diff --git a/.travis.yml b/.travis.yml index 91e2c719..d62455ee 100644 --- a/.travis.yml +++ b/.travis.yml @@ -10,10 +10,10 @@ script: - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi - if (julia -e 'VERSION < v"0.5" && exit(1)'); then julia -e 'include(joinpath(JULIA_HOME, Base.DATAROOTDIR, "julia", "build_sysimg.jl")); build_sysimg(force=true)'; - julia -e 'Pkg.clone(pwd()); Pkg.build("ForwardDiff"); Pkg.test("ForwardDiff"; coverage=true)'; + julia -e 'Pkg.clone(pwd()); Pkg.build("ForwardDiff"); Pkg.checkout("DiffBase"); Pkg.test("ForwardDiff"; coverage=true)'; julia -O3 -e 'include(joinpath(Pkg.dir("ForwardDiff"), "test/SIMDTest.jl"))'; else - julia -e 'Pkg.clone(pwd()); Pkg.build("ForwardDiff"); Pkg.test("ForwardDiff"; coverage=true)'; + julia -e 'Pkg.clone(pwd()); Pkg.build("ForwardDiff"); Pkg.checkout("DiffBase"); Pkg.test("ForwardDiff"; coverage=true)'; fi after_success: - julia -e 'cd(Pkg.dir("ForwardDiff")); Pkg.add("Coverage"); using Coverage; Coveralls.submit(Coveralls.process_folder())' diff --git a/docs/_rst/source/advanced_usage.rst b/docs/_rst/source/advanced_usage.rst index 414e6acd..576cc4ee 100644 --- a/docs/_rst/source/advanced_usage.rst +++ b/docs/_rst/source/advanced_usage.rst @@ -117,6 +117,43 @@ Note that it is usually best to pick a chunk size which divides evenly into the dimension. Otherwise, ForwardDiff has to construct and utilize an extra "remainder" chunk to complete the calculation. +Fixing issues with NaN/Inf return values +---------------------------------------- + +ForwardDiff's default behavior is to return ``NaN`` for undefined derivatives (or otherwise +mirror the behavior of the function in ``Base``, if it would return an error). This is +usually the correct thing to do, but in some cases can erroneously "poison" values which +aren't sensitive to the input and thus cause ForwardDiff to incorrectly return ``NaN`` or +``Inf`` derivatives. For example: + +.. code-block:: julia + + # the dual number's perturbation component is zero, so this + # variable should not propagate derivative information + julia> log(ForwardDiff.Dual(0.0, 0.0)) + Dual(-Inf,NaN) # oops, this NaN should be 0.0 + +Here, ForwardDiff computes the derivative of ``log(0.0)`` as ``NaN`` and then propagates +this derivative by multiplying it by the perturbation component. Usually, ForwardDiff can +rely on the identity ``x * 0.0 == 0.0`` to prevent the derivatives from propagating when +the perturbation component is ``0.0``. However, this identity doesn't hold if ``isnan(y)`` +or ``isinf(y)``, in which case a ``NaN`` derivative will be propagated instead. + +It is possible to fix this behavior by checking that the perturbation component is zero +before attempting to propagate derivative information, but this check can noticeably +decrease performance (~5%-10% on our benchmarks). + +In order to preserve performance in the majority of use cases, ForwardDiff disables this +check by default. If your code is affected by this ``NaN`` behvaior, you can enable +ForwardDiff's ``NaN``-safe mode by setting ``NANSAFE_MODE_ENABLED`` to ``true`` in +ForwardDiff's source (this constant is located in ``src/ForwardDiff.jl`` in the +package's directory). + +In the future, we plan on allowing users and downstream library authors to dynamically +enable ``NaN``-safe mode via the ``AbstractConfig`` API (see `the relevant issue +`_). + + Hessian of a vector-valued function ----------------------------------- diff --git a/docs/_sources/advanced_usage.txt b/docs/_sources/advanced_usage.txt index 414e6acd..576cc4ee 100644 --- a/docs/_sources/advanced_usage.txt +++ b/docs/_sources/advanced_usage.txt @@ -117,6 +117,43 @@ Note that it is usually best to pick a chunk size which divides evenly into the dimension. Otherwise, ForwardDiff has to construct and utilize an extra "remainder" chunk to complete the calculation. +Fixing issues with NaN/Inf return values +---------------------------------------- + +ForwardDiff's default behavior is to return ``NaN`` for undefined derivatives (or otherwise +mirror the behavior of the function in ``Base``, if it would return an error). This is +usually the correct thing to do, but in some cases can erroneously "poison" values which +aren't sensitive to the input and thus cause ForwardDiff to incorrectly return ``NaN`` or +``Inf`` derivatives. For example: + +.. code-block:: julia + + # the dual number's perturbation component is zero, so this + # variable should not propagate derivative information + julia> log(ForwardDiff.Dual(0.0, 0.0)) + Dual(-Inf,NaN) # oops, this NaN should be 0.0 + +Here, ForwardDiff computes the derivative of ``log(0.0)`` as ``NaN`` and then propagates +this derivative by multiplying it by the perturbation component. Usually, ForwardDiff can +rely on the identity ``x * 0.0 == 0.0`` to prevent the derivatives from propagating when +the perturbation component is ``0.0``. However, this identity doesn't hold if ``isnan(y)`` +or ``isinf(y)``, in which case a ``NaN`` derivative will be propagated instead. + +It is possible to fix this behavior by checking that the perturbation component is zero +before attempting to propagate derivative information, but this check can noticeably +decrease performance (~5%-10% on our benchmarks). + +In order to preserve performance in the majority of use cases, ForwardDiff disables this +check by default. If your code is affected by this ``NaN`` behvaior, you can enable +ForwardDiff's ``NaN``-safe mode by setting ``NANSAFE_MODE_ENABLED`` to ``true`` in +ForwardDiff's source (this constant is located in ``src/ForwardDiff.jl`` in the +package's directory). + +In the future, we plan on allowing users and downstream library authors to dynamically +enable ``NaN``-safe mode via the ``AbstractConfig`` API (see `the relevant issue +`_). + + Hessian of a vector-valued function ----------------------------------- diff --git a/docs/_static/basic.css b/docs/_static/basic.css index 9fa77d88..2b513f0c 100644 --- a/docs/_static/basic.css +++ b/docs/_static/basic.css @@ -4,7 +4,7 @@ * * Sphinx stylesheet -- basic theme. * - * :copyright: Copyright 2007-2015 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2016 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ @@ -52,6 +52,8 @@ div.sphinxsidebar { width: 230px; margin-left: -100%; font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; } div.sphinxsidebar ul { @@ -83,10 +85,6 @@ div.sphinxsidebar #searchbox input[type="text"] { width: 170px; } -div.sphinxsidebar #searchbox input[type="submit"] { - width: 30px; -} - img { border: 0; max-width: 100%; @@ -187,6 +185,13 @@ div.genindex-jumpbox { /* -- general body styles --------------------------------------------------- */ +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + a.headerlink { visibility: hidden; } diff --git a/docs/_static/css/theme.css b/docs/_static/css/theme.css index 57b98fe6..7be93399 100644 --- a/docs/_static/css/theme.css +++ b/docs/_static/css/theme.css @@ -1,5 +1,5 @@ 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+ }, + + initOnKeyListeners: function() { + $(document).keyup(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box or textarea + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT') { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); } }; @@ -260,4 +284,4 @@ _ = Documentation.gettext; $(document).ready(function() { Documentation.init(); -}); +}); \ No newline at end of file diff --git a/docs/_static/fonts/Inconsolata-Bold.ttf b/docs/_static/fonts/Inconsolata-Bold.ttf index 360a232d..58c9fef3 100644 Binary files a/docs/_static/fonts/Inconsolata-Bold.ttf and b/docs/_static/fonts/Inconsolata-Bold.ttf 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- reset(); - win.on('hashchange', reset); - - // Set scrolling - win.on('scroll', function () { - if (!linkScroll) { - winScroll = true; - } - }); - setInterval(function () { - if (winScroll) { - winScroll = false; - var newWinPosition = win.scrollTop(), - navPosition = navBar.scrollTop(), - newNavPosition = navPosition + (newWinPosition - winPosition); - navBar.scrollTop(newNavPosition); - winPosition = newWinPosition; - } - }, 25); - }, - init = function () { - navBar = jquery('nav.wy-nav-side:first'); - win = jquery(window); - }, - reset = function () { - // Get anchor from URL and open up nested nav - var anchor = encodeURI(window.location.hash); - if (anchor) { - try { - var link = $('.wy-menu-vertical') - .find('[href="' + anchor + '"]'); - $('.wy-menu-vertical li.toctree-l1 li.current') - .removeClass('current'); - link.closest('li.toctree-l2').addClass('current'); - link.closest('li.toctree-l3').addClass('current'); - link.closest('li.toctree-l4').addClass('current'); - } - catch (err) { - console.log("Error expanding nav for anchor", err); - } - } - }, - hashChange = function () { - linkScroll = true; - win.one('hashchange', function () { - linkScroll = false; - }); - }; - jquery(init); - return { - enable: enable, - hashChange: hashChange - }; - }()); - return { - StickyNav: stickyNav }; -}($)); + + nav.toggleCurrent = function (elem) { + var parent_li = elem.closest('li'); + parent_li.siblings('li.current').removeClass('current'); + parent_li.siblings().find('li.current').removeClass('current'); + parent_li.find('> ul li.current').removeClass('current'); + parent_li.toggleClass('current'); + } + + return nav; +}; + +module.exports.ThemeNav = ThemeNav(); + +if (typeof(window) != 'undefined') { + window.SphinxRtdTheme = { StickyNav: module.exports.ThemeNav }; +} + +},{"jquery":"jquery"}]},{},["sphinx-rtd-theme"]); diff --git a/docs/_static/pygments.css b/docs/_static/pygments.css index 57eadc03..8213e90b 100644 --- a/docs/_static/pygments.css +++ b/docs/_static/pygments.css @@ -4,8 +4,10 @@ .highlight .err { border: 1px solid #FF0000 } /* Error */ .highlight .k { color: #007020; font-weight: bold } /* Keyword */ .highlight .o { color: #666666 } /* Operator */ +.highlight .ch { color: #408090; font-style: italic } /* Comment.Hashbang */ .highlight .cm { color: #408090; font-style: italic } /* Comment.Multiline */ .highlight .cp { color: #007020 } /* Comment.Preproc */ +.highlight .cpf { color: #408090; font-style: italic } /* Comment.PreprocFile */ .highlight .c1 { color: #408090; font-style: italic } /* Comment.Single */ .highlight .cs { color: #408090; background-color: #fff0f0 } /* Comment.Special */ .highlight .gd { color: #A00000 } /* Generic.Deleted */ diff --git a/docs/_static/searchtools.js b/docs/_static/searchtools.js index 0e794fd3..066857ce 100644 --- a/docs/_static/searchtools.js +++ b/docs/_static/searchtools.js @@ -2,14 +2,15 @@ * searchtools.js_t * ~~~~~~~~~~~~~~~~ * - * Sphinx JavaScript utilties for the full-text search. + * Sphinx JavaScript utilities for the full-text search. * - * :copyright: Copyright 2007-2015 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2016 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ +/* Non-minified version JS is _stemmer.js if file is provided */ /** * Porter Stemmer */ @@ -373,8 +374,7 @@ var Search = { } // lookup as search terms in fulltext - results = results.concat(this.performTermsSearch(searchterms, excluded, terms, Scorer.term)) - .concat(this.performTermsSearch(searchterms, excluded, titleterms, Scorer.title)); + results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms)); // let the scorer override scores with a custom scoring function if (Scorer.score) { @@ -538,23 +538,47 @@ var Search = { /** * search for full-text terms in the index */ - performTermsSearch : function(searchterms, excluded, terms, score) { + performTermsSearch : function(searchterms, excluded, terms, titleterms) { var filenames = this._index.filenames; var titles = this._index.titles; - var i, j, file, files; + var i, j, file; var fileMap = {}; + var scoreMap = {}; var results = []; // perform the search on the required terms for (i = 0; i < searchterms.length; i++) { var word = searchterms[i]; + var files = []; + var _o = [ + {files: terms[word], score: Scorer.term}, + {files: titleterms[word], score: Scorer.title} + ]; + // no match but word was a required one - if ((files = terms[word]) === undefined) + if ($u.every(_o, function(o){return o.files === undefined;})) { break; - if (files.length === undefined) { - files = [files]; } + // found search word in contents + $u.each(_o, function(o) { + var _files = o.files; + if (_files === undefined) + return + + if (_files.length === undefined) + _files = [_files]; + files = files.concat(_files); + + // set score for the word in each file to Scorer.term + for (j = 0; j < _files.length; j++) { + file = _files[j]; + if (!(file in scoreMap)) + scoreMap[file] = {} + scoreMap[file][word] = o.score; + } + }); + // create the mapping for (j = 0; j < files.length; j++) { file = files[j]; @@ -576,7 +600,9 @@ var Search = { // ensure that none of the excluded terms is in the search result for (i = 0; i < excluded.length; i++) { if (terms[excluded[i]] == file || - $u.contains(terms[excluded[i]] || [], file)) { + titleterms[excluded[i]] == file || + $u.contains(terms[excluded[i]] || [], file) || + $u.contains(titleterms[excluded[i]] || [], file)) { valid = false; break; } @@ -584,6 +610,9 @@ var Search = { // if we have still a valid result we can add it to the result list if (valid) { + // select one (max) score for the file. + // for better ranking, we should calculate ranking by using words statistics like basic tf-idf... + var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]})); results.push([filenames[file], titles[file], '', null, score]); } } @@ -594,7 +623,7 @@ var Search = { * helper function to return a node containing the * search summary for a given text. keywords is a list * of stemmed words, hlwords is the list of normal, unstemmed - * words. the first one is used to find the occurance, the + * words. the first one is used to find the occurrence, the * latter for highlighting it. */ makeSearchSummary : function(text, keywords, hlwords) { diff --git a/docs/_static/websupport.js b/docs/_static/websupport.js index 28d65db4..98e7f40b 100644 --- a/docs/_static/websupport.js +++ b/docs/_static/websupport.js @@ -2,9 +2,9 @@ * websupport.js * ~~~~~~~~~~~~~ * - * sphinx.websupport utilties for all documentation. + * sphinx.websupport utilities for all documentation. * - * :copyright: Copyright 2007-2015 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2016 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ diff --git a/docs/advanced_usage.html b/docs/advanced_usage.html index 4b94fab9..47bc8814 100644 --- a/docs/advanced_usage.html +++ b/docs/advanced_usage.html @@ -45,17 +45,27 @@
@@ -136,7 +120,13 @@
-
+ + + + + + +
  • Docs »
    • @@ -151,7 +141,8 @@
-
+
+

