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.form-horizontal .form-actions{padding-left:180px;}
table{max-width:100%;background-color:transparent;border-collapse:collapse;border-spacing:0;}
.table{width:100%;margin-bottom:20px;}.table th,.table td{padding:8px;line-height:20px;text-align:left;vertical-align:top;border-top:1px solid #dddddd;}
.table th{font-weight:bold;}
.table thead th{vertical-align:bottom;}
.table caption+thead tr:first-child th,.table caption+thead tr:first-child td,.table colgroup+thead tr:first-child th,.table colgroup+thead tr:first-child td,.table thead:first-child tr:first-child th,.table thead:first-child tr:first-child td{border-top:0;}
.table tbody+tbody{border-top:2px solid #dddddd;}
.table .table{background-color:#ffffff;}
.table-condensed th,.table-condensed td{padding:4px 5px;}
.table-bordered{border:1px solid #dddddd;border-collapse:separate;*border-collapse:collapse;border-left:0;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}.table-bordered th,.table-bordered td{border-left:1px solid #dddddd;}
.table-bordered caption+thead tr:first-child th,.table-bordered caption+tbody tr:first-child th,.table-bordered caption+tbody tr:first-child td,.table-bordered colgroup+thead tr:first-child th,.table-bordered colgroup+tbody tr:first-child th,.table-bordered colgroup+tbody tr:first-child td,.table-bordered thead:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child td{border-top:0;}
.table-bordered thead:first-child tr:first-child>th:first-child,.table-bordered tbody:first-child tr:first-child>td:first-child,.table-bordered tbody:first-child tr:first-child>th:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;}
.table-bordered thead:first-child tr:first-child>th:last-child,.table-bordered tbody:first-child tr:first-child>td:last-child,.table-bordered tbody:first-child tr:first-child>th:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px;}
.table-bordered thead:last-child tr:last-child>th:first-child,.table-bordered tbody:last-child tr:last-child>td:first-child,.table-bordered tbody:last-child tr:last-child>th:first-child,.table-bordered tfoot:last-child tr:last-child>td:first-child,.table-bordered tfoot:last-child tr:last-child>th:first-child{-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px;}
.table-bordered thead:last-child tr:last-child>th:last-child,.table-bordered tbody:last-child tr:last-child>td:last-child,.table-bordered tbody:last-child tr:last-child>th:last-child,.table-bordered tfoot:last-child tr:last-child>td:last-child,.table-bordered tfoot:last-child tr:last-child>th:last-child{-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px;}
.table-bordered tfoot+tbody:last-child tr:last-child td:first-child{-webkit-border-bottom-left-radius:0;-moz-border-radius-bottomleft:0;border-bottom-left-radius:0;}
.table-bordered tfoot+tbody:last-child tr:last-child td:last-child{-webkit-border-bottom-right-radius:0;-moz-border-radius-bottomright:0;border-bottom-right-radius:0;}
.table-bordered caption+thead tr:first-child th:first-child,.table-bordered caption+tbody tr:first-child td:first-child,.table-bordered colgroup+thead tr:first-child th:first-child,.table-bordered colgroup+tbody tr:first-child td:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;}
.table-bordered caption+thead tr:first-child th:last-child,.table-bordered caption+tbody tr:first-child td:last-child,.table-bordered colgroup+thead tr:first-child th:last-child,.table-bordered colgroup+tbody tr:first-child td:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px;}
.table-striped tbody>tr:nth-child(odd)>td,.table-striped tbody>tr:nth-child(odd)>th{background-color:#f9f9f9;}
.table-hover tbody tr:hover>td,.table-hover tbody tr:hover>th{background-color:#f5f5f5;}
table td[class*="span"],table th[class*="span"],.row-fluid table td[class*="span"],.row-fluid table th[class*="span"]{display:table-cell;float:none;margin-left:0;}
.table td.span1,.table th.span1{float:none;width:44px;margin-left:0;}
.table td.span2,.table th.span2{float:none;width:124px;margin-left:0;}
.table td.span3,.table th.span3{float:none;width:204px;margin-left:0;}
.table td.span4,.table th.span4{float:none;width:284px;margin-left:0;}
.table td.span5,.table th.span5{float:none;width:364px;margin-left:0;}
.table td.span6,.table th.span6{float:none;width:444px;margin-left:0;}
.table td.span7,.table th.span7{float:none;width:524px;margin-left:0;}
.table td.span8,.table th.span8{float:none;width:604px;margin-left:0;}
.table td.span9,.table th.span9{float:none;width:684px;margin-left:0;}
.table td.span10,.table th.span10{float:none;width:764px;margin-left:0;}
.table td.span11,.table th.span11{float:none;width:844px;margin-left:0;}
.table td.span12,.table th.span12{float:none;width:924px;margin-left:0;}
.table tbody tr.success>td{background-color:#dff0d8;}
.table tbody tr.error>td{background-color:#f2dede;}
.table tbody tr.warning>td{background-color:#fcf8e3;}
.table tbody tr.info>td{background-color:#d9edf7;}
.table-hover tbody tr.success:hover>td{background-color:#d0e9c6;}
.table-hover tbody tr.error:hover>td{background-color:#ebcccc;}
.table-hover tbody tr.warning:hover>td{background-color:#faf2cc;}
