Copyright (c) 2002, 2018, Oracle and/or its affiliates. All rights reserved. DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. This code is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 2 only, as published by the Free Software Foundation. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License version 2 for more details (a copy is included in the LICENSE file that accompanied this code). You should have received a copy of the GNU General Public License version 2 along with this work; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA or visit www.oracle.com if you need additional information or have any questions. Strength Reduction ------------------ Strength reduction replaces an expansive operation by a cheaper one, such as multiplication by addition or subtraction, multiplication instead of exponentiation; use compound assignment operators such as += wherever possible, changing code of the form a[i] = a[i] + x to a[i] += x, since they result in fewer bytecode instructions; use shifts instead of multiplication by powers of two, etc. For example: x ** 2 = x * x 2.0 * x = x + x x / 2 = x * 0.5 Induction Variable ------------------ A variable is called an induction variables of a loop if every time the variable changes values it is incremented or decrmented by some constant. Basic induction variables i whose only assignments within the loop is of the form i += c, where c is a constant.