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date Fri, 27 Oct 2017 22:46:09 +0900
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1 -- CXG2001.A
2 --
3 -- Grant of Unlimited Rights
4 --
5 -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
6 -- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
7 -- unlimited rights in the software and documentation contained herein.
8 -- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
9 -- this public release, the Government intends to confer upon all
10 -- recipients unlimited rights equal to those held by the Government.
11 -- These rights include rights to use, duplicate, release or disclose the
12 -- released technical data and computer software in whole or in part, in
13 -- any manner and for any purpose whatsoever, and to have or permit others
14 -- to do so.
15 --
16 -- DISCLAIMER
17 --
18 -- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
19 -- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
20 -- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
21 -- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
22 -- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
23 -- PARTICULAR PURPOSE OF SAID MATERIAL.
24 --*
25 --
26 -- OBJECTIVE:
27 -- Check that the floating point attributes Model_Mantissa,
28 -- Machine_Mantissa, Machine_Radix, and Machine_Rounds
29 -- are properly reported.
30 --
31 -- TEST DESCRIPTION:
32 -- This test uses a generic package to compute and check the
33 -- values of the Machine_ attributes listed above. The
34 -- generic package is instantiated with the standard FLOAT
35 -- type and a floating point type for the maximum number
36 -- of digits of precision.
37 --
38 -- APPLICABILITY CRITERIA:
39 -- This test applies only to implementations supporting the
40 -- Numerics Annex.
41 --
42 --
43 -- CHANGE HISTORY:
44 -- 26 JAN 96 SAIC Initial Release for 2.1
45 --
46 --!
47
48 -- References:
49 --
50 -- "Algorithms To Reveal Properties of Floating-Point Arithmetic"
51 -- Michael A. Malcolm; CACM November 1972; pgs 949-951.
52 --
53 -- Software Manual for Elementary Functions; W. J. Cody and W. Waite;
54 -- Prentice-Hall; 1980
55 -----------------------------------------------------------------------
56 --
57 -- This test relies upon the fact that
58 -- (A+2.0)-A is not necessarily 2.0. If A is large enough then adding
59 -- a small value to A does not change the value of A. Consider the case
60 -- where we have a decimal based floating point representation with 4
61 -- digits of precision. A floating point number would logically be
62 -- represented as "DDDD * 10 ** exp" where D is a value in the range 0..9.
63 -- The first loop of the test starts A at 2.0 and doubles it until
64 -- ((A+1.0)-A)-1.0 is no longer zero. For our decimal floating point
65 -- number this will be 1638 * 10**1 (the value 16384 rounded or truncated
66 -- to fit in 4 digits).
67 -- The second loop starts B at 2.0 and keeps doubling B until (A+B)-A is
68 -- no longer 0. This will keep looping until B is 8.0 because that is
69 -- the first value where rounding (assuming our machine rounds and addition
70 -- employs a guard digit) will change the upper 4 digits of the result:
71 -- 1638_
72 -- + 8
73 -- -------
74 -- 1639_
75 -- Without rounding the second loop will continue until
76 -- B is 16:
77 -- 1638_
78 -- + 16
79 -- -------
80 -- 1639_
81 --
82 -- The radix is then determined by (A+B)-A which will give 10.
83 --
84 -- The use of Tmp and ITmp in the test is to force values to be
85 -- stored into memory in the event that register precision is greater
86 -- than the stored precision of the floating point values.
87 --
88 --
89 -- The test for rounding is (ignoring the temporary variables used to
90 -- get the stored precision) is
91 -- Rounds := A + Radix/2.0 - A /= 0.0 ;
92 -- where A is the value determined in the first step that is the smallest
93 -- power of 2 such that A + 1.0 = A. This means that the true value of
94 -- A has one more digit in its value than 'Machine_Mantissa.
95 -- This check will detect the case where a value is always rounded.
96 -- There is an additional case where values are rounded to the nearest
97 -- even value. That is referred to as IEEE style rounding in the test.
