Changeset 44694


Ignore:
Timestamp:
Apr 21, 2008, 1:00:16 PM (10 years ago)
Author:
John Maddock
Message:

Merged changes from the Sandbox, and rebuilt the docs.
Also added some missing files.

Location:
trunk/libs/math/doc/sf_and_dist
Files:
23 added
58 edited

Legend:

Unmodified
Added
Removed
  • trunk/libs/math/doc/sf_and_dist/credits.qbk

    r44091 r44694  
    3737[@http://www.w3.org/ W3C] standard
    3838[@http://www.svg.org/ Scalable Vector Graphic (SVG)] format
    39 using a program created by Jacob Voytko during a Google 'Summer of Code'.
     39using a program created by Jacob Voytko during a
     40[@http://code.google.com/soc/2007/ Google Summer of Code (2007)].
    4041Since browser support for rendering SVG is still not universal
    4142(Microsoft Internet Explorer, even IE 8 beta, still lacks native SVG support
     
    5051- for their many helpful comments.
    5152
    52 [endsect][/section:roadmap Roadmap]
     53[endsect] [/section:credits Credits and Acknowledgements]
    5354
    5455[/
    55   Copyright 2006 - 2008 John Maddock and Paul A. Bristow.
     56  Copyright 2006, 2007, 2008 John Maddock and Paul A. Bristow.
    5657  Distributed under the Boost Software License, Version 1.0.
    5758  (See accompanying file LICENSE_1_0.txt or copy at
  • trunk/libs/math/doc/sf_and_dist/erf.qbk

    r44091 r44694  
    170170
    171171For `z <= 0.5` then a rational approximation to erf is used, based on the
    172 observation that:
    173 
    174    erf(z)/z ~ 1.12....
    175    
    176 Therefore erf is calculated using:
    177 
    178    erf(z) = z * (1.125F + R(z));
    179    
    180 where the rational approximation R(z) is optimised for absolute error:
    181 as long as its absolute error is small enough compared to 1.125, then any
    182 round-off error incurred during the computation of R(z) will effectively
     172observation that erf is an odd function and therefore erf is calculated using:
     173
     174   erf(z) = z * (C + R(z*z));
     175   
     176where the rational approximation R(z*z) is optimised for absolute error:
     177as long as its absolute error is small enough compared to the constant C, then any
     178round-off error incurred during the computation of R(z*z) will effectively
    183179disappear from the result.  As a result the error for erf and erfc in this
    184180region is very low: the last bit is incorrect in only a very small number of
     
    193189Therefore for `z > 0.5` we calculate erfc using:
    194190
    195    erfc(z) = exp(-z*z) * (c + R(z)) / z;
    196    
    197 Again R(z) is optimised for absolute error, and the constant `c` is
     191   erfc(z) = exp(-z*z) * (C + R(z - B)) / z;
     192   
     193Again R(z - B) is optimised for absolute error, and the constant `C` is
    198194the average of `erfc(z) * exp(z*z) * z` taken at the endpoints of the range.
    199 Once again, as long as the absolute error in R(z) is small
    200 compared to `c` then `c + R(z)` will be correctly rounded, and the error
     195Once again, as long as the absolute error in R(z - B) is small
     196compared to `c` then `c + R(z - B)` will be correctly rounded, and the error
    201197in the result will depend only on the accuracy of the exp function.  In practice,
    202198in all but a very small number of cases, the error is confined to the last bit
    203 of the result.
     199of the result.  The constant `B` is chosen so that the left hand end of the range
     200of the rational approximation is 0.
     201
     202For large `z` over a range \[a, +[infin]\] the above approximation is modified to:
     203
     204   erfc(z) = exp(-z*z) * (C + R(1 / z)) / z;
    204205
    205206[endsect]
  • trunk/libs/math/doc/sf_and_dist/fpclassify.qbk

    r39791 r44694  
    1 [section:fpclass Floating Point Classification: Infinities and NaN's]
     1[section:fpclass Floating-Point Classification: Infinities and NaN's]
    22
    33[h4 Synopsis]
     
    1313
    1414   template <class T>
    15    bool isfinite(T z);
     15   bool isfinite(T z); // Neither infinity nor NaN.
    1616
    1717   template <class T>
    18    bool isinf(T t);
     18   bool isinf(T t); // Infinity (+ or -).
    1919
    2020   template <class T>
    21    bool isnan(T t);
     21   bool isnan(T t); // NaN.
    2222
    2323   template <class T>
    24    bool isnormal(T t);
     24   bool isnormal(T t); // isfinite and not denormalised.
     25   
     26   #include <boost\math\special_functions\fpclassify.hpp>
     27
     28to use these functions.
    2529
    2630[h4 Description]
     
    5054   (boost::math::isnan)(z);
    5155   //
    52    // This will cause a compiler error is isnan is a native macro:
     56   // This will cause a compiler error if isnan is a native macro:
    5357   boost::math::isnan(z);
    54    // So always use (boost::math::isnan)(z); instead.
     58   // So always use instead:
     59   (boost::math::isnan)(z);
     60   //
     61   // You can also add a using statment,
     62   // globally to a .cpp file, or to a local function in a .hpp file.
     63   using boost::math::isnan;
     64   // so you can write the shorter and less cluttered
     65   (isnan)(z)
     66   // But, as above, if isnan is a native macro, this causes a compiler error,
     67   // because the macro always 'gets' the name first, unless enclosed in () brackets.
    5568   
    5669Detailed descriptions for each of these functions follows:
     
    8396   bool isnan(T t);
    8497
    85 Returns true only if /z/ is a NaN.
     98Returns true only if /z/ is a [@http://en.wikipedia.org/wiki/NaN NaN].
    8699
    87100   template <class T>
     
    93106
    94107[/
    95   Copyright 2006 John Maddock and Paul A. Bristow.
     108  Copyright 2006, 2008 John Maddock and Paul A. Bristow.
    96109  Distributed under the Boost Software License, Version 1.0.
    97110  (See accompanying file LICENSE_1_0.txt or copy at
  • trunk/libs/math/doc/sf_and_dist/html/index.html

    r44093 r44694  
    292292        Part Splitting (modf)</a></span></dt>
    293293</dl></dd>
    294 <dt><span class="section"><a href="math_toolkit/special/fpclass.html"> Floating Point Classification:
     294<dt><span class="section"><a href="math_toolkit/special/fpclass.html"> Floating-Point Classification:
    295295      Infinities and NaN's</a></span></dt>
    296296</dl></dd>
     
    423423</div>
    424424<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    425 <td align="left"><p><small>Last revised: April 07, 2008 at 16:18:49 GMT</small></p></td>
     425<td align="left"><p><small>Last revised: April 21, 2008 at 12:48:57 GMT</small></p></td>
    426426<td align="right"><div class="copyright-footer"></div></td>
    427427</tr></table>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html

    r44093 r44694  
    3434      </p>
    3535<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
    36 <a name="id806336"></a>
     36<a name="id806718"></a>
    3737        <a href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
    3838        philosophy</a>
     
    8686      </p>
    8787<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
    88 <a name="id806447"></a>
     88<a name="id806828"></a>
    8989        <a href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
    9090        and Representation of Test Values</a>
     
    131131      </p>
    132132<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
    133 <a name="id806691"></a>
     133<a name="id807060"></a>
    134134        <a href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
    135135        of Tests</a>
     
    157157      </p>
    158158<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
    159 <a name="id806751"></a>
     159<a name="id807120"></a>
    160160        <a href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
    161161        Unsuitable Arguments</a>
     
    243243</table></div>
    244244<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
    245 <a name="id806975"></a>
     245<a name="id807345"></a>
    246246        <a href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
    247247        of Functions that are Not Mathematically defined</a>
     
    277277</table></div>
    278278<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
    279 <a name="id807116"></a>
     279<a name="id807486"></a>
    280280        <a href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
    281281        of distributions</a>
     
    310310      </p>
    311311<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
    312 <a name="id807261"></a>
     312<a name="id807630"></a>
    313313        <a href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
    314314        of Floating-Point Infinity</a>
     
    354354      </p>
    355355<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
    356 <a name="id807419"></a>
     356<a name="id807788"></a>
    357357        <a href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
    358358        Shape and Location</a>
     
    381381      </p>
    382382<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
    383 <a name="id807884"></a>
     383<a name="id808253"></a>
    384384        <a href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
    385385        on Implementation of Specific Functions &amp; Distributions</a>
     
    393393        </li></ul></div>
    394394<a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a><h5>
    395 <a name="id807924"></a>
     395<a name="id808293"></a>
    396396        <a href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
    397397        Approximations Used</a>
     
    436436      </p>
    437437<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
    438 <a name="id808021"></a>
     438<a name="id808389"></a>
    439439        <a href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
    440440        of Mathematical Constants</a>
     
    497497</span></pre>
    498498<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
    499 <a name="id808568"></a>
     499<a name="id808958"></a>
    500500        <a href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
    501501        safety</a>
     
    522522      </p>
    523523<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
    524 <a name="id808633"></a>
     524<a name="id809023"></a>
    525525        <a href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
    526526        of Test Data</a>
     
    566566      </p>
    567567<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
    568 <a name="id808743"></a>
     568<a name="id809134"></a>
    569569        <a href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
    570570        and Managing the Equations</a>
     
    727727      </p>
    728728<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
    729 <a name="id809122"></a>
     729<a name="id809512"></a>
    730730        <a href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
    731731        Graphs</a>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html

    r44093 r44694  
    2828</h3></div></div></div>
    2929<a name="math_toolkit.backgrounders.lanczos.motivation"></a><h5>
    30 <a name="id809523"></a>
     30<a name="id809891"></a>
    3131        <a href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
    3232      </h5>
     
    9999      </p>
    100100<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
    101 <a name="id809896"></a>
     101<a name="id810268"></a>
    102102        <a href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
    103103        Approximation</a>
     
    161161</table></div>
    162162<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
    163 <a name="id810159"></a>
     163<a name="id810531"></a>
    164164        <a href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
    165165        the Coefficients</a>
     
    205205      </p>
    206206<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
    207 <a name="id810365"></a>
     207<a name="id810737"></a>
    208208        <a href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
    209209        the Right Parameters</a>
     
