- Fixes #20298 for vertical button group spacing
- Fixes #20784 for horizontal (default) button group spacing
- Alternate fix to #20823 which only applied a fix for vertical button groups

- Really we didn't need to do any of that strip units stuff to generate six new variables, two for each button size
- Using sibling selectors, we can target those split button dropdown toggles using the .dropdown-toggle-split class, and adjust padding and margin as needed
- Now, we nuke the margin-left from the ::after generated caret and tighten up the padding so that those split toggles don't look huge next to their main button

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- New vars
- New function for stripping units so we can combine rems and ems in math functions
- Add new classes for sizing and spacing around the split dropdown toggle so that the caret isn't misaligned

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Both widgets need to use the same border width because of input groups.
Thus:
$btn-border-width   => $input-btn-border-width
$input-border-width => $input-btn-border-width

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Fixes half of #18425
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- no real need for everything to be 100% shared
- padding looked and felt too large for inputs but not for buttons
- tying forms and buttons seems fine, but throwing in pagination feels wrong

commit 81324491f4913d6797c3c9e4df83a1aefd7d9116
Author: Daniel <dano.husar@gmail.com>
Date:   Sat May 10 17:37:29 2014 +0100

    use opacity mixin

commit 694b0a3fcd196e8cba9e4c23850f903c0804cb44
Author: Daniel Husar <dano.husar@gmail.com>
Date:   Fri May 9 13:47:35 2014 +0100

    Update button-groups.less

It seems that dropdown-menu in justified button-group appears at the far
left of the group. Check the problem in [Bootstrap
site](http://getbootstrap.com/components/#btn-groups-justified).

Instead of not rendering the element at all with display:none, use opacity:0 and z-index:-1 so the radio element has a defined position on the document and user agents can show the required message in the right place.

* Floats any `.input-group` within a toolbar
* Simplifies the CSS to remove sibling selectors and instead use a
negative amrgin on the parent with only `margin-left`

See it in action: http://jsbin.com/aGEcUqAT/1/.

Original discussion:
https://github.com/less/less.js/issues/1437#issuecomment-21383639.

Since we’re switching to `grunt-contrib-less`, we can take advantage of
newer LESS features than what RECESS supported. Included in that is the
ability to `:extend`, and not only that, but `:extend(.mixin-name
all)`. By doing so, we remove duplicate CSS for all our elements that
were being clearfix-ed.

Fixes #8947, #8968, #8991, #9257, #9268, #9291, #9430, #9604, #9686,
#9929, #10731, #10793, #11305, #11498, #11533, #11570, #11604, #11652.

(dem issues, tho)

Example of issue here.
https://dl.dropboxusercontent.com/u/14037764/Development/stackoverflow/bootstrap/vertical-btn.PNG