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1 ------------------------------------------------------------------------------
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2 -- --
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3 -- GNAT COMPILER COMPONENTS --
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4 -- --
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5 -- U I N T P --
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6 -- --
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7 -- S p e c --
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8 -- --
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145
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9 -- Copyright (C) 1992-2019, Free Software Foundation, Inc. --
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111
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10 -- --
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11 -- GNAT is free software; you can redistribute it and/or modify it under --
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12 -- terms of the GNU General Public License as published by the Free Soft- --
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13 -- ware Foundation; either version 3, or (at your option) any later ver- --
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14 -- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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15 -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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16 -- or FITNESS FOR A PARTICULAR PURPOSE. --
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17 -- --
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18 -- As a special exception under Section 7 of GPL version 3, you are granted --
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19 -- additional permissions described in the GCC Runtime Library Exception, --
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20 -- version 3.1, as published by the Free Software Foundation. --
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21 -- --
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22 -- You should have received a copy of the GNU General Public License and --
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23 -- a copy of the GCC Runtime Library Exception along with this program; --
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24 -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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25 -- <http://www.gnu.org/licenses/>. --
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26 -- --
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27 -- GNAT was originally developed by the GNAT team at New York University. --
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28 -- Extensive contributions were provided by Ada Core Technologies Inc. --
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29 -- --
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30 ------------------------------------------------------------------------------
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31
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32 -- Support for universal integer arithmetic
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33
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34 -- WARNING: There is a C version of this package. Any changes to this
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35 -- source file must be properly reflected in the C header file uintp.h
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36
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37 with Alloc;
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38 with Table;
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39 pragma Elaborate_All (Table);
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40 with Types; use Types;
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41
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42 package Uintp is
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43
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44 -------------------------------------------------
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45 -- Basic Types and Constants for Uintp Package --
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46 -------------------------------------------------
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47
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48 type Uint is private;
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49 -- The basic universal integer type
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50
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51 No_Uint : constant Uint;
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52 -- A constant value indicating a missing or unset Uint value
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53
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54 Uint_0 : constant Uint;
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55 Uint_1 : constant Uint;
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56 Uint_2 : constant Uint;
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57 Uint_3 : constant Uint;
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58 Uint_4 : constant Uint;
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59 Uint_5 : constant Uint;
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60 Uint_6 : constant Uint;
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61 Uint_7 : constant Uint;
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62 Uint_8 : constant Uint;
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63 Uint_9 : constant Uint;
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64 Uint_10 : constant Uint;
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65 Uint_11 : constant Uint;
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66 Uint_12 : constant Uint;
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67 Uint_13 : constant Uint;
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68 Uint_14 : constant Uint;
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69 Uint_15 : constant Uint;
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70 Uint_16 : constant Uint;
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71 Uint_24 : constant Uint;
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72 Uint_32 : constant Uint;
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73 Uint_63 : constant Uint;
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74 Uint_64 : constant Uint;
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75 Uint_80 : constant Uint;
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76 Uint_128 : constant Uint;
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77
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78 Uint_Minus_1 : constant Uint;
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79 Uint_Minus_2 : constant Uint;
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80 Uint_Minus_3 : constant Uint;
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81 Uint_Minus_4 : constant Uint;
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82 Uint_Minus_5 : constant Uint;
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83 Uint_Minus_6 : constant Uint;
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84 Uint_Minus_7 : constant Uint;
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85 Uint_Minus_8 : constant Uint;
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86 Uint_Minus_9 : constant Uint;
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87 Uint_Minus_12 : constant Uint;
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88 Uint_Minus_36 : constant Uint;
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89 Uint_Minus_63 : constant Uint;
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90 Uint_Minus_80 : constant Uint;
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91 Uint_Minus_128 : constant Uint;
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92
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93 type UI_Vector is array (Pos range <>) of Int;
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94 -- Vector containing the integer values of a Uint value
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95
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96 -- Note: An earlier version of this package used pointers of arrays of Ints
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97 -- (dynamically allocated) for the Uint type. The change leads to a few
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98 -- less natural idioms used throughout this code, but eliminates all uses
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99 -- of the heap except for the table package itself. For example, Uint
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100 -- parameters are often converted to UI_Vectors for internal manipulation.
