#include "EXTERN.h"
#include "perl.h"
#include "XSUB.h"
/* We're not using anything for which we need ppport.h */
#include <string.h>
#include <gmp.h>
#include "ptypes.h"
#include "gmp_main.h"
#include "primality.h"
#include "small_factor.h"
#include "ecm.h"
#include "simpqs.h"
#include "bls75.h"
#include "ecpp.h"
#include "aks.h"
#include "utility.h"
#include "factor.h"
#include "isaac.h"
#include "random_prime.h"
#define _GMP_ECM_FACTOR(n, f, b1, ncurves) \
_GMP_ecm_factor_projective(n, f, b1, 0, ncurves)
/* Instead of trying to suck in lots of Math::BigInt::GMP and be terribly
* clever (and brittle), just do all C<->Perl bigints via strings. It's
* crude but seems to work pretty well.
*/
static void validate_string_number(CV* cv, const char* var, const char* s)
{
const char* p;
if (s == 0)
croak("%s (%s): null string pointer as input", GvNAME(CvGV(cv)),var);
if (*s == 0)
croak("%s (%s): empty string as input", GvNAME(CvGV(cv)),var);
p = s;
while (*p != 0) {
if (!isdigit(*p))
croak("%s (%s): input '%s' must be a positive integer", GvNAME(CvGV(cv)), var, s);
p++;
}
}
#define VALIDATE_AND_SET(var, str) \
do { \
const char* s = str; \
if (*s == '+') s++; \
validate_string_number(cv,#var,s); \
mpz_init_set_str(var, s, 10); \
} while (0)
static char* cert_with_header(char* proof, mpz_t n) {
char *str, *strptr;
if (proof == 0) {
New(0, str, 1, char);
str[0] = '\0';
} else {
New(0, str, strlen(proof) + 100 + mpz_sizeinbase(n,10), char);
strptr = str;
strptr += gmp_sprintf(strptr, "[MPU - Primality Certificate]\nVersion 1.0\n\nProof for:\nN %Zd\n\n", n);
strcat(strptr, proof);
Safefree(proof);
}
return str;
}
MODULE = Math::Prime::Util::GMP PACKAGE = Math::Prime::Util::GMP
PROTOTYPES: ENABLE
void _GMP_init()
void _GMP_destroy()
void _GMP_set_verbose(IN int v)
PPCODE:
set_verbose_level(v);
void seed_csprng(IN UV bytes, IN unsigned char* seed)
PPCODE:
isaac_init(bytes, seed);
UV irand()
ALIAS:
irand64 = 1
is_csprng_well_seeded = 2
CODE:
switch (ix) {
#if BITS_PER_WORD >= 64
case 0: RETVAL = isaac_rand32(); break;
case 1: RETVAL = (((UV)isaac_rand32()) << 32) | isaac_rand32(); break;
#else
case 0:
case 1: RETVAL = isaac_rand32(); break;
#endif
case 2:
default: RETVAL = isaac_seeded(); break;
}
OUTPUT:
RETVAL
NV drand(NV m = 1.0)
CODE:
RETVAL = m * drand64();
OUTPUT:
RETVAL
int
is_pseudoprime(IN char* strn, ...)
ALIAS:
is_euler_pseudoprime = 1
is_strong_pseudoprime = 2
PREINIT:
int i;
mpz_t n, a;
CODE:
if (items < 2) croak("%s: no bases", GvNAME(CvGV(cv)));
validate_string_number(cv,"n",strn);
if (strn[1] == 0) {
switch (strn[0]) {
case '2': case '3': case '5': case '7': XSRETURN_IV(1); break;
case '0': case '1': case '4': case '6': case '8': XSRETURN_IV(0); break;
default: break; /* let 9 fall through */
}
}
mpz_init_set_str(n, strn, 10);
for (i = 1; i < items; i++) {
const char* strbase = SvPV_nolen(ST(i));
validate_string_number(cv, "base", strbase);
mpz_init_set_str(a, strbase, 10);
switch (ix) {
case 0: RETVAL = is_pseudoprime(n, a); break;
case 1: RETVAL = is_euler_pseudoprime(n, a); break;
case 2:
default: RETVAL = miller_rabin(n, a); break;
}
mpz_clear(a);
if (!RETVAL) break;
}
mpz_clear(n);
OUTPUT:
RETVAL
int miller_rabin_random(IN char* strn, IN IV nbases = 1, IN char* seedstr = 0)
PREINIT:
mpz_t n;
CODE:
if (nbases < 0)
croak("Parameter '%"IVdf"' must be a positive integer\n", nbases);
VALIDATE_AND_SET(n, strn);
RETVAL = miller_rabin_random(n, nbases, seedstr);
mpz_clear(n);
OUTPUT:
RETVAL
