1 |
149 |
jeremybenn |
-- CXG2022.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 multiplication and division of binary fixed point
|
28 |
|
|
-- numbers with compatible 'small values produce exact results.
|
29 |
|
|
--
|
30 |
|
|
-- TEST DESCRIPTION:
|
31 |
|
|
-- Signed, unsigned, and a mixture of signed and unsigned
|
32 |
|
|
-- binary fixed point values are multiplied and divided.
|
33 |
|
|
-- The result is checked against the expected "perfect result set"
|
34 |
|
|
--
|
35 |
|
|
-- SPECIAL REQUIREMENTS
|
36 |
|
|
-- The Strict Mode for the numerical accuracy must be
|
37 |
|
|
-- selected. The method by which this mode is selected
|
38 |
|
|
-- is implementation dependent.
|
39 |
|
|
--
|
40 |
|
|
-- APPLICABILITY CRITERIA:
|
41 |
|
|
-- This test applies only to implementations supporting the
|
42 |
|
|
-- Numerics Annex.
|
43 |
|
|
-- This test only applies to the Strict Mode for numerical
|
44 |
|
|
-- accuracy.
|
45 |
|
|
--
|
46 |
|
|
--
|
47 |
|
|
-- CHANGE HISTORY:
|
48 |
|
|
-- 1 Apr 96 SAIC Initial release for 2.1
|
49 |
|
|
-- 29 Jan 1998 EDS Repaired fixed point errors ("**" and
|
50 |
|
|
-- assumptions about 'Small)
|
51 |
|
|
--!
|
52 |
|
|
|
53 |
|
|
with System;
|
54 |
|
|
with Report;
|
55 |
|
|
procedure CXG2022 is
|
56 |
|
|
Verbose : constant Boolean := False;
|
57 |
|
|
|
58 |
|
|
procedure Check_Signed is
|
59 |
|
|
type Pairs is delta 2.0 range -2.0 ** (System.Max_Mantissa) ..
|
60 |
|
|
2.0 ** (System.Max_Mantissa) - 1.0;
|
61 |
|
|
type Halves is delta 0.5 range -2.0 ** (System.Max_Mantissa-2) ..
|
62 |
|
|
2.0 ** (System.Max_Mantissa-2) - 1.0;
|
63 |
|
|
P1, P2, P3, P4 : Pairs;
|
64 |
|
|
H1, H2, H3, H4 : Halves;
|
65 |
|
|
|
66 |
|
|
procedure Dont_Opt is
|
67 |
|
|
-- keep optimizer from knowing the constant value of expressions
|
68 |
|
|
begin
|
69 |
|
|
if Report.Ident_Bool (False) then
|
70 |
|
|
P1 := 2.0; P2 := 4.0; P3 := 6.0;
|
71 |
|
|
H1 := -2.0; H2 := 9.0; H3 := 3.0;
|
72 |
|
|
end if;
|
73 |
|
|
end Dont_Opt;
|
74 |
|
|
|
75 |
|
|
begin
|
76 |
|
|
H1 := -0.5;
|
77 |
|
|
H2 := Halves'First;
|
78 |
|
|
H3 := 1.0;
|
79 |
|
|
P1 := 12.0;
|
80 |
|
|
P2 := Pairs'First;
|
81 |
|
|
P3 := Pairs'Last;
|
82 |
|
|
Dont_Opt;
|
83 |
|
|
|
84 |
|
|
P4 := Pairs (P1 * H1); -- 12.0 * -0.5
|
85 |
|
|
if P4 /= -6.0 then
|
86 |
|
|
Report.Failed ("12.0 * -0.5 = " & Pairs'Image (P4));
|
87 |
|
|
end if;
|
88 |
|
|
|
89 |
|
|
H4 := Halves (P1 / H1); -- 12.0 / -0.5
|
90 |
|
|
if H4 /= -24.0 then
|
91 |
|
|
Report.Failed ("12.0 / -0.5 = " & Halves'Image (H4));
|
92 |
|
|
end if;
|
93 |
|
|
|
94 |
|
|
P4 := P3 * H3; -- Pairs'Last * 1.0
|
95 |
|
|
if P4 /= Pairs'Last then
|
96 |
|
|
Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));
|
97 |
|
|
end if;
|
98 |
|
|
|
99 |
|
|
P4 := P3 / H3; -- Pairs'Last / 1.0
|
100 |
|
|
if P4 /= Pairs'Last then
|
101 |
|
|
Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));
|
102 |
|
|
end if;
|
103 |
|
|
|
104 |
|
|
