mp.h

这是一个同样来自贝尔实验室的和UNIX有着渊源的操作系统, 其简洁的设计和实现易于我们学习和理解

#define _MPINT 1

// 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*);