diff --git a/include/mcl/fp_tower.hpp b/include/mcl/fp_tower.hpp
index 31a54a4..f2faebe 100644
--- a/include/mcl/fp_tower.hpp
+++ b/include/mcl/fp_tower.hpp
@@ -379,11 +379,16 @@ public:
 	}
 
 	static uint32_t get_xi_a() { return Fp::getOp().xi_a; }
-	static void init()
+	static void init(bool *pb)
 	{
 //		assert(Fp::maxSize <= 256);
 		mcl::fp::Op& op = Fp::op_;
 		assert(op.xi_a);
+		// assume p < W/4 where W = 1 << (N * sizeof(Unit) * 8)
+		if ((op.p[op.N - 1] >> (sizeof(fp::Unit) * 8 - 2)) != 0) {
+			*pb = false;
+			return;
+		}
 		mul_xi = 0;
 #ifdef MCL_XBYAK_DIRECT_CALL
 		add = fp::func_ptr_cast<void (*)(Fp2T& z, const Fp2T& x, const Fp2T& y)>(op.fp2_addA_);
@@ -440,6 +445,12 @@ public:
 		}
 	}
 #ifndef CYBOZU_DONT_USE_EXCEPTION
+	static void init()
+	{
+		bool b;
+		init(&b);
+		if (!b) throw cybozu::Exception("Fp2::init");
+	}
 	template<class InputStream>
 	void load(InputStream& is, int ioMode = IoSerialize)
 	{
diff --git a/test/fp_tower_test.cpp b/test/fp_tower_test.cpp
index b5e77db..5dd3a70 100644
--- a/test/fp_tower_test.cpp
+++ b/test/fp_tower_test.cpp
@@ -400,9 +400,11 @@ void test(const char *p, mcl::fp::Mode mode)
 {
 	const int xi_a = 1;
 	Fp::init(xi_a, p, mode);
-	printf("mode=%s\n", mcl::fp::ModeToStr(mode));
 	if (Fp::getOp().isFullBit) return;
-	Fp2::init();
+	bool b;
+	Fp2::init(&b);
+	if (!b) return;
+	printf("mode=%s\n", mcl::fp::ModeToStr(mode));
 	printf("bitSize=%d\n", (int)Fp::getBitSize());
 #if 0
 	if (Fp::getBitSize() > 256) {