P4 := P2 * 0.25; -- Pairs'First * 0.25
|
105 |
|
|
if P4 /= Pairs (-2.0 ** (System.Max_Mantissa - 2)) then
|
106 |
|
|
Report.Failed ("Pairs'First * 0.25 = " & Pairs'Image (P4));
|
107 |
|
|
end if;
|
108 |
|
|
|
109 |
|
|
P4 := 100.5 / H1; -- 100.5 / -0.5
|
110 |
|
|
if P4 = -201.0 then
|
111 |
|
|
null; -- Perfect result
|
112 |
|
|
elsif Pairs'Small = 2.0 and ( P4 = -200.0 or P4 = -202.0 ) then
|
113 |
|
|
null; -- Allowed variation
|
114 |
|
|
else
|
115 |
|
|
Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &
|
116 |
|
|
" and 100.5/-0.5 = " & Pairs'Image (P4) );
|
117 |
|
|
end if;
|
118 |
|
|
|
119 |
|
|
H4 := H1 * H2; -- -0.5 * Halves'First
|
120 |
|
|
if H4 /= Halves (2.0 ** (System.Max_Mantissa-3)) then
|
121 |
|
|
Report.Failed ("-0.5 * Halves'First =" & Halves'Image (H4) &
|
122 |
|
|
" instead of " &
|
123 |
|
|
Halves'Image( Halves(2.0 ** (System.Max_Mantissa-3))));
|
124 |
|
|
end if;
|
125 |
|
|
|
126 |
|
|
exception
|
127 |
|
|
when others =>
|
128 |
|
|
Report.Failed ("unexpected exception in Check_Signed");
|
129 |
|
|
end Check_Signed;
|
130 |
|
|
|
131 |
|
|
|
132 |
|
|
|
133 |
|
|
procedure Check_Unsigned is
|
134 |
|
|
type Pairs is delta 2.0 range 0.0 .. 2.0 ** (System.Max_Mantissa+1) - 1.0;
|
135 |
|
|
type Halves is delta 0.5 range 0.0 .. 2.0 ** (System.Max_Mantissa-1) - 1.0;
|
136 |
|
|
P1, P2, P3, P4 : Pairs;
|
137 |
|
|
H1, H2, H3, H4 : Halves;
|
138 |
|
|
|
139 |
|
|
procedure Dont_Opt is
|
140 |
|
|
-- keep optimizer from knowing the constant value of expressions
|
141 |
|
|
begin
|
142 |
|
|
if Report.Ident_Bool (False) then
|
143 |
|
|
P1 := 2.0; P2 := 4.0; P3 := 6.0;
|
144 |
|
|
H1 := 2.0; H2 := 9.0; H3 := 3.0;
|
145 |
|
|
end if;
|
146 |
|
|
end Dont_Opt;
|
147 |
|
|
|
148 |
|
|
begin
|
149 |
|
|
H1 := 10.5;
|
150 |
|
|
H2 := Halves(2.0 ** (System.Max_Mantissa - 6));
|
151 |
|
|
H3 := 1.0;
|
152 |
|
|
P1 := 12.0;
|
153 |
|
|
P2 := Pairs'Last / 2;
|
154 |
|
|
P3 := Pairs'Last;
|
155 |
|
|
Dont_Opt;
|
156 |
|
|
|
157 |
|
|
P4 := Pairs (P1 * H1); -- 12.0 * 10.5
|
158 |
|
|
if P4 /= 126.0 then
|
159 |
|
|
Report.Failed ("12.0 * 10.5 = " & Pairs'Image (P4));
|
160 |
|
|
end if;
|
161 |
|
|
|
162 |
|
|
H4 := Halves (P1 / H1); -- 12.0 / 10.5
|
163 |
|
|
if H4 /= 1.0 and H4 /= 1.5 then
|
164 |
|
|
Report.Failed ("12.0 / 10.5 = " & Halves'Image (H4));
|
165 |
|
|
end if;
|
166 |
|
|
|
167 |
|
|
P4 := P3 * H3; -- Pairs'Last * 1.0
|
168 |
|
|
if P4 /= Pairs'Last then
|
169 |
|
|
Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));
|
170 |
|
|
end if;
|
171 |
|
|
|
172 |
|
|
P4 := P3 / H3; -- Pairs'Last / 1.0
|
173 |
|
|
if P4 /= Pairs'Last then
|
174 |
|
|
Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));
|
175 |
|
|
end if;
|
176 |
|
|
|
177 |
|
|
P4 := P1 * 0.25; -- 12.0 * 0.25
|
178 |
|
|
if P4 /= 2.0 and P4 /= 4.0 then
|
179 |
|
|
Report.Failed ("12.0 * 0.25 = " & Pairs'Image (P4));
|
180 |
|
|
end if;
|
181 |
|
|
|
182 |
|
|
P4 := 100.5 / H1; -- 100.5 / 10.5 = 9.571...