    229229      </p>
    230230<div class="table">
    231 <a name="id810448"></a><p class="title"><b>Table 52. Optimal choices for N and g when computing with
     231<a name="id810820"></a><p class="title"><b>Table 52. Optimal choices for N and g when computing with
    232232      guard digits (source: Pugh)</b></p>
    233233<div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with
     
    372372      </p>
    373373<div class="table">
    374 <a name="id810775"></a><p class="title"><b>Table 53. Optimum value for N and g when computing at fixed
     374<a name="id811142"></a><p class="title"><b>Table 53. Optimum value for N and g when computing at fixed
    375375      precision</b></p>
    376376<div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed
     
    537537      </p>
    538538<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
    539 <a name="id811053"></a>
     539<a name="id811420"></a>
    540540        <a href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
    541541      </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html

    r44093 r44694  
    2828</h3></div></div></div>
    2929<a name="math_toolkit.backgrounders.refs.general_references"></a><h5>
    30 <a name="id812417"></a>
     30<a name="id812783"></a>
    3131        <a href="refs.html#math_toolkit.backgrounders.refs.general_references">General
    3232        references</a>
     
    9292      </p>
    9393<a name="math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__"></a><h5>
    94 <a name="id812591"></a>
     94<a name="id812957"></a>
    9595        <a href="refs.html#math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__">Calculators*
    9696        that we found (and used to cross-check - as far as their widely-varying accuracy
     
    102102      </p>
    103103<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
    104 <a name="id812636"></a>
     104<a name="id813002"></a>
    105105        <a href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
    106106      </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html

    r44093 r44694  
    8282      </p>
    8383<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
    84 <a name="id809422"></a>
     84<a name="id809813"></a>
    8585        <a href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
    8686        Impossibility of Zero Error</a>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html

    r44093 r44694  
    9595      </p>
    9696<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
    97 <a name="id811304"></a>
     97<a name="id811671"></a>
    9898        <a href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
    9999        Method</a>
     
    175175</table></div>
    176176<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
    177 <a name="id811524"></a>
     177<a name="id811891"></a>
    178178        <a href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
    179179        1</a>
     
    206206      </p>
    207207<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
    208 <a name="id811630"></a>
     208<a name="id811997"></a>
    209209        <a href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
    210210        2</a>
     
    235235      </p>
    236236<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
    237 <a name="id811690"></a>
     237<a name="id812057"></a>
    238238        <a href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
    239239      </h5>
     
    251251      </p>
    252252<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
    253 <a name="id811752"></a>
     253<a name="id812118"></a>
    254254        <a href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
    255255        Approximations</a>
     
    300300      </p>
    301301<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
    302 <a name="id811874"></a>
     302<a name="id812241"></a>
    303303        <a href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
    304304        Considerations</a>
     
    408408      </p>
    409409<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
    410 <a name="id812133"></a>
     410<a name="id812499"></a>
    411411        <a href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
    412412        Method Checklist</a>
     
    462462</ul></div>
    463463<a name="math_toolkit.backgrounders.remez.references"></a><h5>
    464 <a name="id812236"></a>
     464<a name="id812602"></a>
    465465        <a href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
    466466      </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html

    r44093 r44694  
    232232        </p>
    233233<p>
    234           Sandbox and trunk last synchonised at revision: 44092.
     234          Sandbox and trunk last synchonised at revision: 44694.
    235235        </p>
    236236<p>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html

    r44093 r44694  
    3636      </p>
    3737<div class="table">
    38 <a name="id800269"></a><p class="title"><b>Table 47. Performance Comparison of Various Windows Compilers</b></p>
     38<a name="id800657"></a><p class="title"><b>Table 47. Performance Comparison of Various Windows Compilers</b></p>
    3939<div class="table-contents"><table class="table" summary="Performance Comparison of Various Windows Compilers">
    4040<colgroup>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html

    r44093 r44694  
    4747</table></div>
    4848<a name="math_toolkit.perf.comparisons.comparison_to_gsl_1_9_and_cephes"></a><h5>
    49 <a name="id802743"></a>
     49<a name="id803124"></a>
    5050        <a href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_gsl_1_9_and_cephes">Comparison
    5151        to GSL-1.9 and Cephes</a>
     
    214214              <p>
    215215                +INF
    216                 <sup>[<a name="id803110" href="#ftn.id803110">1</a>]</sup>
     216                <sup>[<a name="id803491" href="#ftn.id803491">1</a>]</sup>
    217217              </p>
    218218              </td>
     
    285285</tr>
    286286</tbody>
    287 <tbody class="footnotes"><tr><td colspan="4"><div class="footnote"><p><sup>[<a name="ftn.id803110" href="#id803110">1</a>] </sup>
     287<tbody class="footnotes"><tr><td colspan="4"><div class="footnote"><p><sup>[<a name="ftn.id803491" href="#id803491">1</a>] </sup>
    288288                    Cephes gets stuck in an infinite loop while trying to execute
    289289                    our test cases.
     
    291291</table></div>
    292292<a name="math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_windows"></a><h5>
    293 <a name="id803279"></a>
     293<a name="id803660"></a>
    294294        <a href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_windows">Comparison
    295295        to the R Statistical Library on Windows</a>
     
    302302      </p>
    303303<div class="table">
    304 <a name="id803306"></a><p class="title"><b>Table 50. A Comparison to the R Statistical Library on Windows
     304<a name="id803688"></a><p class="title"><b>Table 50. A Comparison to the R Statistical Library on Windows
    305305      XP</b></p>
    306306<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Windows
     
    375375              </p>
    376376<p>74.66
    377               <sup>[<a name="id803447" href="#ftn.id803447">1</a>]</sup>
     377              <sup>[<a name="id803828" href="#ftn.id803828">1</a>]</sup>
    378378              </p>
    379379<p> </p>
     
    793793              </p>
    794794<p>53.59
    795               <sup>[<a name="id804296" href="#ftn.id804296">2</a>]</sup>
     795              <sup>[<a name="id804677" href="#ftn.id804677">2</a>]</sup>
    796796              </p>
    797797<p> </p>
     
    10111011</tbody>
    10121012<tbody class="footnotes"><tr><td colspan="3">
    1013 <div class="footnote"><p><sup>[<a name="ftn.id803447" href="#id803447">1</a>] </sup>
     1013<div class="footnote"><p><sup>[<a name="ftn.id803828" href="#id803828">1</a>] </sup>
    10141014                  There are a small number of our test cases where the R library
    10151015                  fails to converge on a result: these tend to dominate the performance
    10161016                  result.
    10171017                </p></div>
    1018 <div class="footnote"><p><sup>[<a name="ftn.id804296" href="#id804296">2</a>] </sup>
     1018<div class="footnote"><p><sup>[<a name="ftn.id804677" href="#id804677">2</a>] </sup>
    10191019                  The R library appears to use a linear-search strategy, that can
    10201020                  perform very badly in a small number of pathological cases, but
     
    10251025</div>
    10261026<br class="table-break"><a name="math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux"></a><h5>
    1027 <a name="id804746"></a>
     1027<a name="id805127"></a>
    10281028        <a href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux">Comparison
    10291029        to the R Statistical Library on Linux</a>
     
    10341034      </p>
    10351035<div class="table">
    1036 <a name="id804771"></a><p class="title"><b>Table 51. A Comparison to the R Statistical Library on Linux</b></p>
     1036<a name="id805152"></a><p class="title"><b>Table 51. A Comparison to the R Statistical Library on Linux</b></p>
    10371037<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Linux">
    10381038<colgroup>
     
    11051105              </p>
    11061106<p>44.06
    1107               <sup>[<a name="id804910" href="#ftn.id804910">1</a>]</sup>
     1107              <sup>[<a name="id805292" href="#ftn.id805292">1</a>]</sup>
    11081108              </p>
    11091109<p> </p>
     
    15231523              </p>
    15241524<p>30.07
    1525               <sup>[<a name="id805755" href="#ftn.id805755">2</a>]</sup>
     1525              <sup>[<a name="id806136" href="#ftn.id806136">2</a>]</sup>
    15261526              </p>
    15271527<p> </p>
     
    17411741</tbody>
    17421742<tbody class="footnotes"><tr><td colspan="3">
    1743 <div class="footnote"><p><sup>[<a name="ftn.id804910" href="#id804910">1</a>] </sup>
     1743<div class="footnote"><p><sup>[<a name="ftn.id805292" href="#id805292">1</a>] </sup>
    17441744                  There are a small number of our test cases where the R library
    17451745                  fails to converge on a result: these tend to dominate the performance
    17461746                  result.
    17471747                </p></div>
    1748 <div class="footnote"><p><sup>[<a name="ftn.id805755" href="#id805755">2</a>] </sup>
     1748<div class="footnote"><p><sup>[<a name="ftn.id806136" href="#id806136">2</a>] </sup>
    17491749                  The R library appears to use a linear-search strategy, that can
    17501750                  perform very badly in a small number of pathological cases, but
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html

    r44093 r44694  
    3434      </p>
    3535<div class="table">
    36 <a name="id799698"></a><p class="title"><b>Table 46. Performance Comparison of Release and Debug Settings</b></p>
     36<a name="id800086"></a><p class="title"><b>Table 46. Performance Comparison of Release and Debug Settings</b></p>
    3737<div class="table-contents"><table class="table" summary="Performance Comparison of Release and Debug Settings">
    3838<colgroup>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/tuning.html

    r44093 r44694  
    235235      </p>
    236236<div class="table">
    237 <a name="id801392"></a><p class="title"><b>Table 48. A Comparison of Polynomial Evaluation Methods</b></p>
     237<a name="id801773"></a><p class="title"><b>Table 48. A Comparison of Polynomial Evaluation Methods</b></p>
    238238<div class="table-contents"><table class="table" summary="A Comparison of Polynomial Evaluation Methods">
    239239<colgroup>
     
