efd3ac8a23
instead of testing for special field primes each time in mpmod(), make it explicit with a mpfiled() function that tests a modulus N to be of some special form that can be reduced more efficiently with some precalculation, and replaces N with a Mfield* when it can. the Mfield*'s are recognized by mpmod() as they have the MPfield flag set and provide a function pointer that executes the fast reduction.
182 lines
6.1 KiB
C
182 lines
6.1 KiB
C
#pragma src "/sys/src/libmp"
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#pragma lib "libmp.a"
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#define _MPINT 1
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/*
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* the code assumes mpdigit to be at least an int
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* mpdigit must be an atomic type. mpdigit is defined
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* in the architecture specific u.h
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*/
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typedef struct mpint mpint;
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struct mpint
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{
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int sign; /* +1 or -1 */
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int size; /* allocated digits */
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int top; /* significant digits */
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mpdigit *p;
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char flags;
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};
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enum
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{
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MPstatic= 0x01, /* static constant */
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MPnorm= 0x02, /* normalization status */
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MPtimesafe= 0x04, /* request time invariant computation */
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MPfield= 0x08, /* this mpint is a field modulus */
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Dbytes= sizeof(mpdigit), /* bytes per digit */
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Dbits= Dbytes*8 /* bits per digit */
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};
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/* allocation */
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void mpsetminbits(int n); /* newly created mpint's get at least n bits */
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mpint* mpnew(int n); /* create a new mpint with at least n bits */
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void mpfree(mpint *b);
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void mpbits(mpint *b, int n); /* ensure that b has at least n bits */
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mpint* mpnorm(mpint *b); /* dump leading zeros */
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mpint* mpcopy(mpint *b);
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void mpassign(mpint *old, mpint *new);
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/* random bits */
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mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b);
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/* return uniform random [0..n-1] */
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mpint* mpnrand(mpint *n, void (*gen)(uchar*, int), mpint *b);
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/* conversion */
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mpint* strtomp(char*, char**, int, mpint*); /* ascii */
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int mpfmt(Fmt*);
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char* mptoa(mpint*, int, char*, int);
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mpint* letomp(uchar*, uint, mpint*); /* byte array, little-endian */
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int mptole(mpint*, uchar*, uint, uchar**);
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void mptolel(mpint *b, uchar *p, int n);
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mpint* betomp(uchar*, uint, mpint*); /* byte array, big-endian */
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int mptobe(mpint*, uchar*, uint, uchar**);
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void mptober(mpint *b, uchar *p, int n);
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uint mptoui(mpint*); /* unsigned int */
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mpint* uitomp(uint, mpint*);
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int mptoi(mpint*); /* int */
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mpint* itomp(int, mpint*);
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uvlong mptouv(mpint*); /* unsigned vlong */
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mpint* uvtomp(uvlong, mpint*);
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vlong mptov(mpint*); /* vlong */
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mpint* vtomp(vlong, mpint*);
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/* divide 2 digits by one */
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void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
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/* in the following, the result mpint may be */
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/* the same as one of the inputs. */
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void mpadd(mpint *b1, mpint *b2, mpint *sum); /* sum = b1+b2 */
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void mpsub(mpint *b1, mpint *b2, mpint *diff); /* diff = b1-b2 */
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void mpleft(mpint *b, int shift, mpint *res); /* res = b<<shift */
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void mpright(mpint *b, int shift, mpint *res); /* res = b>>shift */
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void mpmul(mpint *b1, mpint *b2, mpint *prod); /* prod = b1*b2 */
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void mpexp(mpint *b, mpint *e, mpint *m, mpint *res); /* res = b**e mod m */
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void mpmod(mpint *b, mpint *m, mpint *remainder); /* remainder = b mod m */
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/* logical operations */
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void mpand(mpint *b1, mpint *b2, mpint *res);
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void mpbic(mpint *b1, mpint *b2, mpint *res);
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void mpor(mpint *b1, mpint *b2, mpint *res);
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void mpnot(mpint *b, mpint *res);
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void mpxor(mpint *b1, mpint *b2, mpint *res);
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void mptrunc(mpint *b, int n, mpint *res);
