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Subject: [Boost-commit] svn:boost r83545 - in sandbox/precision/libs/precision/doc: . html html/precision
From: pbristow_at_[hidden]
Date: 2013-03-24 12:52:52


Author: pbristow
Date: 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
New Revision: 83545
URL: http://svn.boost.org/trac/boost/changeset/83545

Log:
More refinement, including changing types to typedefs where appropriate. Added cmath functions needed. Still some Chris TODOs near end.
Binary files modified:
   sandbox/precision/libs/precision/doc/precision.pdf
Text files modified:
   sandbox/precision/libs/precision/doc/html/index.html | 30 ++++---
   sandbox/precision/libs/precision/doc/html/precision/abstract.html | 20 +++--
   sandbox/precision/libs/precision/doc/html/precision/background.html | 18 ++--
   sandbox/precision/libs/precision/doc/html/precision/introduction.html | 53 +++++---------
   sandbox/precision/libs/precision/doc/html/precision/references.html | 110 +++++++++++++++---------------
   sandbox/precision/libs/precision/doc/html/precision/suffixes.html | 25 +++---
   sandbox/precision/libs/precision/doc/html/precision/version_id.html | 6
   sandbox/precision/libs/precision/doc/html4_symbols.qbk | 1
   sandbox/precision/libs/precision/doc/precision.qbk | 142 ++++++++++++++++++++++++---------------
   9 files changed, 213 insertions(+), 192 deletions(-)

Modified: sandbox/precision/libs/precision/doc/html/index.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/index.html (original)
+++ sandbox/precision/libs/precision/doc/html/index.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -1,10 +1,10 @@
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>Specific-Width Floating-Point Types</title>
+<title>Specific-Width Floating-Point Typedefs</title>
 <link rel="stylesheet" href="./boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="index.html" title="Specific-Width Floating-Point Types">
+<link rel="home" href="index.html" title="Specific-Width Floating-Point Typedefs">
 <link rel="next" href="precision/abstract.html" title="Abstract">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -22,7 +22,7 @@
 <div class="titlepage">
 <div>
 <div><h2 class="title">
-<a name="precision"></a>Specific-Width Floating-Point Types</h2></div>
+<a name="precision"></a>Specific-Width Floating-Point Typedefs</h2></div>
 <div><div class="authorgroup">
 <div class="author"><h3 class="author">
 <span class="firstname">Paul A.</span> <span class="surname">Bristow</span>
@@ -50,18 +50,17 @@
 <dt><span class="section">Abstract</span></dt>
 <dt><span class="section">Background</span></dt>
 <dt><span class="section">Introduction</span></dt>
-<dt><span class="section">The proposed types and potential extensions</span></dt>
-<dt><span class="section"><a href="precision/suffixes.html">How to specify constants with quad
- and half precision?</a></span></dt>
-<dt><span class="section">Specifying Precision</span></dt>
-<dd><dl>
-<dt><span class="section"><a href="precision/precision/integerfixedtypes.html">Existing Specific
- precision integer types</a></span></dt>
-<dt><span class="section">Proposed new section</span></dt>
-</dl></dd>
-<dt><span class="section">Interaction with complex</span></dt>
+<dt><span class="section"><a href="precision/thetypedefs.html">The proposed typedefs and potential
+ extensions</a></span></dt>
+<dt><span class="section"><a href="precision/suffixes.html">How to define floating-point literal
+ suffixes?</a></span></dt>
+<dt><span class="section">Place in the standard</span></dt>
+<dt><span class="section">Interaction with <limits></span></dt>
+<dt><span class="section">Interoperation with <cmath></span></dt>
+<dt><span class="section">Interoperation with <complex></span></dt>
 <dt><span class="section"><a href="precision/microfpu.html">Improved efficiency and robustness
     for microcontrollers</a></span></dt>
+<dt><span class="section">The context within existing implementations</span></dt>
 <dt><span class="section">References</span></dt>
 <dt><span class="section">Version Info</span></dt>
 </dl>
@@ -69,6 +68,9 @@
 <p>
     ISO/IEC JTC1 SC22 WG21/SG6 Numerics N??? - 2013-4-??
   </p>
+<p>
+ ]
+ </p>
 <div class="important"><table border="0" summary="Important">
 <tr>
 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="images/important.png"></td>
@@ -89,7 +91,7 @@
 </table></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: March 24, 2013 at 09:21:29 GMT</small></p></td>
+<td align="left"><p><small>Last revised: March 24, 2013 at 16:50:00 GMT</small></p></td>
 <td align="right"><div class="copyright-footer"></div></td>
 </tr></table>
 <hr>