Advanced Usage Guide

@@ -181,7 +172,7 @@

Configuring Chunk Size

For example:

-
julia> import ForwardDiff
+
julia> import ForwardDiff
 
 # let's use a Rosenbrock function as our target function
 julia> function rosenbrock(x)
@@ -211,25 +202,25 @@ 
Configuring Chunk Sizejulia> cfg10 = ForwardDiff.GradientConfig{10}(x);
 
 # (input length of 10000) / (chunk size of 1) = (10000 1-element chunks)
-julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg1);
+julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg1);
   0.408305 seconds (4 allocations: 160 bytes)
 
 # (input length of 10000) / (chunk size of 4) = (2500 4-element chunks)
-julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg4);
+julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg4);
   0.295764 seconds (4 allocations: 160 bytes)
 
 # (input length of 10000) / (chunk size of 10) = (1000 10-element chunks)
-julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg10);
+julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg10);
   0.267396 seconds (4 allocations: 160 bytes)
 

 

 
If you do not explicity provide a chunk size, ForwardDiff will try to guess one for you
 based on your input vector:

-
# The GradientConfig constructor will automatically select a
+
# The GradientConfig constructor will automatically select a
 # chunk size in one is not explicitly provided
 julia> cfg = ForwardDiff.GradientConfig(x);
 
-julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg);
+julia> @time ForwardDiff.gradient!(out, rosenbrock, x, cfg);
 0.266920 seconds (4 allocations: 160 bytes)
 

 

@@ -241,11 +232,11 @@ 
Configuring Chunk SizeIf your input dimension is a runtime variable, you can rely on ForwardDiff’s heuristic
 without sacrificing type stability by manually asserting the output type, or - even better -
 by using the in-place API functions:

-
# will be type-stable since you're asserting the output type
+
# will be type-stable since you're asserting the output type
 ForwardDiff.gradient(rosenbrock, x)::Vector{Float64}
 
 # will be type-stable since `out` is returned, and Julia knows the type of `out`
-ForwardDiff.gradient!(out, rosenbrock, x)
+ForwardDiff.gradient!(out, rosenbrock, x)
 

 

 
One final question remains: How should you select a chunk size? The answer is essentially
@@ -256,22 +247,51 @@ 
Configuring Chunk Size
 

+

+
Fixing issues with NaN/Inf return values

+
ForwardDiff’s default behavior is to return NaN for undefined derivatives (or otherwise
+mirror the behavior of the function in Base, if it would return an error). This is
+usually the correct thing to do, but in some cases can erroneously “poison” values which
+aren’t sensitive to the input and thus cause ForwardDiff to incorrectly return NaN or
+Inf derivatives. For example:

+
# the dual number's perturbation component is zero, so this
+# variable should not propagate derivative information
+julia> log(ForwardDiff.Dual(0.0, 0.0))
+Dual(-Inf,NaN) # oops, this NaN should be 0.0
+

+

+
Here, ForwardDiff computes the derivative of log(0.0) as NaN and then propagates
+this derivative by multiplying it by the perturbation component. Usually, ForwardDiff can
+rely on the identity x * 0.0 == 0.0 to prevent the derivatives from propagating when
+the perturbation component is 0.0. However, this identity doesn’t hold if isnan(y)
+or isinf(y), in which case a NaN derivative will be propagated instead.

+
It is possible to fix this behavior by checking that the perturbation component is zero
+before attempting to propagate derivative information, but this check can noticeably
+decrease performance (~5%-10% on our benchmarks).

+
In order to preserve performance in the majority of use cases, ForwardDiff disables this
+check by default. If your code is affected by this NaN behvaior, you can enable
+ForwardDiff’s NaN-safe mode by setting NANSAFE_MODE_ENABLED to true in
+ForwardDiff’s source (this constant is located in src/ForwardDiff.jl in the
+package’s directory).

+
In the future, we plan on allowing users and downstream library authors to dynamically
+enable NaN-safe mode via the AbstractConfig API (see the relevant issue).