    635635      </p>
    636636<div class="table">
    637 <a name="id802147"></a><p class="title"><b>Table 49. Performance Comparison with and Without Internal
     637<a name="id802528"></a><p class="title"><b>Table 49. Performance Comparison with and Without Internal
    638638      Promotion to long double</b></p>
    639639<div class="table-contents"><table class="table" summary="Performance Comparison with and Without Internal
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html

    r44093 r44694  
    5656        </p>
    5757<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.real"></a><h6>
    58 <a name="id789797"></a>
     58<a name="id790180"></a>
    5959          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.real">real</a>
    6060        </h6>
     
    9494        </p>
    9595<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_outwards"></a><h6>
    96 <a name="id790284"></a>
     96<a name="id790666"></a>
    9797          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_outwards">integer_round_outwards</a>
    9898        </h6>
     
    152152        </p>
    153153<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_inwards"></a><h6>
    154 <a name="id790803"></a>
     154<a name="id791185"></a>
    155155          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_inwards">integer_round_inwards</a>
    156156        </h6>
     
    215215        </p>
    216216<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_down"></a><h6>
    217 <a name="id791456"></a>
     217<a name="id791839"></a>
    218218          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_down">integer_round_down</a>
    219219        </h6>
     
    223223        </p>
    224224<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_up"></a><h6>
    225 <a name="id791488"></a>
     225<a name="id791870"></a>
    226226          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_up">integer_round_up</a>
    227227        </h6>
     
    231231        </p>
    232232<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_nearest"></a><h6>
    233 <a name="id791519"></a>
     233<a name="id791902"></a>
    234234          <a href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_nearest">integer_round_nearest</a>
    235235        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html

    r44093 r44694  
    4040</ul></div>
    4141<a name="math_toolkit.policy.pol_ref.error_handling_policies.available_actions_when_an_error_is_raised"></a><h5>
    42 <a name="id784074"></a>
     42<a name="id784456"></a>
    4343          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.available_actions_when_an_error_is_raised">Available
    4444          Actions When an Error is Raised</a>
     
    6363        </p>
    6464<a name="math_toolkit.policy.pol_ref.error_handling_policies.throw_on_error"></a><h6>
    65 <a name="id784327"></a>
     65<a name="id784708"></a>
    6666          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.throw_on_error">throw_on_error</a>
    6767        </h6>
     
    163163</table></div>
    164164<a name="math_toolkit.policy.pol_ref.error_handling_policies.errno_on_error"></a><h6>
    165 <a name="id784509"></a>
     165<a name="id784891"></a>
    166166          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.errno_on_error">errno_on_error</a>
    167167        </h6>
     
    264264</table></div>
    265265<a name="math_toolkit.policy.pol_ref.error_handling_policies.ignore_error"></a><h6>
    266 <a name="id784708"></a>
     266<a name="id785090"></a>
    267267          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.ignore_error">ignore_error</a>
    268268        </h6>
     
    365365</table></div>
    366366<a name="math_toolkit.policy.pol_ref.error_handling_policies.user_error"></a><h6>
    367 <a name="id784909"></a>
     367<a name="id785291"></a>
    368368          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.user_error">user_error</a>
    369369        </h6>
     
    411411        </p>
    412412<a name="math_toolkit.policy.pol_ref.error_handling_policies.kinds_of_error_raised"></a><h5>
    413 <a name="id785978"></a>
     413<a name="id786360"></a>
    414414          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.kinds_of_error_raised">Kinds
    415415          of Error Raised</a>
     
    625625</table></div>
    626626<a name="math_toolkit.policy.pol_ref.error_handling_policies.examples"></a><h5>
    627 <a name="id786983"></a>
     627<a name="id787365"></a>
    628628          <a href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.examples">Examples</a>
    629629        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html

    r44093 r44694  
    8585</table></div>
    8686<a name="math_toolkit.policy.pol_ref.internal_promotion.examples"></a><h5>
    87 <a name="id788298"></a>
     87<a name="id788680"></a>
    8888          <a href="internal_promotion.html#math_toolkit.policy.pol_ref.internal_promotion.examples">Examples</a>
    8989        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html

    r44093 r44694  
    6262        </p>
    6363<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_domain_error_policy"></a><h6>
    64 <a name="id793322"></a>
     64<a name="id793704"></a>
    6565          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_domain_error_policy">BOOST_MATH_DOMAIN_ERROR_POLICY</a>
    6666        </h6>
     
    7272        </p>
    7373<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_pole_error_policy"></a><h6>
    74 <a name="id793415"></a>
     74<a name="id793797"></a>
    7575          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_pole_error_policy">BOOST_MATH_POLE_ERROR_POLICY</a>
    7676        </h6>
     
    8282        </p>
    8383<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_overflow_error_policy"></a><h6>
    84 <a name="id793507"></a>
     84<a name="id793889"></a>
    8585          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_overflow_error_policy">BOOST_MATH_OVERFLOW_ERROR_POLICY</a>
    8686        </h6>
     
    9292        </p>
    9393<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_rounding_error_policy"></a><h6>
    94 <a name="id793600"></a>
     94<a name="id793982"></a>
    9595          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_rounding_error_policy">BOOST_MATH_ROUNDING_ERROR_POLICY</a>
    9696        </h6>
     
    102102        </p>
    103103<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_evaluation_error_policy"></a><h6>
    104 <a name="id793693"></a>
     104<a name="id794075"></a>
    105105          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_evaluation_error_policy">BOOST_MATH_EVALUATION_ERROR_POLICY</a>
    106106        </h6>
     
    112112        </p>
    113113<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_underflow_error_policy"></a><h6>
    114 <a name="id793786"></a>
     114<a name="id794168"></a>
    115115          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_underflow_error_policy">BOOST_MATH_UNDERFLOW_ERROR_POLICY</a>
    116116        </h6>
     
    122122        </p>
    123123<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_denorm_error_policy"></a><h6>
    124 <a name="id793879"></a>
     124<a name="id794261"></a>
    125125          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_denorm_error_policy">BOOST_MATH_DENORM_ERROR_POLICY</a>
    126126        </h6>
     
    132132        </p>
    133133<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_digits10_policy"></a><h6>
    134 <a name="id793971"></a>
     134<a name="id794353"></a>
    135135          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_digits10_policy">BOOST_MATH_DIGITS10_POLICY</a>
    136136        </h6>
     
    143143        </p>
    144144<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_float_policy"></a><h6>
    145 <a name="id794020"></a>
     145<a name="id794402"></a>
    146146          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_float_policy">BOOST_MATH_PROMOTE_FLOAT_POLICY</a>
    147147        </h6>
     
    155155        </p>
    156156<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_double_policy"></a><h6>
    157 <a name="id794112"></a>
     157<a name="id794494"></a>
    158158          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_double_policy">BOOST_MATH_PROMOTE_DOUBLE_POLICY</a>
    159159        </h6>
     
    167167        </p>
    168168<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_discrete_quantile_policy"></a><h6>
    169 <a name="id794211"></a>
     169<a name="id794592"></a>
    170170          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_discrete_quantile_policy">BOOST_MATH_DISCRETE_QUANTILE_POLICY</a>
    171171        </h6>
     
    178178        </p>
    179179<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_assert_undefined_policy"></a><h6>
    180 <a name="id794328"></a>
     180<a name="id794709"></a>
    181181          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_assert_undefined_policy">BOOST_MATH_ASSERT_UNDEFINED_POLICY</a>
    182182        </h6>
     
    191191        </p>
    192192<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_series_iteration_policy"></a><h6>
    193 <a name="id794393"></a>
     193<a name="id794773"></a>
    194194          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_series_iteration_policy">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</a>
    195195        </h6>
     
    200200        </p>
    201201<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_root_iteration_policy"></a><h6>
    202 <a name="id794435"></a>
     202<a name="id794815"></a>
    203203          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_root_iteration_policy">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</a>
    204204        </h6>
     
    209209        </p>
    210210<a name="math_toolkit.policy.pol_ref.policy_defaults.example"></a><h6>
    211 <a name="id794476"></a>
     211<a name="id794857"></a>
    212212          <a href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.example">Example</a>
    213213        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html

    r44093 r44694  
    178178        </p>
    179179<a name="math_toolkit.policy.pol_tutorial.understand_dis_quant.other_rounding_policies_are_available"></a><h6>
    180 <a name="id780576"></a>
     180<a name="id780971"></a>
    181181          <a href="understand_dis_quant.html#math_toolkit.policy.pol_tutorial.understand_dis_quant.other_rounding_policies_are_available">Other
    182182          Rounding Policies are Available</a>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special.html

    r44091 r44694  
    150150        Part Splitting (modf)</a></span></dt>
    151151</dl></dd>
    152 <dt><span class="section"><a href="special/fpclass.html"> Floating Point Classification:
     152<dt><span class="section"><a href="special/fpclass.html"> Floating-Point Classification:
    153153      Infinities and NaN's</a></span></dt>
    154154</dl></div>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.bessel.bessel.synopsis"></a><h5>
    31 <a name="id682628"></a>
     31<a name="id682793"></a>
    3232          <a href="bessel.html#math_toolkit.special.bessel.bessel.synopsis">Synopsis</a>
    3333        </h5>
     
    4545</pre>
    4646<a name="math_toolkit.special.bessel.bessel.description"></a><h5>
    47 <a name="id683136"></a>
     47<a name="id683301"></a>
    4848          <a href="bessel.html#math_toolkit.special.bessel.bessel.description">Description</a>
    4949        </h5>
     
    111111        </p>
    112112<a name="math_toolkit.special.bessel.bessel.testing"></a><h5>
    113 <a name="id683537"></a>
     113<a name="id683702"></a>
    114114          <a href="bessel.html#math_toolkit.special.bessel.bessel.testing">Testing</a>
    115115        </h5>
     
    120120        </p>
    121121<a name="math_toolkit.special.bessel.bessel.accuracy"></a><h5>
    122 <a name="id683576"></a>
     122<a name="id683741"></a>
    123123          <a href="bessel.html#math_toolkit.special.bessel.bessel.accuracy">Accuracy</a>
    124124        </h5>
     
    136136        </p>
    137137<div class="table">
    138 <a name="id683632"></a><p class="title"><b>Table 35. Errors Rates in cyl_bessel_j</b></p>
     138<a name="id683798"></a><p class="title"><b>Table 35. Errors Rates in cyl_bessel_j</b></p>
    139139<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_j">
    140140<colgroup>
     