#define PRIMALITY_START(name, small_retval, test_small_factors) \
/* Negative numbers return 0 */ \
if ((strn != 0) && (strn[0] == '-') ) \
XSRETURN_IV(0); \
validate_string_number(cv, "n", strn); \
/* Handle single digit numbers */ \
if (strn[1] == 0) { \
int q_is_prime = 0; \
switch (strn[0]) { \
case '2': case '3': case '5': case '7': q_is_prime = small_retval; \
break; \
} \
XSRETURN_IV(q_is_prime); \
} \
/* Test for small multiples while it is still a string */ \
if (test_small_factors) { \
UV digsum = 0; \
int i, slen = strlen(strn); \
/* Multiples of 2 and 5 return 0 */ \
switch (strn[slen-1]-'0') { \
case 0: case 2: case 4: case 5: case 6: case 8: \
XSRETURN_IV(0); break; \
} \
/* Multiples of 3 return 0 */ \
for (i = 0; i < slen; i++) digsum += strn[i]-'0'; \
if (digsum % 3 == 0) XSRETURN_IV(0); \
} \
mpz_init_set_str(n, strn, 10);
int
is_lucas_pseudoprime(IN char* strn)
ALIAS:
is_strong_lucas_pseudoprime = 1
is_extra_strong_lucas_pseudoprime = 2
is_frobenius_underwood_pseudoprime = 3
is_frobenius_khashin_pseudoprime = 4
is_euler_plumb_pseudoprime = 5
PREINIT:
mpz_t n;
CODE:
if ((strn != 0) && (strn[0] == '-') )
croak("Parameter '%s' must be a positive integer\n", strn);
PRIMALITY_START("is_lucas_pseudoprime", 1, 0);
switch (ix) {
case 0: RETVAL = _GMP_is_lucas_pseudoprime(n, 0); break;
case 1: RETVAL = _GMP_is_lucas_pseudoprime(n, 1); break;
case 2: RETVAL = _GMP_is_lucas_pseudoprime(n, 2); break;
case 3: RETVAL = _GMP_is_frobenius_underwood_pseudoprime(n); break;
case 4: RETVAL = _GMP_is_frobenius_khashin_pseudoprime(n); break;
case 5:
default:RETVAL = is_euler_plumb_pseudoprime(n); break;
}
mpz_clear(n);
OUTPUT:
RETVAL
int
is_almost_extra_strong_lucas_pseudoprime(IN char* strn, IN UV increment = 1)
PREINIT:
mpz_t n;
CODE:
if ((strn != 0) && (strn[0] == '-') )
croak("Parameter '%s' must be a positive integer\n", strn);
if (increment == 0 || increment > 65535)
croak("Increment parameter must be >0 and < 65536");
PRIMALITY_START("is_almost_extra_strong_lucas_pseudoprime", 1, 0);
RETVAL = _GMP_is_almost_extra_strong_lucas_pseudoprime(n, increment);
mpz_clear(n);
OUTPUT:
RETVAL
int
is_frobenius_pseudoprime(IN char* strn, IN IV P = 0, IN IV Q = 0)
PREINIT:
mpz_t n;
CODE:
if ((strn != 0) && (strn[0] == '-') )
croak("Parameter '%s' must be a positive integer\n", strn);
PRIMALITY_START("is_frobenius_pseudoprime", 1, 0);
RETVAL = is_frobenius_pseudoprime(n, P, Q);
mpz_clear(n);
OUTPUT:
RETVAL
int
is_prime(IN char* strn)
ALIAS:
is_prob_prime = 1
is_aks_prime = 2
is_llr_prime = 3
is_proth_prime = 4
is_nminus1_prime = 5
is_nplus1_prime = 6
is_bls75_prime = 7
is_ecpp_prime = 8
is_bpsw_prime = 9
PREINIT:
mpz_t n;
int ret;
CODE:
/* Returns arg for single-dig primes, 0 for multiples of 2, 3, 5, or neg */
PRIMALITY_START("is_prime", 2, 1);
switch (ix) {
case 0: ret = _GMP_is_prime(n); break;
case 1: ret = _GMP_is_prob_prime(n); break;
case 2: ret = is_aks_prime(n); break;
case 3: ret = llr(n); break;
case 4: ret = proth(n); break;
case 5: ret = (_GMP_primality_bls_nm1(n, 100, 0) == 2) ? 1 : 0; break;
case 6: ret = (_GMP_primality_bls_np1(n, 100, 0) == 2) ? 1 : 0; break;
case 7: ret = (bls75_hybrid(n, 100, 0) == 2) ? 1 : 0; break;
case 8: ret = _GMP_ecpp(n, 0); break;
case 9:
default:ret = _GMP_BPSW(n); break;
}
RETVAL = ret;
mpz_clear(n);
OUTPUT:
RETVAL
void
_is_provable_prime(IN char* strn, IN int wantproof = 0)
ALIAS:
is_miller_prime = 1
is_perrin_pseudoprime = 2
PREINIT:
int result;
mpz_t n;