+

 

 
Hessian of a vector-valued function

 
While ForwardDiff does not have a built-in function for taking Hessians of vector-valued
 functions, you can easily compose calls to ForwardDiff.jacobian to accomplish this.
 For example:

-
julia> ForwardDiff.jacobian(x -> ForwardDiff.jacobian(sin, x), [1,2,3])
-9×3 Array{Float64,2}:
- -0.841471   0.0        0.0
- -0.0       -0.0       -0.0
- -0.0       -0.0       -0.0
- 0.0        0.0        0.0
- -0.0       -0.909297  -0.0
- -0.0       -0.0       -0.0
- 0.0        0.0        0.0
- -0.0       -0.0       -0.0
- -0.0       -0.0       -0.14112
+
julia> ForwardDiff.jacobian(x -> ForwardDiff.jacobian(sin, x), [1,2,3])
+9×3 Array{Float64,2}:
+ -0.841471   0.0        0.0
+ -0.0       -0.0       -0.0
+ -0.0       -0.0       -0.0
+ 0.0        0.0        0.0
+ -0.0       -0.909297  -0.0
+ -0.0       -0.0       -0.0
+ 0.0        0.0        0.0
+ -0.0       -0.0       -0.0
+ -0.0       -0.0       -0.14112
 

 

 
Since this functionality is composed from ForwardDiff’s existing API rather than built into
@@ -279,29 +299,29 @@ 
Hessian of a vector-valued functionreshape (note that reshape does not copy data, so it’s not an
 expensive operation):

-
julia> function vector_hessian(f, x)
-       n = length(x)
-       out = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x)
-       return reshape(out, n, n, n)
-   end
-vector_hessian (generic function with 1 method)
-
-julia> vector_hessian(sin, [1, 2, 3])
-3×3×3 Array{Float64,3}:
-[:, :, 1] =
- -0.841471   0.0   0.0
- -0.0       -0.0  -0.0
- -0.0       -0.0  -0.0
-
-[:, :, 2] =
-  0.0   0.0        0.0
- -0.0  -0.909297  -0.0
- -0.0  -0.0       -0.0
-
-[:, :, 3] =
-  0.0   0.0   0.0
- -0.0  -0.0  -0.0
- -0.0  -0.0  -0.14112
+
julia> function vector_hessian(f, x)
+       n = length(x)
+       out = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x)
+       return reshape(out, n, n, n)
+   end
+vector_hessian (generic function with 1 method)
+
+julia> vector_hessian(sin, [1, 2, 3])
+3×3×3 Array{Float64,3}:
+[:, :, 1] =
+ -0.841471   0.0   0.0
+ -0.0       -0.0  -0.0
+ -0.0       -0.0  -0.0
+
+[:, :, 2] =
+  0.0   0.0        0.0
+ -0.0  -0.909297  -0.0
+ -0.0  -0.0       -0.0
+
+[:, :, 3] =
+  0.0   0.0   0.0
+ -0.0  -0.0  -0.0
+ -0.0  -0.0  -0.14112
 

 

 
Likewise, you could write a version of vector_hessian which supports functions of the
@@ -317,7 +337,7 @@ 
SIMD VectorizationDual numbers without
 SIMD instructions (i.e. not starting Julia with -O3):

-
julia> using ForwardDiff: Dual
+
julia> using ForwardDiff: Dual
 
 julia> a = Dual(1., 2., 3., 4.)
 Dual(1.0,2.0,3.0,4.0)
@@ -363,7 +383,7 @@ 
SIMD Vectorization-O3 instead, the call to @code_llvm will show that LLVM
 can SIMD-vectorize the addition:

-
julia> @code_llvm a + b
+
julia> @code_llvm a + b
 
 define void @"julia_+_70842"(%Dual* noalias sret, %Dual*, %Dual*) #0 {
 top:
@@ -385,6 +405,7 @@ 
SIMD Vectorization
     

         © Copyright 2015, Jarrett Revels, Theodore Papamarkou, Miles Lubin, and other contributors.
+
     

   

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/basic_api.html b/docs/basic_api.html
index fdf0edda..882019e8 100644
--- a/docs/basic_api.html
+++ b/docs/basic_api.html
@@ -45,17 +45,27 @@
 
     
     
 
     

@@ -136,7 +120,13 @@
       
       

         

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+

   
    
     
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@@ -151,7 +141,8 @@
   

   

 

-          

+          

+           

             
   

 
Basic ForwardDiff API

@@ -314,6 +305,7 @@ 
The AbstractConfig
 
 
+           

           

           

   
@@ -332,9 +324,10 @@ 
The AbstractConfig
     

         © Copyright 2015, Jarrett Revels, Theodore Papamarkou, Miles Lubin, and other contributors.
+
     

   

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/contributing.html b/docs/contributing.html
index 5814b4f0..a2102a06 100644
--- a/docs/contributing.html
+++ b/docs/contributing.html
@@ -44,17 +44,27 @@
 
     
     
 
     

@@ -135,7 +120,13 @@
       
       

         

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+          
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+ 
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-          

+          

+           

             
   

 
How to Contribute

@@ -167,25 +159,25 @@ 
How to Contribute
 
Manually Optimizing Unary Functions

 
To see a list of functions to pick from, look at ForwardDiff.AUTO_DEFINED_UNARY_FUNCS:

-
julia> import ForwardDiff
-
-julia> ForwardDiff.AUTO_DEFINED_UNARY_FUNCS
-57-element Array{Symbol,1}:
- :sqrt
- :cbrt
- :abs2
- :inv
- :log
- :log10
- :log2
- :log1p
- :exp
- :exp2
- :expm1
- :sin
- :cos
- :tan
- ⋮
+
julia> import ForwardDiff
+
+julia> ForwardDiff.AUTO_DEFINED_UNARY_FUNCS
+57-element Array{Symbol,1}:
+ :sqrt
+ :cbrt
+ :abs2
+ :inv
+ :log
+ :log10
+ :log2
+ :log1p
+ :exp
+ :exp2
+ :expm1
+ :sin
+ :cos
+ :tan
+ ⋮
 

 

 
Some of these functions may have already been manually optimized. To see what functions have
@@ -224,6 +216,7 @@ 
Manually Adding Functions to ForwardDiff
     

         © Copyright 2015, Jarrett Revels, Theodore Papamarkou, Miles Lubin, and other contributors.
+
     

   

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/genindex.html b/docs/genindex.html
index c6b848d0..ee28917c 100644
--- a/docs/genindex.html
+++ b/docs/genindex.html
@@ -44,17 +44,27 @@
 