.table-hover tbody tr.info:hover>td{background-color:#c4e3f3;}
[class^="icon-"],[class*=" icon-"]{display:inline-block;width:14px;height:14px;*margin-right:.3em;line-height:14px;vertical-align:text-top;background-image:url("../img/glyphicons-halflings.png");background-position:14px 14px;background-repeat:no-repeat;margin-top:1px;}
.icon-white,.nav-pills>.active>a>[class^="icon-"],.nav-pills>.active>a>[class*=" icon-"],.nav-list>.active>a>[class^="icon-"],.nav-list>.active>a>[class*=" icon-"],.navbar-inverse .nav>.active>a>[class^="icon-"],.navbar-inverse .nav>.active>a>[class*=" icon-"],.dropdown-menu>li>a:hover>[class^="icon-"],.dropdown-menu>li>a:focus>[class^="icon-"],.dropdown-menu>li>a:hover>[class*=" icon-"],.dropdown-menu>li>a:focus>[class*=" icon-"],.dropdown-menu>.active>a>[class^="icon-"],.dropdown-menu>.active>a>[class*=" icon-"],.dropdown-submenu:hover>a>[class^="icon-"],.dropdown-submenu:focus>a>[class^="icon-"],.dropdown-submenu:hover>a>[class*=" icon-"],.dropdown-submenu:focus>a>[class*=" icon-"]{background-image:url("../img/glyphicons-halflings-white.png");}
.icon-glass{background-position:0 0;}
.icon-music{background-position:-24px 0;}
.icon-search{background-position:-48px 0;}
.icon-envelope{background-position:-72px 0;}
.icon-heart{background-position:-96px 0;}
.icon-star{background-position:-120px 0;}
.icon-star-empty{background-position:-144px 0;}
.icon-user{background-position:-168px 0;}
.icon-film{background-position:-192px 0;}
.icon-th-large{background-position:-216px 0;}
.icon-th{background-position:-240px 0;}
.icon-th-list{background-position:-264px 0;}
.icon-ok{background-position:-288px 0;}
.icon-remove{background-position:-312px 0;}
.icon-zoom-in{background-position:-336px 0;}
.icon-zoom-out{background-position:-360px 0;}
.icon-off{background-position:-384px 0;}
.icon-signal{background-position:-408px 0;}
.icon-cog{background-position:-432px 0;}
.icon-trash{background-position:-456px 0;}
.icon-home{background-position:0 -24px;}
.icon-file{background-position:-24px -24px;}
.icon-time{background-position:-48px -24px;}
.icon-road{background-position:-72px -24px;}
.icon-download-alt{background-position:-96px -24px;}
.icon-download{background-position:-120px -24px;}
.icon-upload{background-position:-144px -24px;}
.icon-inbox{background-position:-168px -24px;}
.icon-play-circle{background-position:-192px -24px;}
.icon-repeat{background-position:-216px -24px;}
.icon-refresh{background-position:-240px -24px;}
.icon-list-alt{background-position:-264px -24px;}
.icon-lock{background-position:-287px -24px;}
.icon-flag{background-position:-312px -24px;}
.icon-headphones{background-position:-336px -24px;}
.icon-volume-off{background-position:-360px -24px;}
.icon-volume-down{background-position:-384px -24px;}
.icon-volume-up{background-position:-408px -24px;}
.icon-qrcode{background-position:-432px -24px;}
.icon-barcode{background-position:-456px -24px;}
.icon-tag{background-position:0 -48px;}
.icon-tags{background-position:-25px -48px;}
.icon-book{background-position:-48px -48px;}
.icon-bookmark{background-position:-72px -48px;}
.icon-print{background-position:-96px -48px;}
.icon-camera{background-position:-120px -48px;}
.icon-font{background-position:-144px -48px;}
.icon-bold{background-position:-167px -48px;}
.icon-italic{background-position:-192px -48px;}
.icon-text-height{background-position:-216px -48px;}
.icon-text-width{background-position:-240px -48px;}
.icon-align-left{background-position:-264px -48px;}
.icon-align-center{background-position:-288px -48px;}
.icon-align-right{background-position:-312px -48px;}
.icon-align-justify{background-position:-336px -48px;}
.icon-list{background-position:-360px -48px;}
.icon-indent-left{background-position:-384px -48px;}
.icon-indent-right{background-position:-408px -48px;}
.icon-facetime-video{background-position:-432px -48px;}
.icon-picture{background-position:-456px -48px;}
.icon-pencil{background-position:0 -72px;}
.icon-map-marker{background-position:-24px -72px;}
.icon-adjust{background-position:-48px -72px;}
.icon-tint{background-position:-72px -72px;}
.icon-edit{background-position:-96px -72px;}
.icon-share{background-position:-120px -72px;}
.icon-check{background-position:-144px -72px;}
.icon-move{background-position:-168px -72px;}
.icon-step-backward{background-position:-192px -72px;}
.icon-fast-backward{background-position:-216px -72px;}
.icon-backward{background-position:-240px -72px;}
.icon-play{background-position:-264px -72px;}
.icon-pause{background-position:-288px -72px;}
.icon-stop{background-position:-312px -72px;}
.icon-forward{background-position:-336px -72px;}
.icon-fast-forward{background-position:-360px -72px;}
.icon-step-forward{background-position:-384px -72px;}
.icon-eject{background-position:-408px -72px;}
.icon-chevron-left{background-position:-432px -72px;}
.icon-chevron-right{background-position:-456px -72px;}
.icon-plus-sign{background-position:0 -96px;}
.icon-minus-sign{background-position:-24px -96px;}
.icon-remove-sign{background-position:-48px -96px;}
.icon-ok-sign{background-position:-72px -96px;}
.icon-question-sign{background-position:-96px -96px;}
.icon-info-sign{background-position:-120px -96px;}
.icon-screenshot{background-position:-144px -96px;}
