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*To*: <stds-754@xxxxxxxx>, <stds-754@xxxxxxxxxxx>*Subject*: Re: Motion: Update transcendental functions with crlibm progress.*From*: "Eric Postpischil" <stds-754+ieee.org@xxxxxxx>*Date*: Mon, 7 Aug 2006 21:33:57 -0700*Importance*: Normal*List-help*: <http://listserv.ieee.org/cgi-bin/wa?LIST=STDS-754>, <mailto:LISTSERV@LISTSERV.IEEE.ORG?body=INFO STDS-754>*List-owner*: <mailto:STDS-754-request@LISTSERV.IEEE.ORG>*List-subscribe*: <mailto:STDS-754-subscribe-request@LISTSERV.IEEE.ORG>*List-unsubscribe*: <mailto:STDS-754-unsubscribe-request@LISTSERV.IEEE.ORG>*Sender*: stds-754@xxxxxxxxxxxxxxxxx

I would like to amend my motion with corrections and suggestions from Jim Thomas. The changes are: Remove the editorial note about sin not underflowing for single- and double-precision (this does not substantively change the motion): Operation: sin Function: sin(x) Domain: [-pi, +pi] Exceptions: |x| = infinity: invalid; underflow Separate sinpi and cospi and note that sinpi may underflow: Operation: sinpi Function: sin(pi*x) Domain: empty Exceptions: |x| = infinity: invalid; underflow Operation: cospi Function: cos(pi*x) Domain: empty Exceptions: |x| = infinity: invalid Add a footnote about exceptions that can occur in weird formats (and license the editors to change the phrasing): Some functions, such as cospi and log, can be made to underflow and/or overflow in an abnormal format with a huge precision and a small exponent field. These are not noted in table D.1 and are not anticipated to occur in common practice. The entire new text of the motion follows. -- edp (Eric Postpischil) http://edp.org Motion: Update Table D.1 with new results from crlibm 0.14. Rationale: The crlibm project has new results showing the feasibility of these new intervals. Edits: [[Text in double brackets is comment, not part of the motion.]] [[I use the format below because it is easier to compose, and, I judge, read, in plain text email than trying to produce a table format. This motion is not intended to change the draft's table format to this format. "Domain" stands for the "Correctly-rounded Domain" column.]] Change Table D.1 to: Operation: exp Function: e^x Domain: [-infinity, +infinity] [[Complete.]] Exceptions: overflow; underflow Operation: log, log2, log10 Function: log[e](x), log[2](x), log[10](x) Domain: (0, +infinity] [[Complete.]] Exceptions: x = 0: division by zero; x < 0: invalid Operation: sinh, cosh Function: sinh(x), cosh(x) Domain: [-infinity, +infinity] [[Complete.]] Exceptions: overflow Operation: sin Function: sin(x) Domain: [-pi, +pi] Exceptions: |x| = infinity: invalid; underflow Operation: cos Function: cos(x) Domain: [-pi, +pi] Exceptions: |x| = infinity: invalid; underflow [[Even if cos does not underflow for any single- or double-precision number, it might for other precisions.]] Operation: tan Function: tan(x) Domain: [-pi, +pi] Exceptions: |x| = infinity: invalid; underflow; overflow [[Even if tan does not underflow or overflow for any single- or double-precision number, it might for other precisions.]] Operation: asin Function: asin(x) Domain: [-1, +1] [[Complete.]] Exceptions: x not in [-1, +1]: invalid Operation: acos Function: acos(x) Domain: [-1, 1] [[Complete.]] Exceptions: x not in [-1, +1]: invalid Operation: atan Function: atan(x) Domain: [-infinity, +infinity] [[Complete.]] Exceptions: underflow [[Retain existing notes about atan.]] Operation: expm1 Function: e^x-1 Domain: [-infinity, +infinity] [[Complete.]] Exceptions: overflow; underflow Operation: log1p Function: log[e](1+x) Domain: (-1, +infinity] [[Complete.]] Exceptions: x = -1: division by zero; x < -1: invalid Operation: sinpi Function: sin(pi*x) Domain: empty Exceptions: |x| = infinity: invalid; underflow Operation: cospi Function: cos(pi*x) Domain: empty Exceptions: |x| = infinity: invalid Operation: atanpi Function: atan(x)/pi Domain: empty Exceptions: underflow Add a footnote to table D.1. about exceptions that can occur in weird formats (and license the editors to change the phrasing): Some functions, such as cospi and log, can be made to underflow and/or overflow in an abnormal format with a huge precision and a small exponent field. These are not noted in table D.1 and are not anticipated to occur in common practice.

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