     
     
 
     

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@@ -148,7 +131,8 @@
   

   

 

-          

+          

+           

             
 
 
Index

@@ -187,6 +171,7 @@ 
F

 
 
 
+           

           

           

   
@@ -196,9 +181,10 @@ 
F

   

     

         © Copyright 2015, Jarrett Revels, Theodore Papamarkou, Miles Lubin, and other contributors.
+
     

   

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 

 
diff --git a/docs/how_it_works.html b/docs/how_it_works.html
index 5748cff1..b662c2f1 100644
--- a/docs/how_it_works.html
+++ b/docs/how_it_works.html
@@ -45,17 +45,27 @@
 
     
     
 
     

@@ -136,7 +117,13 @@
       
       

         

-          

+          
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@@ -151,7 +138,8 @@
   

   

 

-          

+          

+           

             
   

 
How ForwardDiff Works

@@ -160,13 +148,13 @@ 
How ForwardDiff Works
 
Dual Number Implementation

 
Partial derivatives are stored in the Partials{N,T} type:

-
immutable Partials{N,T}
+
immutable Partials{N,T}
     values::NTuple{N,T}
 end
 

 

 
Overtop of this container type, ForwardDiff implements the Dual{N,T} type:

-
immutable Dual{N,T<:Real} <: Real
+
immutable Dual{N,T<:Real} <: Real
     value::T
     partials::Partials{N,T}
 end
@@ -183,7 +171,7 @@ 
Dual Number ImplementationBase.sin
 can be overloaded on Dual like so:

-
Base.sin(d::Dual) = Dual(sin(value(d)), cos(value(d)) * partials(d))
+
Base.sin(d::Dual) = Dual(sin(value(d)), cos(value(d)) * partials(d))
 

 

 
If we assume that a general function f is composed of entirely of these elementary
@@ -229,31 +217,32 @@ 
ForwardDiff’s API\(f\) to evaluate the gradient:

 

-\[\begin{split}\vec{x} = \begin{bmatrix}
+\[ \begin{align}\begin{aligned}\begin{split}\vec{x} = \begin{bmatrix}
                x_1 \\
                x_2 \\
                x_3 \\
                x_4
-           \end{bmatrix}\end{split}\]\[\begin{split}\vec{x}_{\epsilon} = \begin{bmatrix}
+           \end{bmatrix}\end{split}\\\begin{split}\vec{x}_{\epsilon} = \begin{bmatrix}
                         x_1 + \epsilon_1 \\
                         x_2 + \epsilon_2 \\
                         x_3 \\
                         x_4
                      \end{bmatrix}
 \to
-f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_1} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_2} \epsilon_2\end{split}\]\[\begin{split}\vec{x}_{\epsilon} = \begin{bmatrix}
+f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_1} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_2} \epsilon_2\end{split}\\\begin{split}\vec{x}_{\epsilon} = \begin{bmatrix}
                         x_1 \\
                         x_2 \\
                         x_3 + \epsilon_1 \\
                         x_4 + \epsilon_2
                      \end{bmatrix}
 \to
-f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2\end{split}\]

+f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2\end{split}\end{aligned}\end{align} \]

 
This seeding process is similar for Jacobians, so we won’t rehash it here.

 

 

 
 
+           

           

           

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/index.html b/docs/index.html
index 4377144a..15dd0f4d 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -44,17 +44,27 @@
 
     
     
 
     

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-          

+          

+           

             
   
Go to ForwardDiff on GitHub

 

@@ -174,6 +158,7 @@ 
ForwardDiff.jlAdvanced Usage Guide
@@ -207,19 +192,20 @@ 
ForwardDiff.jl
 
Publications

 
If you find ForwardDiff useful in your work, we kindly request that you cite the following paper:

-
@article{RevelsLubinPapamarkou2016,
-   title = {Forward-Mode Automatic Differentiation in Julia},
-  author = {{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.},
- journal = {arXiv:1607.07892 [cs.MS]},
-    year = {2016},
-    url = {https://arxiv.org/abs/1607.07892}
-}
+
@article{RevelsLubinPapamarkou2016,
+   title = {Forward-Mode Automatic Differentiation in Julia},
+  author = {{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.},
+ journal = {arXiv:1607.07892 [cs.MS]},
+    year = {2016},
+    url = {https://arxiv.org/abs/1607.07892}
+}
 

 

 

 

 
 
+           

           

           

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+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/install.html b/docs/install.html
index a14237d1..ef01aaa8 100644
--- a/docs/install.html
+++ b/docs/install.html
@@ -45,17 +45,27 @@
 
     
     
 
     

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-          

+          

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Installation and Version Requirements

 
To install ForwardDiff, simply use Julia’s package manager:

-
julia> Pkg.add("ForwardDiff")
+
julia> Pkg.add("ForwardDiff")
 

 

 
The current version of ForwardDiff supports Julia v0.4 and v0.5.

 

 
 
+           

           

           

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/limitations.html b/docs/limitations.html
index 2f7023d3..f994cac3 100644
--- a/docs/limitations.html
+++ b/docs/limitations.html
@@ -45,17 +45,27 @@
 
     
     
 
     

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Limitations of ForwardDiff

@@ -169,6 +153,7 @@ 
Limitations of ForwardDiff
     

         © Copyright 2015, Jarrett Revels, Theodore Papamarkou, Miles Lubin, and other contributors.
+
     

   

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/docs/objects.inv b/docs/objects.inv
index 7f382b95..7396bc2e 100644
Binary files a/docs/objects.inv and b/docs/objects.inv differ
diff --git a/docs/search.html b/docs/search.html
index 0b8c552c..da0d1bf4 100644
--- a/docs/search.html
+++ b/docs/search.html
@@ -43,17 +43,27 @@
 
     
     
 
     