.icon-remove-circle{background-position:-168px -96px;}
.icon-ok-circle{background-position:-192px -96px;}
.icon-ban-circle{background-position:-216px -96px;}
.icon-arrow-left{background-position:-240px -96px;}
.icon-arrow-right{background-position:-264px -96px;}
.icon-arrow-up{background-position:-289px -96px;}
.icon-arrow-down{background-position:-312px -96px;}
.icon-share-alt{background-position:-336px -96px;}
.icon-resize-full{background-position:-360px -96px;}
.icon-resize-small{background-position:-384px -96px;}
.icon-plus{background-position:-408px -96px;}
.icon-minus{background-position:-433px -96px;}
.icon-asterisk{background-position:-456px -96px;}
.icon-exclamation-sign{background-position:0 -120px;}
.icon-gift{background-position:-24px -120px;}
.icon-leaf{background-position:-48px -120px;}
.icon-fire{background-position:-72px -120px;}
.icon-eye-open{background-position:-96px -120px;}
.icon-eye-close{background-position:-120px -120px;}
.icon-warning-sign{background-position:-144px -120px;}
.icon-plane{background-position:-168px -120px;}
.icon-calendar{background-position:-192px -120px;}
.icon-random{background-position:-216px -120px;width:16px;}
.icon-comment{background-position:-240px -120px;}
.icon-magnet{background-position:-264px -120px;}
.icon-chevron-up{background-position:-288px -120px;}
.icon-chevron-down{background-position:-313px -119px;}
.icon-retweet{background-position:-336px -120px;}
.icon-shopping-cart{background-position:-360px -120px;}
.icon-folder-close{background-position:-384px -120px;width:16px;}
.icon-folder-open{background-position:-408px -120px;width:16px;}
.icon-resize-vertical{background-position:-432px -119px;}
.icon-resize-horizontal{background-position:-456px -118px;}
.icon-hdd{background-position:0 -144px;}
.icon-bullhorn{background-position:-24px -144px;}
.icon-bell{background-position:-48px -144px;}
.icon-certificate{background-position:-72px -144px;}
.icon-thumbs-up{background-position:-96px -144px;}
.icon-thumbs-down{background-position:-120px -144px;}
.icon-hand-right{background-position:-144px -144px;}
.icon-hand-left{background-position:-168px -144px;}
.icon-hand-up{background-position:-192px -144px;}
.icon-hand-down{background-position:-216px -144px;}
.icon-circle-arrow-right{background-position:-240px -144px;}
.icon-circle-arrow-left{background-position:-264px -144px;}
.icon-circle-arrow-up{background-position:-288px -144px;}
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.icon-globe{background-position:-336px -144px;}
.icon-wrench{background-position:-360px -144px;}
.icon-tasks{background-position:-384px -144px;}
.icon-filter{background-position:-408px -144px;}
.icon-briefcase{background-position:-432px -144px;}
.icon-fullscreen{background-position:-456px -144px;}
.dropup,.dropdown{position:relative;}
.dropdown-toggle{*margin-bottom:-3px;}
.dropdown-toggle:active,.open .dropdown-toggle{outline:0;}
.caret{display:inline-block;width:0;height:0;vertical-align:top;border-top:4px solid #000000;border-right:4px solid transparent;border-left:4px solid transparent;content:"";}
.dropdown .caret{margin-top:8px;margin-left:2px;}
.dropdown-menu{position:absolute;top:100%;left:0;z-index:1000;display:none;float:left;min-width:160px;padding:5px 0;margin:2px 0 0;list-style:none;background-color:#ffffff;border:1px solid #ccc;border:1px solid rgba(0, 0, 0, 0.2);*border-right-width:2px;*border-bottom-width:2px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);-moz-box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box;}.dropdown-menu.pull-right{right:0;left:auto;}
.dropdown-menu .divider{*width:100%;height:1px;margin:9px 1px;*margin:-5px 0 5px;overflow:hidden;background-color:#e5e5e5;border-bottom:1px solid #ffffff;}
.dropdown-menu>li>a{display:block;padding:3px 20px;clear:both;font-weight:normal;line-height:20px;color:#333333;white-space:nowrap;}
.dropdown-menu>li>a:hover,.dropdown-menu>li>a:focus,.dropdown-submenu:hover>a,.dropdown-submenu:focus>a{text-decoration:none;color:#ffffff;background-color:#0081c2;background-image:-moz-linear-gradient(top, #0088cc, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#0088cc), to(#0077b3));background-image:-webkit-linear-gradient(top, #0088cc, #0077b3);background-image:-o-linear-gradient(top, #0088cc, #0077b3);background-image:linear-gradient(to bottom, #0088cc, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0);}
.dropdown-menu>.active>a,.dropdown-menu>.active>a:hover,.dropdown-menu>.active>a:focus{color:#ffffff;text-decoration:none;outline:0;background-color:#0081c2;background-image:-moz-linear-gradient(top, #0088cc, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#0088cc), to(#0077b3));background-image:-webkit-linear-gradient(top, #0088cc, #0077b3);background-image:-o-linear-gradient(top, #0088cc, #0077b3);background-image:linear-gradient(to bottom, #0088cc, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0);}
.dropdown-menu>.disabled>a,.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{color:#999999;}
.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{text-decoration:none;background-color:transparent;background-image:none;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);cursor:default;}