Modified: sandbox/precision/libs/precision/doc/html/precision/abstract.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/abstract.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/abstract.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -4,9 +4,9 @@
 <title>Abstract</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="prev" href="../index.html" title="Specific-Width Floating-Point Types">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="prev" href="../index.html" title="Specific-Width Floating-Point Typedefs">
 <link rel="next" href="background.html" title="Background">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -28,7 +28,7 @@
 </h2></div></div></div>
 <p>
       It is proposed to add to the C++ standard several optional typedefs for floating-point
- types with specified widths. In particular, the optional types include <code class="computeroutput"><span class="identifier">float16_t</span></code>, <code class="computeroutput"><span class="identifier">float32_t</span></code>,
+ types having specified width. In particular, the optional types include <code class="computeroutput"><span class="identifier">float16_t</span></code>, <code class="computeroutput"><span class="identifier">float32_t</span></code>,
       <code class="computeroutput"><span class="identifier">float64_t</span></code>, <code class="computeroutput"><span class="identifier">float128_t</span></code>,
       and their corresponding fast and least types. The optional floating-point types
       are to conform with the corresponding types <code class="computeroutput"><span class="identifier">binary16</span></code>,
@@ -38,11 +38,13 @@
       format</a>.
     </p>
 <p>
- The optional floating-point types with specified widths are to be contained
+ The optional floating-point types having specified width are to be contained
       in a new standard library header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cstdfloat</span><span class="special">&gt;</span></code>.
- Any of the optional floating-point types with specified widths included in
- the implementation must have full support for the functions in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span></code> and seamlessly interoperate with <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span></code>.
- The proposed new floating-point types with specified widths will be defined
+ Any of the optional floating-point types having specified width included in
+ the implementation should have full support for the functions in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span></code> and seamlessly interoperate with <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span></code>. Any of the optional floating-point types
+ having specified width included in the implementation must template specializations
+ of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span></code>.
+ The proposed new floating-point types having specified width will be defined
       in the global and <code class="computeroutput"><span class="identifier">std</span></code> namespaces.
     </p>
 <p>
@@ -52,7 +54,7 @@
       <span class="keyword">double</span></code>.
     </p>
 <p>
- Floating-point types with specified widths are expected to significantly improve
+ Floating-point types having specified width are expected to significantly improve
       clarity of code and portability of floating-point calculations. Analogous improvements
       for integer calculations were recently achieved via standardization of integer
       types having specified width such as <code class="computeroutput"><span class="identifier">int8_t</span></code>,

Modified: sandbox/precision/libs/precision/doc/html/precision/background.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/background.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/background.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -4,8 +4,8 @@
 <title>Background</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
 <link rel="prev" href="abstract.html" title="Abstract">
 <link rel="next" href="introduction.html" title="Introduction">
 </head>
@@ -52,8 +52,8 @@
     </p>
 <p>
       There is also progress in C++ in the area of multiprecision, including support
- of multiprecision floating-point numbers. In particular, the acceptance and
- release of Boost.Multiprecision
+ of user-defined multiprecision floating-point numbers. In particular, the acceptance
+ and release of Boost.Multiprecision
       provides much higher precision than built-in <code class="computeroutput"><span class="keyword">long</span>
       <span class="keyword">double</span></code> with its cpp_dec_float
       data type. Boost.Multiprecision
@@ -68,8 +68,8 @@
       Since Boost.Multiprecision
       and Boost.Math
       work seamlessly, a <code class="computeroutput"><span class="identifier">float_type</span> <span class="keyword">typedef</span></code> can be used to switch from a built-in
- type to hundreds of decimal digits. This allows all the special functions and
- distributions in Boost.Math
+ type to a multiprecision type with tens or even hundreds of decimal digits.
+ This allows all the special functions and distributions in Boost.Math
       to be used at any chosen precision.
     </p>
 <p>
@@ -85,9 +85,9 @@
     </p>
 <p>
       All these development have made C++ much more attractive to the scientific
- and engeering community, especially those needing mathematical functions and
- higher (or lower) precision for some of their calculations. Previously these
- domains were predominantly covered by computer algebra systems.
+ and engineering community, especially those needing mathematical functions
+ and higher (or lower) precision for some of their calculations. Previously
+ these domains were predominantly covered by computer algebra systems.
     </p>
 <div class="footnotes">
 <br><hr style="width:100; align:left;">