    305305</div>
    306306<br class="table-break"><div class="table">
    307 <a name="id683937"></a><p class="title"><b>Table 36. Errors Rates in cyl_neumann</b></p>
     307<a name="id684102"></a><p class="title"><b>Table 36. Errors Rates in cyl_neumann</b></p>
    308308<div class="table-contents"><table class="table" summary="Errors Rates in cyl_neumann">
    309309<colgroup>
     
    495495        </p>
    496496<a name="math_toolkit.special.bessel.bessel.implementation"></a><h5>
    497 <a name="id688639"></a>
     497<a name="id688792"></a>
    498498          <a href="bessel.html#math_toolkit.special.bessel.bessel.implementation">Implementation</a>
    499499        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.bessel.bessel_over.ordinary_bessel_functions"></a><h5>
    31 <a name="id681639"></a>
     31<a name="id681804"></a>
    3232          <a href="bessel_over.html#math_toolkit.special.bessel.bessel_over.ordinary_bessel_functions">Ordinary
    3333          Bessel Functions</a>
     
    104104        </p>
    105105<a name="math_toolkit.special.bessel.bessel_over.modified_bessel_functions"></a><h5>
    106 <a name="id682056"></a>
     106<a name="id682221"></a>
    107107          <a href="bessel_over.html#math_toolkit.special.bessel.bessel_over.modified_bessel_functions">Modified
    108108          Bessel Functions</a>
     
    168168        </p>
    169169<a name="math_toolkit.special.bessel.bessel_over.spherical_bessel_functions"></a><h5>
    170 <a name="id682452"></a>
     170<a name="id682617"></a>
    171171          <a href="bessel_over.html#math_toolkit.special.bessel.bessel_over.spherical_bessel_functions">Spherical
    172172          Bessel Functions</a>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.bessel.mbessel.synopsis"></a><h5>
    31 <a name="id689427"></a>
     31<a name="id689580"></a>
    3232          <a href="mbessel.html#math_toolkit.special.bessel.mbessel.synopsis">Synopsis</a>
    3333        </h5>
     
    4545</pre>
    4646<a name="math_toolkit.special.bessel.mbessel.description"></a><h5>
    47 <a name="id689937"></a>
     47<a name="id690090"></a>
    4848          <a href="mbessel.html#math_toolkit.special.bessel.mbessel.description">Description</a>
    4949        </h5>
     
    110110        </p>
    111111<a name="math_toolkit.special.bessel.mbessel.testing"></a><h5>
    112 <a name="id690326"></a>
     112<a name="id690479"></a>
    113113          <a href="mbessel.html#math_toolkit.special.bessel.mbessel.testing">Testing</a>
    114114        </h5>
     
    119119        </p>
    120120<a name="math_toolkit.special.bessel.mbessel.accuracy"></a><h5>
    121 <a name="id690365"></a>
     121<a name="id690518"></a>
    122122          <a href="mbessel.html#math_toolkit.special.bessel.mbessel.accuracy">Accuracy</a>
    123123        </h5>
     
    130130        </p>
    131131<div class="table">
    132 <a name="id690405"></a><p class="title"><b>Table 37. Errors Rates in cyl_bessel_i</b></p>
     132<a name="id690558"></a><p class="title"><b>Table 37. Errors Rates in cyl_bessel_i</b></p>
    133133<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_i">
    134134<colgroup>
     
    227227</div>
    228228<br class="table-break"><div class="table">
    229 <a name="id690560"></a><p class="title"><b>Table 38. Errors Rates in cyl_bessel_k</b></p>
     229<a name="id690713"></a><p class="title"><b>Table 38. Errors Rates in cyl_bessel_k</b></p>
    230230<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_k">
    231231<colgroup>
     
    327327</div>
    328328<br class="table-break"><a name="math_toolkit.special.bessel.mbessel.implementation"></a><h5>
    329 <a name="id690728"></a>
     329<a name="id690881"></a>
    330330          <a href="mbessel.html#math_toolkit.special.bessel.mbessel.implementation">Implementation</a>
    331331        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.bessel.sph_bessel.synopsis"></a><h5>
    31 <a name="id691406"></a>
     31<a name="id691559"></a>
    3232          <a href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.synopsis">Synopsis</a>
    3333        </h5>
     
    4545</pre>
    4646<a name="math_toolkit.special.bessel.sph_bessel.description"></a><h5>
    47 <a name="id691915"></a>
     47<a name="id692068"></a>
    4848          <a href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.description">Description</a>
    4949        </h5>
     
    9898        </p>
    9999<a name="math_toolkit.special.bessel.sph_bessel.testing"></a><h5>
    100 <a name="id692195"></a>
     100<a name="id692348"></a>
    101101          <a href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.testing">Testing</a>
    102102        </h5>
     
    107107        </p>
    108108<a name="math_toolkit.special.bessel.sph_bessel.accuracy"></a><h5>
    109 <a name="id692234"></a>
     109<a name="id692387"></a>
    110110          <a href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.accuracy">Accuracy</a>
    111111        </h5>
     
    117117        </p>
    118118<a name="math_toolkit.special.bessel.sph_bessel.implementation"></a><h5>
    119 <a name="id692284"></a>
     119<a name="id692437"></a>
    120120          <a href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.implementation">Implementation</a>
    121121        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.ellint.ellint_1.synopsis"></a><h6>
    31 <a name="id697975"></a>
     31<a name="id698129"></a>
    3232          <a href="ellint_1.html#math_toolkit.special.ellint.ellint_1.synopsis">Synopsis</a>
    3333        </h6>
     
    5656</span></pre>
    5757<a name="math_toolkit.special.ellint.ellint_1.description"></a><h6>
    58 <a name="id698538"></a>
     58<a name="id698692"></a>
    5959          <a href="ellint_1.html#math_toolkit.special.ellint.ellint_1.description">Description</a>
    6060        </h6>
     
    124124        </p>
    125125<a name="math_toolkit.special.ellint.ellint_1.accuracy"></a><h6>
    126 <a name="id699197"></a>
     126<a name="id699351"></a>
    127127          <a href="ellint_1.html#math_toolkit.special.ellint.ellint_1.accuracy">Accuracy</a>
    128128        </h6>
     
    135135        </p>
    136136<div class="table">
    137 <a name="id699231"></a><p class="title"><b>Table 40. Errors Rates in the Elliptic Integrals of the
     137<a name="id699385"></a><p class="title"><b>Table 40. Errors Rates in the Elliptic Integrals of the
    138138        First Kind</b></p>
    139139<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
     
    238238</div>
    239239<br class="table-break"><a name="math_toolkit.special.ellint.ellint_1.testing"></a><h6>
    240 <a name="id699393"></a>
     240<a name="id699547"></a>
    241241          <a href="ellint_1.html#math_toolkit.special.ellint.ellint_1.testing">Testing</a>
    242242        </h6>
     
    248248        </p>
    249249<a name="math_toolkit.special.ellint.ellint_1.implementation"></a><h6>
    250 <a name="id699432"></a>
     250<a name="id699587"></a>
    251251          <a href="ellint_1.html#math_toolkit.special.ellint.ellint_1.implementation">Implementation</a>
    252252        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.ellint.ellint_2.synopsis"></a><h6>
    31 <a name="id699548"></a>
     31<a name="id699703"></a>
    3232          <a href="ellint_2.html#math_toolkit.special.ellint.ellint_2.synopsis">Synopsis</a>
    3333        </h6>
     
    5656</span></pre>
    5757<a name="math_toolkit.special.ellint.ellint_2.description"></a><h6>
    58 <a name="id700110"></a>
     58<a name="id700264"></a>
    5959          <a href="ellint_2.html#math_toolkit.special.ellint.ellint_2.description">Description</a>
    6060        </h6>
     
    124124        </p>
    125125<a name="math_toolkit.special.ellint.ellint_2.accuracy"></a><h6>
    126 <a name="id700769"></a>
     126<a name="id700923"></a>
    127127          <a href="ellint_2.html#math_toolkit.special.ellint.ellint_2.accuracy">Accuracy</a>
    128128        </h6>
     
    135135        </p>
    136136<div class="table">
    137 <a name="id700802"></a><p class="title"><b>Table 41. Errors Rates in the Elliptic Integrals of the
     137<a name="id700956"></a><p class="title"><b>Table 41. Errors Rates in the Elliptic Integrals of the
    138138        Second Kind</b></p>
    139139<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
     
    238238</div>
    239239<br class="table-break"><a name="math_toolkit.special.ellint.ellint_2.testing"></a><h6>
    240 <a name="id700965"></a>
     240<a name="id701119"></a>
    241241          <a href="ellint_2.html#math_toolkit.special.ellint.ellint_2.testing">Testing</a>
    242242        </h6>
     
    248248        </p>
    249249<a name="math_toolkit.special.ellint.ellint_2.implementation"></a><h6>
    250 <a name="id701004"></a>
     250<a name="id701158"></a>
    251251          <a href="ellint_2.html#math_toolkit.special.ellint.ellint_2.implementation">Implementation</a>
    252252        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.ellint.ellint_3.synopsis"></a><h6>
    31 <a name="id701120"></a>
     31<a name="id701274"></a>
    3232          <a href="ellint_3.html#math_toolkit.special.ellint.ellint_3.synopsis">Synopsis</a>
    3333        </h6>
     
    5656</span></pre>
    5757<a name="math_toolkit.special.ellint.ellint_3.description"></a><h6>
    58 <a name="id701819"></a>
     58<a name="id701973"></a>
    5959          <a href="ellint_3.html#math_toolkit.special.ellint.ellint_3.description">Description</a>
    6060        </h6>
     
    136136        </p>
    137137<a name="math_toolkit.special.ellint.ellint_3.accuracy"></a><h6>
    138 <a name="id702662"></a>
     138<a name="id702817"></a>
    139139          <a href="ellint_3.html#math_toolkit.special.ellint.ellint_3.accuracy">Accuracy</a>
    140140        </h6>
     
    147147        </p>
    148148<div class="table">
    149 <a name="id702696"></a><p class="title"><b>Table 42. Errors Rates in the Elliptic Integrals of the
     149<a name="id702851"></a><p class="title"><b>Table 42. Errors Rates in the Elliptic Integrals of the
    150150        Third Kind</b></p>
    151151<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
     