.open{*z-index:1000;}.open>.dropdown-menu{display:block;}
.dropdown-backdrop{position:fixed;left:0;right:0;bottom:0;top:0;z-index:990;}
.pull-right>.dropdown-menu{right:0;left:auto;}
.dropup .caret,.navbar-fixed-bottom .dropdown .caret{border-top:0;border-bottom:4px solid #000000;content:"";}
.dropup .dropdown-menu,.navbar-fixed-bottom .dropdown .dropdown-menu{top:auto;bottom:100%;margin-bottom:1px;}
.dropdown-submenu{position:relative;}
.dropdown-submenu>.dropdown-menu{top:0;left:100%;margin-top:-6px;margin-left:-1px;-webkit-border-radius:0 6px 6px 6px;-moz-border-radius:0 6px 6px 6px;border-radius:0 6px 6px 6px;}
.dropdown-submenu:hover>.dropdown-menu{display:block;}
.dropup .dropdown-submenu>.dropdown-menu{top:auto;bottom:0;margin-top:0;margin-bottom:-2px;-webkit-border-radius:5px 5px 5px 0;-moz-border-radius:5px 5px 5px 0;border-radius:5px 5px 5px 0;}
.dropdown-submenu>a:after{display:block;content:" ";float:right;width:0;height:0;border-color:transparent;border-style:solid;border-width:5px 0 5px 5px;border-left-color:#cccccc;margin-top:5px;margin-right:-10px;}
.dropdown-submenu:hover>a:after{border-left-color:#ffffff;}
.dropdown-submenu.pull-left{float:none;}.dropdown-submenu.pull-left>.dropdown-menu{left:-100%;margin-left:10px;-webkit-border-radius:6px 0 6px 6px;-moz-border-radius:6px 0 6px 6px;border-radius:6px 0 6px 6px;}
.dropdown .dropdown-menu .nav-header{padding-left:20px;padding-right:20px;}
.typeahead{z-index:1051;margin-top:2px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
.well{min-height:20px;padding:19px;margin-bottom:20px;background-color:#f5f5f5;border:1px solid #e3e3e3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:inset 0 1px 1px rgba(0, 0, 0, 0.05);-moz-box-shadow:inset 0 1px 1px rgba(0, 0, 0, 0.05);box-shadow:inset 0 1px 1px rgba(0, 0, 0, 0.05);}.well blockquote{border-color:#ddd;border-color:rgba(0, 0, 0, 0.15);}
.well-large{padding:24px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;}
.well-small{padding:9px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px;}
.fade{opacity:0;-webkit-transition:opacity 0.15s linear;-moz-transition:opacity 0.15s linear;-o-transition:opacity 0.15s linear;transition:opacity 0.15s linear;}.fade.in{opacity:1;}
.collapse{position:relative;height:0;overflow:hidden;-webkit-transition:height 0.35s ease;-moz-transition:height 0.35s ease;-o-transition:height 0.35s ease;transition:height 0.35s ease;}.collapse.in{height:auto;}
.close{float:right;font-size:20px;font-weight:bold;line-height:20px;color:#000000;text-shadow:0 1px 0 #ffffff;opacity:0.2;filter:alpha(opacity=20);}.close:hover,.close:focus{color:#000000;text-decoration:none;cursor:pointer;opacity:0.4;filter:alpha(opacity=40);}
button.close{padding:0;cursor:pointer;background:transparent;border:0;-webkit-appearance:none;}
.btn{display:inline-block;*display:inline;*zoom:1;padding:4px 12px;margin-bottom:0;font-size:13px;line-height:20px;text-align:center;vertical-align:middle;cursor:pointer;color:#333333;text-shadow:0 1px 1px rgba(255, 255, 255, 0.75);background-color:#f5f5f5;background-image:-moz-linear-gradient(top, #ffffff, #e6e6e6);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ffffff), to(#e6e6e6));background-image:-webkit-linear-gradient(top, #ffffff, #e6e6e6);background-image:-o-linear-gradient(top, #ffffff, #e6e6e6);background-image:linear-gradient(to bottom, #ffffff, #e6e6e6);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffffff', endColorstr='#ffe6e6e6', GradientType=0);border-color:#e6e6e6 #e6e6e6 #bfbfbf;border-color:rgba(0, 0, 0, 0.1) rgba(0, 0, 0, 0.1) rgba(0, 0, 0, 0.25);*background-color:#e6e6e6;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);border:1px solid #cccccc;*border:0;border-bottom-color:#b3b3b3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;*margin-left:.3em;-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);}.btn:hover,.btn:focus,.btn:active,.btn.active,.btn.disabled,.btn[disabled]{color:#333333;background-color:#e6e6e6;*background-color:#d9d9d9;}
.btn:active,.btn.active{background-color:#cccccc \9;}
.btn:hover,.btn:focus,.btn:active,.btn.active,.btn.disabled,.btn[disabled]{color:#333333;background-color:#e6e6e6;*background-color:#d9d9d9;}
.btn:active,.btn.active{background-color:#cccccc \9;}
.btn:first-child{*margin-left:0;}
.btn:first-child{*margin-left:0;}
.btn:hover,.btn:focus{color:#333333;text-decoration:none;background-position:0 -15px;-webkit-transition:background-position 0.1s linear;-moz-transition:background-position 0.1s linear;-o-transition:background-position 0.1s linear;transition:background-position 0.1s linear;}
.btn:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px;}
.btn.active,.btn:active{background-image:none;outline:0;-webkit-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);}
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.btn-large{padding:11px 19px;font-size:16.25px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;}
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.btn-block+.btn-block{margin-top:5px;}
input[type="submit"].btn-block,input[type="reset"].btn-block,input[type="button"].btn-block{width:100%;}