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101 -- This is done by creating the local UI_Vector using the function N_Digits
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102 -- on the Uint to find the size needed for the vector, and then calling
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103 -- Init_Operand to copy the values out of the table into the vector.
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104
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105 -----------------
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106 -- Subprograms --
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107 -----------------
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108
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109 procedure Initialize;
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110 -- Initialize Uint tables. Note that Initialize must not be called if
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111 -- Tree_Read is used. Note also that there is no lock routine in this
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112 -- unit, these are among the few tables that can be expanded during
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113 -- gigi processing.
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114
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115 procedure Tree_Read;
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116 -- Initializes internal tables from current tree file using the relevant
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117 -- Table.Tree_Read routines. Note that Initialize should not be called if
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118 -- Tree_Read is used. Tree_Read includes all necessary initialization.
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119
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120 procedure Tree_Write;
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121 -- Writes out internal tables to current tree file using the relevant
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122 -- Table.Tree_Write routines.
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123
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124 function UI_Abs (Right : Uint) return Uint;
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125 pragma Inline (UI_Abs);
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126 -- Returns abs function of universal integer
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127
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128 function UI_Add (Left : Uint; Right : Uint) return Uint;
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129 function UI_Add (Left : Int; Right : Uint) return Uint;
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130 function UI_Add (Left : Uint; Right : Int) return Uint;
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131 -- Returns sum of two integer values
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132
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133 function UI_Decimal_Digits_Hi (U : Uint) return Nat;
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134 -- Returns an estimate of the number of decimal digits required to
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135 -- represent the absolute value of U. This estimate is correct or high,
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136 -- i.e. it never returns a value that is too low. The accuracy of the
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137 -- estimate affects only the effectiveness of comparison optimizations
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138 -- in Urealp.
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139
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140 function UI_Decimal_Digits_Lo (U : Uint) return Nat;
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141 -- Returns an estimate of the number of decimal digits required to
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142 -- represent the absolute value of U. This estimate is correct or low,
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143 -- i.e. it never returns a value that is too high. The accuracy of the
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144 -- estimate affects only the effectiveness of comparison optimizations
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145 -- in Urealp.
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146
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147 function UI_Div (Left : Uint; Right : Uint) return Uint;
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148 function UI_Div (Left : Int; Right : Uint) return Uint;
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149 function UI_Div (Left : Uint; Right : Int) return Uint;
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150 -- Returns quotient of two integer values. Fatal error if Right = 0
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151
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152 function UI_Eq (Left : Uint; Right : Uint) return Boolean;
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153 function UI_Eq (Left : Int; Right : Uint) return Boolean;
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154 function UI_Eq (Left : Uint; Right : Int) return Boolean;
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155 pragma Inline (UI_Eq);
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156 -- Compares integer values for equality
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157
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158 function UI_Expon (Left : Uint; Right : Uint) return Uint;
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159 function UI_Expon (Left : Int; Right : Uint) return Uint;
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160 function UI_Expon (Left : Uint; Right : Int) return Uint;
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161 function UI_Expon (Left : Int; Right : Int) return Uint;
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162 -- Returns result of exponentiating two integer values.
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163 -- Fatal error if Right is negative.
