Merge pull request github#1296 from RasmusSemmle/master

Add pythagorean query

Author: Mark Shannon

python/ql/src/Numerics/Pythagorean.py

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+# We know that a^2 + b^2 = c^2, and wish to use this to compute c
+from math import sqrt, hypot
+
+a = 3e154 # a^2 > 1e308
+b = 4e154 # b^2 > 1e308
+# with these, c = 5e154 which is less that 1e308
+
+def longSideDirect():
+    return sqrt(a**2 + b**2) # this will overflow
+
+def longSideBuiltin():
+    return hypot(a, b) # better to use built-in function

python/ql/src/Numerics/Pythagorean.qhelp

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+<!DOCTYPE qhelp PUBLIC
+  "-//Semmle//qhelp//EN"
+  "qhelp.dtd">
+<qhelp>
+
+<overview>
+<p>
+Calculating the length of the hypotenuse using the standard formula <code>c = sqrt(a**2 + b**2)</code> may lead to overflow if the two other sides are both very large.
+Even though <code>c</code> will not be much bigger than <code>max(a, b)</code>, either <code>a**2</code> or <code>b**2</code> (or both) will.
+Thus, the calculation could overflow, even though the result is well within representable range.
+</p>
+</overview>
+
+<recommendation>
+<p>
+Rather than <code>sqrt(a**2 + b**2)</code>, use the built-in function <code>hypot(a,b)</code> from the <code>math</code> library.
+</p>
+</recommendation>
+
+<example>
+<p>
+The following code shows two different ways of computing the hypotenuse.
+The first is a direct rewrite of the Pythagorean theorem, the second uses the built-in function.
+</p>
+
+<sample src="Pythagorean.py" />
+</example>
+
+<references>
+<li>Python Language Reference: <a href="https://docs.python.org/library/math.html#math.hypot">The hypot function</a></li>
+<li>Wikipedia: <a href="https://en.wikipedia.org/wiki/Hypot">Hypot</a>.</li>
+</references>
+</qhelp>

python/ql/src/Numerics/Pythagorean.ql

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+/**
+ * @name Pythagorean calculation with sub-optimal numerics
+ * @description Calculating the length of the hypotenuse using the standard formula may lead to overflow.
+ * @kind problem
+ * @tags accuracy
+ * @problem.severity warning
+ * @sub-severity low
+ * @precision medium
+ * @id py/pythagorean
+ */
+
+import python
+
+predicate squareOp(BinaryExpr e) {
+  e.getOp() instanceof Pow and e.getRight().(IntegerLiteral).getN() = "2"
+}
+
+predicate squareMul(BinaryExpr e) {
+  e.getOp() instanceof Mult and e.getRight().(Name).getId() = e.getLeft().(Name).getId()
+}
+
+predicate squareRef(Name e) {
+  e.isUse() and
+  exists(SsaVariable v, Expr s |
+    v.getVariable() = e.getVariable() |
+    s = v.getDefinition().getNode().getParentNode().(AssignStmt).getValue() and
+    square(s)
+  )
+}
+
+predicate square(Expr e) {
+  squareOp(e)
+  or
+  squareMul(e)
+  or
+  squareRef(e)
+}
+
+from
+  Call c,
+  BinaryExpr s
+where
+  c.getFunc().toString() = "sqrt" and
+  c.getArg(0) = s and
+  s.getOp() instanceof Add and
+  square(s.getLeft()) and square(s.getRight())
+select
+  c, "Pythagorean calculation with sub-optimal numerics"

python/ql/test/query-tests/Numerics/Pythagorean.expected

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+| pythagorean_test.py:6:12:6:28 | sqrt() | Pythagorean calculation with sub-optimal numerics |
+| pythagorean_test.py:9:12:9:26 | sqrt() | Pythagorean calculation with sub-optimal numerics |
+| pythagorean_test.py:14:12:14:24 | sqrt() | Pythagorean calculation with sub-optimal numerics |

python/ql/test/query-tests/Numerics/Pythagorean.qlref

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+Numerics/Pythagorean.ql

python/ql/test/query-tests/Numerics/pythagorean_test.py

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+# Computing the Euclidian norm using the Pythagorean Theorem
+
+from math import sqrt
+
+def withPow(a, b):
+    return sqrt(a**2 + b**2)
+
+def withMul(a, b):
+    return sqrt(a*a + b*b)
+
+def withRef(a, b):
+    a2 = a**2
+    b2 = b*b
+    return sqrt(a2 + b2)