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.btn-link,.btn-link:active,.btn-link[disabled]{background-color:transparent;background-image:none;-webkit-box-shadow:none;-moz-box-shadow:none;box-shadow:none;}
.btn-link{border-color:transparent;cursor:pointer;color:#0088cc;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0;}
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.btn-group:first-child{*margin-left:0;}
.btn-group+.btn-group{margin-left:5px;}
.btn-toolbar{font-size:0;margin-top:10px;margin-bottom:10px;}.btn-toolbar>.btn+.btn,.btn-toolbar>.btn-group+.btn,.btn-toolbar>.btn+.btn-group{margin-left:5px;}
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.btn-group>.btn+.btn{margin-left:-1px;}
.btn-group>.btn,.btn-group>.dropdown-menu,.btn-group>.popover{font-size:13px;}
.btn-group>.btn-mini{font-size:9.75px;}
.btn-group>.btn-small{font-size:11.049999999999999px;}
.btn-group>.btn-large{font-size:16.25px;}
.btn-group>.btn:first-child{margin-left:0;-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px;}
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.btn-group>.btn+.dropdown-toggle{padding-left:8px;padding-right:8px;-webkit-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);*padding-top:5px;*padding-bottom:5px;}
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.btn-group>.btn-small+.dropdown-toggle{*padding-top:5px;*padding-bottom:4px;}
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.btn-group.open .btn-info.dropdown-toggle{background-color:#2f96b4;}
.btn-group.open .btn-inverse.dropdown-toggle{background-color:#222222;}
.btn .caret{margin-top:8px;margin-left:0;}
.btn-large .caret{margin-top:6px;}
.btn-large .caret{border-left-width:5px;border-right-width:5px;border-top-width:5px;}
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.dropup .btn-large .caret{border-bottom-width:5px;}
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.alert{padding:8px 35px 8px 14px;margin-bottom:20px;text-shadow:0 1px 0 rgba(255, 255, 255, 0.5);background-color:#fcf8e3;border:1px solid #fbeed5;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
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.alert h4{margin:0;}
.alert .close{position:relative;top:-2px;right:-21px;line-height:20px;}
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.alert-success h4{color:#468847;}
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.alert-danger h4,.alert-error h4{color:#b94a48;}
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.alert-block p+p{margin-top:5px;}
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.modal-footer .btn-block+.btn-block{margin-left:0;}
.tooltip{position:absolute;z-index:1030;display:block;visibility:visible;font-size:11px;line-height:1.4;opacity:0;filter:alpha(opacity=0);}.tooltip.in{opacity:0.8;filter:alpha(opacity=80);}
.tooltip.top{margin-top:-3px;padding:5px 0;}
.tooltip.right{margin-left:3px;padding:0 5px;}
.tooltip.bottom{margin-top:3px;padding:5px 0;}
.tooltip.left{margin-left:-3px;padding:0 5px;}
.tooltip-inner{max-width:200px;padding:8px;color:#ffffff;text-align:center;text-decoration:none;background-color:#000000;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
.tooltip-arrow{position:absolute;width:0;height:0;border-color:transparent;border-style:solid;}
.tooltip.top .tooltip-arrow{bottom:0;left:50%;margin-left:-5px;border-width:5px 5px 0;border-top-color:#000000;}
.tooltip.right .tooltip-arrow{top:50%;left:0;margin-top:-5px;border-width:5px 5px 5px 0;border-right-color:#000000;}
.tooltip.left .tooltip-arrow{top:50%;right:0;margin-top:-5px;border-width:5px 0 5px 5px;border-left-color:#000000;}
.tooltip.bottom .tooltip-arrow{top:0;left:50%;margin-left:-5px;border-width:0 5px 5px;border-bottom-color:#000000;}
.popover{position:absolute;top:0;left:0;z-index:1010;display:none;max-width:276px;padding:1px;text-align:left;background-color:#ffffff;-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box;border:1px solid #ccc;border:1px solid rgba(0, 0, 0, 0.2);-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);-moz-box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);box-shadow:0 5px 10px rgba(0, 0, 0, 0.2);white-space:normal;}.popover.top{margin-top:-10px;}
.popover.right{margin-left:10px;}
.popover.bottom{margin-top:10px;}
.popover.left{margin-left:-10px;}
.popover-title{margin:0;padding:8px 14px;font-size:14px;font-weight:normal;line-height:18px;background-color:#f7f7f7;border-bottom:1px solid #ebebeb;-webkit-border-radius:5px 5px 0 0;-moz-border-radius:5px 5px 0 0;border-radius:5px 5px 0 0;}.popover-title:empty{display:none;}
.popover-content{padding:9px 14px;}
.popover .arrow,.popover .arrow:after{position:absolute;display:block;width:0;height:0;border-color:transparent;border-style:solid;}
.popover .arrow{border-width:11px;}
.popover .arrow:after{border-width:10px;content:"";}
.popover.top .arrow{left:50%;margin-left:-11px;border-bottom-width:0;border-top-color:#999;border-top-color:rgba(0, 0, 0, 0.25);bottom:-11px;}.popover.top .arrow:after{bottom:1px;margin-left:-10px;border-bottom-width:0;border-top-color:#ffffff;}
.popover.right .arrow{top:50%;left:-11px;margin-top:-11px;border-left-width:0;border-right-color:#999;border-right-color:rgba(0, 0, 0, 0.25);}.popover.right .arrow:after{left:1px;bottom:-10px;border-left-width:0;border-right-color:#ffffff;}