Modified: sandbox/precision/libs/precision/doc/html/precision/introduction.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/introduction.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/introduction.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -4,10 +4,10 @@
 <title>Introduction</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
 <link rel="prev" href="background.html" title="Background">
-<link rel="next" href="thetypes.html" title="The proposed types and potential extensions">
+<link rel="next" href="thetypedefs.html" title="The proposed typedefs and potential extensions">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
 <table cellpadding="2" width="100%"><tr>
@@ -20,7 +20,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="background.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thetypes.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="background.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thetypedefs.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 <div class="section precision_introduction">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -37,8 +37,8 @@
 <p>
       It is, however, emphasized that floating-point adherence to <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_
       floating-point format</a> is not mandated by the current C++ language standard.
- Nor does the standard specify the widths or precisions of its built-in types
- <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>,
+ Nor does the standard specify the widths, precisions or lyaout of its built-in
+ types <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>,
       and <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
       This can lead to portability problems, introduce poor efficiency on cost-sensitive
       microcontroller architectures, and reduce reliability and safety.
@@ -58,46 +58,29 @@
       of floating-point calculations in C++ by ensuring that the actual precision
       of a floating-point type can be exactly determined both at compile-time as
       well as during the run of a calculation. Strong interest in floating-point
- types with specified widths has, for example, recently been expressed on the
- <a href="http://lists.boost.org/Archives/boost/2013/03/201786.php" target="_top">Boost
+ <code class="computeroutput"><span class="identifier">typedefs</span></code> having specified width
+ has, for example, recently been expressed on the <a href="http://lists.boost.org/Archives/boost/2013/03/201786.php" target="_top">Boost
       list discussion of precise floating-point types</a>.
     </p>
 <p>
- Recent specification of integer types having specified widths in C99, C11,
+ Recent specification of integer typedefs having specified width in C99, C11,
       C++11, and <a href="http://open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3376.pdf" target="_top">C++
       draft specification</a> has drastically improved integer algorithm portability
       and range.
     </p>
 <p>
- One example of how integer types having specified widths have proven to be
+ One example of how integer typedefs having specified width have proven to be
       essential is described by Robert Ramey <a href="http://lists.boost.org/Archives/boost/2002/11/40432.php" target="_top">Usefulness
       of fixed integer sizes in portability (for Boost serialization library).</a>
     </p>
 <p>
- &#8220;
-Fundamental types in C++ are <code class="computeroutput"><span class="keyword">unsigned</span>
- <span class="keyword">char</span><span class="special">,</span> <span class="keyword">signed</span> <span class="keyword">char</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">short</span> <span class="keyword">int</span><span class="special">,</span>
- <span class="keyword">signed</span> <span class="keyword">short</span>
- <span class="keyword">int</span><span class="special">,</span> <span class="special">...</span> <span class="keyword">unsigned</span> <span class="keyword">long</span><span class="special">,</span> <span class="keyword">signed</span>
- <span class="keyword">long</span></code>. In addition to the above some
- compilers define <code class="computeroutput"><span class="identifier">int32_t</span></code>, and
- other as fundamental types. It is a unfortunate accident of history that the
- nomenclature is confusing. It is an unfortunate original design choice that
- this size of int, char etc were not defined as a specific number of bits. However
- at the time there were in common usage machines with 9, 16, 18, 24, 32, 36
- and 48 bit words. What else were the authors to do? It is common among programers
- to define types <code class="computeroutput"><span class="identifier">int16_t</span></code>, ...,
- etc using the <code class="computeroutput"><span class="keyword">typedef</span></code> facility
- to map integers of a specific size between machines. This does no harm and
- can facilitate portability. However it in no way alters the fundamental types
- that are available on a given platform. &#8221;
- </p>
-<p>
- The motivations to provide floating-point types with specified widths are analogous
- to those that led to the introduction of integers with specified widths such
- as <code class="computeroutput"><span class="identifier">int8_t</span></code>, <code class="computeroutput"><span class="identifier">int16_t</span></code>,
- <code class="computeroutput"><span class="identifier">int32_t</span></code>, and <code class="computeroutput"><span class="identifier">int64_t</span></code>. The specification of floating-point
- types with specified widths and adherence to <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_
+ The motivations to provide floating-point <code class="computeroutput"><span class="keyword">typedef</span></code>s
+ having specified width are analogous to those that led to the introduction
+ of integers having specified width such as <code class="computeroutput"><span class="identifier">int8_t</span></code>,
+ <code class="computeroutput"><span class="identifier">int16_t</span></code>, <code class="computeroutput"><span class="identifier">int32_t</span></code>,
+ and <code class="computeroutput"><span class="identifier">int64_t</span></code>. The specification
+ of floating-point <code class="computeroutput"><span class="keyword">typedef</span></code>s having
+ specified width and adherence to <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_
       floating-point format</a> can potentially improve the C++ language significantly,
       especially in the scientific and engineering communities where other languages
       have found benefit from types that conform exactly to the <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_
@@ -122,7 +105,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="background.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thetypes.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="background.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thetypedefs.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 </body>
 </html>

