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
|
#ifndef __MP_H__
#define __MP_H__ 1
#ifdef __cplusplus
extern "C" {
#endif
/*
#pragma src "/sys/src/libmp"
#pragma lib "libmp.a"
*/
#define _MPINT 1
typedef long mpdigit;
// the code assumes mpdigit to be at least an int
// mpdigit must be an atomic type. mpdigit is defined
// in the architecture specific u.h
typedef struct mpint mpint;
struct mpint
{
int sign; // +1 or -1
int size; // allocated digits
int top; // significant digits
mpdigit *p;
char flags;
};
enum
{
MPstatic= 0x01,
Dbytes= sizeof(mpdigit), // bytes per digit
Dbits= Dbytes*8 // bits per digit
};
// allocation
void mpsetminbits(int n); // newly created mpint's get at least n bits
mpint* mpnew(int n); // create a new mpint with at least n bits
void mpfree(mpint *b);
void mpbits(mpint *b, int n); // ensure that b has at least n bits
void mpnorm(mpint *b); // dump leading zeros
mpint* mpcopy(mpint *b);
void mpassign(mpint *old, mpint *new);
// random bits
mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b);
// conversion
mpint* strtomp(char*, char**, int, mpint*); // ascii
int mpfmt(Fmt*);
char* mptoa(mpint*, int, char*, int);
mpint* letomp(uchar*, uint, mpint*); // byte array, little-endian
int mptole(mpint*, uchar*, uint, uchar**);
mpint* betomp(uchar*, uint, mpint*); // byte array, little-endian
int mptobe(mpint*, uchar*, uint, uchar**);
uint mptoui(mpint*); // unsigned int
mpint* uitomp(uint, mpint*);
int mptoi(mpint*); // int
mpint* itomp(int, mpint*);
uvlong mptouv(mpint*); // unsigned vlong
mpint* uvtomp(uvlong, mpint*);
vlong mptov(mpint*); // vlong
mpint* vtomp(vlong, mpint*);
// divide 2 digits by one
void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
// in the following, the result mpint may be
// the same as one of the inputs.
void mpadd(mpint *b1, mpint *b2, mpint *sum); // sum = b1+b2
void mpsub(mpint *b1, mpint *b2, mpint *diff); // diff = b1-b2
void mpleft(mpint *b, int shift, mpint *res); // res = b<<shift
void mpright(mpint *b, int shift, mpint *res); // res = b>>shift
void mpmul(mpint *b1, mpint *b2, mpint *prod); // prod = b1*b2
void mpexp(mpint *b, mpint *e, mpint *m, mpint *res); // res = b**e mod m
void mpmod(mpint *b, mpint *m, mpint *remainder); // remainder = b mod m
// quotient = dividend/divisor, remainder = dividend % divisor
void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder);
// return neg, 0, pos as b1-b2 is neg, 0, pos
int mpcmp(mpint *b1, mpint *b2);
// extended gcd return d, x, and y, s.t. d = gcd(a,b) and ax+by = d
void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y);
// res = b**-1 mod m
void mpinvert(mpint *b, mpint *m, mpint *res);
// bit counting
int mpsignif(mpint*); // number of sigificant bits in mantissa
int mplowbits0(mpint*); // k, where n = 2**k * q for odd q
// well known constants
extern mpint *mpzero, *mpone, *mptwo;
// sum[0:alen] = a[0:alen-1] + b[0:blen-1]
// prereq: alen >= blen, sum has room for alen+1 digits
void mpvecadd(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *sum);
// diff[0:alen-1] = a[0:alen-1] - b[0:blen-1]
// prereq: alen >= blen, diff has room for alen digits
void mpvecsub(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *diff);
// p[0:n] += m * b[0:n-1]
// prereq: p has room for n+1 digits
void mpvecdigmuladd(mpdigit *b, int n, mpdigit m, mpdigit *p);
// p[0:n] -= m * b[0:n-1]
// prereq: p has room for n+1 digits
int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p);
// p[0:alen*blen-1] = a[0:alen-1] * b[0:blen-1]
// prereq: alen >= blen, p has room for m*n digits
void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
// sign of a - b or zero if the same
int mpveccmp(mpdigit *a, int alen, mpdigit *b, int blen);
// divide the 2 digit dividend by the one digit divisor and stick in quotient
// we assume that the result is one digit - overflow is all 1's
void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
// playing with magnitudes
int mpmagcmp(mpint *b1, mpint *b2);
void mpmagadd(mpint *b1, mpint *b2, mpint *sum); // sum = b1+b2
void mpmagsub(mpint *b1, mpint *b2, mpint *sum); // sum = b1+b2
// chinese remainder theorem
typedef struct CRTpre CRTpre; // precomputed values for converting
// twixt residues and mpint
typedef struct CRTres CRTres; // residue form of an mpint
struct CRTres
{
int n; // number of residues
mpint *r[1]; // residues
};
CRTpre* crtpre(int, mpint**); // precompute conversion values
CRTres* crtin(CRTpre*, mpint*); // convert mpint to residues
void crtout(CRTpre*, CRTres*, mpint*); // convert residues to mpint
void crtprefree(CRTpre*);
void crtresfree(CRTres*);
/* #pragma varargck type "B" mpint* */
#ifdef __cplusplus
}
#endif
#endif
|