.popover.bottom .arrow{left:50%;margin-left:-11px;border-top-width:0;border-bottom-color:#999;border-bottom-color:rgba(0, 0, 0, 0.25);top:-11px;}.popover.bottom .arrow:after{top:1px;margin-left:-10px;border-top-width:0;border-bottom-color:#ffffff;}
.popover.left .arrow{top:50%;right:-11px;margin-top:-11px;border-right-width:0;border-left-color:#999;border-left-color:rgba(0, 0, 0, 0.25);}.popover.left .arrow:after{right:1px;border-right-width:0;border-left-color:#ffffff;bottom:-10px;}
.thumbnails{margin-left:-20px;list-style:none;*zoom:1;}.thumbnails:before,.thumbnails:after{display:table;content:"";line-height:0;}
.thumbnails:after{clear:both;}
.thumbnails:before,.thumbnails:after{display:table;content:"";line-height:0;}
.thumbnails:after{clear:both;}
.row-fluid .thumbnails{margin-left:0;}
.thumbnails>li{float:left;margin-bottom:20px;margin-left:20px;}
.thumbnail{display:block;padding:4px;line-height:20px;border:1px solid #ddd;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 3px rgba(0, 0, 0, 0.055);-moz-box-shadow:0 1px 3px rgba(0, 0, 0, 0.055);box-shadow:0 1px 3px rgba(0, 0, 0, 0.055);-webkit-transition:all 0.2s ease-in-out;-moz-transition:all 0.2s ease-in-out;-o-transition:all 0.2s ease-in-out;transition:all 0.2s ease-in-out;}
a.thumbnail:hover,a.thumbnail:focus{border-color:#0088cc;-webkit-box-shadow:0 1px 4px rgba(0, 105, 214, 0.25);-moz-box-shadow:0 1px 4px rgba(0, 105, 214, 0.25);box-shadow:0 1px 4px rgba(0, 105, 214, 0.25);}
.thumbnail>img{display:block;max-width:100%;margin-left:auto;margin-right:auto;}
.thumbnail .caption{padding:9px;color:#555555;}
.media,.media-body{overflow:hidden;*overflow:visible;zoom:1;}
.media,.media .media{margin-top:15px;}
.media:first-child{margin-top:0;}
.media-object{display:block;}
.media-heading{margin:0 0 5px;}
.media>.pull-left{margin-right:10px;}
.media>.pull-right{margin-left:10px;}
.media-list{margin-left:0;list-style:none;}
.label,.badge{display:inline-block;padding:2px 4px;font-size:10.998px;font-weight:bold;line-height:14px;color:#ffffff;vertical-align:baseline;white-space:nowrap;text-shadow:0 -1px 0 rgba(0, 0, 0, 0.25);background-color:#999999;}
.label{-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px;}
.badge{padding-left:9px;padding-right:9px;-webkit-border-radius:9px;-moz-border-radius:9px;border-radius:9px;}
.label:empty,.badge:empty{display:none;}
a.label:hover,a.label:focus,a.badge:hover,a.badge:focus{color:#ffffff;text-decoration:none;cursor:pointer;}
.label-important,.badge-important{background-color:#b94a48;}
.label-important[href],.badge-important[href]{background-color:#953b39;}
.label-warning,.badge-warning{background-color:#f89406;}
.label-warning[href],.badge-warning[href]{background-color:#c67605;}
.label-success,.badge-success{background-color:#468847;}
.label-success[href],.badge-success[href]{background-color:#356635;}
.label-info,.badge-info{background-color:#3a87ad;}
.label-info[href],.badge-info[href]{background-color:#2d6987;}
.label-inverse,.badge-inverse{background-color:#333333;}
.label-inverse[href],.badge-inverse[href]{background-color:#1a1a1a;}
.btn .label,.btn .badge{position:relative;top:-1px;}
.btn-mini .label,.btn-mini .badge{top:0;}
@-webkit-keyframes progress-bar-stripes{from{background-position:40px 0;} to{background-position:0 0;}}@-moz-keyframes progress-bar-stripes{from{background-position:40px 0;} to{background-position:0 0;}}@-ms-keyframes progress-bar-stripes{from{background-position:40px 0;} to{background-position:0 0;}}@-o-keyframes progress-bar-stripes{from{background-position:0 0;} to{background-position:40px 0;}}@keyframes progress-bar-stripes{from{background-position:40px 0;} to{background-position:0 0;}}.progress{overflow:hidden;height:20px;margin-bottom:20px;background-color:#f7f7f7;background-image:-moz-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#f5f5f5), to(#f9f9f9));background-image:-webkit-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-o-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:linear-gradient(to bottom, #f5f5f5, #f9f9f9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fff5f5f5', endColorstr='#fff9f9f9', GradientType=0);-webkit-box-shadow:inset 0 1px 2px rgba(0, 0, 0, 0.1);-moz-box-shadow:inset 0 1px 2px rgba(0, 0, 0, 0.1);box-shadow:inset 0 1px 2px rgba(0, 0, 0, 0.1);-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
.progress .bar{width:0%;height:100%;color:#ffffff;float:left;font-size:12px;text-align:center;text-shadow:0 -1px 0 rgba(0, 0, 0, 0.25);background-color:#0e90d2;background-image:-moz-linear-gradient(top, #149bdf, #0480be);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#149bdf), to(#0480be));background-image:-webkit-linear-gradient(top, #149bdf, #0480be);background-image:-o-linear-gradient(top, #149bdf, #0480be);background-image:linear-gradient(to bottom, #149bdf, #0480be);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff149bdf', endColorstr='#ff0480be', GradientType=0);-webkit-box-shadow:inset 0 -1px 0 rgba(0, 0, 0, 0.15);-moz-box-shadow:inset 0 -1px 0 rgba(0, 0, 0, 0.15);box-shadow:inset 0 -1px 0 rgba(0, 0, 0, 0.15);-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;-webkit-transition:width 0.6s ease;-moz-transition:width 0.6s ease;-o-transition:width 0.6s ease;transition:width 0.6s ease;}