Modified: sandbox/precision/libs/precision/doc/html/precision/references.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/references.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/references.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -4,9 +4,9 @@
 <title>References</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="prev" href="microfpu.html" title="Improved efficiency and robustness for microcontrollers">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="prev" href="context.html" title="The context within existing implementations">
 <link rel="next" href="version_id.html" title="Version Info">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,61 +20,63 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="microfpu.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="version_id.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="context.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="version_id.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 <div class="section precision_references">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 <a name="precision.references"></a><a class="link" href="references.html" title="References">References</a>
 </h2></div></div></div>
-<p>
- <a href="http://isocpp.org/std/meetings-and-participation/papers-and-mailings" target="_top">isocpp.org
- C++ papers and mailings</a>
- </p>
-<p>
- <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html" target="_top">C++
- Binary Fixed-Point Arithmetic, N3352, Lawrence Crowl</a>
- </p>
-<p>
- <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html" target="_top">Proposal
- to Add Decimal Floating Point Support to C++, N3407 Dietmar Kuhl</a>
- </p>
-<p>
- The C committee is working on a Decimal TR as TR 24732. The decimal support
- in C uses built-in types _Decimal32, _Decimal64, and _Decimal128. <a href="http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf" target="_top">128-bit
- decimal floating point in IEEE 754:2008</a>
- </p>
-<p>
- <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">lists binary16,
- 32, 64 and 128</a>
- </p>
-<p>
- (and also decimal 32, 64, and 128) <a href="http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4610933" target="_top">IEEE
- Std 754-2008</a>
- </p>
-<p>
- <a href="http://dx.doi.org/10.1109/IEEESTD.2008.4610935" target="_top">IEEE Standard for
- Floating-point Arithmetic, IEEE Std 754-2008</a>
- </p>
-<p>
- <a href="http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf" target="_top">How
- to Read Floating Point Numbers Accurately, William D Clinger</a>
- </p>
-<p>
- <a href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2013/n3548.pdf" target="_top">Conditionally-supported
- Special Math Functions for C++14, N3584, Walter E. Brown</a>
- </p>
-<p>
- <a href="../www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3515.pdf" target="_top">Walter
- E.Brown, Opaque Typedefs</a>
- </p>
-<p>
- <a href="http://open-std.org/jtc1/sc22/wg21/docs/papers/2013/n????.pdf" target="_top">Specification
- of Extended Precision Floating-point and Integer Types, Christopher Kormanyos,
- John Maddock</a>
- </p>
-<p>
- X8087 notes
- </p>
+<div class="orderedlist"><ol class="orderedlist" type="1">
+<li class="listitem">
+ <a href="http://isocpp.org/std/meetings-and-participation/papers-and-mailings" target="_top">isocpp.org
+ C++ papers and mailings</a>
+ </li>
+<li class="listitem">
+ <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html" target="_top">C++
+ Binary Fixed-Point Arithmetic, N3352, Lawrence Crowl</a>
+ </li>
+<li class="listitem">
+ <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html" target="_top">Proposal
+ to Add Decimal Floating Point Support to C++, N3407 Dietmar Kuhl</a>
+ </li>
+<li class="listitem">
+ The C committee is working on a Decimal TR as TR 24732. The decimal support
+ in C uses built-in types _Decimal32, _Decimal64, and _Decimal128. <a href="http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf" target="_top">128-bit
+ decimal floating point in IEEE 754:2008</a>
+ </li>
+<li class="listitem">
+ <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">lists binary16,
+ 32, 64 and 128</a> (and also decimal 32, 64, and 128)
+ </li>
+<li class="listitem">
+ <a href="http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4610933" target="_top">IEEE
+ Std 754-2008</a>
+ </li>
+<li class="listitem">
+ <a href="http://dx.doi.org/10.1109/IEEESTD.2008.4610935" target="_top">IEEE Standard
+ for Floating-point Arithmetic, IEEE Std 754-2008</a>
+ </li>
+<li class="listitem">
+ <a href="http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf" target="_top">How
+ to Read Floating Point Numbers Accurately, William D Clinger</a>
+ </li>
+<li class="listitem">
+ <a href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2013/n3548.pdf" target="_top">Conditionally-supported
+ Special Math Functions for C++14, N3584, Walter E. Brown</a>
+ </li>
+<li class="listitem">
+ <a href="../www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3515.pdf" target="_top">Walter
+ E.Brown, Opaque Typedefs</a>
+ </li>
+<li class="listitem">
+ <a href="http://open-std.org/jtc1/sc22/wg21/docs/papers/2013/n????.pdf" target="_top">Specification
+ of Extended Precision Floating-point and Integer Types, Christopher Kormanyos,
+ John Maddock</a>
+ </li>
+<li class="listitem">
+ X8087 notes
+ </li>
+</ol></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
@@ -86,7 +88,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="microfpu.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="version_id.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="context.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="version_id.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 </body>
 </html>

Modified: sandbox/precision/libs/precision/doc/html/precision/suffixes.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/suffixes.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/suffixes.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -1,13 +1,13 @@
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>How to specify constants with quad and half precision?</title>
+<title>How to define floating-point literal suffixes?</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="prev" href="thetypes.html" title="The proposed types and potential extensions">
-<link rel="next" href="precision.html" title="Specifying Precision">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="prev" href="thetypedefs.html" title="The proposed typedefs and potential extensions">
+<link rel="next" href="thestandard.html" title="Place in the standard">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
 <table cellpadding="2" width="100%"><tr>
@@ -20,12 +20,12 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="thetypes.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="precision.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="thetypedefs.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thestandard.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 <div class="section precision_suffixes">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="precision.suffixes"></a><a class="link" href="suffixes.html" title="How to specify constants with quad and half precision?">How to specify constants with quad
- and half precision?</a>
+<a name="precision.suffixes"></a><a class="link" href="suffixes.html" title="How to define floating-point literal suffixes?">How to define floating-point literal
+ suffixes?</a>
 </h2></div></div></div>
 <p>
       The standard specifies that the type of a floating-point literal is double
@@ -62,7 +62,7 @@
     </p>
 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cstdfloat</span><span class="special">&gt;</span>
 
-<span class="identifier">constexpr</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float16_t</span> <span class="identifier">euler_gamma</span> <span class="special">=</span> <span class="number">0.577216</span><span class="identifier">H</span><span class="special">;</span>
+<span class="identifier">constexpr</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float16_t</span> <span class="identifier">euler</span> <span class="special">=</span> <span class="number">0.577216</span><span class="identifier">H</span><span class="special">;</span>
 </pre>
 <p>
       Higher precisions also require construction from floating-point literals. As
@@ -85,14 +85,13 @@
 