98 --
99 -----------------------------------------------------------------------
100
101 with System;
102 with Report;
103 with Ada.Numerics.Generic_Elementary_Functions;
104 procedure CXG2001 is
105 Verbose : constant Boolean := False;
106
107 -- if one of the attribute computation loops exceeds Max_Iterations
108 -- it is most likely due to the compiler reordering an expression
109 -- that should not be reordered.
110 Illegal_Optimization : exception;
111 Max_Iterations : constant := 10_000;
112
113 generic
114 type Real is digits <>;
115 package Chk_Attrs is
116 procedure Do_Test;
117 end Chk_Attrs;
118
119 package body Chk_Attrs is
120 package EF is new Ada.Numerics.Generic_Elementary_Functions (Real);
121 function Log (X : Real) return Real renames EF.Log;
122
123
124 -- names used in paper
125 Radix : Integer; -- Beta
126 Mantissa_Digits : Integer; -- t
127 Rounds : Boolean; -- RND
128
129 -- made global to Determine_Attributes to help thwart optimization
130 A, B : Real := 2.0;
131 Tmp, Tmpa, Tmp1 : Real;
132 ITmp : Integer;
133 Half_Radix : Real;
134
135 -- special constants - not declared as constants so that
136 -- the "stored" precision will be used instead of a "register"
137 -- precision.
138 Zero : Real := 0.0;
139 One : Real := 1.0;
140 Two : Real := 2.0;
141
142
143 procedure Thwart_Optimization is
144 -- the purpose of this procedure is to reference the
145 -- global variables used by Determine_Attributes so
146 -- that the compiler is not likely to keep them in
147 -- a higher precision register for their entire lifetime.
148 begin
149 if Report.Ident_Bool (False) then
150 -- never executed
151 A := A + 5.0;
152 B := B + 6.0;
153 Tmp := Tmp + 1.0;
154 Tmp1 := Tmp1 + 2.0;
155 Tmpa := Tmpa + 2.0;
156 One := 12.34; Two := 56.78; Zero := 90.12;
157 end if;
158 end Thwart_Optimization;
159
160
161 -- determines values for Radix, Mantissa_Digits, and Rounds
162 -- This is mostly a straight translation of the C code.
163 -- The only significant addition is the iteration count
164 -- to prevent endless looping if things are really screwed up.
165 procedure Determine_Attributes is
166 Iterations : Integer;
167 begin
168 Rounds := True;
169
170 Iterations := 0;
171 Tmp := Real'Machine (((A + One) - A) - One);
172 while Tmp = Zero loop
173 A := Real'Machine(A + A);
174 Tmp := Real'Machine(A + One);
175 Tmp1 := Real'Machine(Tmp - A);
176 Tmp := Real'Machine(Tmp1 - One);
177
178 Iterations := Iterations + 1;
179 if Iterations > Max_Iterations then
180 raise Illegal_Optimization;
181 end if;
182 end loop;
183
184 Iterations := 0;
185 Tmp := Real'Machine(A + B);
186 ITmp := Integer (Tmp - A);
187 while ITmp = 0 loop
188 B := Real'Machine(B + B);
189 Tmp := Real'Machine(A + B);
190 ITmp := Integer (Tmp - A);
191
192 Iterations := Iterations + 1;
193 if Iterations > Max_Iterations then
194 raise Illegal_Optimization;
195 end if;
196 end loop;
197
198 Radix := ITmp;
199
200 Mantissa_Digits := 0;
201 B := 1.0;
202 Tmp := Real'Machine(((B + One) - B) - One);
203 Iterations := 0;
204 while (Tmp = Zero) loop
205 Mantissa_Digits := Mantissa_Digits + 1;
206 B := B * Real (Radix);
207 Tmp := Real'Machine(B + One);
208 Tmp1 := Real'Machine(Tmp - B);
209 Tmp := Real'Machine(Tmp1 - One);