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164
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165 function UI_GCD (Uin, Vin : Uint) return Uint;
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166 -- Computes GCD of input values. Assumes Uin >= Vin >= 0
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167
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168 function UI_Ge (Left : Uint; Right : Uint) return Boolean;
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169 function UI_Ge (Left : Int; Right : Uint) return Boolean;
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170 function UI_Ge (Left : Uint; Right : Int) return Boolean;
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171 pragma Inline (UI_Ge);
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172 -- Compares integer values for greater than or equal
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173
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174 function UI_Gt (Left : Uint; Right : Uint) return Boolean;
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175 function UI_Gt (Left : Int; Right : Uint) return Boolean;
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176 function UI_Gt (Left : Uint; Right : Int) return Boolean;
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177 pragma Inline (UI_Gt);
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178 -- Compares integer values for greater than
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179
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180 function UI_Is_In_Int_Range (Input : Uint) return Boolean;
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181 pragma Inline (UI_Is_In_Int_Range);
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182 -- Determines if universal integer is in Int range
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183
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184 function UI_Le (Left : Uint; Right : Uint) return Boolean;
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185 function UI_Le (Left : Int; Right : Uint) return Boolean;
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186 function UI_Le (Left : Uint; Right : Int) return Boolean;
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187 pragma Inline (UI_Le);
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188 -- Compares integer values for less than or equal
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189
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190 function UI_Lt (Left : Uint; Right : Uint) return Boolean;
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191 function UI_Lt (Left : Int; Right : Uint) return Boolean;
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192 function UI_Lt (Left : Uint; Right : Int) return Boolean;
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193 -- Compares integer values for less than
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194
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195 function UI_Max (Left : Uint; Right : Uint) return Uint;
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196 function UI_Max (Left : Int; Right : Uint) return Uint;
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197 function UI_Max (Left : Uint; Right : Int) return Uint;
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198 -- Returns maximum of two integer values
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199
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200 function UI_Min (Left : Uint; Right : Uint) return Uint;
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201 function UI_Min (Left : Int; Right : Uint) return Uint;
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202 function UI_Min (Left : Uint; Right : Int) return Uint;
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203 -- Returns minimum of two integer values
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204
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205 function UI_Mod (Left : Uint; Right : Uint) return Uint;
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206 function UI_Mod (Left : Int; Right : Uint) return Uint;
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207 function UI_Mod (Left : Uint; Right : Int) return Uint;
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208 pragma Inline (UI_Mod);
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209 -- Returns mod function of two integer values
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210
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211 function UI_Mul (Left : Uint; Right : Uint) return Uint;
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212 function UI_Mul (Left : Int; Right : Uint) return Uint;
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213 function UI_Mul (Left : Uint; Right : Int) return Uint;
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214 -- Returns product of two integer values
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215
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216 function UI_Ne (Left : Uint; Right : Uint) return Boolean;
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217 function UI_Ne (Left : Int; Right : Uint) return Boolean;
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218 function UI_Ne (Left : Uint; Right : Int) return Boolean;
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219 pragma Inline (UI_Ne);
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220 -- Compares integer values for inequality
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221
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222 function UI_Negate (Right : Uint) return Uint;
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223 pragma Inline (UI_Negate);
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224 -- Returns negative of universal integer
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225
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226 function UI_Rem (Left : Uint; Right : Uint) return Uint;
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227 function UI_Rem (Left : Int; Right : Uint) return Uint;
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228 function UI_Rem (Left : Uint; Right : Int) return Uint;
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229 -- Returns rem of two integer values
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230
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231 function UI_Sub (Left : Uint; Right : Uint) return Uint;
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232 function UI_Sub (Left : Int; Right : Uint) return Uint;
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233 function UI_Sub (Left : Uint; Right : Int) return Uint;
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234 pragma Inline (UI_Sub);
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235 -- Returns difference of two integer values
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236
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237 function UI_Modular_Exponentiation
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238 (B : Uint;
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239 E : Uint;
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240 Modulo : Uint) return Uint;
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241 -- Efficiently compute (B**E) rem Modulo
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242
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243 function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint;
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244 -- Compute the multiplicative inverse of N in modular arithmetics with the
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245 -- given Modulo (uses Euclid's algorithm). Note: the call is considered
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246 -- to be erroneous (and the behavior is undefined) if n is not invertible.
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247
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248 function UI_From_Int (Input : Int) return Uint;
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249 -- Converts Int value to universal integer form
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250
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145
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251 generic
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252 type In_T is range <>;
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253 function UI_From_Integral (Input : In_T) return Uint;
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254 -- Likewise, but converts from any integer type. Must not be applied to
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255 -- biased types (instantiation will provide a warning if actual is a biased
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256 -- type).