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void mpxtend(mpint *b, int n, mpint *res);
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/* modular arithmetic, time invariant when 0≤b1≤m-1 and 0≤b2≤m-1 */
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void mpmodadd(mpint *b1, mpint *b2, mpint *m, mpint *sum); /* sum = b1+b2 % m */
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void mpmodsub(mpint *b1, mpint *b2, mpint *m, mpint *diff); /* diff = b1-b2 % m */
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void mpmodmul(mpint *b1, mpint *b2, mpint *m, mpint *prod); /* prod = b1*b2 % m */
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/* quotient = dividend/divisor, remainder = dividend % divisor */
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void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder);
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/* return neg, 0, pos as b1-b2 is neg, 0, pos */
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int mpcmp(mpint *b1, mpint *b2);
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/* res = s != 0 ? b1 : b2 */
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void mpsel(int s, mpint *b1, mpint *b2, mpint *res);
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/* extended gcd return d, x, and y, s.t. d = gcd(a,b) and ax+by = d */
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void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y);
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/* res = b**-1 mod m */
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void mpinvert(mpint *b, mpint *m, mpint *res);
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/* bit counting */
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int mpsignif(mpint*); /* number of sigificant bits in mantissa */
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int mplowbits0(mpint*); /* k, where n = 2**k * q for odd q */
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/* well known constants */
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extern mpint *mpzero, *mpone, *mptwo;
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/* sum[0:alen] = a[0:alen-1] + b[0:blen-1] */
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/* prereq: alen >= blen, sum has room for alen+1 digits */
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void mpvecadd(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *sum);
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/* diff[0:alen-1] = a[0:alen-1] - b[0:blen-1] */
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/* prereq: alen >= blen, diff has room for alen digits */
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void mpvecsub(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *diff);
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/* p[0:n] += m * b[0:n-1] */
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/* prereq: p has room for n+1 digits */
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void mpvecdigmuladd(mpdigit *b, int n, mpdigit m, mpdigit *p);
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/* p[0:n] -= m * b[0:n-1] */
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/* prereq: p has room for n+1 digits */
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int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p);
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/* p[0:alen+blen-1] = a[0:alen-1] * b[0:blen-1] */
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/* prereq: alen >= blen, p has room for m*n digits */
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void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
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void mpvectsmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
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/* sign of a - b or zero if the same */
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int mpveccmp(mpdigit *a, int alen, mpdigit *b, int blen);
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int mpvectscmp(mpdigit *a, int alen, mpdigit *b, int blen);
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/* divide the 2 digit dividend by the one digit divisor and stick in quotient */
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/* we assume that the result is one digit - overflow is all 1's */
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void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
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/* playing with magnitudes */
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int mpmagcmp(mpint *b1, mpint *b2);
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void mpmagadd(mpint *b1, mpint *b2, mpint *sum); /* sum = b1+b2 */
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void mpmagsub(mpint *b1, mpint *b2, mpint *sum); /* sum = b1+b2 */
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/* chinese remainder theorem */
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typedef struct CRTpre CRTpre; /* precomputed values for converting */
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/* twixt residues and mpint */
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typedef struct CRTres CRTres; /* residue form of an mpint */
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#pragma incomplete CRTpre
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struct CRTres
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{
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int n; /* number of residues */
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mpint *r[1]; /* residues */
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};
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CRTpre* crtpre(int, mpint**); /* precompute conversion values */
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CRTres* crtin(CRTpre*, mpint*); /* convert mpint to residues */
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void crtout(CRTpre*, CRTres*, mpint*); /* convert residues to mpint */
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void crtprefree(CRTpre*);
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void crtresfree(CRTres*);
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/* fast field arithmetic */
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typedef struct Mfield Mfield;
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struct Mfield
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{
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mpint;
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int (*reduce)(Mfield*, mpint*, mpint*);
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};
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mpint *mpfield(mpint*);
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Mfield *gmfield(mpint*);
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Mfield *cnfield(mpint*);
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#pragma varargck type "B" mpint*
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