210
211 Iterations := Iterations + 1;
212 if Iterations > Max_Iterations then
213 raise Illegal_Optimization;
214 end if;
215 end loop;
216
217 Rounds := False;
218 Half_Radix := Real (Radix) / Two;
219 Tmp := Real'Machine(A + Half_Radix);
220 Tmp1 := Real'Machine(Tmp - A);
221 if (Tmp1 /= Zero) then
222 Rounds := True;
223 end if;
224 Tmpa := Real'Machine(A + Real (Radix));
225 Tmp := Real'Machine(Tmpa + Half_Radix);
226 if not Rounds and (Tmp - TmpA /= Zero) then
227 Rounds := True;
228 if Verbose then
229 Report.Comment ("IEEE style rounding");
230 end if;
231 end if;
232
233 exception
234 when others =>
235 Thwart_Optimization;
236 raise;
237 end Determine_Attributes;
238
239
240 procedure Do_Test is
241 Show_Results : Boolean := Verbose;
242 Min_Mantissa_Digits : Integer;
243 begin
244 -- compute the actual Machine_* attribute values
245 Determine_Attributes;
246
247 if Real'Machine_Radix /= Radix then
248 Report.Failed ("'Machine_Radix incorrectly reports" &
249 Integer'Image (Real'Machine_Radix));
250 Show_Results := True;
251 end if;
252
253 if Real'Machine_Mantissa /= Mantissa_Digits then
254 Report.Failed ("'Machine_Mantissa incorrectly reports" &
255 Integer'Image (Real'Machine_Mantissa));
256 Show_Results := True;
257 end if;
258
259 if Real'Machine_Rounds /= Rounds then
260 Report.Failed ("'Machine_Rounds incorrectly reports " &
261 Boolean'Image (Real'Machine_Rounds));
262 Show_Results := True;
263 end if;
264
265 if Show_Results then
266 Report.Comment ("computed Machine_Mantissa is" &
267 Integer'Image (Mantissa_Digits));
268 Report.Comment ("computed Radix is" &
269 Integer'Image (Radix));
270 Report.Comment ("computed Rounds is " &
271 Boolean'Image (Rounds));
272 end if;
273
274 -- check the model attributes against the machine attributes
275 -- G.2.2(3)/3;6.0
276 if Real'Model_Mantissa > Real'Machine_Mantissa then
277 Report.Failed ("model mantissa > machine mantissa");
278 end if;
279
280 -- G.2.2(3)/2;6.0
281 -- 'Model_Mantissa >= ceiling(d*log(10)/log(radix))+1
282 Min_Mantissa_Digits :=
283 Integer (
284 Real'Ceiling (
285 Real(Real'Digits) * Log(10.0) / Log(Real(Real'Machine_Radix))
286 ) ) + 1;
287 if Real'Model_Mantissa < Min_Mantissa_Digits then
288 Report.Failed ("Model_Mantissa [" &
289 Integer'Image (Real'Model_Mantissa) &
290 "] < minimum mantissa digits [" &
291 Integer'Image (Min_Mantissa_Digits) &
292 "]");
293 end if;
294
295 exception
296 when Illegal_Optimization =>
297 Report.Failed ("illegal optimization of" &
298 " floating point expression");
299 end Do_Test;
300 end Chk_Attrs;
301
302 package Chk_Float is new Chk_Attrs (Float);
303
304 -- check the floating point type with the most digits
305 type A_Long_Float is digits System.Max_Digits;
306 package Chk_A_Long_Float is new Chk_Attrs (A_Long_Float);
307 begin
308 Report.Test ("CXG2001",
309 "Check the attributes Model_Mantissa," &
310 " Machine_Mantissa, Machine_Radix," &
311 " and Machine_Rounds");
312
313 Report.Comment ("checking Standard.Float");
314 Chk_Float.Do_Test;
315
316 Report.Comment ("checking a digits" &
317 Integer'Image (System.Max_Digits) &
318 " floating point type");
319 Chk_A_Long_Float.Do_Test;
320
321 Report.Result;
322 end CXG2001;