PPCODE:
PRIMALITY_START("is_provable_prime", 2, ix != 2);
if (ix == 1) {
result = is_miller_prime(n, wantproof); /* Assume GRH or not */
mpz_clear(n);
XSRETURN_IV(result);
}
if (ix == 2) {
result = is_perrin_pseudoprime(n, wantproof); /* Restricted or not */
mpz_clear(n);
XSRETURN_IV(result);
}
if (wantproof == 0) {
result = _GMP_is_provable_prime(n, 0);
XPUSHs(sv_2mortal(newSViv( result )));
} else {
char* prooftext = 0;
result = _GMP_is_provable_prime(n, &prooftext);
XPUSHs(sv_2mortal(newSViv( result )));
if (prooftext) {
XPUSHs(sv_2mortal(newSVpv(prooftext, 0)));
Safefree(prooftext);
} else {
XPUSHs(sv_2mortal(newSVpv("", 0)));
}
}
mpz_clear(n);
int
_validate_ecpp_curve(IN char* stra, IN char* strb, IN char* strn, IN char* strpx, IN char* strpy, IN char* strm, IN char* strq)
PREINIT:
mpz_t a, b, n, px, py, m, q, t1, t2;
CODE:
VALIDATE_AND_SET(a, stra);
VALIDATE_AND_SET(b, strb); /* Unused */
VALIDATE_AND_SET(n, strn);
VALIDATE_AND_SET(px, strpx);
VALIDATE_AND_SET(py, strpy);
VALIDATE_AND_SET(m, strm);
VALIDATE_AND_SET(q, strq);
mpz_init(t1); mpz_init(t2);
RETVAL = (ecpp_check_point(px, py, m, q, a, n, t1, t2) == 2) ? 1 : 0;
mpz_clear(t1); mpz_clear(t2);
mpz_clear(a); mpz_clear(b); mpz_clear(n); mpz_clear(px); mpz_clear(py);
mpz_clear(m); mpz_clear(q);
OUTPUT:
RETVAL
UV
is_power(IN char* strn, IN UV a = 0)
PREINIT:
mpz_t n;
int isneg;
CODE:
isneg = (strn[0] == '-');
if (isneg) strn++;
validate_string_number(cv, "n", strn);
RETVAL = 0;
if (!isneg || (a == 0 || a & 1)) {
mpz_init_set_str(n, strn, 10);
RETVAL = is_power(n, a);
mpz_clear(n);
}
if (isneg && a == 0 && RETVAL != 0) {
UV r = RETVAL;
while (!(r & 1)) r >>= 1;
RETVAL = (r == 1) ? 0 : r;
}
OUTPUT:
RETVAL
#define XPUSH_MPZ(n) \
do { \
/* Push as a scalar if <= min(ULONG_MAX,UV_MAX), string otherwise */ \
UV _v = mpz_get_ui(n); \
if (!mpz_cmp_ui(n, _v)) { \
XPUSHs(sv_2mortal(newSVuv( _v ))); \
} else { \
char* str; \
int nsize = mpz_sizeinbase(n, 10) + 2; \
New(0, str, nsize, char); \
mpz_get_str(str, 10, n); \
XPUSHs(sv_2mortal(newSVpv(str, 0))); \
Safefree(str); \
} \
} while (0)
void
next_prime(IN char* strn)
ALIAS:
prev_prime = 1
PREINIT:
mpz_t n;
PPCODE:
VALIDATE_AND_SET(n, strn);
if (ix == 1 && mpz_cmp_ui(n,3) < 0) { mpz_clear(n); XSRETURN_UNDEF; }
if (ix == 0) _GMP_next_prime(n);
else _GMP_prev_prime(n);
XPUSH_MPZ(n);
mpz_clear(n);
void
prime_count(IN char* strlo, IN char* strhi = 0)
ALIAS:
random_prime = 1
urandomr = 2
PREINIT:
mpz_t lo, hi, res;
int retundef;
PPCODE:
if (strhi == 0) {
mpz_init_set_ui(lo, 0);
VALIDATE_AND_SET(hi, strlo);
} else {
VALIDATE_AND_SET(lo, strlo);
VALIDATE_AND_SET(hi, strhi);
}
if (ix == 2 && mpz_sizeinbase(hi,2) <= 32) {
uint32_t ulo = mpz_get_ui(lo), uhi = mpz_get_ui(hi);
if (ulo <= uhi) {
mpz_clear(lo); mpz_clear(hi);
XSRETURN_IV( ulo + isaac_rand(uhi-ulo+1) );
}
}
retundef = 0;
mpz_init(res);
if (ix == 0) {
count_primes(res, lo, hi);
} else if (ix == 1) {
retundef = !mpz_random_prime(res, lo, hi);
} else {
if (mpz_cmp(lo,hi) > 0) {
retundef = 1;
} else {
mpz_sub(hi,hi,lo);
mpz_add_ui(hi,hi,1);
mpz_isaac_urandomm(res, hi);
mpz_add(res,res,lo);
}
}
if (!retundef) XPUSH_MPZ(res);
mpz_clear(res);
mpz_clear(hi);
mpz_clear(lo);
if (retundef) XSRETURN_UNDEF;
void
totient(IN char* strn)
ALIAS:
carmichael_lambda = 1
exp_mangoldt = 2
bernfrac = 3
harmfrac = 4
znprimroot = 5
ramanujan_tau = 6
sqrtint = 7
is_prime_power = 8
urandomm = 9
PREINIT:
mpz_t res, n;
PPCODE:
if (strn != 0 && strn[0] == '-') { /* If input is negative... */
