add isOne and isNegative

include/mcl/fp.hpp

@@ -106,6 +106,12 @@ public:
 	"\n", mode, op_.useMont);
 #endif
 		op_.init(mstr, base, maxBitSize, mode);
+		{
+			FpT x = 1;
+			op_.copy(op_.oneRep, x.v_);
+			mpz_class half = (op_.mp - 1) / 2;
+			Gmp::getArray(op_.half, op_.N, half);
+		}
 	}
 	static inline void getModulo(std::string& pstr)
 	{
@@ -299,6 +305,18 @@ public:
 		powerArray(z, x, Gmp::getUnit(y), abs(y.get_mpz_t()->_mp_size), y < 0);
 	}
 	bool isZero() const { return op_.isZero(v_); }
+	bool isOne() const { return fp::isEqualArray(v_, op_.oneRep, op_.N); }
+	/*
+		return true if p/2 < x < p
+		return false if 0 <= x <= p/2
+		note p/2 == (p-1)/2 because of p is odd
+	*/
+	bool isNegative() const
+	{
+		fp::Block b;
+		getBlock(b);
+		return fp::compareArray(b.p, op_.half, op_.N) > 0;
+	}
 	bool isValid() const
 	{
 		return fp::compareArray(v_, op_.p, op_.N) < 0;

include/mcl/op.hpp

@@ -54,6 +54,8 @@ struct Op {
 	mpz_class mp;
 	mcl::SquareRoot sq;
 	Unit p[maxOpUnitSize];
+	Unit half[maxOpUnitSize]; // (p - 1) / 2
+	Unit oneRep[maxOpUnitSize]; // 1(=inv R if Montgomery)
 	/*
 		for Montgomery
 		one = 1

test/mont_fp_test.cpp

@@ -365,6 +365,38 @@ struct Test {
 				CYBOZU_TEST_ASSERT(x != y);
 			}
 		}
+		{
+			Fp x(1);
+			CYBOZU_TEST_ASSERT(x.isOne());
+			x = 2;
+			CYBOZU_TEST_ASSERT(!x.isOne());
+		}
+		{
+			const struct {
+				int v;
+				bool expected;
+			} tbl[] = {
+				{ 0, false },
+				{ 1, false },
+				{ -1, true },
+			};
+			for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
+				Fp x = tbl[i].v;
+				PUT(x);
+				CYBOZU_TEST_EQUAL(x.isNegative(), tbl[i].expected);
+			}
+			std::string str;
+			Fp::getModulo(str);
+			mpz_class half(str);
+			half = (half - 1) / 2;
+			Fp x;
+			x.setMpz(half - 1);
+			CYBOZU_TEST_ASSERT(!x.isNegative());
+			x.setMpz(half);
+			CYBOZU_TEST_ASSERT(!x.isNegative());
+			x.setMpz(half + 1);
+			CYBOZU_TEST_ASSERT(x.isNegative());
+		}
 	}
 
 	void modulo()