add sqrT

misc/low_test.cpp

@@ -69,6 +69,39 @@ CYBOZU_TEST_AUTO(mulT)
 {
 	mulTest<8>();
 	mulTest<12>();
+	mulTest<16>();
+}
+
+template<size_t N>
+void sqrTest()
+{
+	printf("N=%zd (%zdbit)\n", N, N * 32);
+	cybozu::XorShift rg;
+	uint32_t x[N];
+	uint32_t y[N * 2];
+	for (size_t i = 0; i < 1000; i++) {
+		setRand(x, N, rg);
+		// remove MSB
+		x[N - 1] &= 0x7fffffff;
+		mcl::Vint vx;
+		vx.setArray(x, N);
+		vx *= vx;
+		mcl::sqrT<N>(y, x);
+		CYBOZU_TEST_EQUAL_ARRAY(y, vx.getUnit(), N * 2);
+#if 0
+		memset(z, 0, sizeof(z));
+		mcl::karatsubaT<N>(z, x, y);
+		CYBOZU_TEST_EQUAL_ARRAY(z, vx.getUnit(), N * 2);
+#endif
+	}
+	CYBOZU_BENCH_C("sqrT", 10000, mcl::sqrT<N>, y, x);
+}
+
+CYBOZU_TEST_AUTO(sqrT)
+{
+	sqrTest<8>();
+	sqrTest<12>();
+	sqrTest<16>();
 }
 
 struct Montgomery {

src/low_funct.hpp

@@ -101,6 +101,54 @@ void mulT(uint32_t z[N * 2], const uint32_t x[N], const uint32_t y[N])
 	}
 }
 
+template<size_t N>
+uint32_t mulUnitWithTblT(uint32_t z[N], const uint64_t *tbl_j)
+{
+	uint32_t H = 0;
+	for (size_t i = 0; i < N; i++) {
+		uint64_t v = tbl_j[i];
+		v += H;
+		z[i] = uint32_t(v);
+		H = uint32_t(v >> 32);
+	}
+	return H;
+}
+
+template<size_t N>
+uint32_t addMulUnitWithTblT(uint32_t z[N], const uint64_t *tbl_j)
+{
+	uint32_t H = 0;
+	for (size_t i = 0; i < N; i++) {
+		uint64_t v = tbl_j[i];
+		v += H;
+		v += z[i];
+		z[i] = uint32_t(v);
+		H = uint32_t(v >> 32);
+	}
+	return H;
+}
+
+
+// y[N * 2] = x[N] * x[N]
+template<size_t N>
+void sqrT(uint32_t y[N * 2], const uint32_t x[N])
+{
+	uint64_t tbl[N * N]; // x[i]x[j]
+	for (size_t i = 0; i < N; i++) {
+		uint64_t xi = x[i];
+		tbl[i * N + i] = xi * xi;
+		for (size_t j = i + 1; j < N; j++) {
+			uint64_t v = xi * x[j];
+			tbl[i * N + j] = v;
+			tbl[j * N + i] = v;
+		}
+	}
+	y[N] = mulUnitWithTblT<N>(y, tbl);
+	for (size_t i = 1; i < N; i++) {
+		y[N + i] = addMulUnitWithTblT<N>(&y[i], tbl + N * i);
+	}
+}
+
 /*
 	z[N * 2] = x[N] * y[N]
 	H = N/2