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257
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111
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258 function UI_From_CC (Input : Char_Code) return Uint;
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259 -- Converts Char_Code value to universal integer form
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260
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261 function UI_To_Int (Input : Uint) return Int;
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262 -- Converts universal integer value to Int. Constraint_Error if value is
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263 -- not in appropriate range.
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264
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265 function UI_To_CC (Input : Uint) return Char_Code;
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266 -- Converts universal integer value to Char_Code. Constraint_Error if value
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267 -- is not in Char_Code range.
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268
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269 function Num_Bits (Input : Uint) return Nat;
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270 -- Approximate number of binary bits in given universal integer. This
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271 -- function is used for capacity checks, and it can be one bit off
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272 -- without affecting its usage.
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273
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274 function Vector_To_Uint
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275 (In_Vec : UI_Vector;
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276 Negative : Boolean) return Uint;
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277 -- Functions that calculate values in UI_Vectors, call this function to
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278 -- create and return the Uint value. In_Vec contains the multiple precision
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279 -- (Base) representation of a non-negative value. Leading zeroes are
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280 -- permitted. Negative is set if the desired result is the negative of the
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281 -- given value. The result will be either the appropriate directly
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282 -- represented value, or a table entry in the proper canonical format is
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283 -- created and returned.
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284 --
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285 -- Note that Init_Operand puts a signed value in the result vector, but
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286 -- Vector_To_Uint is always presented with a non-negative value. The
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287 -- processing of signs is something that is done by the caller before
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288 -- calling Vector_To_Uint.
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289
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290 ---------------------
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291 -- Output Routines --
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292 ---------------------
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293
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294 type UI_Format is (Hex, Decimal, Auto);
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295 -- Used to determine whether UI_Image/UI_Write output is in hexadecimal
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296 -- or decimal format. Auto, the default setting, lets the routine make a
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297 -- decision based on the value.
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298
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299 UI_Image_Max : constant := 48; -- Enough for a 128-bit number
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300 UI_Image_Buffer : String (1 .. UI_Image_Max);
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301 UI_Image_Length : Natural;
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302 -- Buffer used for UI_Image as described below
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303
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304 procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
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305 -- Places a representation of Uint, consisting of a possible minus sign,
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306 -- followed by the value in UI_Image_Buffer. The form of the value is an
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307 -- integer literal in either decimal (no base) or hexadecimal (base 16)
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308 -- format. If Hex is True on entry, then hex mode is forced, otherwise
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309 -- UI_Image makes a guess at which output format is more convenient. The
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310 -- value must fit in UI_Image_Buffer. The actual length of the result is
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311 -- returned in UI_Image_Length. If necessary to meet this requirement, the
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312 -- result is an approximation of the proper value, using an exponential
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313 -- format. The image of No_Uint is output as a single question mark.
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314
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315 function UI_Image (Input : Uint; Format : UI_Format := Auto) return String;
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316 -- Functional form, in which the result is returned as a string. This call
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317 -- also leaves the result in UI_Image_Buffer/Length as described above.
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318
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319 procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
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320 -- Writes a representation of Uint, consisting of a possible minus sign,
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321 -- followed by the value to the output file. The form of the value is an
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322 -- integer literal in either decimal (no base) or hexadecimal (base 16)
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323 -- format as appropriate. UI_Format shows which format to use. Auto, the
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324 -- default, asks UI_Write to make a guess at which output format will be
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325 -- more convenient to read.
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326
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327 procedure pid (Input : Uint);
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328 pragma Export (Ada, pid);
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329 -- Writes representation of Uint in decimal with a terminating line
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330 -- return. This is intended for use from the debugger.
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331
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332 procedure pih (Input : Uint);
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333 pragma Export (Ada, pih);
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334 -- Writes representation of Uint in hex with a terminating line return.
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335 -- This is intended for use from the debugger.
