Re: [Stds-754] Motion: Update transcendental functions with crlibm progress.

[r754@xxxxxxxxxxxxxx]

        Item 19 has been so amended.  - Dan

> From: "Eric Postpischil" <stds-754+ieee.org@xxxxxxx>
> Date: Mon, 7 Aug 2006 21:33:57 -0700
> Subject: Re: [Stds-754] Motion: Update transcendental functions with crlibm
>       progress.
>
> 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.