if (ix == 2) XSRETURN_IV(1); /* exp_mangoldt return 1 */
if (ix == 5) strn++; /* znprimroot flip sign */
if (ix == 8) XSRETURN_IV(0); /* is_prime_power return 0 */
}
VALIDATE_AND_SET(n, strn);
mpz_init(res);
switch (ix) {
case 0: totient(res, n); break;
case 1: carmichael_lambda(res, n); break;
case 2: exp_mangoldt(res, n); break;
case 3: bernfrac(n, res, n);
XPUSH_MPZ(n);
break;
case 4: harmfrac(n, res, n);
XPUSH_MPZ(n);
break;
case 5: znprimroot(res, n); break;
case 6: ramanujan_tau(res, n); break;
case 7: mpz_sqrt(res, n); break;
case 8: mpz_set_ui(res, prime_power(res, n)); break;
case 9:
default: mpz_isaac_urandomm(res, n); break;
}
if (ix == 5 && !mpz_sgn(res) && mpz_cmp_ui(n,1) != 0)
{ mpz_clear(n); mpz_clear(res); XSRETURN_UNDEF; }
XPUSH_MPZ(res);
mpz_clear(n);
mpz_clear(res);
void harmreal(IN char* strn, IN UV prec = 40)
ALIAS:
bernreal = 1
zeta = 2
riemannr = 3
lambertw = 4
surround_primes = 5
PREINIT:
mpz_t n;
mpf_t f;
char* res;
int retundef;
PPCODE:
if (ix == 5) { /* surround_primes */
UV prev, next;
VALIDATE_AND_SET(n, strn);
next = 1 + (mpz_sgn(n)==0);
if (mpz_cmp_ui(n,2) > 0) {
surround_primes(n, &prev, &next, (items == 1) ? 0 : prec);
XPUSHs(sv_2mortal(newSVuv(prev)));
} else {
XPUSHs(sv_2mortal(newSV(0)));
}
XPUSHs(sv_2mortal(newSVuv(next)));
mpz_clear(n);
} else {
retundef = 0;
res = 0;
if (ix == 2 || ix == 3 || ix == 4) {
unsigned long bits = 64 + (unsigned long)(prec*3.32193);
mpf_init2(f, bits);
if (mpf_set_str(f, strn, 10) != 0)
croak("Not valid base-10 floating point input: %s", strn);
switch (ix) {
case 2: res = zetareal(f, prec); break;
case 3: res = riemannrreal(f, prec); break;
case 4:
default: res = lambertwreal(f, prec); break;
}
if (res == 0) retundef = 1;
mpf_clear(f);
} else {
VALIDATE_AND_SET(n, strn);
res = (ix == 0) ? harmreal(n, prec) : bernreal(n, prec);
mpz_clear(n);
}
if (retundef)
XSRETURN_UNDEF;
XPUSHs(sv_2mortal(newSVpv(res, 0)));
Safefree(res);
}
void
gcd(...)
PROTOTYPE: @
ALIAS:
lcm = 1
vecsum = 2
vecprod = 3
PREINIT:
int i;
mpz_t ret, n;
PPCODE:
if (items == 0) XSRETURN_IV( (ix == 3) ? 1 : 0);
if (ix == 3) {
mpz_t* list;
New(0, list, items, mpz_t);
for (i = 0; i < items; i++) {
char* strn = SvPV_nolen(ST(i));
validate_string_number(cv, "arg", (strn[0]=='-') ? strn+1 : strn);
mpz_init_set_str(list[i], strn, 10);
}
mpz_product(list, 0, items-1);
XPUSH_MPZ(list[0]);
for (i = 0; i < items; i++) mpz_clear(list[i]);
Safefree(list);
XSRETURN(1);
}
mpz_init(n);
mpz_init_set_ui(ret, (ix == 1 || ix == 3) ? 1 : 0);
for (i = 0; i < items; i++) {
char* strn = SvPV_nolen(ST(i));
validate_string_number(cv,"arg", (strn[0]=='-') ? strn+1 : strn);
if (ix <= 1 && strn != 0 && strn[0] == '-') strn++;
mpz_set_str(n, strn, 10);
switch (ix) {
case 0: mpz_gcd(ret, ret, n); break;
case 1: mpz_lcm(ret, ret, n); break;
case 2: mpz_add(ret, ret, n); break;
case 3:
default: mpz_mul(ret, ret, n); break;
}
}
XPUSH_MPZ(ret);
mpz_clear(n);
mpz_clear(ret);
int
kronecker(IN char* stra, IN char* strb)
ALIAS:
valuation = 1
PREINIT:
mpz_t a, b;
CODE:
validate_string_number(cv,"a", (stra[0]=='-') ? stra+1 : stra);
validate_string_number(cv,"b", (strb[0]=='-') ? strb+1 : strb);
mpz_init_set_str(a, stra, 10);
mpz_init_set_str(b, strb, 10);
if (ix == 0) {
RETVAL = mpz_kronecker(a, b);
} else {
mpz_abs(a,a);
mpz_abs(b,b);
if (mpz_cmp_ui(a,1) <= 0 || mpz_cmp_ui(b,1) <= 0) {
RETVAL = 0;
} else if (mpz_cmp_ui(b,2) == 0) {
RETVAL = mpz_scan1(a, 0);
} else {