.progress .bar+.bar{-webkit-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);-moz-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);}
.progress-striped .bar{background-color:#149bdf;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(0.25, rgba(255, 255, 255, 0.15)), color-stop(0.25, transparent), color-stop(0.5, transparent), color-stop(0.5, rgba(255, 255, 255, 0.15)), color-stop(0.75, rgba(255, 255, 255, 0.15)), color-stop(0.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);-webkit-background-size:40px 40px;-moz-background-size:40px 40px;-o-background-size:40px 40px;background-size:40px 40px;}
.progress.active .bar{-webkit-animation:progress-bar-stripes 2s linear infinite;-moz-animation:progress-bar-stripes 2s linear infinite;-ms-animation:progress-bar-stripes 2s linear infinite;-o-animation:progress-bar-stripes 2s linear infinite;animation:progress-bar-stripes 2s linear infinite;}
.progress-danger .bar,.progress .bar-danger{background-color:#dd514c;background-image:-moz-linear-gradient(top, #ee5f5b, #c43c35);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ee5f5b), to(#c43c35));background-image:-webkit-linear-gradient(top, #ee5f5b, #c43c35);background-image:-o-linear-gradient(top, #ee5f5b, #c43c35);background-image:linear-gradient(to bottom, #ee5f5b, #c43c35);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffee5f5b', endColorstr='#ffc43c35', GradientType=0);}
.progress-danger.progress-striped .bar,.progress-striped .bar-danger{background-color:#ee5f5b;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(0.25, rgba(255, 255, 255, 0.15)), color-stop(0.25, transparent), color-stop(0.5, transparent), color-stop(0.5, rgba(255, 255, 255, 0.15)), color-stop(0.75, rgba(255, 255, 255, 0.15)), color-stop(0.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);}
.progress-success .bar,.progress .bar-success{background-color:#5eb95e;background-image:-moz-linear-gradient(top, #62c462, #57a957);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#62c462), to(#57a957));background-image:-webkit-linear-gradient(top, #62c462, #57a957);background-image:-o-linear-gradient(top, #62c462, #57a957);background-image:linear-gradient(to bottom, #62c462, #57a957);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff62c462', endColorstr='#ff57a957', GradientType=0);}
.progress-success.progress-striped .bar,.progress-striped .bar-success{background-color:#62c462;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(0.25, rgba(255, 255, 255, 0.15)), color-stop(0.25, transparent), color-stop(0.5, transparent), color-stop(0.5, rgba(255, 255, 255, 0.15)), color-stop(0.75, rgba(255, 255, 255, 0.15)), color-stop(0.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);}
.progress-info .bar,.progress .bar-info{background-color:#4bb1cf;background-image:-moz-linear-gradient(top, #5bc0de, #339bb9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#5bc0de), to(#339bb9));background-image:-webkit-linear-gradient(top, #5bc0de, #339bb9);background-image:-o-linear-gradient(top, #5bc0de, #339bb9);background-image:linear-gradient(to bottom, #5bc0de, #339bb9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff5bc0de', endColorstr='#ff339bb9', GradientType=0);}
.progress-info.progress-striped .bar,.progress-striped .bar-info{background-color:#5bc0de;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(0.25, rgba(255, 255, 255, 0.15)), color-stop(0.25, transparent), color-stop(0.5, transparent), color-stop(0.5, rgba(255, 255, 255, 0.15)), color-stop(0.75, rgba(255, 255, 255, 0.15)), color-stop(0.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);}
.progress-warning .bar,.progress .bar-warning{background-color:#faa732;background-image:-moz-linear-gradient(top, #fbb450, #f89406);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fbb450), to(#f89406));background-image:-webkit-linear-gradient(top, #fbb450, #f89406);background-image:-o-linear-gradient(top, #fbb450, #f89406);background-image:linear-gradient(to bottom, #fbb450, #f89406);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fffbb450', endColorstr='#fff89406', GradientType=0);}
.progress-warning.progress-striped .bar,.progress-striped .bar-warning{background-color:#fbb450;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(0.25, rgba(255, 255, 255, 0.15)), color-stop(0.25, transparent), color-stop(0.5, transparent), color-stop(0.5, rgba(255, 255, 255, 0.15)), color-stop(0.75, rgba(255, 255, 255, 0.15)), color-stop(0.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);}
.accordion{margin-bottom:20px;}
.accordion-group{margin-bottom:2px;border:1px solid #e5e5e5;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;}
.accordion-heading{border-bottom:0;}
.accordion-heading .accordion-toggle{display:block;padding:8px 15px;}
.accordion-toggle{cursor:pointer;}
.accordion-inner{padding:9px 15px;border-top:1px solid #e5e5e5;}
.carousel{position:relative;margin-bottom:20px;line-height:1;}
.carousel-inner{overflow:hidden;width:100%;position:relative;}
