113 lines
3.3 KiB
C#
113 lines
3.3 KiB
C#
namespace PerfectNumbers.Core;
|
|
|
|
public class MersenneResidueStepper
|
|
{
|
|
private UInt128 m;
|
|
private ulong p;
|
|
private UInt128 pow2_mod;
|
|
private UInt128 M_mod;
|
|
|
|
public MersenneResidueStepper(UInt128 modulus, ulong p0, UInt128 M_mod_m_at_p0)
|
|
{
|
|
if (modulus == 0)
|
|
{
|
|
throw new ArgumentException("Modulus must be positive.");
|
|
}
|
|
|
|
m = modulus;
|
|
p = p0;
|
|
|
|
// Inputs are already reduced in production; keep the old modulo guard commented for debugging reference.
|
|
// TODO: Confirm whether GPU execution ever constructs this stepper; if so, split the CPU/GPU initialization so
|
|
// the accelerator path retains the modulo reductions that prevent divergence.
|
|
// M_mod = M_mod_m_at_p0 % m;
|
|
// pow2_mod = (M_mod + 1) % m;
|
|
M_mod = M_mod_m_at_p0;
|
|
pow2_mod = M_mod + 1;
|
|
if (pow2_mod >= m)
|
|
{
|
|
pow2_mod -= m;
|
|
}
|
|
}
|
|
|
|
// TODO: Inline this accessor into callers so the hot residue path reads the backing fields directly
|
|
// instead of jumping through a wrapper method every iteration.
|
|
public (ulong, UInt128) State() => (p, M_mod);
|
|
|
|
public (ulong, UInt128) Step(long delta)
|
|
{
|
|
if (delta == 0)
|
|
{
|
|
return State();
|
|
}
|
|
|
|
ulong absDelta = (ulong)Math.Abs(delta);
|
|
UInt128 g = absDelta.PowMod(m);
|
|
|
|
if (delta > 0)
|
|
{
|
|
// Reuse the cached 2^p residue and only multiply by the adaptive pow2 step computed above.
|
|
pow2_mod = (pow2_mod * g) % m;
|
|
}
|
|
else
|
|
{
|
|
// Modular inverse for negative delta
|
|
// TODO: Switch to a cached divisor-cycle remainder instead of computing a fresh modular inverse for every
|
|
// backward jump; the divisor cycle benchmarks demonstrated significant savings once shared cycle data was used.
|
|
UInt128 inverse = ModInverse(g, m);
|
|
pow2_mod = (pow2_mod * inverse) % m;
|
|
}
|
|
|
|
p = (ulong)((long)p + delta);
|
|
|
|
// TODO: Use the shared pow2mod remainder cache here so this `%` becomes a subtraction-based fold instead of the
|
|
// slower modulo operator for large moduli.
|
|
M_mod = (pow2_mod + m - 1) % m;
|
|
|
|
return State();
|
|
}
|
|
|
|
public (ulong, UInt128) To(ulong p_target)
|
|
{
|
|
// TODO: Collapse this wrapper once callers can invoke Step directly; the extra indirection shows up
|
|
// in the profiler when residue adjustments happen per candidate.
|
|
long delta = (long)p_target - (long)p;
|
|
|
|
return Step(delta);
|
|
}
|
|
|
|
private static UInt128 ModInverse(UInt128 a, UInt128 m)
|
|
{
|
|
UInt128 m0 = m;
|
|
UInt128 t;
|
|
UInt128 q;
|
|
UInt128 x0 = 0;
|
|
UInt128 x1 = 1;
|
|
|
|
if (m == 1)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
while (a > 1)
|
|
{
|
|
// TODO: Replace this division-heavy Euclidean loop with the binary modular inverse that reuses divisor
|
|
// cycles so we drop repeated `/` and `%` operations during backtracking steps.
|
|
q = a / m;
|
|
t = m;
|
|
m = a % m;
|
|
a = t;
|
|
t = x0;
|
|
x0 = x1 - q * x0;
|
|
x1 = t;
|
|
}
|
|
|
|
if (x1 < 0)
|
|
{
|
|
x1 += m0;
|
|
}
|
|
|
|
return x1;
|
|
}
|
|
}
|