Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Numbers/multprec_natural_numbers.ads, Revision 1.1.1.1
1.1 maekawa 1: package Multprec_Natural_Numbers is
2:
3: -- DESCRIPTION :
4: -- This package allows to manipulate natural numbers of arbitrary length.
5:
6: -- DATA STRUCTURES :
7:
8: type Array_of_Naturals is array ( natural range <> ) of natural;
9: type Natural_Number is private;
10:
11: -- CREATORS :
12:
13: function Create ( n : natural ) return Array_of_Naturals;
14:
15: -- DESCRIPTION :
16: -- Returns the representation of the natural number as coefficient vector.
17:
18: function Create ( n : natural ) return Natural_Number;
19:
20: -- DESCRIPTION :
21: -- Returns the representation of n as a natural number.
22:
23: function Create ( n : Array_of_Naturals ) return Natural_Number;
24:
25: -- DESCRIPTION :
26: -- Creates a number from the coefficients in n.
27:
28: -- REQUIRED : n'range = 0..n'last and n(i) < Base, for i in n'range.
29:
30: function Create ( n : Natural_Number ) return natural;
31:
32: -- DESCRIPTION :
33: -- Returns the representation of n as a standard natural.
34:
35: -- REQUIRED : n < Base.
36:
37: -- SELECTORS :
38:
39: function Base return natural;
40:
41: -- DESCRIPTION :
42: -- Returns the base of the number representation.
43:
44: function Exponent return natural;
45:
46: -- DESCRIPTION :
47: -- Returns the exponent: the number of decimal places in the base.
48:
49: function Empty ( n : Natural_Number ) return boolean;
50:
51: -- DESCRIPTION :
52: -- Returns true if the number has not been created yet, or when it has
53: -- been destroyed by the operation Clear; otherwise false is returned.
54: -- An empty number is considered as zero.
55:
56: function Size ( n : Natural_Number ) return natural;
57:
58: -- DESCRIPTION :
59: -- Returns the index of the last entry in the coefficient representation.
60:
61: function Decimal_Places ( n : natural ) return natural;
62:
63: -- DESCRIPTION :
64: -- Returns the number of decimal places n occupies, Decimal_Places(0) = 0.
65:
66: function Decimal_Places ( n : Natural_Number ) return natural;
67:
68: -- DESCRIPTION :
69: -- Returns the number of decimal places n occupies, Decimal_Places(0) = 0.
70: -- Since n can be arbitrarily large, also the number of return should
71: -- have no constraints on its size. However, the current implementation
72: -- would not support the manipulation of numbers whose size causes this
73: -- function to crash.
74:
75: function Coefficient ( n : Natural_Number; i : natural ) return natural;
76:
77: -- DESCRIPTION :
78: -- Returns the ith entry in the coefficient representation.
79:
80: function Coefficients ( n : Natural_Number ) return Array_of_Naturals;
81:
82: -- DESCRIPTION :
83: -- Returns the coefficient representation of n, of range 0..Size(n).
84: -- The number n equals then the sum of Coefficient(n,i)*Base**i,
85: -- for i in 0..Size(n).
86:
87: -- COMPARISON AND COPYING :
88:
89: function Equal ( n1 : Natural_Number; n2 : natural ) return boolean;
90: function Equal ( n1,n2 : Natural_Number ) return boolean;
91:
92: -- DESCRIPTION :
93: -- Returns true when both numbers n1 and n2 are equal, false otherwise.
94:
95: function "<" ( n1 : Natural_Number; n2 : natural ) return boolean;
96: function "<" ( n1 : natural; n2 : Natural_Number ) return boolean;
97: function "<" ( n1,n2 : Natural_Number ) return boolean;
98:
99: -- DESCRIPTION :
100: -- Returns true if n1 < n2, false otherwise.
101:
102: function ">" ( n1 : Natural_Number; n2 : natural ) return boolean;
103: function ">" ( n1 : natural; n2 : Natural_Number ) return boolean;
104: function ">" ( n1,n2 : Natural_Number ) return boolean;
105:
106: -- DESCRIPTION :
107: -- Returns true if n1 > n2, false otherwise.