    250250</div>
    251251<br class="table-break"><a name="math_toolkit.special.ellint.ellint_3.testing"></a><h6>
    252 <a name="id702859"></a>
     252<a name="id703014"></a>
    253253          <a href="ellint_3.html#math_toolkit.special.ellint.ellint_3.testing">Testing</a>
    254254        </h6>
     
    260260        </p>
    261261<a name="math_toolkit.special.ellint.ellint_3.implementation"></a><h6>
    262 <a name="id702898"></a>
     262<a name="id703052"></a>
    263263          <a href="ellint_3.html#math_toolkit.special.ellint.ellint_3.implementation">Implementation</a>
    264264        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.ellint.ellint_carlson.synopsis"></a><h6>
    31 <a name="id693855"></a>
     31<a name="id694009"></a>
    3232          <a href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.synopsis">Synopsis</a>
    3333        </h6>
     
    101101</span></pre>
    102102<a name="math_toolkit.special.ellint.ellint_carlson.description"></a><h6>
    103 <a name="id695626"></a>
     103<a name="id695779"></a>
    104104          <a href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.description">Description</a>
    105105        </h6>
     
    237237        </p>
    238238<a name="math_toolkit.special.ellint.ellint_carlson.testing"></a><h6>
    239 <a name="id697394"></a>
     239<a name="id697548"></a>
    240240          <a href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.testing">Testing</a>
    241241        </h6>
     
    266266        </p>
    267267<a name="math_toolkit.special.ellint.ellint_carlson.accuracy"></a><h6>
    268 <a name="id697464"></a>
     268<a name="id697618"></a>
    269269          <a href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.accuracy">Accuracy</a>
    270270        </h6>
     
    277277        </p>
    278278<div class="table">
    279 <a name="id697499"></a><p class="title"><b>Table 39. Errors Rates in the Carlson Elliptic Integrals</b></p>
     279<a name="id697653"></a><p class="title"><b>Table 39. Errors Rates in the Carlson Elliptic Integrals</b></p>
    280280<div class="table-contents"><table class="table" summary="Errors Rates in the Carlson Elliptic Integrals">
    281281<colgroup>
     
    420420</div>
    421421<br class="table-break"><a name="math_toolkit.special.ellint.ellint_carlson.implementation"></a><h6>
    422 <a name="id697730"></a>
     422<a name="id697884"></a>
    423423          <a href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.implementation">Implementation</a>
    424424        </h6>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html

    r44093 r44694  
    6262        </p>
    6363<a name="math_toolkit.special.ellint.ellint_intro.notation"></a><h5>
    64 <a name="id692512"></a>
     64<a name="id692665"></a>
    6565          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.notation">Notation</a>
    6666        </h5>
     
    6969        </p>
    7070<a name="ellint_def"></a><a name="math_toolkit.special.ellint.ellint_intro.definition"></a><h5>
    71 <a name="id692549"></a>
     71<a name="id692702"></a>
    7272          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.definition">Definition</a>
    7373        </h5>
     
    258258</table></div>
    259259<a name="ellint_theorem"></a><a name="math_toolkit.special.ellint.ellint_intro.duplication_theorem"></a><h5>
    260 <a name="id693304"></a>
     260<a name="id693458"></a>
    261261          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.duplication_theorem">Duplication
    262262          Theorem</a>
     
    270270        </p>
    271271<a name="ellint_formula"></a><a name="math_toolkit.special.ellint.ellint_intro.carlson_s_formulas"></a><h5>
    272 <a name="id693379"></a>
     272<a name="id693533"></a>
    273273          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.carlson_s_formulas">Carlson's
    274274          Formulas</a>
     
    288288        </p>
    289289<a name="math_toolkit.special.ellint.ellint_intro.numerical_algorithms"></a><h5>
    290 <a name="id693474"></a>
     290<a name="id693627"></a>
    291291          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.numerical_algorithms">Numerical
    292292          Algorithms</a>
     
    302302        </p>
    303303<a name="ellint_refs"></a><a name="math_toolkit.special.ellint.ellint_intro.references"></a><h5>
    304 <a name="id693536"></a>
     304<a name="id693689"></a>
    305305          <a href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.references">References</a>
    306306        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/fpclass.html

    r44093 r44694  
    22<head>
    33<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
    4 <title>Floating Point Classification: Infinities and NaN's</title>
     4<title>Floating-Point Classification: Infinities and NaN's</title>
    55<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
    66<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
     
    2525<div class="section" lang="en">
    2626<div class="titlepage"><div><div><h3 class="title">
    27 <a name="math_toolkit.special.fpclass"></a><a href="fpclass.html" title="Floating Point Classification: Infinities and NaN's"> Floating Point Classification:
     27<a name="math_toolkit.special.fpclass"></a><a href="fpclass.html" title="Floating-Point Classification: Infinities and NaN's"> Floating-Point Classification:
    2828      Infinities and NaN's</a>
    2929</h3></div></div></div>
    3030<a name="math_toolkit.special.fpclass.synopsis"></a><h5>
    31 <a name="id719333"></a>
     31<a name="id719474"></a>
    3232        <a href="fpclass.html#math_toolkit.special.fpclass.synopsis">Synopsis</a>
    3333      </h5>
     
    4242
    4343<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
    44 <span class="keyword">bool</span> <span class="identifier">isfinite</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
    45 
    46 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
    47 <span class="keyword">bool</span> <span class="identifier">isinf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
    48 
    49 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
    50 <span class="keyword">bool</span> <span class="identifier">isnan</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
    51 
    52 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
    53 <span class="keyword">bool</span> <span class="identifier">isnormal</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
    54 </pre>
     44<span class="keyword">bool</span> <span class="identifier">isfinite</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span> <span class="comment">// Neither infinity nor NaN.
     45</span>
     46<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
     47<span class="keyword">bool</span> <span class="identifier">isinf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// Infinity (+ or -).
     48</span>
     49<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
     50<span class="keyword">bool</span> <span class="identifier">isnan</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// NaN.
     51</span>
     52<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
     53<span class="keyword">bool</span> <span class="identifier">isnormal</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// isfinite and not denormalised.
     54</span>
     55<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">\</span><span class="identifier">math</span><span class="special">\</span><span class="identifier">special_functions</span><span class="special">\</span><span class="identifier">fpclassify</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
     56</pre>
     57<p>
     58        to use these functions.
     59      </p>
    5560<a name="math_toolkit.special.fpclass.description"></a><h5>
    56 <a name="id719773"></a>
     61<a name="id720008"></a>
    5762        <a href="fpclass.html#math_toolkit.special.fpclass.description">Description</a>
    5863      </h5>
     
    8489</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">);</span>
    8590<span class="comment">//
    86 </span><span class="comment">// This will cause a compiler error is isnan is a native macro:
     91</span><span class="comment">// This will cause a compiler error if isnan is a native macro:
    8792</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
    88 <span class="comment">// So always use (boost::math::isnan)(z); instead.
     93<span class="comment">// So always use instead:
     94</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">);</span>
     95<span class="comment">//
     96</span><span class="comment">// You can also add a using statment,
     97</span><span class="comment">// globally to a .cpp file, or to a local function in a .hpp file.
     98</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">;</span>
     99<span class="comment">// so you can write the shorter and less cluttered
     100</span><span class="special">(</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">)</span>
     101<span class="comment">// But, as above, if isnan is a native macro, this causes a compiler error,
     102</span><span class="comment">// because the macro always 'gets' the name first, unless enclosed in () brackets.
    89103</span></pre>
    90104<p>
     
    194208</pre>
    195209<p>
    196         Returns true only if <span class="emphasis"><em>z</em></span> is a NaN.
     210        Returns true only if <span class="emphasis"><em>z</em></span> is a <a href="http://en.wikipedia.org/wiki/NaN" target="_top">NaN</a>.
    197211      </p>
    198212<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html

    r44093 r44694  
    7272        </p>
    7373<a name="math_toolkit.special.powers.cbrt.accuracy"></a><h5>
    74 <a name="id709131"></a>
     74<a name="id709273"></a>
    7575          <a href="cbrt.html#math_toolkit.special.powers.cbrt.accuracy">Accuracy</a>
    7676        </h5>
     
    8080        </p>
    8181<a name="math_toolkit.special.powers.cbrt.testing"></a><h5>
    82 <a name="id709172"></a>
     82<a name="id709314"></a>
    8383          <a href="cbrt.html#math_toolkit.special.powers.cbrt.testing">Testing</a>
    8484        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html

    r44093 r44694  
    8181        </p>
    8282<a name="math_toolkit.special.powers.expm1.accuracy"></a><h5>
    83 <a name="id708631"></a>
     83<a name="id708773"></a>
    8484          <a href="expm1.html#math_toolkit.special.powers.expm1.accuracy">Accuracy</a>
    8585        </h5>
     
    8989        </p>
    9090<a name="math_toolkit.special.powers.expm1.testing"></a><h5>
    91 <a name="id708672"></a>
     91<a name="id708814"></a>
    9292          <a href="expm1.html#math_toolkit.special.powers.expm1.testing">Testing</a>
    9393        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html

    r44093 r44694  
    5959        </p>
    6060<a name="math_toolkit.special.powers.hypot.implementation"></a><h5>
    61 <a name="id710713"></a>
     61<a name="id710855"></a>
    6262          <a href="hypot.html#math_toolkit.special.powers.hypot.implementation">Implementation</a>
    6363        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html

    r44093 r44694  
    9494        </p>
    9595<a name="math_toolkit.special.powers.log1p.accuracy"></a><h5>
    96 <a name="id708035"></a>
     96<a name="id708178"></a>
    9797          <a href="log1p.html#math_toolkit.special.powers.log1p.accuracy">Accuracy</a>
    9898        </h5>
     
    102102        </p>
    103103<a name="math_toolkit.special.powers.log1p.testing"></a><h5>
    104 <a name="id708076"></a>
     104<a name="id708218"></a>
    105105          <a href="log1p.html#math_toolkit.special.powers.log1p.testing">Testing</a>
    106106        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html

    r44093 r44694  
    7575        </p>
    7676<a name="math_toolkit.special.powers.powm1.accuracy"></a><h5>
    77 <a name="id710274"></a>
     77<a name="id710416"></a>
    7878          <a href="powm1.html#math_toolkit.special.powers.powm1.accuracy">Accuracy</a>
    7979        </h5>
     
