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date Fri, 27 Oct 2017 22:46:09 +0900
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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
34 with Types; use Types;
35 with Uintp; use Uintp;
36
37 package 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
344 private
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
369 end Urealp;