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336
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337 ------------------------
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338 -- Operator Renamings --
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339 ------------------------
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340
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341 function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
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342 function "+" (Left : Int; Right : Uint) return Uint renames UI_Add;
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343 function "+" (Left : Uint; Right : Int) return Uint renames UI_Add;
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344
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345 function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
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346 function "/" (Left : Int; Right : Uint) return Uint renames UI_Div;
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347 function "/" (Left : Uint; Right : Int) return Uint renames UI_Div;
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348
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349 function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
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350 function "*" (Left : Int; Right : Uint) return Uint renames UI_Mul;
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351 function "*" (Left : Uint; Right : Int) return Uint renames UI_Mul;
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352
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353 function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
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354 function "-" (Left : Int; Right : Uint) return Uint renames UI_Sub;
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355 function "-" (Left : Uint; Right : Int) return Uint renames UI_Sub;
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356
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357 function "**" (Left : Uint; Right : Uint) return Uint renames UI_Expon;
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358 function "**" (Left : Uint; Right : Int) return Uint renames UI_Expon;
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359 function "**" (Left : Int; Right : Uint) return Uint renames UI_Expon;
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360 function "**" (Left : Int; Right : Int) return Uint renames UI_Expon;
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361
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362 function "abs" (Real : Uint) return Uint renames UI_Abs;
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363
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364 function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
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365 function "mod" (Left : Int; Right : Uint) return Uint renames UI_Mod;
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366 function "mod" (Left : Uint; Right : Int) return Uint renames UI_Mod;
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367
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368 function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
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369 function "rem" (Left : Int; Right : Uint) return Uint renames UI_Rem;
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370 function "rem" (Left : Uint; Right : Int) return Uint renames UI_Rem;
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371
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372 function "-" (Real : Uint) return Uint renames UI_Negate;
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373
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374 function "=" (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
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375 function "=" (Left : Int; Right : Uint) return Boolean renames UI_Eq;
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376 function "=" (Left : Uint; Right : Int) return Boolean renames UI_Eq;
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377
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378 function ">=" (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
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379 function ">=" (Left : Int; Right : Uint) return Boolean renames UI_Ge;
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380 function ">=" (Left : Uint; Right : Int) return Boolean renames UI_Ge;
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381
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382 function ">" (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
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383 function ">" (Left : Int; Right : Uint) return Boolean renames UI_Gt;
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384 function ">" (Left : Uint; Right : Int) return Boolean renames UI_Gt;
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385
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386 function "<=" (Left : Uint; Right : Uint) return Boolean renames UI_Le;
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387 function "<=" (Left : Int; Right : Uint) return Boolean renames UI_Le;
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388 function "<=" (Left : Uint; Right : Int) return Boolean renames UI_Le;
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389
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390 function "<" (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
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391 function "<" (Left : Int; Right : Uint) return Boolean renames UI_Lt;
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392 function "<" (Left : Uint; Right : Int) return Boolean renames UI_Lt;
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393
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394 -----------------------------
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395 -- Mark/Release Processing --
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396 -----------------------------
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397
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398 -- The space used by Uint data is not automatically reclaimed. However, a
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399 -- mark-release regime is implemented which allows storage to be released
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400 -- back to a previously noted mark. This is used for example when doing
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401 -- comparisons, where only intermediate results get stored that do not
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402 -- need to be saved for future use.
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403
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404 type Save_Mark is private;
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405
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406 function Mark return Save_Mark;
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407 -- Note mark point for future release
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408
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409 procedure Release (M : Save_Mark);
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410 -- Release storage allocated since mark was noted
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411
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412 procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
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413 -- Like Release, except that the given Uint value (which is typically among
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414 -- the data being released) is recopied after the release, so that it is
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415 -- the most recent item, and UI is updated to point to its copied location.
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416
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417 procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
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418 -- Like Release, except that the given Uint values (which are typically
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419 -- among the data being released) are recopied after the release, so that
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420 -- they are the most recent items, and UI1 and UI2 are updated if necessary
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421 -- to point to the copied locations. This routine is careful to do things
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422 -- in the right order, so that the values do not clobber one another.