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diff --git a/docs/searchindex.js b/docs/searchindex.js
index 6e63b6b2..61ed8ea5 100644
--- a/docs/searchindex.js
+++ b/docs/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
+Search.setIndex({envversion:49,filenames:["advanced_usage","index"],objects:{},objnames:{},objtypes:{},terms:{"byte":0,"case":0,"default":0,"final":0,"import":0,"new":1,"true":0,"try":0,"void":0,"while":[0,1],_70842:0,_70852:0,abl:0,about:1,abstractconfig:[0,1],accomplish:0,accuraci:1,actual:0,add:0,addit:0,advantag:1,affect:0,algorithm:1,align:0,all:0,alloc:0,allow:0,almost:0,also:0,amen:0,ani:1,answer:0,api:[0,1],appropri:0,aren:0,arg:0,arithmet:0,arrai:0,articl:1,arxiv:1,assert:0,attempt:0,author:[0,1],automat:[0,1],bandwidth:0,base:0,basic:[0,1],befor:0,behavior:0,behvaior:0,benchmark:0,best:0,better:0,binari:0,bitcast:0,bitcod:0,block:0,both:1,bring:0,buffer:0,build:0,built:0,calcul:0,call:0,callabl:1,can:[0,1],cast:0,caus:0,certain:0,cfg10:0,cfg1:0,cfg4:0,cfg:0,check:0,cite:1,code:0,code_llvm:0,common:1,compil:0,complet:0,compon:0,compos:0,comput:0,conjunct:0,constant:0,construct:0,constructor:0,consult:0,contribut:1,copi:0,correct:0,cost:0,could:0,cours:0,creat:1,data:0,decreas:0,defin:0,depend:[0,1],deriv:[0,1],describ:0,develop:1,diffbas:0,differenc:1,different:0,differenti:1,diffresult:0,dimens:0,directori:0,disabl:0,divid:0,document:[0,1],doe:0,doesn:0,doubl:0,downstream:0,dual:[0,1],dure:0,dynam:0,each:0,easili:0,element:0,eltyp:0,emit:0,enabl:[0,1],end:0,entir:0,erron:0,error:0,essenti:0,evalu:[0,1],even:0,evenli:0,exampl:0,execut:0,exist:0,expens:0,explic:0,explicitli:0,extra:0,fadd:0,featur:0,fell:0,find:1,fine:0,finit:1,first:0,flag:0,float64:0,follow:1,form:0,forward:1,forwarddiff:0,free:0,from:[0,1],futur:0,gener:[0,1],getelementptr:0,github:1,gradient:[0,1],gradientconfig:0,guess:0,have:0,heavili:0,here:0,heurist:0,higher:[0,1],hold:0,horribl:0,how:[0,1],howev:0,http:1,i32:0,i64:0,ident:0,imag:0,implement:1,inbound:0,incorrectli:0,increas:0,inform:0,inher:0,input:0,insert:0,installat:1,instead:0,instruct:0,isinf:0,isnan:0,jacobian:[0,1],journal:1,julia:[0,1],julia_:0,kindli:1,know:0,larger:0,learn:[0,1],length:0,let:0,librari:0,likewis:0,limit:1,llvm:0,load:0,local:0,locat:0,log:0,lubin:1,machin:0,major:0,make:0,mani:0,manual:[0,1],matrix:0,memori:0,method:[0,1],might:0,mirror:0,mode:[0,1],modul:0,more:0,multipli:0,multithread:1,mutat:0,nansafe_mode_enabled:0,nativ:1,need:0,noalia:0,non:1,note:0,notic:0,number:[0,1],object:1,older:1,one:0,onli:0,oop:0,oper:0,optim:0,optimiz:1,org:1,other:[0,1],otherwis:0,our:0,out:0,outperform:1,output:0,over:1,overcom:0,own:0,packag:0,page:1,papamark:1,paper:1,partial:0,perform:[0,1],perhap:0,perturb:0,pick:0,place:0,plan:0,pleas:0,poison:0,possibl:0,pre:0,preserv:0,prevent:0,primal:0,process:0,propag:0,proport:0,provid:0,question:0,rand:0,rather:0,realiti:0,realli:1,reason:0,rebuild:0,reduc:0,redund:0,relev:0,reli:0,remain:0,remaind:0,request:1,requir:[0,1],reshap:0,resourc:1,ret:0,retriev:[0,1],revel:1,revelslubinpapamarkou2016:1,rosenbrock:0,run:0,runtim:0,sacrif:0,safe:0,sai:0,scope:0,second:0,see:0,seen:0,select:0,sensit:0,set:[0,1],sever:0,shape:0,should:0,show:0,similar:0,sin:0,sinc:0,slpvectorizerpass:0,smaller:0,some:0,sourc:0,specif:0,speed:1,speedup:0,squar:0,src:0,sret:0,stabil:0,stabl:0,start:0,state:0,store:0,suit:0,support:0,swoop:0,system:0,take:[0,1],target:0,task:0,techniqu:[0,1],tensor:0,than:0,thi:[0,1],thing:0,thu:0,time:0,titl:1,top:0,tune:0,two:0,type:[0,1],unari:1,undefin:0,unexport:1,unstabl:0,upgrade:1,url:1,user:[0,1],usual:0,usualli:0,util:0,vari:1,variabl:0,vector_hessian:0,version:[0,1],via:0,wai:0,want:0,well:0,what:0,when:0,where:0,wherea:0,whether:0,which:0,wikipedia:1,without:0,word:0,work:[0,1],would:0,write:0,year:1,yield:0,you:[0,1],your:[0,1],zero:0},titles:["Advanced Usage Guide","ForwardDiff.jl"],titleterms:{"function":0,"public":1,"return":0,access:0,advanc:0,chunk:0,configur:0,fix:0,forwarddiff:1,guid:0,hessian:0,inf:0,issu:0,lower:0,nan:0,order:0,result:0,simd:0,size:0,usage:0,valu:0,vector:0}})
\ No newline at end of file
diff --git a/docs/upgrade.html b/docs/upgrade.html
index 72c7e866..eb86c1f4 100644
--- a/docs/upgrade.html
+++ b/docs/upgrade.html
@@ -45,17 +45,27 @@
 
     
     
 
     

@@ -136,7 +121,13 @@
       
       

         

-          

+          
+
+ 
+
+
+
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  • Docs »
    • 
       
@@ -151,7 +142,8 @@
   

   

 

-          

+          

+           

             
   

 
Upgrading from Older Versions of ForwardDiff

@@ -162,7 +154,7 @@ 
Upgrading from Older Versions of ForwardDiff

 
In order to avoid namespace conflicts with other packages, ForwardDiff’s API functions are no longer exported by default. Thus, you must now fully qualify the
 functions to reference them:

-
# old v0.1 style
+
# old v0.1 style
 using ForwardDiff
 hessian(f, x)
 
@@ -174,7 +166,7 @@ 
Unexported API Functions
 
Setting Chunk Size

-
# old v0.1 style
+
# old v0.1 style
 ForwardDiff.gradient(f, x; chunk_size = 10)
 
 # old v0.2 style
@@ -187,7 +179,7 @@ 
Setting Chunk Size
 
Enabling Multithreading

-
# old v0.1/v0.2 style
+
# old v0.1/v0.2 style
 ForwardDiff.gradient(f, x; multithread = true)
 
 # current v0.3 style
@@ -198,7 +190,7 @@ 
Enabling Multithreading
 
Retrieving Lower-Order Results

 
For more detail, see our documentation on retrieving lower-order results.

