1------------------------------------------------------------------------------ 2-- -- 3-- GNAT COMPILER COMPONENTS -- 4-- -- 5-- U R E A L P -- 6-- -- 7-- S p e c -- 8-- -- 9-- Copyright (C) 1992-2013, Free Software Foundation, Inc. -- 10-- -- 11-- GNAT is free software; you can redistribute it and/or modify it under -- 12-- terms of the GNU General Public License as published by the Free Soft- -- 13-- ware Foundation; either version 3, or (at your option) any later ver- -- 14-- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- 15-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- 16-- or FITNESS FOR A PARTICULAR PURPOSE. -- 17-- -- 18-- As a special exception under Section 7 of GPL version 3, you are granted -- 19-- additional permissions described in the GCC Runtime Library Exception, -- 20-- version 3.1, as published by the Free Software Foundation. -- 21-- -- 22-- You should have received a copy of the GNU General Public License and -- 23-- a copy of the GCC Runtime Library Exception along with this program; -- 24-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- 25-- <http://www.gnu.org/licenses/>. -- 26-- -- 27-- GNAT was originally developed by the GNAT team at New York University. -- 28-- Extensive contributions were provided by Ada Core Technologies Inc. -- 29-- -- 30------------------------------------------------------------------------------ 31 32-- Support for universal real arithmetic 33 34with Types; use Types; 35with Uintp; use Uintp; 36 37package Urealp is 38 39 --------------------------------------- 40 -- Representation of Universal Reals -- 41 --------------------------------------- 42 43 -- A universal real value is represented by a single value (which is 44 -- an index into an internal table). These values are not hashed, so 45 -- the equality operator should not be used on Ureal values (instead 46 -- use the UR_Eq function). 47 48 -- A Ureal value represents an arbitrary precision universal real value, 49 -- stored internally using four components: 50 51 -- the numerator (Uint, always non-negative) 52 -- the denominator (Uint, always non-zero, always positive if base = 0) 53 -- a real base (Nat, either zero, or in the range 2 .. 16) 54 -- a sign flag (Boolean), set if negative 55 56 -- Negative numbers are represented by the sign flag being True. 57 58 -- If the base is zero, then the absolute value of the Ureal is simply 59 -- numerator/denominator, where denominator is positive. If the base is 60 -- non-zero, then the absolute value is numerator / (base ** denominator). 61 -- In that case, since base is positive, (base ** denominator) is also 62 -- positive, even when denominator is negative or null. 63 64 -- A normalized Ureal value has base = 0, and numerator/denominator 65 -- reduced to lowest terms, with zero itself being represented as 0/1. 66 -- This is a canonical format, so that for normalized Ureal values it 67 -- is the case that two equal values always have the same denominator 68 -- and numerator values. 69 70 -- Note: a value of minus zero is legitimate, and the operations in 71 -- Urealp preserve the handling of signed zeroes in accordance with 72 -- the rules of IEEE P754 ("IEEE floating point"). 73 74 ------------------------------ 75 -- Types for Urealp Package -- 76 ------------------------------ 77 78 type Ureal is private; 79 -- Type used for representation of universal reals 80 81 No_Ureal : constant Ureal; 82 -- Constant used to indicate missing or unset Ureal value 83 84 --------------------- 85 -- Ureal Constants -- 86 --------------------- 87 88 function Ureal_0 return Ureal; 89 -- Returns value 0.0 90 91 function Ureal_M_0 return Ureal; 92 -- Returns value -0.0 93 94 function Ureal_Tenth return Ureal; 95 -- Returns value 0.1 96 97 function Ureal_Half return Ureal; 98 -- Returns value 0.5 99 100 function Ureal_1 return Ureal; 101 -- Returns value 1.0 102 103 function Ureal_2 return Ureal; 104 -- Returns value 2.0 105 106 function Ureal_10 return Ureal; 107 -- Returns value 10.0 108 109 function Ureal_100 return Ureal; 110 -- Returns value 100.0 111 112 function Ureal_2_80 return Ureal; 113 -- Returns value 2.0 ** 80 114 115 function Ureal_2_M_80 return Ureal; 116 -- Returns value 2.0 ** (-80) 117 118 function Ureal_2_128 return Ureal; 119 -- Returns value 2.0 ** 128 120 121 function Ureal_2_M_128 return Ureal; 122 -- Returns value 2.0 ** (-128) 123 124 function Ureal_10_36 return Ureal; 125 -- Returns value 10.0 ** 36 126 127 function Ureal_M_10_36 return Ureal; 128 -- Returns value -10.0 ** 36 129 130 ----------------- 131 -- Subprograms -- 132 ----------------- 133 134 procedure Initialize; 135 -- Initialize Ureal tables. Note that Initialize must not be called if 136 -- Tree_Read is used. Note also that there is no Lock routine in this 137 -- unit. These tables are among the few tables that can be expanded 138 -- during Gigi processing. 