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423
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424 -----------------------------------
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425 -- Representation of Uint Values --
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426 -----------------------------------
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427
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428 private
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429
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430 type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
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431 for Uint'Size use 32;
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432
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433 No_Uint : constant Uint := Uint (Uint_Low_Bound);
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434
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435 -- Uint values are represented as multiple precision integers stored in
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436 -- a multi-digit format using Base as the base. This value is chosen so
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437 -- that the product Base*Base is within the range of allowed Int values.
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438
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439 -- Base is defined to allow efficient execution of the primitive operations
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440 -- (a0, b0, c0) defined in the section "The Classical Algorithms"
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441 -- (sec. 4.3.1) of Donald Knuth's "The Art of Computer Programming",
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442 -- Vol. 2. These algorithms are used in this package. In particular,
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443 -- the product of two single digits in this base fits in a 32-bit integer.
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444
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445 Base_Bits : constant := 15;
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446 -- Number of bits in base value
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447
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448 Base : constant Int := 2**Base_Bits;
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449
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450 -- Values in the range -(Base-1) .. Max_Direct are encoded directly as
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451 -- Uint values by adding a bias value. The value of Max_Direct is chosen
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452 -- so that a directly represented number always fits in two digits when
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453 -- represented in base format.
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454
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455 Min_Direct : constant Int := -(Base - 1);
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456 Max_Direct : constant Int := (Base - 1) * (Base - 1);
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457
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458 -- The following values define the bias used to store Uint values which
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459 -- are in this range, as well as the biased values for the first and last
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460 -- values in this range. We use a new derived type for these constants to
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461 -- avoid accidental use of Uint arithmetic on these values, which is never
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462 -- correct.
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463
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464 type Ctrl is new Int;
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465
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466 Uint_Direct_Bias : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
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467 Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
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468 Uint_Direct_Last : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
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469
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470 Uint_0 : constant Uint := Uint (Uint_Direct_Bias + 0);
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471 Uint_1 : constant Uint := Uint (Uint_Direct_Bias + 1);
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472 Uint_2 : constant Uint := Uint (Uint_Direct_Bias + 2);
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473 Uint_3 : constant Uint := Uint (Uint_Direct_Bias + 3);
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474 Uint_4 : constant Uint := Uint (Uint_Direct_Bias + 4);
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475 Uint_5 : constant Uint := Uint (Uint_Direct_Bias + 5);
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476 Uint_6 : constant Uint := Uint (Uint_Direct_Bias + 6);
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477 Uint_7 : constant Uint := Uint (Uint_Direct_Bias + 7);
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478 Uint_8 : constant Uint := Uint (Uint_Direct_Bias + 8);
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479 Uint_9 : constant Uint := Uint (Uint_Direct_Bias + 9);
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480 Uint_10 : constant Uint := Uint (Uint_Direct_Bias + 10);
