NAME
mpsetminbits, mpnew, mpfree, mpbits, mpnorm, mpcopy, mpassign,
mprand, strtomp, mpfmt,mptoa, betomp, mptobe, letomp, mptole,
mptoui, uitomp, mptoi, itomp, uvtomp, mptouv, vtomp, mptov, mpdigdiv,
mpadd, mpsub, mpleft, mpright, mpmul, mpexp, mpmod, mpdiv, mpcmp,
mpextendedgcd, mpinvert,
mpsignif, mplowbits0, mpvecdigmuladd, mpvecdigmulsub, mpvecadd,
mpvecsub, mpveccmp, mpvecmul, mpmagcmp, mpmagadd, mpmagsub, crtpre,
crtin, crtout, crtprefree, crtresfree – extended precision arithmetic |
SYNOPSIS
#include <u.h> #include <libc.h> #include <mp.h> mpint* mpnew(int n) void mpfree(mpint *b) void mpsetminbits(int n) void mpbits(mpint *b, int n) void mpnorm(mpint *b) mpint* mpcopy(mpint *b) void mpassign(mpint *old, mpint *new) mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b) mpint* strtomp(char *buf, char **rptr, int base, mpint *b) char* mptoa(mpint *b, int base, char *buf, int blen) int mpfmt(Fmt*) mpint* betomp(uchar *buf, uint blen, mpint *b) int mptobe(mpint *b, uchar *buf, uint blen, uchar **bufp) mpint* letomp(uchar *buf, uint blen, mpint *b) int mptole(mpint *b, uchar *buf, uint blen, uchar **bufp) uint mptoui(mpint*) mpint* uitomp(uint, mpint*) int mptoi(mpint*) mpint* itomp(int, mpint*) mpint* vtomp(vlong, mpint*) vlong mptov(mpint*) mpint* uvtomp(uvlong, mpint*) uvlong mptouv(mpint*) void mpadd(mpint *b1, mpint *b2, mpint *sum) void mpmagadd(mpint *b1, mpint *b2, mpint *sum) void mpsub(mpint *b1, mpint *b2, mpint *diff) void mpmagsub(mpint *b1, mpint *b2, mpint *diff) void mpleft(mpint *b, int shift, mpint *res) void mpright(mpint *b, int shift, mpint *res) void mpmul(mpint *b1, mpint *b2, mpint *prod) void mpexp(mpint *b, mpint *e, mpint *m, mpint *res) void mpmod(mpint *b, mpint *m, mpint *remainder)
void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient,
int mpmagcmp(mpint *b1, mpint *b2)
void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x,
int mpsignif(mpint *b) int mplowbits0(mpint *b)
void mpdigdiv(mpdigit *dividend, mpdigit divisor,
int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p)
void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen,
CRTpre* crtpre(int nfactors, mpint **factors) CRTres* crtin(CRTpre *crt, mpint *x) void crtout(CRTpre *crt, CRTres *r, mpint *x) void crtprefree(CRTpre *cre) void crtresfree(CRTres *res)
mpint *mpzero, *mpone, *mptwo |
DESCRIPTION
These routines perform extended precision integer arithmetic.
The basic type is mpint, which points to an array of mpdigits,
stored in little–endian order:
The size of mpdigit is architecture–dependent and defined in /$cputype/include/u.h. Mpints are dynamically allocated and must be explicitly freed. Operations grow the array of digits as needed. In general, the result parameters are last in the argument list. Routines that return an mpint will allocate the mpint if the result parameter is nil. This includes strtomp, itomp, uitomp, and btomp. These functions, in addition to mpnew and mpcopy, will return nil if the allocation fails. Input and result parameters may point to the same mpint. The routines check and copy where necessary. Mpnew creates an mpint with an initial allocation of n bits. If n is zero, the allocation will be whatever was specified in the last call to mpsetminbits or to the initial value, 1056. Mpfree frees an mpint. Mpbits grows the allocation of b to fit at least n bits. If b–>top doesn't cover n bits, mpbits increases it to do so. Unless you are writing new basic operations, you can restrict yourself to mpnew(0) and mpfree(b). Mpnorm normalizes the representation by trimming any high order zero digits. All routines except mpbits return normalized results. Mpcopy creates a new mpint with the same value as b while mpassign sets the value of new to be that of old. Mprand creates an n bit random number using the generator gen. Gen takes a pointer to a string of uchar's and the number to fill in. Strtomp and mptoa convert between ASCII and mpint representations using the base indicated. Only the bases 10, 16, 32, and 64 are supported. Anything else defaults to 16. Strtomp skips any leading spaces or tabs. Strtomp's scan stops when encountering a digit not valid in the base. If rptr is not zero, *rptr is set to point to the character immediately after the string converted. If the parse pterminates before any digits are found, strtomp return nil. Mptoa returns a pointer to the filled buffer. If the parameter buf is nil, the buffer is allocated. Mpfmt can be used with fmtinstall(2) and print(2) to print hexadecimal representations of mpints. The conventional verb is B, for which mp.h provides a pragma. Mptobe and mptole convert an mpint to a byte array. The former creates a big endian representation, the latter a little endian one. If the destination buf is not nil, it specifies the buffer of length blen for the result. If the representation is less than blen bytes, the rest of the buffer is zero filled. If buf is nil, then a buffer is allocated and a pointer to it is deposited in the location pointed to by bufp. Sign is ignored in these conversions, i.e., the byte array version is always positive. Betomp, and letomp convert from a big or little endian byte array at buf of length blen to an mpint. If b is not nil, it refers to a preallocated mpint for the result. If b is nil, a new integer is allocated and returned as the result.
The integer conversions are: When converting to the base integer types, if the integer is too large, the largest integer of the appropriate sign and size is returned.
The mathematical functions are: Mpextendedgcd computes the greatest common denominator, d, of a and b. It also computes x and y such that a*x + b*y = d. Both a and b are required to be positive. If called with negative arguments, it will return a gcd of 0. Mpinverse computes the multiplicative inverse of b mod m. Mpsignif returns the number of significant bits in b. Mplowbits0 returns the number of consecutive zero bits at the low end of the significant bits. For example, for 0x14, mpsignif returns 5 and mplowbits0 returns 2. For 0, mpsignif and mplowbits0 both return 0.
The remaining routines all work on arrays of mpdigit rather than
mpint's. They are the basis of all the other routines. They are
separated out to allow them to be rewritten in assembler for each
architecture. There is also a portable C version for each one.
mptwo, mpone and mpzero are the constants 2, 1 and 0. These cannot
be freed. Chinese remainder theorem When computing in a non–prime modulus, n, it is possible to perform the computations on the residues modulo the prime factors of n instead. Since these numbers are smaller, multiplication and exponentiation can be much faster.
Crtin computes the residues of x and returns them in a newly allocated
structure:
Crepre saves a copy of the factors and precomputes the constants necessary for converting the residue form back into a number modulo the product of the factors. It returns a newly allocated structure containing values.
Crtprefree and crtresfree free CRTpre and CRTres structures respectively. |
SOURCE
/sys/src/libmp |