static S64 FindFactor(S64 n, U32 seed)
{
// Pollard's rho algorithm.
U64 n2 = (S64)n;
for (; ; )
{
if (n2 % 2 == 0)
return 2;
if (_prime((S64)n2))
return (S64)n2;
U64 a = (U64)XorShift(&seed) << 32;
a |= (U64)XorShift(&seed);
U64 y = a % (n2 + 1);
U64 c = (U64)XorShift(&seed) + 1;
U64 m = (U64)XorShift(&seed) + 1;
U64 g;
U64 r = 1;
U64 q = 1;
U64 ys = 0;
U64 x;
U64 i;
do
{
x = y;
for (i = 0; i < r; i++)
y = (ModMul(y, y, n2) + c) % n2;
U64 k = 0;
do
{
ys = y;
U64 min_value = m < r - k ? m : r - k;
for (i = 0; i < min_value; i++)
{
y = (ModMul(y, y, n2) + c) % n2;
q = ModMul(q, x > y ? x - y : y - x, n2);
}
g = _gcd((S64)q, (S64)n2);
k += m;
} while (k < r && g <= 1);
r *= 2;
} while (g <= 1);
if (g == n2)
{
do
{
ys = (ModMul(ys, ys, n2) + c) % n2;
g = _gcd((S64)(x > ys ? x - ys : ys - x), (S64)n2);
} while (g <= 1);
}
if (g == n2)
seed++;
else
n2 = g;
}
}
static U64 ModPow(U64 value, U64 exponent, U64 modulus)
{
U64 w = 1;
while (exponent > 0)
{
if ((exponent & 1) != 0)
w = ModMul(w, value, modulus);
value = ModMul(value, value, modulus);
exponent >>= 1;
}
return w;
}
/* Begin the complex ModInt functions */
void
CmplxModMul(CmplxModInt *Prod, CmplxModInt *a, CmplxModInt *b)
{CmplxModInt P;
ModInt T1,T2;
ModMul(&T1,&a->r,&b->r);
ModMul(&T2,&a->i,&b->i);
ModSub(&P.r,&T1,&T2);
ModMul(&T1,&a->r,&b->i);
ModMul(&T2,&a->i,&b->r);
ModAdd(&P.i,&T1,&T2);
*Prod=P;
}
EXPORT S64 _modMul(S64 a, S64 b, S64 modulus)
{
THROWDBG(a < 0, 0xe9170006);
THROWDBG(b < 0, 0xe9170006);
THROWDBG(modulus < 0, 0xe9170006);
return (S64)ModMul((U64)a, (U64)b, (U64)modulus);
}
void
ModPow(ModInt *Prod,ModInt *Base,ModInt *Expon)
{ModInt b;
b=*Base;
while (!ModTestLowBit(Expon)) {ModMul(&b,&b,&b);RAW_ShiftR(Expon);}
*Prod=b;
RAW_ShiftR(Expon);
while (!IsModZero(Expon))
{
ModMul(&b,&b,&b);
if (ModTestLowBit(Expon)) ModMul(Prod,Prod,&b);
RAW_ShiftR(Expon);
}
}
void
IModPow(ModInt *Prod,UINT32 base,UINT32 expon)
/* Raise an integer to an integer power, returning a ModInt */
{ModInt b;
if (expon==0) {ModSet(Prod,1);return;}
ModSet(&b,base);
while (!(expon&1))
{
ModMul(&b,&b,&b);
expon>>=1;
}
*Prod=b;
while (expon>>=1)
{
ModMul(&b,&b,&b);
if (expon&1) ModMul(Prod,Prod,&b);
}
}
