1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
|
(************************************************************************)
(* This file is part of SKS. SKS is free software; you can
redistribute it and/or modify it under the terms of the GNU General
Public License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
USA *)
(***********************************************************************)
(** Field of integers mod p (for a settable prime p) *)
open StdLabels
open MoreLabels
module Unix=UnixLabels
open Printf
open Number2
open Big_int
type t = big_int
type tref = big_int ref
type zzarray = big_int array
let order = ref two
let nbits = ref 0
let nbytes = ref 0
let rec num_bits x =
if x =! zero then 0
else 1 + num_bits (x /! two)
let set_order value =
order := value;
nbits := num_bits !order;
nbytes := !nbits / 8 + (if !nbits mod 8 = 0 then 0 else 1)
let modulo = mod_big_int
let num_bytes () = !nbytes
let of_bytes bytes = bigint_of_bytes bytes
let to_bytes n = bigint_to_bytes ~nbytes:!nbytes (modulo n !order)
let of_int i = modulo (big_int_of_int i) !order
let to_N x = x
let of_N x = modulo x !order
let add x y = modulo (x +! y) !order
let mul x y = modulo (x *! y) !order
let mult x y = modulo (x *! y) !order
let imult x y = modulo (mult_int_big_int x y) !order
let add_fast x y = (x +! y)
let mul_fast x y = (x *! y)
let mult_fast x y = (x *! y)
let canonicalize x = modulo x !order
let shl x i =
x *! power_int_positive_int 2 i
let square x = modulo (x *! x) !order
let square_fast x = x *! x
let imul x y = modulo (mult_big_int y x) !order
let neg x = !order -! x
let inv x =
if x = zero then raise (Invalid_argument "ZZp.inv: Attempt to invert 0");
let u = gcd_big_int x !order in
modulo u !order
let div x y = modulo (x *! (inv y)) !order
let sub_fast x y = x -! y
let sub x y = modulo (x -! y) !order
let lt = lt_big_int
let gt = gt_big_int
let eq = eq_big_int
let neq x y = not (eq_big_int x y)
let to_string x = string_of_big_int x
let print x = print_string (to_string x)
let points n =
Array.init n
~f:(fun i ->
let ival = ((i + 1) / 2) * (if i mod 2 = 0 then 1 else (-1)) in
big_int_of_int ival)
let svalues n =
Array.init n ~f:(fun i -> one)
(* In-place operations. Since we're using Big_int, there are no in-place operations,
so we just fake it. *)
let mult_in v x y =
v := mult x y
let mult_fast_in v x y =
v := mult_fast x y
let add_in v x y =
v := add x y
let add_fast_in v x y =
v := add_fast x y
let sub_in v x y =
v := sub x y
let sub_fast_in v x y =
v := x -! y
let copy_in v x = v := x
let copy_out v = !v
let make_ref x = ref x
let look = copy_out
let canonicalize_in v = v := modulo !v !order
(* Array-wise functions for adding elements to svalues *)
let add_el_array ~points el =
Array.init (Array.length points)
~f:( fun i ->
let rval = modulo (points.(i) -! el) !order in
if eq rval zero
then failwith "Sample point added to set"
else rval )
let del_el_array ~points el =
Array.map ~f:inv (add_el_array ~points el)
let mult_array ~svalues array =
if Array.length svalues <> Array.length array
then raise (Invalid_argument "ZZp.add_el: array lengths don't match");
for i = 0 to Array.length array - 1 do
svalues.(i) <- mult svalues.(i) array.(i)
done
(** Element-based functions for adding elements to svalues *)
let add_el ~svalues ~points el =
if Array.length svalues <> Array.length points
then raise (Invalid_argument "ZZp.add_el: array lengths don't match");
for i = 0 to Array.length points - 1 do
svalues.(i) <- mult svalues.(i) (points.(i) -! el)
done
(* needs checking *)
let del_el ~svalues ~points el =
if Array.length svalues <> Array.length points
then raise (Invalid_argument "ZZp.del_el: array lengths don't match");
for i = 0 to Array.length points - 1 do
svalues.(i) <- div svalues.(i) (points.(i) -! el)
done
let array_mult x y =
let len = Array.length x in
Array.init len ~f:(fun i -> mult x.(i) y.(i))
let zzarray_div x y =
Array.init (Array.length x) ~f:(fun i -> x.(i) /! y.(i))
let zzarray_copy ar = Array.copy ar
let cmp = compare_big_int
let length array = Array.length array
let zzarray_to_array array = Array.copy array
let zzarray_of_array array = Array.copy array
let to_string_array x =
Array.init 1 ~f:(fun i -> to_bytes x)
|