-
# old v0.1 style
+
# old v0.1 style
 answer, results = ForwardDiff.hessian(f, x, AllResults)
 v = ForwardDiff.value(results)
 g = ForwardDiff.gradient(results)
@@ -206,7 +198,7 @@ 
Retrieving Lower-Order Results# old v0.2 style
 out = HessianResult(x)
-ForwardDiff.hessian!(out, f, x)
+ForwardDiff.hessian!(out, f, x)
 v = ForwardDiff.value(out)
 g = ForwardDiff.gradient(out)
 h = ForwardDiff.hessian(out)
@@ -214,7 +206,7 @@ 
Retrieving Lower-Order Results# current v0.3 style
 using DiffBase
 out = DiffBase.HessianResult(x)
-ForwardDiff.hessian!(out, f, x)
+ForwardDiff.hessian!(out, f, x)
 v = DiffBase.value(out)
 g = DiffBase.gradient(out)
 h = DiffBase.hessian(out)
@@ -227,7 +219,7 @@ 
Higher-Order Differentiationtensor function. Instead, users can take higher-order/higher-dimensional
 derivatives by composing existing API functions. For example, here’s how to reimplement
 tensor:

-
# old v0.1 style
+
# old v0.1 style
 ForwardDiff.tensor(f, x)
 
 # current v0.3 style (since v0.2)
@@ -247,33 +239,34 @@ 
Creating Differentiation Functionsour API documentation.

-
# old v0.1 style
+
# old v0.1 style
 df = ForwardDiff.derivative(f)
 
 # current v0.3 style (since v0.2)
 df = x -> ForwardDiff.derivative(f, x)
 

 

-
# old v0.1 style
+
# old v0.1 style
 # in-place gradient function of f
-gf! = ForwardDiff.gradient(f, mutates = true)
+gf! = ForwardDiff.gradient(f, mutates = true)
 
 # current v0.3 style (since v0.2)
-gf! = (out, x) -> ForwardDiff.gradient!(out, f, x)
+gf! = (out, x) -> ForwardDiff.gradient!(out, f, x)
 

 

-
# old v0.1 style
+
# old v0.1 style
 # in-place Jacobian function of f!(y, x):
-jf! = ForwardDiff.jacobian(f!, mutates = true, output_length = length(y))
+jf! = ForwardDiff.jacobian(f!, mutates = true, output_length = length(y))
 
 # current v0.3 style (since v0.2)
-jf! = (out, y, x) -> ForwardDiff.jacobian!(out, f!, y, x)
+jf! = (out, y, x) -> ForwardDiff.jacobian!(out, f!, y, x)
 

 

 

 

 
 
+           

           

           

-  Built with Sphinx using a theme provided by Read the Docs.
+  Built with Sphinx using a theme provided by Read the Docs. 
 
 
 
diff --git a/src/ForwardDiff.jl b/src/ForwardDiff.jl
index 8d8bacfb..c9294129 100644
--- a/src/ForwardDiff.jl
+++ b/src/ForwardDiff.jl
@@ -13,6 +13,11 @@ import NaNMath
 # types/functions/constants #
 #############################
 
+# NaN-safe mode switch #
+#----------------------#
+
+const NANSAFE_MODE_ENABLED = false
+
 # multithreading #
 #----------------#
 
diff --git a/src/partials.jl b/src/partials.jl
index 9c74bc7c..e070275f 100644
--- a/src/partials.jl
+++ b/src/partials.jl
@@ -75,18 +75,43 @@ Base.convert{N,T}(::Type{Partials{N,T}}, partials::Partials{N,T}) = partials
 @inline @compat(Base.:+){N}(a::Partials{N}, b::Partials{N}) = Partials(add_tuples(a.values, b.values))
 @inline @compat(Base.:-){N}(a::Partials{N}, b::Partials{N}) = Partials(sub_tuples(a.values, b.values))
 @inline @compat(Base.:-)(partials::Partials) = Partials(minus_tuple(partials.values))
-@inline @compat(Base.:*)(partials::Partials, x::Real) = Partials(scale_tuple(partials.values, x))
 @inline @compat(Base.:*)(x::Real, partials::Partials) = partials*x
-@inline @compat(Base.:/)(partials::Partials, x::Real) = Partials(div_tuple_by_scalar(partials.values, x))
 
-@inline function _mul_partials{N}(a::Partials{N}, b::Partials{N}, afactor, bfactor)
-    return Partials(mul_tuples(a.values, b.values, afactor, bfactor))
+@inline function _div_partials(a::Partials, b::Partials, aval, bval)
+    return _mul_partials(a, b, inv(bval), -(aval / (bval*bval)))
 end
 
-@inline function _div_partials(a::Partials, b::Partials, aval, bval)
-    afactor = inv(bval)
-    bfactor = -aval/(bval*bval)
-    return _mul_partials(a, b, afactor, bfactor)
+# NaN/Inf-safe methods #
+#----------------------#
+
+if NANSAFE_MODE_ENABLED
+    @inline function @compat(Base.:*)(partials::Partials, x::Real)
+        x = ifelse(!isfinite(x) && iszero(partials), one(x), x)
+        return Partials(scale_tuple(partials.values, x))
+    end
+
+    @inline function @compat(Base.:/)(partials::Partials, x::Real)
+        x = ifelse(x == zero(x) && iszero(partials), one(x), x)
+        return Partials(div_tuple_by_scalar(partials.values, x))
+    end
+
+    @inline function _mul_partials{N}(a::Partials{N}, b::Partials{N}, x_a, x_b)
+        x_a = ifelse(!isfinite(x_a) && iszero(a), one(x_a), x_a)
+        x_b = ifelse(!isfinite(x_b) && iszero(b), one(x_b), x_b)
+        return Partials(mul_tuples(a.values, b.values, x_a, x_b))
+    end
+else
+    @inline function @compat(Base.:*)(partials::Partials, x::Real)
+        return Partials(scale_tuple(partials.values, x))
+    end
+
+    @inline function @compat(Base.:/)(partials::Partials, x::Real)
+        return Partials(div_tuple_by_scalar(partials.values, x))
+    end
+
+    @inline function _mul_partials{N}(a::Partials{N}, b::Partials{N}, x_a, x_b)
+        return Partials(mul_tuples(a.values, b.values, x_a, x_b))
+    end
 end
 