 <span class="identifier">constexpr</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float128_t</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.1415926535897932384626433832795028841972F</span><span class="number">128</span><span class="special">;</span>
 
-<span class="identifier">constexpr</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float16_t</span> <span class="identifier">euler_gamma</span> <span class="special">=</span> <span class="number">0.577216F</span><span class="number">16</span><span class="special">;</span>
+<span class="identifier">constexpr</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float16_t</span> <span class="identifier">euler</span> <span class="special">=</span> <span class="number">0.577216F</span><span class="number">16</span><span class="special">;</span>
 </pre>
 <p>
       This suffix scheme is unequivocal and it can be easily extended to unlimited
       precision. On the other hand, it may be difficult for programmers to separate
       the character part of the suffix from its numerical part when analyzing source
- code. For example, it is particularly difficult to resolve the suffix in <code class="computeroutput"><span class="identifier">euler_gamma</span></code> above, since the <code class="computeroutput"><span class="number">16F</span><span class="number">16</span></code> obscures
- the <code class="computeroutput"><span class="identifier">F</span></code>.
+ code. For example, it is particularly difficult to resolve the <code class="computeroutput"><span class="identifier">F</span></code> suffix in the initialization of <code class="computeroutput"><span class="identifier">euler</span></code> above.
     </p>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -105,7 +104,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="thetypes.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="precision.html"><img src="../images/next.png" alt="Next"></a>
+<a accesskey="p" href="thetypedefs.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="thestandard.html"><img src="../images/next.png" alt="Next"></a>
 </div>
 </body>
 </html>

Modified: sandbox/precision/libs/precision/doc/html/precision/version_id.html
==============================================================================
--- sandbox/precision/libs/precision/doc/html/precision/version_id.html (original)
+++ sandbox/precision/libs/precision/doc/html/precision/version_id.html 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -4,8 +4,8 @@
 <title>Version Info</title>
 <link rel="stylesheet" href=".././boostbook.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
-<link rel="home" href="../index.html" title="Specific-Width Floating-Point Types">
-<link rel="up" href="../index.html" title="Specific-Width Floating-Point Types">
+<link rel="home" href="../index.html" title="Specific-Width Floating-Point Typedefs">
+<link rel="up" href="../index.html" title="Specific-Width Floating-Point Typedefs">
 <link rel="prev" href="references.html" title="References">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -26,7 +26,7 @@
 <a name="precision.version_id"></a><a class="link" href="version_id.html" title="Version Info">Version Info</a>
 </h2></div></div></div>
 <p>
- Last edit to Quickbook file precision.qbk was at 09:21:29 AM on 2013-Mar-24.
+ Last edit to Quickbook file precision.qbk was at 04:50:00 PM on 2013-Mar-24.
     </p>
 <div class="tip"><table border="0" summary="Tip">
 <tr>

Modified: sandbox/precision/libs/precision/doc/html4_symbols.qbk
==============================================================================
--- sandbox/precision/libs/precision/doc/html4_symbols.qbk (original)
+++ sandbox/precision/libs/precision/doc/html4_symbols.qbk 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -219,7 +219,6 @@
 [template ldquote[]'''&#x201C;'''] [/ left-pointing double quotation mark " ]
 [template rdquote[]'''&#x201D;'''] [/ right-pointing double quotation mark " ]
 
-
 [/
 Copyright 2007, 2010, 2012, 2013 Paul A. Bristow.
 Distributed under the Boost Software License, Version 1.0.

Modified: sandbox/precision/libs/precision/doc/precision.pdf
==============================================================================
Binary files. No diff available.

Modified: sandbox/precision/libs/precision/doc/precision.qbk
==============================================================================
--- sandbox/precision/libs/precision/doc/precision.qbk (original)
+++ sandbox/precision/libs/precision/doc/precision.qbk 2013-03-24 12:52:49 EDT (Sun, 24 Mar 2013)
@@ -1,4 +1,4 @@
-[article Specific-Width Floating-Point Types
+[article Specific-Width Floating-Point Typedefs
     [quickbook 1.5]
     [id precision]
     [copyright 2013 Paul A. Bristow, Christopher Kormanyos, John Maddock]
@@ -13,6 +13,8 @@
 
 [/purpose paper for C++ ISO standards group WG21/SG6 numerics.]
 
