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gcc 7
author kono
date Fri, 27 Oct 2017 22:46:09 +0900
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68:561a7518be6b 111:04ced10e8804
1 ------------------------------------------------------------------------------
2 -- --
3 -- GNAT RUN-TIME COMPONENTS --
4 -- --
5 -- ADA.NUMERICS.GENERIC_ELEMENTARY_FUNCTIONS --
6 -- --
7 -- S p e c --
8 -- --
9 -- Copyright (C) 2012-2017, Free Software Foundation, Inc. --
10 -- --
11 -- This specification is derived from the Ada Reference Manual for use with --
12 -- GNAT. The copyright notice above, and the license provisions that follow --
13 -- apply solely to the Post aspects that have been added to the spec. --
14 -- --
15 -- GNAT is free software; you can redistribute it and/or modify it under --
16 -- terms of the GNU General Public License as published by the Free Soft- --
17 -- ware Foundation; either version 3, or (at your option) any later ver- --
18 -- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
19 -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
20 -- or FITNESS FOR A PARTICULAR PURPOSE. --
21 -- --
22 -- As a special exception under Section 7 of GPL version 3, you are granted --
23 -- additional permissions described in the GCC Runtime Library Exception, --
24 -- version 3.1, as published by the Free Software Foundation. --
25 -- --
26 -- You should have received a copy of the GNU General Public License and --
27 -- a copy of the GCC Runtime Library Exception along with this program; --
28 -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
29 -- <http://www.gnu.org/licenses/>. --
30 -- --
31 -- GNAT was originally developed by the GNAT team at New York University. --
32 -- Extensive contributions were provided by Ada Core Technologies Inc. --
33 -- --
34 ------------------------------------------------------------------------------
35
36 generic
37 type Float_Type is digits <>;
38
39 package Ada.Numerics.Generic_Elementary_Functions with
40 SPARK_Mode => On
41 is
42 pragma Pure;
43
44 -- Preconditions in this unit are meant for analysis only, not for run-time
45 -- checking, so that the expected exceptions are raised when calling
46 -- Assert. This is enforced by setting the corresponding assertion policy
47 -- to Ignore. This is done in the generic spec so that it applies to all
48 -- instances.
49
50 pragma Assertion_Policy (Pre => Ignore);
51
52 function Sqrt (X : Float_Type'Base) return Float_Type'Base with
53 Pre => X >= 0.0,
54 Post => Sqrt'Result >= 0.0
55 and then (if X = 0.0 then Sqrt'Result = 0.0)
56 and then (if X = 1.0 then Sqrt'Result = 1.0)
57
58 -- Finally if X is positive, the result of Sqrt is positive (because
59 -- the sqrt of numbers greater than 1 is greater than or equal to 1,
60 -- and the sqrt of numbers less than 1 is greater than the argument).
61
62 -- This property is useful in particular for static analysis. The
63 -- property that X is positive is not expressed as (X > 0.0), as
64 -- the value X may be held in registers that have larger range and
65 -- precision on some architecture (for example, on x86 using x387
66 -- FPU, as opposed to SSE2). So, it might be possible for X to be
67 -- 2.0**(-5000) or so, which could cause the number to compare as
68 -- greater than 0, but Sqrt would still return a zero result.
69
70 -- Note: we use the comparison with Succ (0.0) here because this is
71 -- more amenable to CodePeer analysis than the use of 'Machine.