|
183 |
|
|
if P4 /= 8.0 and P4 /= 10.0 then
|
184 |
|
|
Report.Failed ("100.5/10.5 = " & Pairs'Image (P4));
|
185 |
|
|
end if;
|
186 |
|
|
|
187 |
|
|
H4 := H2 * 2; -- 2**(max_mantissa-6) * 2
|
188 |
|
|
if H4 /= Halves(2.0 ** (System.Max_Mantissa-5)) then
|
189 |
|
|
Report.Failed ("2**(System.Max_Mantissa-6) * 2=" & Halves'Image (H4) &
|
190 |
|
|
" instead of " &
|
191 |
|
|
Halves'Image( Halves(2.0 ** (System.Max_Mantissa-5))));
|
192 |
|
|
end if;
|
193 |
|
|
|
194 |
|
|
exception
|
195 |
|
|
when others =>
|
196 |
|
|
Report.Failed ("unexpected exception in Check_Unsigned");
|
197 |
|
|
end Check_Unsigned;
|
198 |
|
|
|
199 |
|
|
|
200 |
|
|
|
201 |
|
|
procedure Check_Mixed is
|
202 |
|
|
type Pairs is delta 2.0 range -2.0 ** (System.Max_Mantissa) ..
|
203 |
|
|
2.0 ** (System.Max_Mantissa) - 1.0;
|
204 |
|
|
type Halves is delta 0.5 range 0.0 .. 2.0 ** (System.Max_Mantissa-1) - 1.0;
|
205 |
|
|
P1, P2, P3, P4 : Pairs;
|
206 |
|
|
H1, H2, H3, H4 : Halves;
|
207 |
|
|
|
208 |
|
|
procedure Dont_Opt is
|
209 |
|
|
-- keep optimizer from knowing the constant value of expressions
|
210 |
|
|
begin
|
211 |
|
|
if Report.Ident_Bool (False) then
|
212 |
|
|
P1 := 2.0; P2 := 4.0; P3 := 6.0;
|
213 |
|
|
H1 := 2.0; H2 := 9.0; H3 := 3.0;
|
214 |
|
|
end if;
|
215 |
|
|
end Dont_Opt;
|
216 |
|
|
|
217 |
|
|
begin
|
218 |
|
|
H1 := 10.5;
|
219 |
|
|
H2 := Halves(2.0 ** (System.Max_Mantissa - 6));
|
220 |
|
|
H3 := 1.0;
|
221 |
|
|
P1 := 12.0;
|
222 |
|
|
P2 := -4.0;
|
223 |
|
|
P3 := Pairs'Last;
|
224 |
|
|
Dont_Opt;
|
225 |
|
|
|
226 |
|
|
P4 := Pairs (P1 * H1); -- 12.0 * 10.5
|
227 |
|
|
if P4 /= 126.0 then
|
228 |
|
|
Report.Failed ("12.0 * 10.5 = " & Pairs'Image (P4));
|
229 |
|
|
end if;
|
230 |
|
|
|
231 |
|
|
H4 := Halves (P1 / H1); -- 12.0 / 10.5
|
232 |
|
|
if H4 /= 1.0 and H4 /= 1.5 then
|
233 |
|
|
Report.Failed ("12.0 / 10.5 = " & Halves'Image (H4));
|
234 |
|
|
end if;
|
235 |
|
|
|
236 |
|
|
P4 := P3 * H3; -- Pairs'Last * 1.0
|
237 |
|
|
if P4 /= Pairs'Last then
|
238 |
|
|
Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));
|
239 |
|
|
end if;
|
240 |
|
|
|
241 |
|
|
P4 := P3 / H3; -- Pairs'Last / 1.0
|
242 |
|
|
if P4 /= Pairs'Last then
|
243 |
|
|
Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));
|
244 |
|
|
end if;
|
245 |
|
|
|
246 |
|
|