RETVAL = mpz_remove(a, a, b);
}
}
mpz_clear(b);
mpz_clear(a);
OUTPUT:
RETVAL
void
moebius(IN char* strn, IN char* stro = 0)
PREINIT:
mpz_t n;
PPCODE:
VALIDATE_AND_SET(n, strn);
if (stro == 0) {
int result = moebius(n);
mpz_clear(n);
XSRETURN_IV(result);
} else { /* Ranged result */
mpz_t nhi;
VALIDATE_AND_SET(nhi, stro);
while (mpz_cmp(n, nhi) <= 0) {
XPUSHs(sv_2mortal(newSViv( moebius(n) )));
mpz_add_ui(n, n, 1);
}
mpz_clear(n);
mpz_clear(nhi);
}
void
lucasu(IN IV P, IN IV Q, IN char* strk)
ALIAS:
lucasv = 1
PREINIT:
mpz_t u, v, k;
PPCODE:
VALIDATE_AND_SET(k, strk);
/* We could call mpz_fib_ui / mpz_lucnum_ui when P=1,Q=-1,
* but it is only 10-15% faster so let's not special case. */
mpz_init(u); mpz_init(v);
lucasuv(u, v, P, Q, k);
XPUSH_MPZ( ((ix == 0) ? u : v) );
mpz_clear(v); mpz_clear(u);
mpz_clear(k);
int
liouville(IN char* strn)
ALIAS:
is_semiprime = 1
PREINIT:
mpz_t n;
CODE:
VALIDATE_AND_SET(n, strn);
switch (ix) {
case 0: RETVAL = liouville(n); break;
case 1:
default: RETVAL = is_semiprime(n); break;
}
mpz_clear(n);
OUTPUT:
RETVAL
void
invmod(IN char* stra, IN char* strb)
ALIAS:
binomial = 1
gcdext = 2
jordan_totient = 3
znorder = 4
sqrtmod = 5
is_primitive_root = 6
rootint = 7
PREINIT:
mpz_t a, b, t;
int retundef;
PPCODE:
validate_string_number(cv,"a", (stra[0]=='-') ? stra+1 : stra);
validate_string_number(cv,"b", (strb[0]=='-') ? strb+1 : strb);
mpz_init_set_str(a, stra, 10);
mpz_init_set_str(b, strb, 10);
retundef = 0;
if (ix == 0) {
/* undef if a|b is zero, 0 if b is 1, otherwise result of mpz_invert */
if (!mpz_sgn(b) || !mpz_sgn(a)) retundef = 1;
else if (!mpz_cmp_ui(b,1)) mpz_set_ui(a,0);
else retundef = !mpz_invert(a,a,b);
} else if (ix == 1) {
unsigned long n, k;
if (mpz_sgn(b) < 0) { /* Handle negative k */
if (mpz_sgn(a) >= 0 || mpz_cmp(b,a) > 0) mpz_set_ui(a, 0);
else mpz_sub(b, a, b);
}
n = mpz_get_ui(a);
k = mpz_get_ui(b);
if (k > n || k == 0 || k == n || mpz_sgn(a) < 0) {
mpz_bin_ui(a, a, k);
} else {
if (k > n/2) k = n-k;
/* Note: mpz_bin_uiui is *much* faster than mpz_bin_ui. It is a
* bit faster than our code for small values, and a tiny bit slower
* for larger values. */
if (n > 50000 && k > 1000) binomial(a, n, k);
else mpz_bin_uiui(a, n, k);
}
} else if (ix == 2) {
mpz_init(t);
if (mpz_sgn(a) == 0 && mpz_sgn(b) == 0) {
mpz_set_ui(t, 0); /* This changed in GMP 5.1.2. Enforce new result. */
} else {
gcdext(a, t, b, a, b);
}
XPUSH_MPZ(t); XPUSH_MPZ(b);
mpz_clear(t);
} else if (ix == 3) {
jordan_totient(a, b, mpz_get_ui(a));
} else if (ix == 4) {
znorder(a, a, b);
if (!mpz_sgn(a)) retundef = 1;
} else if (ix == 5) {
retundef = !sqrtmod(a, a, b);
} else if (ix == 6) {
int ret = is_primitive_root(a, b, 0);
mpz_set_si(a, ret);
} else {
if (mpz_sgn(b) <= 0) croak("rootint: k must be > 0");
if (mpz_sgn(a) < 0) croak("rootint: n must be >= 0");
mpz_root(a, a, mpz_get_ui(b));
}
if (!retundef) XPUSH_MPZ(a);
mpz_clear(b); mpz_clear(a);
if (retundef) XSRETURN_UNDEF;
void
addmod(IN char* stra, IN char* strb, IN char* strn)
ALIAS:
mulmod = 1
powmod = 2
divmod = 3
PREINIT:
mpz_t a, b, n;
int retundef;
PPCODE:
validate_string_number(cv,"a", (stra[0]=='-') ? stra+1 : stra);
validate_string_number(cv,"b", (strb[0]=='-') ? strb+1 : strb);
validate_string_number(cv,"n", strn);
mpz_init_set_str(a, stra, 10);
mpz_init_set_str(b, strb, 10);
mpz_init_set_str(n, strn, 10);
retundef = (mpz_sgn(n) <= 0);
if (!retundef && ix == 3) {
if (!mpz_sgn(n) || !mpz_sgn(b)) retundef = 1;