139 140 procedure Tree_Read; 141 -- Initializes internal tables from current tree file using the relevant 142 -- Table.Tree_Read routines. Note that Initialize should not be called if 143 -- Tree_Read is used. Tree_Read includes all necessary initialization. 144 145 procedure Tree_Write; 146 -- Writes out internal tables to current tree file using the relevant 147 -- Table.Tree_Write routines. 148 149 function Rbase (Real : Ureal) return Nat; 150 -- Return the base of the universal real 151 152 function Denominator (Real : Ureal) return Uint; 153 -- Return the denominator of the universal real 154 155 function Numerator (Real : Ureal) return Uint; 156 -- Return the numerator of the universal real 157 158 function Norm_Den (Real : Ureal) return Uint; 159 -- Return the denominator of the universal real after a normalization 160 161 function Norm_Num (Real : Ureal) return Uint; 162 -- Return the numerator of the universal real after a normalization 163 164 function UR_From_Uint (UI : Uint) return Ureal; 165 -- Returns real corresponding to universal integer value 166 167 function UR_To_Uint (Real : Ureal) return Uint; 168 -- Return integer value obtained by accurate rounding of real value. 169 -- The rounding of values half way between two integers is away from 170 -- zero, as required by normal Ada 95 rounding semantics. 171 172 function UR_Trunc (Real : Ureal) return Uint; 173 -- Return integer value obtained by a truncation of real towards zero 174 175 function UR_Ceiling (Real : Ureal) return Uint; 176 -- Return value of smallest integer not less than the given value 177 178 function UR_Floor (Real : Ureal) return Uint; 179 -- Return value of smallest integer not greater than the given value 180 181 -- Conversion table for above four functions 182 183 -- Input To_Uint Trunc Ceiling Floor 184 -- 1.0 1 1 1 1 185 -- 1.2 1 1 2 1 186 -- 1.5 2 1 2 1 187 -- 1.7 2 1 2 1 188 -- 2.0 2 2 2 2 189 -- -1.0 -1 -1 -1 -1 190 -- -1.2 -1 -1 -1 -2 191 -- -1.5 -2 -1 -1 -2 192 -- -1.7 -2 -1 -1 -2 193 -- -2.0 -2 -2 -2 -2 194 195 function UR_From_Components 196 (Num : Uint; 197 Den : Uint; 198 Rbase : Nat := 0; 199 Negative : Boolean := False) 200 return Ureal; 201 -- Builds real value from given numerator, denominator and base. The 202 -- value is negative if Negative is set to true, and otherwise is 203 -- non-negative. 204 205 function UR_Add (Left : Ureal; Right : Ureal) return Ureal; 206 function UR_Add (Left : Ureal; Right : Uint) return Ureal; 207 function UR_Add (Left : Uint; Right : Ureal) return Ureal; 208 -- Returns real sum of operands 209 210 function UR_Div (Left : Ureal; Right : Ureal) return Ureal; 211 function UR_Div (Left : Uint; Right : Ureal) return Ureal; 212 function UR_Div (Left : Ureal; Right : Uint) return Ureal; 213 -- Returns real quotient of operands. Fatal error if Right is zero 214 215 function UR_Mul (Left : Ureal; Right : Ureal) return Ureal; 216 function UR_Mul (Left : Uint; Right : Ureal) return Ureal; 217 function UR_Mul (Left : Ureal; Right : Uint) return Ureal; 218 -- Returns real product of operands 219 220 function UR_Sub (Left : Ureal; Right : Ureal) return Ureal; 221 function UR_Sub (Left : Uint; Right : Ureal) return Ureal; 222 function UR_Sub (Left : Ureal; Right : Uint) return Ureal; 223 -- Returns real difference of operands 224 225 function UR_Exponentiate (Real : Ureal; N : Uint) return Ureal; 226 -- Returns result of raising Ureal to Uint power. 227 -- Fatal error if Left is 0 and Right is negative. 228 229 function UR_Abs (Real : Ureal) return Ureal; 230 -- Returns abs function of real 231 232 function UR_Negate (Real : Ureal) return Ureal; 233 -- Returns negative of real 234 235 function UR_Eq (Left, Right : Ureal) return Boolean; 236 -- Compares reals for equality 237 238 function UR_Max (Left, Right : Ureal) return Ureal; 239 -- Returns the maximum of two reals 240 241 function UR_Min (Left, Right : Ureal) return Ureal; 242 -- Returns the minimum of two reals 243 244 function UR_Ne (Left, Right : Ureal) return Boolean; 245 -- Compares reals for inequality 246 247 function UR_Lt (Left, Right : Ureal) return Boolean; 248 -- Compares reals for less than 249 250 function UR_Le (Left, Right : Ureal) return Boolean; 251 -- Compares reals for less than or equal 252 253 function UR_Gt (Left, Right : Ureal) return Boolean; 254 -- Compares reals for greater than 255 256 function UR_Ge (Left, Right : Ureal) return Boolean; 257 -- Compares reals for greater than or equal 258 259 function UR_Is_Zero (Real : Ureal) return Boolean; 260 -- Tests if real value is zero 261 262 function UR_Is_Negative (Real : Ureal) return Boolean; 263 -- Tests if real value is negative, note that negative zero gives true 264 265 function UR_Is_Positive (Real : Ureal) return Boolean; 266 -- Test if real value is greater than zero 267 268 procedure UR_Write (Real : Ureal; Brackets : Boolean := False); 269 -- Writes value of Real to standard output. Used for debugging and 270 -- tree/source output, and also for -gnatR representation output. If the 271 -- result is easily representable as a standard Ada literal, it will be 272 -- given that way, but as a result of evaluation of static expressions, it 273 -- is possible to generate constants (e.g. 1/13) which have no such 274 -- representation. In such cases (and in cases where it is too much work to 275 -- figure out the Ada literal), the string that is output is of the form 276 -- of some expression such as integer/integer, or integer*integer**integer. 277 -- In the case where an expression is output, if Brackets is set to True, 278 -- the expression is surrounded by square brackets. 279 280 procedure pr (Real : Ureal); 281 pragma Export (Ada, pr); 282 -- Writes value of Real to standard output with a terminating line return, 283 -- using UR_Write as described above. This is for use from the debugger. 284 285 ------------------------ 286 -- Operator Renamings -- 287 ------------------------ 288 289 function "+" (Left : Ureal; Right : Ureal) return Ureal renames UR_Add; 290 function "+" (Left : Uint; Right : Ureal) return Ureal renames UR_Add; 291 function "+" (Left : Ureal; Right : Uint) return Ureal renames UR_Add; 292 293 function "/" (Left : Ureal; Right : Ureal) return Ureal renames UR_Div; 294 function "/" (Left : Uint; Right : Ureal) return Ureal renames UR_Div; 295 function "/" (Left : Ureal; Right : Uint) return Ureal renames UR_Div; 296 297 function "*" (Left : Ureal; Right : Ureal) return Ureal renames UR_Mul; 298 function "*" (Left : Uint; Right : Ureal) return Ureal renames UR_Mul; 299 function "*" (Left : Ureal; Right : Uint) return Ureal renames UR_Mul; 300 301 function "-" (Left : Ureal; Right : Ureal) return Ureal renames UR_Sub; 302 function "-" (Left : Uint; Right : Ureal) return Ureal renames UR_Sub; 303 function "-" (Left : Ureal; Right : Uint) return Ureal renames UR_Sub; 304 305 function "**" (Real : Ureal; N : Uint) return Ureal 306 renames UR_Exponentiate; 307 308 function "abs" (Real : Ureal) return Ureal renames UR_Abs; 309 310 function "-" (Real : Ureal) return Ureal renames UR_Negate; 311 312 function "=" (Left, Right : Ureal) return Boolean renames UR_Eq; 313 314 function "<" (Left, Right : Ureal) return Boolean renames UR_Lt; 315 316 function "<=" (Left, Right : Ureal) return Boolean renames UR_Le; 317 318 function ">=" (Left, Right : Ureal) return Boolean renames UR_Ge; 319 320 function ">" (Left, Right : Ureal) return Boolean renames UR_Gt; 321 322 ----------------------------- 323 -- Mark/Release Processing -- 324 ----------------------------- 325 326 -- The space used by Ureal data is not automatically reclaimed. However, 327 -- a mark-release regime is implemented which allows storage to be 328 -- released back to a previously noted mark. This is used for example 329 -- when doing comparisons, where only intermediate results get stored 330 -- that do not need to be saved for future use. 331 332 type Save_Mark is private; 333 334 function Mark return Save_Mark; 335 -- Note mark point for future release 336 337 procedure Release (M : Save_Mark); 338 -- Release storage allocated since mark was noted 339 340 ------------------------------------ 341 -- Representation of Ureal Values -- 342 ------------------------------------ 343 344private 345 346 type Ureal is new Int range Ureal_Low_Bound .. Ureal_High_Bound; 347 for Ureal'Size use 32; 348 349 No_Ureal : constant Ureal := Ureal'First; 350 351 type Save_Mark is new Int; 352 353 pragma Inline (Denominator); 354 pragma Inline (Mark); 355 pragma Inline (Norm_Num); 356 pragma Inline (Norm_Den); 357 pragma Inline (Numerator); 358 pragma Inline (Rbase); 359 pragma Inline (Release); 360 pragma Inline (Ureal_0); 361 pragma Inline (Ureal_M_0); 362 pragma Inline (Ureal_Tenth); 363 pragma Inline (Ureal_Half); 364 pragma Inline (Ureal_1); 365 pragma Inline (Ureal_2); 366 pragma Inline (Ureal_10); 367 pragma Inline (UR_From_Components); 368 369end Urealp; 370