J3/05-118r1 Date: 31 Jan 2005 To: J3 From: John Reid Subject: HYPOT(NaN,inf), HYPOT(NaN,finite) Here is a draft response for F03/0039, with thanks to Malcolm Cohen for his help. NUMBER: F03/0039 TITLE: HYPOT() KEYWORDS: IEEE-754, hypot() DEFECT TYPE: Erratum STATUS: For consideration QUESTION: What is HYPOT(NaN,infinity)? HYPOT(NaN,finite)? HYPOT(X,Y) when X and/or Y is an infinity (even if the other is a NaN) shall be +infinity. Reason: hypot(), when one of the arguments is an infinity, is +infinity independent of the value of the other argument. So, if the NaN argument is replaced by zero, any finite number, or any infinity, hypot(infinity,NaN) is still infinity. HYPOT(X,Y) when X and/or Y is a NaN (and neither is infinite) shall be a NaN, and should one of the NaN arguments. ANSWER: This example illustrates the use of the features of this section to provide reliable software that is fast in the uncomplicated case. We did not consider what would happen if one of the arguments is a NaN and have therefore edited the text slightly. DISCUSSION: In fact, if either X or Y is a NaN, the first executable statement will set HYPOT to a NaN without signaling an exception. The slower code in the IF construct will therefore not be executed and a NaN will be returned, which is consistent with the way NaNs are handled by intrinsic operators, see paragraph 3 of section 6.2 of the IEEE International Standard. EDITS: Page and line numbers refer to 04-007. [389:12]. Subclause 14.11, Note 14.17, final paragraph, line 2. Before "exception" add "overflow or underflow". SUBMITTED BY: Fred Tydeman HISTORY: J3/05-118 m171 Submitted