P4 := P1 * 0.25; -- 12.0 * 0.25
|
247 |
|
|
if P4 = 3.0 then
|
248 |
|
|
null; -- Perfect result
|
249 |
|
|
elsif Pairs'Small = 2.0 and then ( P4 = 2.0 or P4 = 4.0 ) then
|
250 |
|
|
null; -- Allowed deviation
|
251 |
|
|
else
|
252 |
|
|
Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &
|
253 |
|
|
"and 12.0 * 0.25 = " & Pairs'Image (P4) );
|
254 |
|
|
end if;
|
255 |
|
|
|
256 |
|
|
P4 := 100.5 / H1; -- 100.5 / 10.5 = 9.571...
|
257 |
|
|
if P4 = 9.0 then
|
258 |
|
|
null; -- Perfect result
|
259 |
|
|
elsif Pairs'Small = 2.0 and then ( P4 = 8.0 or P4 = 10.0 ) then
|
260 |
|
|
null; -- Allowed values
|
261 |
|
|
else
|
262 |
|
|
Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &
|
263 |
|
|
"and 100.5/10.5 = " & Pairs'Image (P4) );
|
264 |
|
|
end if;
|
265 |
|
|
|
266 |
|
|
H4 := H2 * 2; -- 2**(max_mantissa-6) * 2
|
267 |
|
|
if H4 /= Halves(2.0 ** (System.Max_Mantissa-5)) then
|
268 |
|
|
Report.Failed ("2**(System.Max_Mantissa-6) * 2=" & Halves'Image (H4) &
|
269 |
|
|
" instead of " &
|
270 |
|
|
Halves'Image( Halves(2.0 ** (System.Max_Mantissa-5))));
|
271 |
|
|
end if;
|
272 |
|
|
|
273 |
|
|
P4 := Pairs(P1 * 6) / P2; -- 12 * 6 / -4
|
274 |
|
|
if (P4 /= -18.0) then
|
275 |
|
|
Report.Failed ("12*6/-4 = " & Pairs'Image(P4));
|
276 |
|
|
end if;
|
277 |
|
|
|
278 |
|
|
P4 := Halves(P1 * 6.0) / P2; -- 12 * 6 / -4
|
279 |
|
|
if (P4 /= -18.0) then
|
280 |
|
|
Report.Failed ("Halves(12*6)/-4 = " & Pairs'Image(P4));
|
281 |
|
|
end if;
|
282 |
|
|
|
283 |
|
|
exception
|
284 |
|
|
when others =>
|
285 |
|
|
Report.Failed ("unexpected exception in Check_Mixed");
|
286 |
|
|
end Check_Mixed;
|
287 |
|
|
|
288 |
|
|
|
289 |
|
|
begin -- main
|
290 |
|
|
Report.Test ("CXG2022",
|
291 |
|
|
"Check the accuracy of multiplication and division" &
|
292 |
|
|
" of binary fixed point numbers");
|
293 |
|
|
if Verbose then
|
294 |
|
|
Report.Comment ("starting signed test");
|
295 |
|
|
end if;
|
296 |
|
|
Check_Signed;
|
297 |
|
|
|
298 |
|
|
if Verbose then
|
299 |
|
|
Report.Comment ("starting unsigned test");
|
300 |
|
|
end if;
|
301 |
|
|
Check_Unsigned;
|
302 |
|
|
|
303 |
|
|
if Verbose then
|
304 |
|
|
Report.Comment ("starting mixed sign test");
|
305 |
|
|
end if;
|
306 |
|
|
Check_Mixed;
|
307 |
|
|
|
308 |
|
|
Report.Result;
|
309 |
|
|
end CXG2022;
|