+ISO/IEC JTC1 SC22 WG21/SG6 Numerics N??? - 2013-4-??
+
 [def __Boost [@http://www.boost.org/ Boost]]
 [def __Boost_Math [@http://www.boost.org/doc/libs/1_53_0/libs/math/doc/html/index.html Boost.Math]]
 [def __gsl [@http://www.gnu.org/software/gsl/ GSL-1.9]]
@@ -36,27 +38,26 @@
 [def __libquadmath [@http://gcc.gnu.org/onlinedocs/libquadmath/ GCC libquadmath]]
 [def __Quad [@http://software.intel.com/en-us/forums/topic/358472 Extended or Quad IEEE FP formats]]
 [def __IEEE754 [@http://dx.doi.org/10.1109/IEEESTD.2008.4610935 IEEE Standard for Floating-point Arithmetic, IEEE Std 754-2008]]
-
 [def __IEEE_Half [@http://en.wikipedia.org/wiki/Half_precision_floating-point_format IEEE half-precision floating-point format]]
 [def __IEEE_Single [@http://en.wikipedia.org/wiki/Single_precision_floating-point_format IEEE single-precision floating-point format]]
 [def __IEEE_Double [@http://en.wikipedia.org/wiki/Double_precision_floating-point_format IEEE double-precision floating-point format]]
 [def __IEEE_Quad [@http://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format Quadruple-precision floating-point format]]
 [def __IEEE_Extended [@http://en.wikipedia.org/wiki/Extended_precision#IEEE_754_extended_precision_formats IEEE 754 extended precision formats and x86 80-bit Extended Precision Format]]
 [def __IEEE_floating_point [@http://en.wikipedia.org/wiki/IEEE_floating_point IEEE_ floating-point format]]
-
+[def __IEEE_80_bit[@ http://en.wikipedia.org/wiki/Extended_precision#IEEE_754_extended_precision_formats# x86 Extended Precision Format]]
 [def __IBM_hexadecimal [@http://en.wikipedia.org/wiki/Extended_precision#IBM_extended_precision_formats IBM extended precision formats]]
 
 [def __C_IEEE_2008 [@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1582.pdf C support for IEEE754:2008 N1582]]
 
-[include html4_symbols.qbk]
+[def __arbitrary_precision [@http://en.wikipedia.org/wiki/Arbitrary_precision arbitrary precision]]
 
-ISO/IEC JTC1 SC22 WG21/SG6 Numerics N??? - 2013-4-??
+[include html4_symbols.qbk]
 
 [important This is NOT an official Boost library.]
 
 [note Comments and suggestions to Paul.A.Bristow pbristow_at_hetp.u-net.com.]
 
-[section:abstract Abstract]
+[section:abstract Abstract]
 
 It is proposed to add to the C++ standard several optional
 typedefs for floating-point types having specified width.
@@ -70,7 +71,7 @@
 The optional floating-point types having specified width
 are to be contained in a new standard library header `<cstdfloat>`.
 Any of the optional floating-point types having specified width
-included in the implementation must have full support for the
+included in the implementation should have full support for the
 functions in `<cmath>` and seamlessly interoperate with `<complex>`.
 Any of the optional floating-point types having specified width
 included in the implementation must template specializations
@@ -147,7 +148,7 @@
 required in numerous programming domains.
 
 All these development have made C++ much more attractive to the
-scientific and engeering community, especially those needing
+scientific and engineering community, especially those needing
 mathematical functions and higher (or lower) precision for some
 of their calculations. Previously these domains were predominantly
 covered by computer algebra systems.
@@ -164,7 +165,7 @@
 
 It is, however, emphasized that floating-point adherence
 to __IEEE_floating_point is not mandated by the current C++ language standard.
-Nor does the standard specify the widths or precisions of its built-in types
+Nor does the standard specify the widths, precisions or lyaout of its built-in types
 `float`, `double`, and `long double`. This can lead to portability problems,
 introduce poor efficiency on cost-sensitive microcontroller architectures,
 and reduce reliability and safety.
@@ -182,23 +183,23 @@
 of floating-point calculations in C++ by ensuring that the actual precision
 of a floating-point type can be exactly determined both at compile-time
 as well as during the run of a calculation.
-Strong interest in floating-point types having specified width
+Strong interest in floating-point `typedefs` having specified width
 has, for example, recently been expressed on
 the [@http://lists.boost.org/Archives/boost/2013/03/201786.php Boost list discussion of precise floating-point types].
 
-Recent specification of integer types having specified width
+Recent specification of integer typedefs having specified width
 in C99, C11, C++11, and [@http://open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3376.pdf C++ draft specification]
 has drastically improved integer algorithm portability and range.
 
-One example of how integer types having specified width
+One example of how integer typedefs having specified width
 have proven to be essential is described by Robert Ramey
 [@http://lists.boost.org/Archives/boost/2002/11/40432.php
 Usefulness of fixed integer sizes in portability (for Boost serialization library).]
 
-The motivations to provide floating-point types having specified width
+The motivations to provide floating-point `typedef`s having specified width
 are analogous to those that led to the introduction of integers
 having specified width such as `int8_t`, `int16_t`, `int32_t`, and `int64_t`.
-The specification of floating-point types having specified width
+The specification of floating-point `typedef`s having specified width
 and adherence to __IEEE_floating_point can potentially
 improve the C++ language significantly, especially in the
 scientific and engineering communities
@@ -214,11 +215,11 @@
 
 [endsect] [/section:introduction Introduction]
 
-[section:thetypes The proposed types and potential extensions]
+[section:thetypedefs The proposed typedefs and potential extensions]
 
-The core of this proposal is based on the types `float16_t`, `float32_t`,
+The core of this proposal is based on the `typedef`s `float16_t`, `float32_t`,
 `float64_t`, `float128_t`, and their corresponding least and fast types.
-These floating-point types have specified widths and they are
+These floating-point `typedef`s have specified widths and they are
 to conform with the corresponding types
 `binary16`, `binary32`, `binary64`, and `binary128`
 specified in __IEEE_floating_point.
@@ -243,10 +244,10 @@
 
 No matter what naming scheme is used, the exact layout and number of significand
 and exponent bits can be confirmed as IEEE754 by checking
-`std::numeric_limits<type>::is_iec559 == true`.
+`std::numeric_limits<type>::is_iec559 == true`, and the byte-order.
 
