[SYSTEMDS-3833] Fix robustness seq() length computation

Size inference and runtime operations all utilize the same primitive
for computing the seq length. However, this primitive must be able
to handle non-integer (from,to,incr) values and as such is prone to
round-off-errors. We now added a compensation that detects such round
off errors and corrects the resulting size.

src/main/java/org/apache/sysds/runtime/util/UtilFunctions.java

@@ -438,14 +438,17 @@ public static long getSeqLength(double from, double to, double incr, boolean che
 		//a very small increment. Hence, we use a different formulation 
 		//that exhibits better numerical stability by avoiding the subtraction
 		//of numbers of different magnitude.
+		//Additionally we check the resulting length and add 1 if this check
+		//allows inferring that round-off errors happened.
 		if( (isSpecial(from) || isSpecial(to) || isSpecial(incr) 
 			|| (from > to && incr > 0) || (from < to && incr < 0)) ) {
 			if( check )
 				throw new RuntimeException("Invalid seq parameters: ("+from+", "+to+", "+incr+")");
 			else
 				return 0; // invalid loop configuration
 		}
-		return 1L + (long) Math.floor(to/incr - from/incr);
+		long tmp = 1L + (long) Math.floor(to/incr - from/incr);
+		return tmp + ((from+tmp*incr <= to) ? 1 : 0);
 	}
 
 	/**

src/test/java/org/apache/sysds/test/functions/io/SeqSizeTest.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+package org.apache.sysds.test.functions.io;
+
+import org.junit.Test;
+import org.apache.sysds.test.AutomatedTestBase;
+import org.apache.sysds.test.TestConfiguration;
+import org.apache.sysds.test.TestUtils;
+
+public class SeqSizeTest extends AutomatedTestBase {
+
+	private final static String TEST_NAME = "SeqSizeTest";
+	private final static String TEST_DIR = "functions/io/";
+	private final static String TEST_CLASS_DIR = TEST_DIR + SeqSizeTest.class.getSimpleName() + "/";
+
+	private final static double eps = 1e-9;
+
+	@Override
+	public void setUp() {
+		TestUtils.clearAssertionInformation();
+		addTestConfiguration(TEST_NAME, 
+			new TestConfiguration(TEST_CLASS_DIR, TEST_NAME, new String[] { "Rout" }) ); 
+	}
+
+	@Test
+	public void runSizeTest() {
+		TestConfiguration config = getTestConfiguration(TEST_NAME);
+		loadTestConfiguration(config);
+		String HOME = SCRIPT_DIR + TEST_DIR;
+		fullDMLScriptName = HOME + TEST_NAME + ".dml";
+		programArgs = new String[]{"-explain", "-args", output("R")};
+		runTest(true, false, null, -1);
+		double dmlScalar = TestUtils.readDMLScalar(output("R")); 
+		TestUtils.compareScalars(dmlScalar, 5, eps);
+	}
+}

src/test/scripts/functions/io/SeqSizeTest.dml

@@ -0,0 +1,23 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+x = length(seq(1,1001,250))
+write(x, $1);