From 08148dcf605117f495545cdf3ce29afb1e9c963e Mon Sep 17 00:00:00 2001
From: MITSUNARI Shigeo <herumi@nifty.com>
Date: Wed, 20 Feb 2019 09:51:34 +0900
Subject: [PATCH] LagrangeInterpolation sets out = yVec[0] if k = 1

---
 include/mcl/bn.h         |  1 +
 include/mcl/lagrange.hpp | 13 +++++++++----
 readme.md                |  1 +
 test/bench.hpp           |  2 ++
 4 files changed, 13 insertions(+), 4 deletions(-)

diff --git a/include/mcl/bn.h b/include/mcl/bn.h
index 6499280..0044d9d 100644
--- a/include/mcl/bn.h
+++ b/include/mcl/bn.h
@@ -379,6 +379,7 @@ MCLBN_DLL_API void mclBn_precomputedMillerLoop2mixed(mclBnGT *f, const mclBnG1 *
 	Lagrange interpolation
 	recover out = y(0) by { (xVec[i], yVec[i]) }
 	return 0 if success else -1
+	@note *out = yVec[0] if k = 1
 	@note k >= 2, xVec[i] != 0, xVec[i] != xVec[j] for i != j
 */
 MCLBN_DLL_API int mclBn_FrLagrangeInterpolation(mclBnFr *out, const mclBnFr *xVec, const mclBnFr *yVec, mclSize k);
diff --git a/include/mcl/lagrange.hpp b/include/mcl/lagrange.hpp
index 7c02188..feca80d 100644
--- a/include/mcl/lagrange.hpp
+++ b/include/mcl/lagrange.hpp
@@ -15,14 +15,19 @@ namespace mcl {
 template<class G, class F>
 void LagrangeInterpolation(bool *pb, G& out, const F *S, const G *vec, size_t k)
 {
+	if (k == 0) {
+		*pb = false;
+		return;
+	}
+	if (k == 1) {
+		out = vec[0];
+		*pb = true;
+		return;
+	}
 	/*
 		delta_{i,S}(0) = prod_{j != i} S[j] / (S[j] - S[i]) = a / b
 		where a = prod S[j], b = S[i] * prod_{j != i} (S[j] - S[i])
 	*/
-	if (k < 2) {
-		*pb = false;
-		return;
-	}
 	F a = S[0];
 	for (size_t i = 1; i < k; i++) {
 		a *= S[i];
diff --git a/readme.md b/readme.md
index 61e5e6e..87c06a1 100644
--- a/readme.md
+++ b/readme.md
@@ -443,6 +443,7 @@ Y. Sakemi, Y. Nogami, K. Okeya, Y. Morikawa, CANS 2008.
 
 # History
 
+* 2019/Feb/20 LagrangeInterpolation sets out = yVec[0] if k = 1
 * 2019/Jan/31 add mclBnFp_mapToG1, mclBnFp2_mapToG2
 * 2019/Jan/31 fix crash on x64-CPU without AVX (thanks to mortdeus)
 
diff --git a/test/bench.hpp b/test/bench.hpp
index b12947a..12868d3 100644
--- a/test/bench.hpp
+++ b/test/bench.hpp
@@ -185,4 +185,6 @@ void testLagrange()
 	Fr s;
 	mcl::LagrangeInterpolation(s, x, y, k);
 	CYBOZU_TEST_EQUAL(s, c[0]);
+	mcl::LagrangeInterpolation(s, x, y, 1);
+	CYBOZU_TEST_EQUAL(s, y[0]);
 }