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481 Uint_11 : constant Uint := Uint (Uint_Direct_Bias + 11);
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482 Uint_12 : constant Uint := Uint (Uint_Direct_Bias + 12);
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483 Uint_13 : constant Uint := Uint (Uint_Direct_Bias + 13);
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484 Uint_14 : constant Uint := Uint (Uint_Direct_Bias + 14);
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485 Uint_15 : constant Uint := Uint (Uint_Direct_Bias + 15);
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486 Uint_16 : constant Uint := Uint (Uint_Direct_Bias + 16);
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487 Uint_24 : constant Uint := Uint (Uint_Direct_Bias + 24);
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488 Uint_32 : constant Uint := Uint (Uint_Direct_Bias + 32);
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489 Uint_63 : constant Uint := Uint (Uint_Direct_Bias + 63);
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490 Uint_64 : constant Uint := Uint (Uint_Direct_Bias + 64);
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491 Uint_80 : constant Uint := Uint (Uint_Direct_Bias + 80);
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492 Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
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493
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494 Uint_Minus_1 : constant Uint := Uint (Uint_Direct_Bias - 1);
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495 Uint_Minus_2 : constant Uint := Uint (Uint_Direct_Bias - 2);
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496 Uint_Minus_3 : constant Uint := Uint (Uint_Direct_Bias - 3);
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497 Uint_Minus_4 : constant Uint := Uint (Uint_Direct_Bias - 4);
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498 Uint_Minus_5 : constant Uint := Uint (Uint_Direct_Bias - 5);
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499 Uint_Minus_6 : constant Uint := Uint (Uint_Direct_Bias - 6);
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500 Uint_Minus_7 : constant Uint := Uint (Uint_Direct_Bias - 7);
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501 Uint_Minus_8 : constant Uint := Uint (Uint_Direct_Bias - 8);
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502 Uint_Minus_9 : constant Uint := Uint (Uint_Direct_Bias - 9);
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503 Uint_Minus_12 : constant Uint := Uint (Uint_Direct_Bias - 12);
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504 Uint_Minus_36 : constant Uint := Uint (Uint_Direct_Bias - 36);
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|
|
505 Uint_Minus_63 : constant Uint := Uint (Uint_Direct_Bias - 63);
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|
|
506 Uint_Minus_80 : constant Uint := Uint (Uint_Direct_Bias - 80);
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|
|
507 Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
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|
|
508
|
|
|
509 Uint_Max_Simple_Mul : constant := Uint_Direct_Bias + 2**15;
|
|
|
510 -- If two values are directly represented and less than or equal to this
|
|
|
511 -- value, then we know the product fits in a 32-bit integer. This allows
|
|
|
512 -- UI_Mul to efficiently compute the product in this case.
|
|
|
513
|
|
|
514 type Save_Mark is record
|
|
|
515 Save_Uint : Uint;
|
|
|
516 Save_Udigit : Int;
|
|
|
517 end record;
|
|
|
518
|
|
|
519 -- Values outside the range that is represented directly are stored using
|
|
|
520 -- two tables. The secondary table Udigits contains sequences of Int values
|
|
|
521 -- consisting of the digits of the number in a radix Base system. The
|
|
|
522 -- digits are stored from most significant to least significant with the
|
|
|
523 -- first digit only carrying the sign.
|
|
|
524
|
|
|
525 -- There is one entry in the primary Uints table for each distinct Uint
|
|
|
526 -- value. This table entry contains the length (number of digits) and
|
|
|
527 -- a starting offset of the value in the Udigits table.
|
|
|
528
|
|
|
529 Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
|
|
|
530
|
|
|
531 -- Some subprograms defined in this package manipulate the Udigits table
|
|
|
532 -- directly, while for others it is more convenient to work with locally
|
|
|
533 -- defined arrays of the digits of the Universal Integers. The type
|
|
|
534 -- UI_Vector is defined for this purpose and some internal subprograms
|
|
|
535 -- used for converting from one to the other are defined.
|
|
|
536
|
|
|
537 type Uint_Entry is record
|
|
|
538 Length : Pos;
|
|
|
539 -- Length of entry in Udigits table in digits (i.e. in words)
|
|
|
540
|
|
|
541 Loc : Int;
|
|
|
542 -- Starting location in Udigits table of this Uint value
|
|
|
543 end record;
|
|
|
544
|
|
|
545 package Uints is new Table.Table (
|
|
|
546 Table_Component_Type => Uint_Entry,
|
|
|
547 Table_Index_Type => Uint'Base,
|
|
|
548 Table_Low_Bound => Uint_First_Entry,
|
|
|
549 Table_Initial => Alloc.Uints_Initial,
|
|
|
550 Table_Increment => Alloc.Uints_Increment,
|
|
|
551 Table_Name => "Uints");
|
|
|
552
|
|
|
553 package Udigits is new Table.Table (
|
|
|
554 Table_Component_Type => Int,
|
|
|
555 Table_Index_Type => Int,
|
|
|
556 Table_Low_Bound => 0,
|
|
|
557 Table_Initial => Alloc.Udigits_Initial,
|
|
|
558 Table_Increment => Alloc.Udigits_Increment,
|
|
|
559 Table_Name => "Udigits");
|
|
|
560
|
|
|
561 -- Note: the reason these tables are defined here in the private part of
|
|
|
562 -- the spec, rather than in the body, is that they are referenced directly
|
|
|
563 -- by gigi.
|
|
|
564
|
|
|
565 end Uintp;
|