else if (!mpz_cmp_ui(b,1)) mpz_set_ui(b,0);
else retundef = !mpz_invert(b,b,n);
}
if (!retundef && ix == 2 && mpz_sgn(b) < 0) {
if (!mpz_cmp_ui(n,1)) mpz_set_ui(b,0);
else retundef = !mpz_invert(a,a,n);
mpz_abs(b,b);
}
if (retundef) {
mpz_clear(n); mpz_clear(b); mpz_clear(a);
XSRETURN_UNDEF;
}
if (ix == 0) {
mpz_add(a,a,b);
mpz_mod(a,a,n);
} else if (ix == 1 || ix == 3) {
mpz_mul(a,a,b);
mpz_mod(a,a,n);
} else if (ix == 2) {
mpz_powm(a, a, b, n);
}
XPUSH_MPZ(a);
mpz_clear(n); mpz_clear(b); mpz_clear(a);
int is_mersenne_prime(IN UV n)
CODE:
RETVAL = lucas_lehmer(n);
OUTPUT:
RETVAL
void Pi(IN UV n)
ALIAS:
random_bytes = 1
PPCODE:
if (ix == 0) {
if (n == 1)
XSRETURN_IV(3);
else if (n > 0) {
char* pi = pidigits(n);
XPUSHs(sv_2mortal(newSVpvn(pi, n+1)));
Safefree(pi);
}
} else {
char* sptr;
SV* sv = newSV(n == 0 ? 1 : n);
SvPOK_only(sv);
SvCUR_set(sv, n);
sptr = SvPVX(sv);
isaac_rand_bytes(n, (unsigned char*)sptr);
sptr[n] = '\0';
PUSHs(sv_2mortal(sv));
XSRETURN(1);
}
void random_nbit_prime(IN UV n)
ALIAS:
random_strong_prime = 1
random_maurer_prime = 2
random_maurer_prime_with_cert = 3
random_shawe_taylor_prime = 4
random_shawe_taylor_prime_with_cert = 5
random_ndigit_prime = 6
urandomb = 7
factorial = 8
partitions = 9
primorial = 10
pn_primorial = 11
consecutive_integer_lcm = 12
PREINIT:
mpz_t p;
char* proof;
PPCODE:
if (ix == 7 && n <= BITS_PER_WORD) {
UV v = irand64(n);
ST(0) = sv_2mortal(newSVuv(v));
XSRETURN(1);
}
mpz_init(p);
proof = 0;
switch (ix) {
case 0: mpz_random_nbit_prime(p, n); break;
case 1: mpz_random_strong_prime(p, n); break;
case 2: mpz_random_maurer_prime(p, n, 0); break;
case 3: mpz_random_maurer_prime(p, n, &proof);
proof = cert_with_header(proof, p);
break;
case 4: mpz_random_shawe_taylor_prime(p, n, 0); break;
case 5: mpz_random_shawe_taylor_prime(p, n, &proof);
proof = cert_with_header(proof, p);
break;
case 6: mpz_random_ndigit_prime(p, n); break;
case 7: mpz_isaac_urandomb(p, n); break;
case 8: mpz_fac_ui(p, n); break; /* swing impl in 5.1+, so fast */
case 9: partitions(p, n); break;
case 10: _GMP_primorial(p, n); break;
case 11: _GMP_pn_primorial(p, n); break;
case 12:
default: consecutive_integer_lcm(p, n); break;
}
XPUSH_MPZ(p);
mpz_clear(p);
if (proof) {
XPUSHs(sv_2mortal(newSVpv(proof, 0)));
Safefree(proof);
}
void
stirling(IN UV n, IN UV m, IN UV type = 1)
PREINIT:
mpz_t r;
PPCODE:
mpz_init(r);
stirling(r, n, m, type);
XPUSH_MPZ( r );
mpz_clear(r);
void
chinese(...)
PROTOTYPE: @
PREINIT:
int i, doretval;
mpz_t* an;
mpz_t ret, lcm;
PPCODE:
if (items == 0)
XSRETURN_IV(0);
mpz_init_set_ui(ret, 0);
New(0, an, 2*items, mpz_t);
for (i = 0; i < items; i++) {
AV* av;
SV** psva;
SV** psvn;
char* strn;
if (!SvROK(ST(i)) || SvTYPE(SvRV(ST(i))) != SVt_PVAV || av_len((AV*)SvRV(ST(i))) != 1)
croak("chinese arguments are two-element array references");
av = (AV*) SvRV(ST(i));
psva = av_fetch(av, 0, 0);
psvn = av_fetch(av, 1, 0);
strn = SvPV_nolen(*psva);
validate_string_number(cv,"a", (strn[0]=='-') ? strn+1 : strn);
mpz_init_set_str(an[i+0], strn, 10);
strn = SvPV_nolen(*psvn);
validate_string_number(cv,"b", (strn[0]=='-') ? strn+1 : strn);
mpz_init_set_str(an[i+items], strn, 10);
}
mpz_init(lcm);
doretval = chinese(ret, lcm, an, an+items, items);
if (doretval) XPUSH_MPZ(ret);
for (i = 0; i < items; i++) {
mpz_clear(an[i+0]);
mpz_clear(an[i+items]);
}
Safefree(an);
mpz_clear(lcm);
mpz_clear(ret);
if (!doretval) XSRETURN_UNDEF;
void
sieve_prime_cluster(IN char* strlow, IN char* strhigh, ...)