108:
109: procedure Copy ( n1 : in natural; n2 : in out Natural_Number );
110: procedure Copy ( n1 : in Natural_Number; n2 : in out Natural_Number );
111:
112: -- DESCRIPTION :
113: -- Clears n2 and makes a copy of n1 to be equal to n2.
114: -- Note that n2 := n1 leads to data sharing.
115:
116: -- ARITHMETIC OPERATIONS as functions (no data sharing) :
117: -- Note that n1 >= n2 is required for subtraction, and n2 /= 0 for division.
118: -- The unary "-" operations have been added to make it ring-like.
119:
120: function "+" ( n1 : Natural_Number; n2 : natural ) return Natural_Number;
121: function "+" ( n1 : natural; n2 : Natural_Number ) return Natural_Number;
122: function "+" ( n1,n2 : Natural_Number ) return Natural_Number;
123:
124: function "-" ( n1 : Natural_Number; n2 : natural ) return Natural_Number;
125: function "-" ( n1 : natural; n2 : Natural_Number ) return Natural_Number;
126: function "-" ( n1,n2 : Natural_Number ) return Natural_Number;
127:
128: function "+" ( n : Natural_Number ) return Natural_Number; -- copies n
129: function "-" ( n : Natural_Number ) return Natural_Number; -- copies n
130:
131: function "*" ( n1 : Natural_Number; n2 : natural ) return Natural_Number;
132: function "*" ( n1 : natural; n2 : Natural_Number ) return Natural_Number;
133: function "*" ( n1,n2 : Natural_Number ) return Natural_Number;
134:
135: function "**" ( n1 : Natural_Number; n2 : natural ) return Natural_Number;
136: function "**" ( n1 : natural; n2 : Natural_Number ) return Natural_Number;
137: function "**" ( n1,n2 : Natural_Number ) return Natural_Number;
138:
139: function "/" ( n1 : Natural_Number; n2 : natural ) return Natural_Number;
140: function "/" ( n1 : natural; n2 : Natural_Number ) return natural;
141: function "/" ( n1,n2 : Natural_Number ) return Natural_Number;
142:
143: function Rmd ( n1 : Natural_Number; n2 : natural ) return natural;
144: function Rmd ( n1 : natural; n2 : Natural_Number ) return natural;
145: function Rmd ( n1,n2 : Natural_Number ) return Natural_Number;
146:
147: -- ARITHMETIC OPERATIONS as procedures for memory management :
148:
149: procedure Add ( n1 : in out Natural_Number; n2 : in natural ); -- "+"
150: procedure Add ( n1 : in out Natural_Number; n2 : in Natural_Number );
151:
152: procedure Sub ( n1 : in out Natural_Number; n2 : in natural ); -- "-"
153: procedure Sub ( n1 : in out Natural_Number; n2 : in Natural_Number );
154: procedure Min ( n : in out Natural_Number );
155:
156: procedure Mul ( n1 : in out Natural_Number; n2 : in natural ); -- "*"
157: procedure Mul ( n1 : in out Natural_Number; n2 : in Natural_Number );
158:
159: procedure Div ( n1 : in out Natural_Number; n2 : in natural ); -- "/"
160: procedure Div ( n1 : in out Natural_Number; n2 : in Natural_Number );
161:
162: procedure Div ( n1 : in Natural_Number; n2 : in natural; -- n1 = n2*q+r
163: q : out Natural_Number; r : out natural );
164: procedure Div ( n1 : in out Natural_Number; n2 : in natural;
165: r : out natural );
166: procedure Div ( n1,n2 : in Natural_Number; q,r : out Natural_Number );
167: procedure Div ( n1 : in out Natural_Number; n2 : in Natural_Number;
168: r : out Natural_Number );
169:
170: -- DESTRUCTOR :
171:
172: procedure Clear ( n : in out Natural_Number );
173:
174: -- DESCRIPTION :
175: -- Deallocation of the memory space. Empty(n) is true on return.
176:
177: private
178:
179: type Natural_Number_Rep;
180: type Natural_Number is access Natural_Number_Rep;
181:
182: end Multprec_Natural_Numbers;
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