add Modp class

include/mcl/gmp_util.hpp

@@ -859,4 +859,55 @@ public:
 #endif
 };
 
+/*
+	Barrett Reduction
+*/
+struct Modp {
+	static const size_t unitBitSize = sizeof(mcl::fp::Unit) * 8;
+	mpz_class p_;
+	mpz_class u_;
+	mpz_class a_;
+	size_t N_;
+	// x &= 1 << (unitBitSize * unitSize)
+	void shrinkSize(mpz_class &x, size_t unitSize) const
+	{
+		size_t u = mcl::gmp::getUnitSize(x);
+		if (u < unitSize) return;
+		bool b;
+		mcl::gmp::setArray(&b, x, mcl::gmp::getUnit(x), unitSize);
+		assert(b);
+	}
+	void init(const mpz_class& p, size_t unitSize)
+	{
+		p_ = p;
+		N_ = unitSize;
+		u_ = (mpz_class(1) << (unitBitSize * 2 * N_)) / p_;
+		a_ = mpz_class(1) << (unitBitSize * (N_ + 1));
+	}
+	void modp(mpz_class& r, const mpz_class& t) const
+	{
+		assert(0 <= t && t < mpz_class(1) << (unitBitSize * 2 * N_));
+		if (t < p_) {
+			r = t;
+			return;
+		}
+		mpz_class q;
+		q = t;
+		q >>= unitBitSize * (N_ - 1);
+		q *= u_;
+		q >>= unitBitSize * (N_ + 1);
+		q *= p_;
+		shrinkSize(q, N_ + 1);
+		r = t;
+		shrinkSize(r, N_ + 1);
+		r -= q;
+		if (r < 0) {
+			r += a_;
+		}
+		if (r >= p_) {
+			r -= p_;
+		}
+	}
+};
+
 } // mcl

test/fp_test.cpp

@@ -777,6 +777,37 @@ void serializeTest()
 	}
 }
 
+void modpTest()
+{
+	const mpz_class& p = Fp::getOp().mp;
+	const mpz_class tbl[] = {
+		0,
+		1,
+		p - 1,
+		p,
+		p + 1,
+		p * 2 - 1,
+		p * 2,
+		p * 2 + 1,
+		p * (p - 1) - 1,
+		p * (p - 1),
+		p * (p - 1) + 1,
+		p * p - 1,
+		p * p,
+		p * p + 1,
+		(mpz_class(1) << Fp::getOp().N * mcl::fp::UnitBitSize * 2) - 1,
+	};
+	mcl::Modp modp;
+	modp.init(p, Fp::getUnitSize());
+	for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
+		const mpz_class& x = tbl[i];
+		mpz_class r1, r2;
+		r1 = x % p;
+		modp.modp(r2, x);
+		CYBOZU_TEST_EQUAL(r1, r2);
+	}
+}
+
 #include <iostream>
 #if (defined(MCL_USE_LLVM) || defined(MCL_USE_XBYAK)) && (MCL_MAX_BIT_SIZE >= 521)
 CYBOZU_TEST_AUTO(mod_NIST_P521)
@@ -886,6 +917,7 @@ void sub(mcl::fp::Mode mode)
 		getStrTest();
 		setHashOfTest();
 		serializeTest();
+		modpTest();
 	}
 	anotherFpTest(mode);
 	setArrayTest2(mode);