ALIAS:
sieve_primes = 1
sieve_twin_primes = 2
PREINIT:
mpz_t low, seghigh, high, t;
UV i, nc, nprimes, maxseg, *list;
PPCODE:
VALIDATE_AND_SET(low, strlow);
VALIDATE_AND_SET(high, strhigh);
mpz_init(seghigh);
mpz_init(t);
nc = items-1;
maxseg = ((UV_MAX > ULONG_MAX) ? ULONG_MAX : UV_MAX);
/* Loop as needed */
while (mpz_cmp(low, high) <= 0) {
mpz_add_ui(seghigh, low, maxseg - 1);
if (mpz_cmp(seghigh, high) > 0)
mpz_set(seghigh, high);
mpz_set(t, seghigh); /* Save in case it is modified */
if (ix == 1) {
UV k = (nc <= 1) ? 0 : SvUV(ST(2));
list = sieve_primes(low, seghigh, k, &nprimes);
} else if (ix == 2) {
list = sieve_twin_primes(low, seghigh, 2, &nprimes);
} else {
uint32_t *cl;
New(0, cl, nc, uint32_t);
cl[0] = 0;
for (i = 1; i < nc; i++) {
UV cval = SvUV(ST(1+i));
if (cval & 1) croak("sieve_prime_cluster: values must be even");
if (cval > 2147483647UL) croak("sieve_prime_cluster: values must be 31-bit");
if (cval <= cl[i-1]) croak("sieve_prime_cluster: values must be increasing");
cl[i] = cval;
}
list = sieve_cluster(low, seghigh, cl, nc, &nprimes);
Safefree(cl);
}
mpz_set(seghigh, t); /* Restore the value we used */
if (list != 0) {
for (i = 0; i < nprimes; i++) {
mpz_add_ui(t, low, list[i]);
XPUSH_MPZ( t );
}
Safefree(list);
}
mpz_add_ui(low, seghigh, 1);
}
mpz_clear(t);
mpz_clear(seghigh);
mpz_clear(high);
mpz_clear(low);
void
sieve_range(IN char* strn, IN UV width, IN UV depth)
PREINIT:
mpz_t low, seghigh, high, t;
UV i, nprimes, maxseg, offset, *list;
PPCODE:
if (width == 0) XSRETURN(0);
if (depth == 0) depth = 1;
VALIDATE_AND_SET(low, strn);
mpz_init(high);
mpz_add_ui(high, low, width-1);
mpz_init(seghigh);
mpz_init(t);
maxseg = ((UV_MAX > ULONG_MAX) ? ULONG_MAX : UV_MAX);
offset = 0;
/* Deal with 0 and 1 inside range */
if (mpz_cmp_ui(low,2) < 0) {
offset = 2 - mpz_get_ui(low);
width = (width < offset) ? 0 : width - offset;
mpz_set_ui(low,2);
}
/* Deal with depth < 2 (no sieving) */
if (depth < 2) {
for (i = 0; i < width; i++)
XPUSHs(sv_2mortal(newSVuv(offset + i)));
mpz_add_ui(low, high, 1);
}
/* Loop as needed */
while (mpz_cmp(low, high) <= 0) {
mpz_add_ui(seghigh, low, maxseg - 1);
if (mpz_cmp(seghigh, high) > 0)
mpz_set(seghigh, high);
mpz_set(t, seghigh); /* Save in case it is modified */
list = sieve_primes(low, seghigh, depth, &nprimes);
mpz_set(seghigh, t); /* Restore the value we used */
if (list != 0) {
for (i = 0; i < nprimes; i++) {
XPUSHs(sv_2mortal(newSVuv( offset + list[i] )));
}
Safefree(list);
}
mpz_add_ui(low, seghigh, 1);
offset += maxseg;
}
mpz_clear(t);
mpz_clear(seghigh);
mpz_clear(high);
mpz_clear(low);
void
lucas_sequence(IN char* strn, IN IV P, IN IV Q, IN char* strk)
PREINIT:
mpz_t U, V, Qk, n, k, t;
PPCODE:
VALIDATE_AND_SET(n, strn);
VALIDATE_AND_SET(k, strk);
mpz_init(U); mpz_init(V); mpz_init(Qk); mpz_init(t);
lucas_seq(U, V, n, P, Q, k, Qk, t);
XPUSH_MPZ(U);
XPUSH_MPZ(V);
XPUSH_MPZ(Qk);
mpz_clear(n); mpz_clear(k);
mpz_clear(U); mpz_clear(V); mpz_clear(Qk); mpz_clear(t);
#define SET_UV_VIA_MPZ_STRING(uva, sva, name) \
{ \
mpz_t t; \
char* stra = SvPV_nolen(sva); \
validate_string_number(cv, name, stra); \
mpz_init_set_str(t, stra, 10); \
uva = mpz_get_ui(t); \
mpz_clear(t); \
}
void
trial_factor(IN char* strn, ...)