 We will now consider several examples showing how various implementations
-might include floating-point types having specified width.
+might include floating-point `typedef`s having specified width.
 
 An implementation that has `float` and `double` corresponding to
 IEEE 754 `binary32`, `binary64`, respectively, could introduce
@@ -262,7 +263,7 @@
 `float256_t` with about 240 binary significand digits of precision.
 In addition, a `float512_t` type with even more precision
 may be considered as a option. Beyond these, there may be
-potential extension to multiprecision types in the future.
+potential extension to multiprecision types, even __arbitrary_precision, in the future.
 
 Consider an implementation for a supercomputer. This platform might have
 `float`, `double`, and `long double` corresponding to IEEE 754
@@ -298,9 +299,7 @@
 The popular [@http://gcc.gnu.org/wiki/x87note Intel X8087 chipset]
 architecture supports a 10-byte floating-point format.
 So it may be useful to provide optional support for `float80_t`.
-In our opinion, there is no type that is analogous to
-`float80_t` in __IEEE_floating_point, but several implementations
-already exist in practice.
+Several implementations using __IEEE_80_bit already exist in practice.
 
 An implementation that supports single-precision `float`,
 double-precision `double`, and 10-byte `long double`
@@ -356,7 +355,7 @@
 for example, `__SIZEOF_LONG_DOUBLE__`.
 But similar macros are not defined for `__float128` nor for `__float80`.
 
-[endsect] [/section:thetypes The proposed types and potential extensions]
+[endsect] [/section:thetypedefs The proposed types and potential extensions]
 
 [section:suffixes How to define floating-point literal suffixes?]
 
@@ -413,9 +412,9 @@
 
 [section:thestandard Place in the standard]
 
-The proper place for floating-point types having specified width
+The proper place for floating-point `typedef`s having specified width
 should be oriented along the lines of the current standard.
-Consider the existing specification of integer types having
+Consider the existing specification of integer `typedef`s having
 specified precision in C++11. A partial synopsis is shown below.
 
 18.4 Integer types [cstdint]
@@ -438,7 +437,7 @@
 
 We propose to add a new header `<cstdfloat>` to the standard library.
 The header `<cstdfloat>` should contain all floating-point
-types having specified width in the implementation.
+`typedef`s having specified width in the implementation.
 Section 18.4 could be extended as shown below.
 
 18.4? Integer and Floating-Point Types Having Specified Width
@@ -490,10 +489,49 @@
 of elementary and transcendental functions (and possibly additional higher transcendental functions)
 is also essential to make the type useful in real-life computational regimes.
 Therefore, the implementation must provide support for the mathematical
-functions in the `std` namespace (TBD: Chris list functions)
-for each of the floating-point types having specified width
+functions in the `std` namespace for each of the floating-point types having specified width
 included in the implementation.
 
+<cmath> contains
+
+Trigonometric functions:
+
+ cos
+ sin
+ tan
+ acos
+ asin
+ atan
+ atan2
+
+Hyperbolic functions:
+
+ cosh
+ sinh
+ tanh
+
+Exponential and logarithmic functions:
+
+ exp
+ frexp
+
+ ldexp
+ log
+ log10
+ modf
+
+Power functions
+
+ pow
+ sqrt
+
+Rounding, absolute value and remainder functions:
+
+ ceil
+ fabs
+ floor
+ fmod
+
 [endsect] [/section:cmathinterop Interoperation with <cmath>]
 
 [section:complexinterop Interoperation with <complex>]
@@ -522,7 +560,7 @@
 Many existing implementations already support `float`, `double`, and `long double`.
 In addition, some of these either are or strive to be compliant with __IEEE_floating_point.
 In these cases, it will be straightforward to support (at least) a subset
-of the proposed floating-point types having specified width using type definitions.
+of the proposed floating-point `typedef`s having specified width using type definitions.
 This was discussed above.
 
 Some implementations for cost-sensitive microcontroller platforms support
@@ -539,27 +577,25 @@
 in a variety of ways, and this has given rise to numerous portability problems.
 For example, suppose we wish to achieve a precision higher than the most common
 IEEE 64-bit floating-point type supported by the X86 chipsets normally used for double
-(http://en.wikipedia.org/wiki/Double_precision providing a precision of between 15 to 17
-decimal digits).
+([@http://en.wikipedia.org/wiki/Double_precision double precision] providing a precision of between 15 and 17 decimal digits).
 
 The options for [@http://en.wikipedia.org/wiki/Long_double long double] are many.
 At least one popular compiler treats `long double` exactly as `double`.
 
