
892 |
|
893 |
|
894 /* XXX: this function does not allow 64-bit arguments */ |
|
895 ft_multo64( (FT_Int32)in_x, (FT_Int32)out_y, &z1 ); |
|
896 ft_multo64( (FT_Int32)in_y, (FT_Int32)out_x, &z2 ); |
|
897 |
|
898 if ( z1.hi > z2.hi ) |
|
899 result = +1; |
|
900 else if ( z1.hi < z2.hi ) |
|
901 result = -1; |
|
902 else if ( z1.lo > z2.lo ) |
|
903 result = +1; |
|
904 else if ( z1.lo < z2.lo ) |
|
905 result = -1; |
|
906 else |
|
907 result = 0; |
|
908 |
|
909 #endif |
|
910 } |
|
911 |
|
912 /* XXX: only the sign of return value, +1/0/-1 must be used */ |
|
913 return (FT_Int)result; |
|
914 } |
|
915 |
|
916 |
|
917 /* documentation is in ftcalc.h */ |
|
918 |
|
919 FT_BASE_DEF( FT_Int ) |
|
920 ft_corner_is_flat( FT_Pos in_x, |
|
921 FT_Pos in_y, |
|
922 FT_Pos out_x, |
|
923 FT_Pos out_y ) |
|
924 { |
|
925 FT_Pos ax = in_x; |
|
926 FT_Pos ay = in_y; |
|
927 |
|
928 FT_Pos d_in, d_out, d_corner; |
|
929 |
|
930 |
|
931 if ( ax < 0 ) |
|
932 ax = -ax; |
|
933 if ( ay < 0 ) |
|
934 ay = -ay; |
|
935 d_in = ax + ay; |
|
936 |
|
937 ax = out_x; |
|
938 if ( ax < 0 ) |
|
939 ax = -ax; |
|
940 ay = out_y; |
|
941 if ( ay < 0 ) |
|
942 ay = -ay; |
|
943 d_out = ax + ay; |
|
944 |
|
945 ax = out_x + in_x; |
|
946 if ( ax < 0 ) |
|
947 ax = -ax; |
|
948 ay = out_y + in_y; |
|
949 if ( ay < 0 ) |
|
950 ay = -ay; |
|
951 d_corner = ax + ay; |
|
952 |
|
953 return ( d_in + d_out - d_corner ) < ( d_corner >> 4 ); |
|
954 } |
|
955 |
|
956 |
|
957 /* END */ |
|