ALIAS:
prho_factor = 1
pbrent_factor = 2
pminus1_factor = 3
pplus1_factor = 4
holf_factor = 5
squfof_factor = 6
ecm_factor = 7
qs_factor = 8
PREINIT:
mpz_t n;
UV arg1, arg2, uf;
static const UV default_arg1[] =
{0, 64000000,64000000,5000000,5000000,256000000,16000000,0, 0 };
/* Trial,Rho, Brent, P-1, P+1, HOLF, SQUFOF, ECM,QS */
PPCODE:
VALIDATE_AND_SET(n, strn);
{
int cmpr = mpz_cmp_ui(n,1);
if (cmpr <= 0) {
mpz_clear(n);
XSRETURN_IV( (cmpr < 0) ? 0 : 1 );
}
}
arg1 = default_arg1[ix];
arg2 = 0;
if (items >= 2) SET_UV_VIA_MPZ_STRING(arg1, ST(1), "specific factor arg 1");
if (items >= 3) SET_UV_VIA_MPZ_STRING(arg2, ST(2), "specific factor arg 2");
while (mpz_even_p(n)) {
XPUSHs(sv_2mortal(newSVuv(2)));
mpz_divexact_ui(n, n, 2);
}
while (mpz_divisible_ui_p(n, 3)) {
XPUSHs(sv_2mortal(newSVuv(3)));
mpz_divexact_ui(n, n, 3);
}
while (mpz_divisible_ui_p(n, 5)) {
XPUSHs(sv_2mortal(newSVuv(5)));
mpz_divexact_ui(n, n, 5);
}
if (mpz_cmp_ui(n,1) > 0 && !_GMP_is_prob_prime(n)) {
mpz_t f;
int success = 0;
mpz_init(f);
switch (ix) {
case 0: if (arg1 == 0) arg1 = 2147483647;
uf = _GMP_trial_factor(n, 2, arg1);
mpz_set_ui(f, uf);
success = (uf > 0);
break;
case 1: success = _GMP_prho_factor(n, f, 3, arg1); break;
case 2: success = _GMP_pbrent_factor(n, f, 3, arg1); break;
case 3: if (arg2 == 0) arg2 = arg1*10;
success = _GMP_pminus1_factor(n, f, arg1,arg2); break;
case 4: if (arg2 == 0) arg2 = arg1*10;
success = _GMP_pplus1_factor(n, f, 0,arg1,arg2); break;
case 5: success = _GMP_holf_factor(n, f, arg1); break;
case 6: success = _GMP_squfof_factor(n, f, arg1); break;
case 7: if (arg2 == 0) arg2 = 100;
if (arg1 == 0) {
success = _GMP_ECM_FACTOR(n, f, 1000, 40)
|| _GMP_ECM_FACTOR(n, f, 10000, 40)
|| _GMP_ECM_FACTOR(n, f, 100000, 40)
|| _GMP_ECM_FACTOR(n, f, 1000000, 40)
|| _GMP_ECM_FACTOR(n, f, 10000000,100);
} else {
success = _GMP_ECM_FACTOR(n, f, arg1, arg2);
}
break;
case 8:
default:{
mpz_t farray[66];
int i, nfactors;
for (i = 0; i < 66; i++)
mpz_init(farray[i]);
nfactors = _GMP_simpqs(n, farray);
for (i = 0; i < nfactors; i++)
XPUSH_MPZ(farray[i]);
for (i = 0; i < 66; i++)
mpz_clear(farray[i]);
if (nfactors > 0)
mpz_set_ui(n, 1);
}
break;
}
if (success) {
XPUSH_MPZ(f);
mpz_divexact(n, n, f);
}
mpz_clear(f);
}
if (mpz_cmp_ui(n,1) > 0)
XPUSH_MPZ(n);
mpz_clear(n);
void
factor(IN char* strn)
ALIAS:
divisors = 1
PREINIT:
mpz_t n;
mpz_t* factors;
int* exponents;
int nfactors, i, j;
PPCODE:
VALIDATE_AND_SET(n, strn);
if (ix == 0) {
nfactors = factor(n, &factors, &exponents);
if (GIMME_V == G_SCALAR) {
for (i = 0, j = 0; i < nfactors; i++)
j += exponents[i];
PUSHs(sv_2mortal(newSVuv(j)));
} else {
for (i = 0; i < nfactors; i++) {
for (j = 0; j < exponents[i]; j++) {
XPUSH_MPZ(factors[i]);
}
}
}
clear_factors(nfactors, &factors, &exponents);
} else {
if (GIMME_V == G_SCALAR) {
sigma(n, n, 0);
XPUSH_MPZ(n);
} else {
factors = divisor_list(&nfactors, n);
EXTEND(SP, nfactors);
for (i = 0; i < nfactors; i++) {
XPUSH_MPZ(factors[i]);
mpz_clear(factors[i]);
}
Safefree(factors);
}
}
mpz_clear(n);
void sigma(IN char* strn, IN UV k = 1)
PREINIT:
mpz_t n;
PPCODE:
VALIDATE_AND_SET(n, strn);
sigma(n, n, k);
XPUSH_MPZ(n);
mpz_clear(n);
void
todigits(IN char* strn, int base=10, int length=-1)
PREINIT:
mpz_t n;
uint32_t bits, d, *digits;
PPCODE:
if (base < 2) croak("invalid base: %d", base);
if (strn[0] == '-' || strn[0] == '+') strn++;
validate_string_number(cv, "n", strn);
if (base == 10) {
uint32_t l = strlen(strn);
New(0, digits, l, uint32_t);
for (d = 0; d < l; d++)
digits[d] = strn[l-d-1]-'0';
} else {
mpz_init_set_str(n, strn, 10);
bits = mpz_sizeinbase(n,2);
New(0, digits, bits, uint32_t);
if (base == 2) {
for (d = 0; d < bits; d++)
digits[d] = mpz_tstbit(n, d);
} else {
for (d = 0; mpz_sgn(n) > 0; mpz_tdiv_q_ui(n, n, base))
digits[d++] = mpz_fdiv_ui(n, base);
}
mpz_clear(n);
}
if (length > 0 || d > 1 || digits[0] != 0) {
if (length < 0) length = d;
EXTEND(SP, length);
for (; length > (int)d; length--)
PUSHs(sv_2mortal(newSVuv( 0 )));
for (; length > 0; length--)
PUSHs(sv_2mortal(newSVuv( digits[length-1] )));
}
Safefree(digits);