    8282        </p>
    8383<a name="math_toolkit.special.powers.powm1.testing"></a><h5>
    84 <a name="id710303"></a>
     84<a name="id710445"></a>
    8585          <a href="powm1.html#math_toolkit.special.powers.powm1.testing">Testing</a>
    8686        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html

    r44093 r44694  
    7777        </p>
    7878<a name="math_toolkit.special.powers.sqrt1pm1.accuracy"></a><h5>
    79 <a name="id709705"></a>
     79<a name="id709847"></a>
    8080          <a href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.accuracy">Accuracy</a>
    8181        </h5>
     
    8585        </p>
    8686<a name="math_toolkit.special.powers.sqrt1pm1.testing"></a><h5>
    87 <a name="id709747"></a>
     87<a name="id709889"></a>
    8888          <a href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.testing">Testing</a>
    8989        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html

    r44093 r44694  
    573573          For <code class="computeroutput"><span class="identifier">z</span> <span class="special">&lt;=</span>
    574574          <span class="number">0.5</span></code> then a rational approximation
    575           to erf is used, based on the observation that:
    576         </p>
    577 <pre class="programlisting"><span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">)/</span><span class="identifier">z</span> <span class="special">~</span> <span class="number">1.12</span><span class="special">....</span>
     575          to erf is used, based on the observation that erf is an odd function and
     576          therefore erf is calculated using:
     577        </p>
     578<pre class="programlisting"><span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">z</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">));</span>
    578579</pre>
    579580<p>
    580           Therefore erf is calculated using:
    581         </p>
    582 <pre class="programlisting"><span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">z</span> <span class="special">*</span> <span class="special">(</span><span class="number">1.125F</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">));</span>
    583 </pre>
    584 <p>
    585           where the rational approximation R(z) is optimised for absolute error:
    586           as long as its absolute error is small enough compared to 1.125, then any
    587           round-off error incurred during the computation of R(z) will effectively
    588           disappear from the result. As a result the error for erf and erfc in this
    589           region is very low: the last bit is incorrect in only a very small number
    590           of cases.
     581          where the rational approximation R(z*z) is optimised for absolute error:
     582          as long as its absolute error is small enough compared to the constant
     583          C, then any round-off error incurred during the computation of R(z*z) will
     584          effectively disappear from the result. As a result the error for erf and
     585          erfc in this region is very low: the last bit is incorrect in only a very
     586          small number of cases.
    591587        </p>
    592588<p>
     
    604600          <span class="number">0.5</span></code> we calculate erfc using:
    605601        </p>
    606 <pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">c</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">;</span>
     602<pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span> <span class="special">-</span> <span class="identifier">B</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">;</span>
    607603</pre>
    608604<p>
    609           Again R(z) is optimised for absolute error, and the constant <code class="computeroutput"><span class="identifier">c</span></code> is the average of <code class="computeroutput"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span>
     605          Again R(z - B) is optimised for absolute error, and the constant <code class="computeroutput"><span class="identifier">C</span></code> is the average of <code class="computeroutput"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span>
    610606          <span class="special">*</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span>
    611607          <span class="identifier">z</span></code> taken at the endpoints of the
    612           range. Once again, as long as the absolute error in R(z) is small compared
    613           to <code class="computeroutput"><span class="identifier">c</span></code> then <code class="computeroutput"><span class="identifier">c</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code> will be correctly rounded, and the error
     608          range. Once again, as long as the absolute error in R(z - B) is small compared
     609          to <code class="computeroutput"><span class="identifier">c</span></code> then <code class="computeroutput"><span class="identifier">c</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span>
     610          <span class="special">-</span> <span class="identifier">B</span><span class="special">)</span></code> will be correctly rounded, and the error
    614611          in the result will depend only on the accuracy of the exp function. In
    615612          practice, in all but a very small number of cases, the error is confined
    616           to the last bit of the result.
    617         </p>
     613          to the last bit of the result. The constant <code class="computeroutput"><span class="identifier">B</span></code>
     614          is chosen so that the left hand end of the range of the rational approximation
     615          is 0.
     616        </p>
     617<p>
     618          For large <code class="computeroutput"><span class="identifier">z</span></code> over a range
     619          [a, +&#8734;] the above approximation is modified to:
     620        </p>
     621<pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="number">1</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">;</span>
     622</pre>
    618623</div>
    619624<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.sf_erf.error_inv.synopsis"></a><h5>
    31 <a name="id667597"></a>
     31<a name="id667755"></a>
    3232          <a href="error_inv.html#math_toolkit.special.sf_erf.error_inv.synopsis">Synopsis</a>
    3333        </h5>
     
    7070        </p>
    7171<a name="math_toolkit.special.sf_erf.error_inv.description"></a><h5>
    72 <a name="id668144"></a>
     72<a name="id668301"></a>
    7373          <a href="error_inv.html#math_toolkit.special.sf_erf.error_inv.description">Description</a>
    7474        </h5>
     
    104104        </p>
    105105<a name="math_toolkit.special.sf_erf.error_inv.accuracy"></a><h5>
    106 <a name="id668689"></a>
     106<a name="id668846"></a>
    107107          <a href="error_inv.html#math_toolkit.special.sf_erf.error_inv.accuracy">Accuracy</a>
    108108        </h5>
     
    114114        </p>
    115115<a name="math_toolkit.special.sf_erf.error_inv.testing"></a><h5>
    116 <a name="id668730"></a>
     116<a name="id668886"></a>
    117117          <a href="error_inv.html#math_toolkit.special.sf_erf.error_inv.testing">Testing</a>
    118118        </h5>
     
    136136</ul></div>
    137137<a name="math_toolkit.special.sf_erf.error_inv.implementation"></a><h5>
    138 <a name="id668797"></a>
     138<a name="id668953"></a>
    139139          <a href="error_inv.html#math_toolkit.special.sf_erf.error_inv.implementation">Implementation</a>
    140140        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html

    r44093 r44694  
    2828</h4></div></div></div>
    2929<a name="math_toolkit.special.sf_poly.hermite.synopsis"></a><h5>
    30 <a name="id677070"></a>
     30<a name="id677225"></a>
    3131          <a href="hermite.html#math_toolkit.special.sf_poly.hermite.synopsis">Synopsis</a>
    3232        </h5>
     
    5252</span></pre>
    5353<a name="math_toolkit.special.sf_poly.hermite.description"></a><h5>
    54 <a name="id677577"></a>
     54<a name="id677731"></a>
    5555          <a href="hermite.html#math_toolkit.special.sf_poly.hermite.description">Description</a>
    5656        </h5>
     
    137137</div>
    138138<a name="math_toolkit.special.sf_poly.hermite.accuracy"></a><h5>
    139 <a name="id678589"></a>
     139<a name="id678743"></a>
    140140          <a href="hermite.html#math_toolkit.special.sf_poly.hermite.accuracy">Accuracy</a>
    141141        </h5>
     
    147147        </p>
    148148<div class="table">
    149 <a name="id678620"></a><p class="title"><b>Table 33. Peak Errors In the Hermite Polynomial</b></p>
     149<a name="id678774"></a><p class="title"><b>Table 33. Peak Errors In the Hermite Polynomial</b></p>
    150150<div class="table-contents"><table class="table" summary="Peak Errors In the Hermite Polynomial">
    151151<colgroup>
     
    254254        </p>
    255255<a name="math_toolkit.special.sf_poly.hermite.testing"></a><h5>
    256 <a name="id678796"></a>
     256<a name="id678951"></a>
    257257          <a href="hermite.html#math_toolkit.special.sf_poly.hermite.testing">Testing</a>
    258258        </h5>
     
    264264        </p>
    265265<a name="math_toolkit.special.sf_poly.hermite.implementation"></a><h5>
    266 <a name="id678835"></a>
     266<a name="id678989"></a>
    267267          <a href="hermite.html#math_toolkit.special.sf_poly.hermite.implementation">Implementation</a>
    268268        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.sf_poly.laguerre.synopsis"></a><h5>
    31 <a name="id673649"></a>
     31<a name="id673804"></a>
    3232          <a href="laguerre.html#math_toolkit.special.sf_poly.laguerre.synopsis">Synopsis</a>
    3333        </h5>
     
    6363</span></pre>
    6464<a name="math_toolkit.special.sf_poly.laguerre.description"></a><h5>
    65 <a name="id674566"></a>
     65<a name="id674721"></a>
    6666          <a href="laguerre.html#math_toolkit.special.sf_poly.laguerre.description">Description</a>
    6767        </h5>
     
    211211</div>
    212212<a name="math_toolkit.special.sf_poly.laguerre.accuracy"></a><h5>
    213 <a name="id676604"></a>
     213<a name="id676759"></a>
    214214          <a href="laguerre.html#math_toolkit.special.sf_poly.laguerre.accuracy">Accuracy</a>
    215215        </h5>
     
    221221        </p>
    222222<div class="table">
    223 <a name="id676635"></a><p class="title"><b>Table 31. Peak Errors In the Laguerre Polynomial</b></p>
     223<a name="id676790"></a><p class="title"><b>Table 31. Peak Errors In the Laguerre Polynomial</b></p>
    224224<div class="table-contents"><table class="table" summary="Peak Errors In the Laguerre Polynomial">
    225225<colgroup>
     
    321321</div>
    322322<br class="table-break"><div class="table">
    323 <a name="id676800"></a><p class="title"><b>Table 32. Peak Errors In the Associated Laguerre
     323<a name="id676955"></a><p class="title"><b>Table 32. Peak Errors In the Associated Laguerre
    324324        Polynomial</b></p>
    325325<div class="table-contents"><table class="table" summary="Peak Errors In the Associated Laguerre
     
    430430        </p>
    431431<a name="math_toolkit.special.sf_poly.laguerre.testing"></a><h5>
    432 <a name="id676977"></a>
     432<a name="id677132"></a>
    433433          <a href="laguerre.html#math_toolkit.special.sf_poly.laguerre.testing">Testing</a>
    434434        </h5>
     