72
73 and then (if X >= Float_Type'Succ (0.0) then Sqrt'Result > 0.0);
74
75 function Log (X : Float_Type'Base) return Float_Type'Base with
76 Pre => X > 0.0,
77 Post => (if X = 1.0 then Log'Result = 0.0);
78
79 function Log (X, Base : Float_Type'Base) return Float_Type'Base with
80 Pre => X > 0.0 and Base > 0.0 and Base /= 1.0,
81 Post => (if X = 1.0 then Log'Result = 0.0);
82
83 function Exp (X : Float_Type'Base) return Float_Type'Base with
84 Post => (if X = 0.0 then Exp'Result = 1.0);
85
86 function "**" (Left, Right : Float_Type'Base) return Float_Type'Base with
87 Pre => (if Left = 0.0 then Right > 0.0) and Left >= 0.0,
88 Post => "**"'Result >= 0.0
89 and then (if Right = 0.0 then "**"'Result = 1.0)
90 and then (if Right = 1.0 then "**"'Result = Left)
91 and then (if Left = 1.0 then "**"'Result = 1.0)
92 and then (if Left = 0.0 then "**"'Result = 0.0);
93
94 function Sin (X : Float_Type'Base) return Float_Type'Base with
95 Post => Sin'Result in -1.0 .. 1.0
96 and then (if X = 0.0 then Sin'Result = 0.0);
97
98 function Sin (X, Cycle : Float_Type'Base) return Float_Type'Base with
99 Pre => Cycle > 0.0,
100 Post => Sin'Result in -1.0 .. 1.0
101 and then (if X = 0.0 then Sin'Result = 0.0);
102
103 function Cos (X : Float_Type'Base) return Float_Type'Base with
104 Post => Cos'Result in -1.0 .. 1.0
105 and then (if X = 0.0 then Cos'Result = 1.0);
106
107 function Cos (X, Cycle : Float_Type'Base) return Float_Type'Base with
108 Pre => Cycle > 0.0,
109 Post => Cos'Result in -1.0 .. 1.0
110 and then (if X = 0.0 then Cos'Result = 1.0);
111
112 function Tan (X : Float_Type'Base) return Float_Type'Base with
113 Post => (if X = 0.0 then Tan'Result = 0.0);
114
115 function Tan (X, Cycle : Float_Type'Base) return Float_Type'Base with
116 Pre => Cycle > 0.0
117 and then abs Float_Type'Base'Remainder (X, Cycle) /= 0.25 * Cycle,
118 Post => (if X = 0.0 then Tan'Result = 0.0);
119
120 function Cot (X : Float_Type'Base) return Float_Type'Base with
121 Pre => X /= 0.0;
122
123 function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base with
124 Pre => Cycle > 0.0
125 and then X /= 0.0
126 and then Float_Type'Base'Remainder (X, Cycle) /= 0.0
127 and then abs Float_Type'Base'Remainder (X, Cycle) = 0.5 * Cycle;
128
129 function Arcsin (X : Float_Type'Base) return Float_Type'Base with
130 Pre => abs X <= 1.0,
131 Post => (if X = 0.0 then Arcsin'Result = 0.0);
132
133 function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base with
134 Pre => Cycle > 0.0 and abs X <= 1.0,
135 Post => (if X = 0.0 then Arcsin'Result = 0.0);
136
137 function Arccos (X : Float_Type'Base) return Float_Type'Base with
138 Pre => abs X <= 1.0,
139 Post => (if X = 1.0 then Arccos'Result = 0.0);
140
141 function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base with
142 Pre => Cycle > 0.0 and abs X <= 1.0,
143 Post => (if X = 1.0 then Arccos'Result = 0.0);
144
145 function Arctan
146 (Y : Float_Type'Base;
147 X : Float_Type'Base := 1.0) return Float_Type'Base
148 with
149 Pre => X /= 0.0 or Y /= 0.0,
150 Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
151
152 function Arctan
153 (Y : Float_Type'Base;
154 X : Float_Type'Base := 1.0;
155 Cycle : Float_Type'Base) return Float_Type'Base
156 with
157 Pre => Cycle > 0.0 and (X /= 0.0 or Y /= 0.0),
158 Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
159
160 function Arccot
161 (X : Float_Type'Base;
162 Y : Float_Type'Base := 1.0) return Float_Type'Base
163 with
164 Pre => X /= 0.0 or Y /= 0.0,
165 Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
166
167 function Arccot
168 (X : Float_Type'Base;
169 Y : Float_Type'Base := 1.0;
170 Cycle : Float_Type'Base) return Float_Type'Base
171 with
172 Pre => Cycle > 0.0 and (X /= 0.0 or Y /= 0.0),
173 Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
174
175 function Sinh (X : Float_Type'Base) return Float_Type'Base with
176 Post => (if X = 0.0 then Sinh'Result = 0.0);
177
178 function Cosh (X : Float_Type'Base) return Float_Type'Base with
179 Post => Cosh'Result >= 1.0
180 and then (if X = 0.0 then Cosh'Result = 1.0);
181
182 function Tanh (X : Float_Type'Base) return Float_Type'Base with
183 Post => Tanh'Result in -1.0 .. 1.0
184 and then (if X = 0.0 then Tanh'Result = 0.0);
185
186 function Coth (X : Float_Type'Base) return Float_Type'Base with
187 Pre => X /= 0.0,
188 Post => abs Coth'Result >= 1.0;
189
190 function Arcsinh (X : Float_Type'Base) return Float_Type'Base with
191 Post => (if X = 0.0 then Arcsinh'Result = 0.0);
192
193 function Arccosh (X : Float_Type'Base) return Float_Type'Base with
194 Pre => X >= 1.0,
195 Post => Arccosh'Result >= 0.0
196 and then (if X = 1.0 then Arccosh'Result = 0.0);
197
198 function Arctanh (X : Float_Type'Base) return Float_Type'Base with
199 Pre => abs X /= 1.0,
200 Post => (if X = 0.0 then Arctanh'Result = 0.0);
201
202 function Arccoth (X : Float_Type'Base) return Float_Type'Base with
203 Pre => X <= 1.0 and abs X /= 1.0;
204
205 end Ada.Numerics.Generic_Elementary_Functions;