-However the [@http://gcc.gnu.org/wiki/x87note Intel X8087 chipset] does do
-calculations using internal 80-bit registers, increasing the significand from 53 to 63 bits,
-and gaining about 3 decimal digits precision from 18 and 21.
+However the [@http://gcc.gnu.org/wiki/x87note Intel X8087 chipset] can do
+calculations using internal 80-bit registers, increasing the significand from 53 to 63 bits, and gaining about 3 decimal digits precision from 18 and 21.
 If we wish to ensure that we use all 80 bits available from Intel 8087 chips to calculate
 [@http://en.wikipedia.org/wiki/Extended_precision Extended precision]
 we would use a `typedef float80_t`, as shown above.
 If the compiler could not generate code this type directly,
 then it would substitute software emulation, perhaps using a
-Boost.Multiprecision type such as `cpp_dec_float_21`.
+Boost.Multiprecision type such as `cpp_dec_float_21` (or in future, `cpp_bin_float_21`).
 
 Some hardware, for example [@http://en.wikipedia.org/wiki/SPARC Sparc],
-provides a 128-bit quadruple precision floating-point chip.
+provides a full 128-bit quadruple precision floating-point chip.
 
 As of gcc 4.3, a quadruple precision is also supported on x86,
-but as the nonstandard type `__float128` rather than `long double`.
+but as the nonstandard type `__float128` rather than as a `long double`.
 
 [@http://www.opensource.apple.com/source/gcc/gcc-5646/gcc/config/rs6000/darwin-ldouble.c Darwin]
 `long double` uses a double-double format developed first by
@@ -576,7 +612,7 @@
 as described in
 [@http://stackoverflow.com/questions/13525774/clang-and-float128-bug-error Clang float128].
 
-in the future, it may be useful on powerful desktop computers and workstations to strive
+In the future, it may be useful on powerful desktop computers and workstations to strive
 to make `long double` equivalent to quadruple-precision (__IEEE_Quad) and to
 type define this to be `float128_t`. Some architectures have hardware support for this.
 Those lacking hardware support for `float128_t` can use software emulation to generate it.
@@ -599,39 +635,38 @@
 
 [section:references References]
 
-[@http://isocpp.org/std/meetings-and-participation/papers-and-mailings isocpp.org C++ papers and mailings]
+# [@http://isocpp.org/std/meetings-and-participation/papers-and-mailings isocpp.org C++ papers and mailings]
 
-[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html C++ Binary Fixed-Point Arithmetic, N3352, Lawrence Crowl]
+# [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html C++ Binary Fixed-Point Arithmetic, N3352, Lawrence Crowl]
 
-[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html Proposal to Add Decimal Floating Point Support to C++, N3407 Dietmar Kuhl]
+# [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html Proposal to Add Decimal Floating Point Support to C++, N3407 Dietmar Kuhl]
 
-The C committee is working on a Decimal TR as TR 24732.
+# The C committee is working on a Decimal TR as TR 24732.
 The decimal support in C uses built-in types _Decimal32, _Decimal64, and _Decimal128.
 [@http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf
 128-bit decimal floating point in IEEE 754:2008]
 
-[@http://en.wikipedia.org/wiki/IEEE_floating_point lists binary16, 32, 64 and 128]
-
+# [@http://en.wikipedia.org/wiki/IEEE_floating_point lists binary16, 32, 64 and 128]
 (and also decimal 32, 64, and 128)
-[@http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4610933 IEEE Std 754-2008]
 
-[@http://dx.doi.org/10.1109/IEEESTD.2008.4610935 IEEE Standard for Floating-point Arithmetic, IEEE Std 754-2008]
+# [@http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4610933 IEEE Std 754-2008]
 
-[@http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf
+# [@http://dx.doi.org/10.1109/IEEESTD.2008.4610935 IEEE Standard for Floating-point Arithmetic, IEEE Std 754-2008]
+
+# [@http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf
 How to Read Floating Point Numbers Accurately, William D Clinger]
 
-[@http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2013/n3548.pdf Conditionally-supported Special Math Functions for C++14, N3584, Walter E. Brown]
+# [@http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2013/n3548.pdf Conditionally-supported Special Math Functions for C++14, N3584, Walter E. Brown]
 
-[@www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3515.pdf
+# [@www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3515.pdf
 Walter E.Brown, Opaque Typedefs]
 
-[@http://open-std.org/jtc1/sc22/wg21/docs/papers/2013/n????.pdf Specification of Extended Precision Floating-point and Integer Types, Christopher Kormanyos, John Maddock]
+# [@http://open-std.org/jtc1/sc22/wg21/docs/papers/2013/n????.pdf Specification of Extended Precision Floating-point and Integer Types, Christopher Kormanyos, John Maddock]
 
-[@ http://gcc.gnu.org/wiki/x87note X8087 notes]
+# [@ http://gcc.gnu.org/wiki/x87note X8087 notes]
 
 [endsect] [/section:references References]
 
-
 [section:version_id Version Info]
 
 Last edit to Quickbook file __FILENAME__ was at __TIME__ on __DATE__.
@@ -652,4 +687,3 @@
   (See accompanying file LICENSE_1_0.txt or copy at
   http://www.boost.org/LICENSE_1_0.txt).
 ]
-


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