 # edge cases where N == 0 #
diff --git a/test/JacobianTest.jl b/test/JacobianTest.jl
index ce6e8402..c448e5d0 100644
--- a/test/JacobianTest.jl
+++ b/test/JacobianTest.jl
@@ -91,7 +91,7 @@ end
 for f in DiffBase.ARRAY_TO_ARRAY_FUNCS
     v = f(X)
     j = ForwardDiff.jacobian(f, X)
-    @test_approx_eq_eps j Calculus.jacobian(f, X, :forward) FINITEDIFF_ERROR
+    @test_approx_eq_eps j Calculus.jacobian(x -> vec(f(x)), X, :forward) FINITEDIFF_ERROR
     for c in CHUNK_SIZES
         cfg = JacobianConfig{c}(X)
 
@@ -99,11 +99,11 @@ for f in DiffBase.ARRAY_TO_ARRAY_FUNCS
         out = ForwardDiff.jacobian(f, X, cfg)
         @test_approx_eq out j
 
-        out = similar(X, length(X), length(X))
+        out = similar(X, length(v), length(X))
         ForwardDiff.jacobian!(out, f, X, cfg)
         @test_approx_eq out j
 
-        out = DiffBase.JacobianResult(X)
+        out = DiffBase.DiffResult(similar(v, length(v)), similar(v, length(v), length(X)))
         ForwardDiff.jacobian!(out, f, X, cfg)
         @test_approx_eq DiffBase.value(out) v
         @test_approx_eq DiffBase.jacobian(out) j
@@ -114,7 +114,7 @@ for f! in DiffBase.INPLACE_ARRAY_TO_ARRAY_FUNCS
     v = zeros(Y)
     f!(v, X)
     j = ForwardDiff.jacobian(f!, zeros(Y), X)
-    @test_approx_eq_eps j Calculus.jacobian(x -> (y = zeros(Y); f!(y, x); y), X, :forward) FINITEDIFF_ERROR
+    @test_approx_eq_eps j Calculus.jacobian(x -> (y = zeros(Y); f!(y, x); vec(y)), X, :forward) FINITEDIFF_ERROR
     for c in CHUNK_SIZES
         cfg = JacobianConfig{c}(X)
         ycfg = JacobianConfig{c}(zeros(Y), X)
diff --git a/test/PartialsTest.jl b/test/PartialsTest.jl
index df8351d1..67bf7115 100644
--- a/test/PartialsTest.jl
+++ b/test/PartialsTest.jl
@@ -9,10 +9,10 @@ samerng() = MersenneTwister(1)
 for N in (0, 3), T in (Int, Float32, Float64)
     println("  ...testing Partials{$N,$T}")
 
-    VALUES = ntuple(n -> rand(T), Val{N})
+    VALUES = (rand(T,N)...)
     PARTIALS = Partials{N,T}(VALUES)
 
-    VALUES2 = ntuple(n -> rand(T), Val{N})
+    VALUES2 = (rand(T,N)...)
     PARTIALS2 = Partials{N,T}(VALUES2)
 
     ##############################
@@ -70,7 +70,7 @@ for N in (0, 3), T in (Int, Float32, Float64)
     @test hash(PARTIALS, hash(1)) == hash(copy(PARTIALS), hash(1))
     @test hash(PARTIALS, hash(1)) == hash(copy(PARTIALS), hash(1))
 
-    const TMPIO = IOBuffer()
+    TMPIO = IOBuffer()
     write(TMPIO, PARTIALS)
     seekstart(TMPIO)
     @test read(TMPIO, typeof(PARTIALS)) == PARTIALS
@@ -84,8 +84,8 @@ for N in (0, 3), T in (Int, Float32, Float64)
     # Conversion/Promotion #
     ########################
 
-    const WIDE_T = widen(T)
-    const WIDE_PARTIALS = convert(Partials{N,WIDE_T}, PARTIALS)
+    WIDE_T = widen(T)
+    WIDE_PARTIALS = convert(Partials{N,WIDE_T}, PARTIALS)
 
     @test typeof(WIDE_PARTIALS) == Partials{N,WIDE_T}
     @test WIDE_PARTIALS == PARTIALS
@@ -101,8 +101,8 @@ for N in (0, 3), T in (Int, Float32, Float64)
     @test (PARTIALS - PARTIALS).values == map(v -> v - v, VALUES)
     @test getfield(-(PARTIALS), :values) == map(-, VALUES)
 
-    const X = rand()
-    const Y = rand()
+    X = rand()
+    Y = rand()
 
     @test X * PARTIALS == PARTIALS * X
     @test (X * PARTIALS).values == map(v -> X * v, VALUES)
@@ -111,6 +111,21 @@ for N in (0, 3), T in (Int, Float32, Float64)
     if N > 0
         @test ForwardDiff._mul_partials(PARTIALS, PARTIALS2, X, Y).values == map((a, b) -> (X * a) + (Y * b), VALUES, VALUES2)
         @test ForwardDiff._div_partials(PARTIALS, PARTIALS2, X, Y) == ForwardDiff._mul_partials(PARTIALS, PARTIALS2, inv(Y), -X/(Y^2))
+
+        if ForwardDiff.NANSAFE_MODE_ENABLED
+            ZEROS = Partials((zeros(T, N)...))
+
+            @test (NaN * ZEROS).values == ZEROS.values
+            @test (Inf * ZEROS).values == ZEROS.values
+            @test (ZEROS / 0).values == ZEROS.values
+
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, X, NaN).values == ZEROS.values
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, NaN, X).values == ZEROS.values
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, X, Inf).values == ZEROS.values
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, Inf, X).values == ZEROS.values
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, Inf, NaN).values == ZEROS.values
+            @test ForwardDiff._mul_partials(ZEROS, ZEROS, NaN, Inf).values == ZEROS.values
+        end
     end
 end