    440440        </p>
    441441<a name="math_toolkit.special.sf_poly.laguerre.implementation"></a><h5>
    442 <a name="id677016"></a>
     442<a name="id677171"></a>
    443443          <a href="laguerre.html#math_toolkit.special.sf_poly.laguerre.implementation">Implementation</a>
    444444        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.special.sf_poly.legendre.synopsis"></a><h5>
    31 <a name="id669318"></a>
     31<a name="id669474"></a>
    3232          <a href="legendre.html#math_toolkit.special.sf_poly.legendre.synopsis">Synopsis</a>
    3333        </h5>
     
    8585        </p>
    8686<a name="math_toolkit.special.sf_poly.legendre.description"></a><h5>
    87 <a name="id670494"></a>
     87<a name="id670651"></a>
    8888          <a href="legendre.html#math_toolkit.special.sf_poly.legendre.description">Description</a>
    8989        </h5>
     
    293293</div>
    294294<a name="math_toolkit.special.sf_poly.legendre.accuracy"></a><h5>
    295 <a name="id672942"></a>
     295<a name="id673098"></a>
    296296          <a href="legendre.html#math_toolkit.special.sf_poly.legendre.accuracy">Accuracy</a>
    297297        </h5>
     
    303303        </p>
    304304<div class="table">
    305 <a name="id672973"></a><p class="title"><b>Table 28. Peak Errors In the Legendre P Function</b></p>
     305<a name="id673129"></a><p class="title"><b>Table 28. Peak Errors In the Legendre P Function</b></p>
    306306<div class="table-contents"><table class="table" summary="Peak Errors In the Legendre P Function">
    307307<colgroup>
     
    432432</div>
    433433<br class="table-break"><div class="table">
    434 <a name="id673171"></a><p class="title"><b>Table 29. Peak Errors In the Associated Legendre
     434<a name="id673327"></a><p class="title"><b>Table 29. Peak Errors In the Associated Legendre
    435435        P Function</b></p>
    436436<div class="table-contents"><table class="table" summary="Peak Errors In the Associated Legendre
     
    534534</div>
    535535<br class="table-break"><div class="table">
    536 <a name="id673329"></a><p class="title"><b>Table 30. Peak Errors In the Legendre Q Function</b></p>
     536<a name="id673485"></a><p class="title"><b>Table 30. Peak Errors In the Legendre Q Function</b></p>
    537537<div class="table-contents"><table class="table" summary="Peak Errors In the Legendre Q Function">
    538538<colgroup>
     
    676676        </p>
    677677<a name="math_toolkit.special.sf_poly.legendre.testing"></a><h5>
    678 <a name="id673555"></a>
     678<a name="id673711"></a>
    679679          <a href="legendre.html#math_toolkit.special.sf_poly.legendre.testing">Testing</a>
    680680        </h5>
     
    686686        </p>
    687687<a name="math_toolkit.special.sf_poly.legendre.implementation"></a><h5>
    688 <a name="id673594"></a>
     688<a name="id673750"></a>
    689689          <a href="legendre.html#math_toolkit.special.sf_poly.legendre.implementation">Implementation</a>
    690690        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html

    r44093 r44694  
    2828</h4></div></div></div>
    2929<a name="math_toolkit.special.sf_poly.sph_harm.synopsis"></a><h5>
    30 <a name="id678890"></a>
     30<a name="id679044"></a>
    3131          <a href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.synopsis">Synopsis</a>
    3232        </h5>
     
    6161</span></pre>
    6262<a name="math_toolkit.special.sf_poly.sph_harm.description"></a><h5>
    63 <a name="id680015"></a>
     63<a name="id680169"></a>
    6464          <a href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.description">Description</a>
    6565        </h5>
     
    156156        </p>
    157157<a name="math_toolkit.special.sf_poly.sph_harm.accuracy"></a><h5>
    158 <a name="id681277"></a>
     158<a name="id681441"></a>
    159159          <a href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.accuracy">Accuracy</a>
    160160        </h5>
     
    171171        </p>
    172172<div class="table">
    173 <a name="id681316"></a><p class="title"><b>Table 34. Peak Errors In the Sperical Harmonic Functions</b></p>
     173<a name="id681481"></a><p class="title"><b>Table 34. Peak Errors In the Sperical Harmonic Functions</b></p>
    174174<div class="table-contents"><table class="table" summary="Peak Errors In the Sperical Harmonic Functions">
    175175<colgroup>
     
    277277        </p>
    278278<a name="math_toolkit.special.sf_poly.sph_harm.testing"></a><h5>
    279 <a name="id681496"></a>
     279<a name="id681660"></a>
    280280          <a href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.testing">Testing</a>
    281281        </h5>
     
    287287        </p>
    288288<a name="math_toolkit.special.sf_poly.sph_harm.implementation"></a><h5>
    289 <a name="id681534"></a>
     289<a name="id681699"></a>
    290290          <a href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.implementation">Implementation</a>
    291291        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/compilers.html

    r44093 r44694  
    3838        </p>
    3939<div class="table">
    40 <a name="id813292"></a><p class="title"><b>Table 54. Supported/Tested Compilers</b></p>
     40<a name="id813658"></a><p class="title"><b>Table 54. Supported/Tested Compilers</b></p>
    4141<div class="table-contents"><table class="table" summary="Supported/Tested Compilers">
    4242<colgroup>
     
    541541<p><br class="table-break"> </p>
    542542<div class="table">
    543 <a name="id814085"></a><p class="title"><b>Table 55. Unsupported Compilers</b></p>
     543<a name="id814456"></a><p class="title"><b>Table 55. Unsupported Compilers</b></p>
    544544<div class="table-contents"><table class="table" summary="Unsupported Compilers">
    545545<colgroup>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/credits.html

    r44091 r44694  
    6464        Plots of the functions and distributions were prepared in <a href="http://www.w3.org/" target="_top">W3C</a>
    6565        standard <a href="http://www.svg.org/" target="_top">Scalable Vector Graphic (SVG)</a>
    66         format using a program created by Jacob Voytko during a Google 'Summer of
    67         Code'. Since browser support for rendering SVG is still not universal (Microsoft
    68         Internet Explorer, even IE 8 beta, still lacks native SVG support but can
    69         be made to work with <a href="http://www.adobe.com/svg/viewer/install/" target="_top">Adobe's
     66        format using a program created by Jacob Voytko during a <a href="http://code.google.com/soc/2007/" target="_top">Google
     67        Summer of Code (2007)</a>. Since browser support for rendering SVG is
     68        still not universal (Microsoft Internet Explorer, even IE 8 beta, still lacks
     69        native SVG support but can be made to work with <a href="http://www.adobe.com/svg/viewer/install/" target="_top">Adobe's
    7070        free SVG viewer</a> plugin), so the SVG files were batch converted to
    7171        JPEG using <a href="http://www.inkscape.org/" target="_top">Inkscape</a>.
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html

    r44093 r44694  
    3131        </p>
    3232<h5>
    33 <a name="id812846"></a>
     33<a name="id813212"></a>
    3434          <a href="history1.html#math_toolkit.status.history1.boost_1_36_0">Boost-1.36.0</a>
    3535        </h5>
     
    6666        </p>
    6767<h5>
    68 <a name="id812913"></a>
     68<a name="id813280"></a>
    6969          <a href="history1.html#math_toolkit.status.history1.boost_1_35_0__post_review_first_official_release">Boost-1.35.0:
    7070          Post Review First Official Release</a>
     
    103103        </p>
    104104<h5>
    105 <a name="id813016"></a>
     105<a name="id813383"></a>
    106106          <a href="history1.html#math_toolkit.status.history1.milestone_4__second_review_candidate__1st_march_2007_">Milestone
    107107          4: Second Review Candidate (1st March 2007)</a>
     
    122122        </p>
    123123<h5>
    124 <a name="id813057"></a>
     124<a name="id813424"></a>
    125125          <a href="history1.html#math_toolkit.status.history1.milestone_3__first_review_candidate__31st_dec_2006_">Milestone
    126126          3: First Review Candidate (31st Dec 2006)</a>
     
    155155        </p>
    156156<h5>
    157 <a name="id813123"></a>
     157<a name="id813490"></a>
    158158          <a href="history1.html#math_toolkit.status.history1.milestone_2__released_september_10th_2006">Milestone
    159159          2: Released September 10th 2006</a>
     
    196196        </p>
    197197<h5>
    198 <a name="id813200"></a>
     198<a name="id813567"></a>
    199199          <a href="history1.html#math_toolkit.status.history1.milestone_1__released_march_31st_2006">Milestone
    200200          1: Released March 31st 2006</a>
     
    231231        </p>
    232232<p>
    233           Sandbox and trunk last synchonised at revision: 44092.
     233          Sandbox and trunk last synchonised at revision: 44694.
    234234        </p>
    235235<p>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html

    r44093 r44694  
    4444      </p>
    4545<a name="math_toolkit.status.issues.tgamma"></a><h5>
    46 <a name="id814269"></a>
     46<a name="id814640"></a>
    4747        <a href="issues.html#math_toolkit.status.issues.tgamma">tgamma</a>
    4848      </h5>
     
    5252        </li></ul></div>
    5353<a name="math_toolkit.status.issues.incomplete_beta"></a><h5>
    54 <a name="id814311"></a>
     54<a name="id814682"></a>
    5555        <a href="issues.html#math_toolkit.status.issues.incomplete_beta">Incomplete Beta</a>
    5656      </h5>
     
    6060        </li></ul></div>
    6161<a name="math_toolkit.status.issues.inverse_gamma"></a><h5>
    62 <a name="id814344"></a>
     62<a name="id814715"></a>
    6363        <a href="issues.html#math_toolkit.status.issues.inverse_gamma">Inverse Gamma</a>
    6464      </h5>
     
    6868        </li></ul></div>
    6969<a name="math_toolkit.status.issues.polynomials"></a><h5>
    70 <a name="id814376"></a>
     70<a name="id814748"></a>
    7171        <a href="issues.html#math_toolkit.status.issues.polynomials">Polynomials</a>
    7272      </h5>
     
    7878        </li></ul></div>
    7979<a name="math_toolkit.status.issues.elliptic_integrals"></a><h5>
    80 <a name="id814413"></a>
     80<a name="id814784"></a>
    8181        <a href="issues.html#math_toolkit.status.issues.elliptic_integrals">Elliptic Integrals</a>
    8282      </h5>
     
    128128</ul></div>
    129129<a name="math_toolkit.status.issues.inverse_hyperbolic_functions"></a><h5>
    130 <a name="id814571"></a>
     130<a name="id814942"></a>
    131131        <a href="issues.html#math_toolkit.status.issues.inverse_hyperbolic_functions">Inverse
    132132        Hyperbolic Functions</a>
     
    138138        </li></ul></div>
    139139<a name="math_toolkit.status.issues.statistical_distributions"></a><h5>
    140 <a name="id814616"></a>
     140<a name="id814988"></a>
    141141        <a href="issues.html#math_toolkit.status.issues.statistical_distributions">Statistical
    142142        distributions</a>
     
    147147        </li></ul></div>
    148148<a name="math_toolkit.status.issues.feature_requests"></a><h5>
    149 <a name="id814651"></a>
     149<a name="id815022"></a>
    150150        <a href="issues.html#math_toolkit.status.issues.feature_requests">Feature Requests</a>
    151151      </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit.html

    r44091 r44694  
    77<link rel="start" href="../index.html" title="Math Toolkit">
    88<link rel="up" href="../index.html" title="Math Toolkit">
    9 <link rel="prev" href="special/fpclass.html" title="Floating Point Classification: Infinities and NaN's">
     9<link rel="prev" href="special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">
    1010<link rel="next" href="toolkit/internals_overview.html" title="Overview">
    1111</head>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.cf.synopsis"></a><h5>
    31 <a name="id722563"></a>
     31<a name="id722948"></a>
    3232          <a href="cf.html#math_toolkit.toolkit.internals1.cf.synopsis">Synopsis</a>
    3333        </h5>
     
    6060</span></pre>
    6161<a name="math_toolkit.toolkit.internals1.cf.description"></a><h5>
    62 <a name="id723284"></a>
     62<a name="id723669"></a>
    6363          <a href="cf.html#math_toolkit.toolkit.internals1.cf.description">Description</a>
    6464        </h5>
     
    158158        </p>
    159159<a name="math_toolkit.toolkit.internals1.cf.implementation"></a><h5>
    160 <a name="id723562"></a>
     160<a name="id723947"></a>
    161161          <a href="cf.html#math_toolkit.toolkit.internals1.cf.implementation">Implementation</a>
    162162        </h5>
     
    168168        </p>
    169169<a name="math_toolkit.toolkit.internals1.cf.examples"></a><h5>
    170 <a name="id723596"></a>
     170<a name="id723981"></a>
    171171          <a href="cf.html#math_toolkit.toolkit.internals1.cf.examples">Examples</a>
    172172        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.minima.synopsis"></a><h5>
    31 <a name="id740279"></a>
     31<a name="id740666"></a>
    3232          <a href="minima.html#math_toolkit.toolkit.internals1.minima.synopsis">synopsis</a>
    3333        </h5>
     
    4646</pre>
    4747<a name="math_toolkit.toolkit.internals1.minima.description"></a><h5>
    48 <a name="id740749"></a>
     48<a name="id741136"></a>
    4949          <a href="minima.html#math_toolkit.toolkit.internals1.minima.description">Description</a>
    5050        </h5>
     
    8989        </p>
    9090<a name="math_toolkit.toolkit.internals1.minima.implementation"></a><h5>
    91 <a name="id740888"></a>
     91<a name="id741275"></a>
    9292          <a href="minima.html#math_toolkit.toolkit.internals1.minima.implementation">Implementation</a>
    9393        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.rational.synopsis"></a><h5>
    31 <a name="id724578"></a>
     31<a name="id724963"></a>
    3232          <a href="rational.html#math_toolkit.toolkit.internals1.rational.synopsis">synopsis</a>
    3333        </h5>
     
    8080</pre>
    8181<a name="math_toolkit.toolkit.internals1.rational.description"></a><h5>
    82 <a name="id726703"></a>
     82<a name="id727088"></a>
    8383          <a href="rational.html#math_toolkit.toolkit.internals1.rational.description">Description</a>
    8484        </h5>
     
    194194        </p>
    195195<a name="math_toolkit.toolkit.internals1.rational.implementation"></a><h5>
    196 <a name="id729166"></a>
     196<a name="id729552"></a>
    197197          <a href="rational.html#math_toolkit.toolkit.internals1.rational.implementation">Implementation</a>
    198198        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.roots.synopsis"></a><h5>
    31 <a name="id729285"></a>
     31<a name="id729670"></a>
    3232          <a href="roots.html#math_toolkit.toolkit.internals1.roots.synopsis">Synopsis</a>
    3333        </h5>
     
    6262</span></pre>
    6363<a name="math_toolkit.toolkit.internals1.roots.description"></a><h5>
    64 <a name="id730440"></a>
     64<a name="id730826"></a>
    6565          <a href="roots.html#math_toolkit.toolkit.internals1.roots.description">Description</a>
    6666        </h5>
     
    177177        </p>
    178178<a name="math_toolkit.toolkit.internals1.roots.newton_raphson_method"></a><h5>
    179 <a name="id730761"></a>
     179<a name="id731147"></a>
    180180          <a href="roots.html#math_toolkit.toolkit.internals1.roots.newton_raphson_method">Newton
    181181          Raphson Method</a>
     
    197197        </p>
    198198<a name="math_toolkit.toolkit.internals1.roots.halley_s_method"></a><h5>
    199 <a name="id730842"></a>
     199<a name="id731228"></a>
    200200          <a href="roots.html#math_toolkit.toolkit.internals1.roots.halley_s_method">Halley's
    201201          Method</a>
     
    221221        </p>
    222222<a name="math_toolkit.toolkit.internals1.roots.schroeder_s_method"></a><h5>
    223 <a name="id730929"></a>
     223<a name="id731315"></a>
    224224          <a href="roots.html#math_toolkit.toolkit.internals1.roots.schroeder_s_method">Schroeder's
    225225          Method</a>
     
    245245        </p>
    246246<a name="math_toolkit.toolkit.internals1.roots.example"></a><h5>
    247 <a name="id731009"></a>
     247<a name="id731395"></a>
    248248          <a href="roots.html#math_toolkit.toolkit.internals1.roots.example">Example</a>
    249249        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.roots2.synopsis"></a><h5>
    31 <a name="id733125"></a>
     31<a name="id733511"></a>
    3232          <a href="roots2.html#math_toolkit.toolkit.internals1.roots2.synopsis">Synopsis</a>
    3333        </h5>
     
    142142</span></pre>
    143143<a name="math_toolkit.toolkit.internals1.roots2.description"></a><h5>
    144 <a name="id735767"></a>
     144<a name="id736154"></a>
    145145          <a href="roots2.html#math_toolkit.toolkit.internals1.roots2.description">Description</a>
    146146        </h5>
     
    560560        </p>
    561561<a name="math_toolkit.toolkit.internals1.roots2.implementation"></a><h5>
    562 <a name="id740212"></a>
     562<a name="id740599"></a>
    563563          <a href="roots2.html#math_toolkit.toolkit.internals1.roots2.implementation">Implementation</a>
    564564        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html

    r44093 r44694  
    2929</h4></div></div></div>
    3030<a name="math_toolkit.toolkit.internals1.series_evaluation.synopsis"></a><h5>
    31 <a name="id720707"></a>
     31<a name="id721093"></a>
    3232          <a href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.synopsis">Synopsis</a>
    3333        </h5>
     
    6262</span></pre>
    6363<a name="math_toolkit.toolkit.internals1.series_evaluation.description"></a><h5>
    64 <a name="id721657"></a>
     64<a name="id722042"></a>
    6565          <a href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.description">Description</a>
    6666        </h5>
     
    118118        </p>
    119119<a name="math_toolkit.toolkit.internals1.series_evaluation.example"></a><h5>
    120 <a name="id721804"></a>
     120<a name="id722189"></a>
    121121          <a href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.example">Example</a>
    122122        </h5>
  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html

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    2929</h4></div></div></div>
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    3232          <a href="error_test.html#math_toolkit.toolkit.internals2.error_test.synopsis">Synopsis</a>
    3333        </h5>
     
    4646</pre>
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    4949          <a href="error_test.html#math_toolkit.toolkit.internals2.error_test.description">Description</a>
    5050        </h5>
     
    166166        </p>
    167167<a name="math_toolkit.toolkit.internals2.error_test.example"></a><h5>
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  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html

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    3131          <a href="polynomials.html#math_toolkit.toolkit.internals2.polynomials.synopsis">Synopsis</a>
    3232        </h5>
     
    104104</span></pre>
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  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html

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    148148</span></pre>
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    152152        </h5>
     
    178178</ul></div>
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    181181          <a href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_1__output_data_for_graph_plotting">Example
    182182          1: Output Data for Graph Plotting</a>
     
    212212        </p>
    213213<a name="math_toolkit.toolkit.internals2.test_data.example_2__creating_test_data"></a><h6>
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    216216          2: Creating Test Data</a>
     
    376376        </p>
    377377<a name="math_toolkit.toolkit.internals2.test_data.example_3__profiling_a_continued_fraction_for_convergence_and_accuracy"></a><h6>
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    380380          3: Profiling a Continued Fraction for Convergence and Accuracy</a>
     
    482482        </p>
    483483<a name="math_toolkit.toolkit.internals2.test_data.reference"></a><h5>
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  • trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html

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    4343      </p>
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    4646        <a href="concepts.html#math_toolkit.using_udt.concepts.basic_arithmetic_requirements">Basic
    4747        Arithmetic Requirements</a>
     
    10351035</table></div>
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    10381038        <a href="concepts.html#math_toolkit.using_udt.concepts.standard_library_support_requirements">Standard
    10391039        Library Support Requirements</a>
  • trunk/libs/math/doc/sf_and_dist/roadmap.qbk

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     74Sandbox and trunk last synchonised at revision: 44694.
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