.carousel-inner>.item{display:none;position:relative;-webkit-transition:0.6s ease-in-out left;-moz-transition:0.6s ease-in-out left;-o-transition:0.6s ease-in-out left;transition:0.6s ease-in-out left;}.carousel-inner>.item>img,.carousel-inner>.item>a>img{display:block;line-height:1;}
.carousel-inner>.active,.carousel-inner>.next,.carousel-inner>.prev{display:block;}
.carousel-inner>.active{left:0;}
.carousel-inner>.next,.carousel-inner>.prev{position:absolute;top:0;width:100%;}
.carousel-inner>.next{left:100%;}
.carousel-inner>.prev{left:-100%;}
.carousel-inner>.next.left,.carousel-inner>.prev.right{left:0;}
.carousel-inner>.active.left{left:-100%;}
.carousel-inner>.active.right{left:100%;}
.carousel-control{position:absolute;top:40%;left:15px;width:40px;height:40px;margin-top:-20px;font-size:60px;font-weight:100;line-height:30px;color:#ffffff;text-align:center;background:#222222;border:3px solid #ffffff;-webkit-border-radius:23px;-moz-border-radius:23px;border-radius:23px;opacity:0.5;filter:alpha(opacity=50);}.carousel-control.right{left:auto;right:15px;}
.carousel-control:hover,.carousel-control:focus{color:#ffffff;text-decoration:none;opacity:0.9;filter:alpha(opacity=90);}
.carousel-indicators{position:absolute;top:15px;right:15px;z-index:5;margin:0;list-style:none;}.carousel-indicators li{display:block;float:left;width:10px;height:10px;margin-left:5px;text-indent:-999px;background-color:#ccc;background-color:rgba(255, 255, 255, 0.25);border-radius:5px;}
.carousel-indicators .active{background-color:#fff;}
.carousel-caption{position:absolute;left:0;right:0;bottom:0;padding:15px;background:#333333;background:rgba(0, 0, 0, 0.75);}
.carousel-caption h4,.carousel-caption p{color:#ffffff;line-height:20px;}
.carousel-caption h4{margin:0 0 5px;}
.carousel-caption p{margin-bottom:0;}
.hero-unit{padding:60px;margin-bottom:30px;font-size:18px;font-weight:200;line-height:30px;color:inherit;background-color:#eeeeee;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;}.hero-unit h1{margin-bottom:0;font-size:60px;line-height:1;color:inherit;letter-spacing:-1px;}
.hero-unit li{line-height:30px;}
.pull-right{float:right;}
.pull-left{float:left;}
.hide{display:none;}
.show{display:block;}
.invisible{visibility:hidden;}
.affix{position:fixed;}
.clearfix{*zoom:1;}.clearfix:before,.clearfix:after{display:table;content:"";line-height:0;}
.clearfix:after{clear:both;}
.hide-text{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0;}
.input-block-level{display:block;width:100%;min-height:30px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;}
@-ms-viewport{width:device-width;}.hidden{display:none;visibility:hidden;}
.visible-phone{display:none !important;}
.visible-tablet{display:none !important;}
.hidden-desktop{display:none !important;}
.visible-desktop{display:inherit !important;}
@media (min-width:768px) and (max-width:979px){.hidden-desktop{display:inherit !important;} .visible-desktop{display:none !important ;} .visible-tablet{display:inherit !important;} .hidden-tablet{display:none !important;}}@media (max-width:767px){.hidden-desktop{display:inherit !important;} .visible-desktop{display:none !important;} .visible-phone{display:inherit !important;} .hidden-phone{display:none !important;}}.visible-print{display:none !important;}
@media print{.visible-print{display:inherit !important;} .hidden-print{display:none !important;}}@media (min-width:1200px){.row{margin-left:-30px;*zoom:1;}.row:before,.row:after{display:table;content:"";line-height:0;} .row:after{clear:both;} .row:before,.row:after{display:table;content:"";line-height:0;} .row:after{clear:both;} [class*="span"]{float:left;min-height:1px;margin-left:30px;} .container,.navbar-static-top .container,.navbar-fixed-top .container,.navbar-fixed-bottom .container{width:1170px;} .span12{width:1170px;} .span11{width:1070px;} .span10{width:970px;} .span9{width:870px;} .span8{width:770px;} .span7{width:670px;} .span6{width:570px;} .span5{width:470px;} .span4{width:370px;} .span3{width:270px;} .span2{width:170px;} .span1{width:70px;} .offset12{margin-left:1230px;} .offset11{margin-left:1130px;} .offset10{margin-left:1030px;} .offset9{margin-left:930px;} .offset8{margin-left:830px;} .offset7{margin-left:730px;} .offset6{margin-left:630px;} 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<h1 id="Julia:-An-LLVM-based-approach-to-scientific-computing">Julia: An LLVM-based approach to scientific computing<a class="anchor-link" href="#Julia:-An-LLVM-based-approach-to-scientific-computing">&#182;</a></h1>
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<p>Keno Fischer</p>
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In&nbsp;[1]:
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<div class="highlight"><pre><span class="n">run</span><span class="p">(</span><span class="sb">`git config --get user.name`</span><span class="p">)</span>
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Keno Fischer
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<li>Julia, the language</li>
<li>A Journey through the CodeGen</li>
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<h1 id="Is-it-any-fast?">Is it any fast?<a class="anchor-link" href="#Is-it-any-fast?">&#182;</a></h1>
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<div class="highlight"><pre><span class="n">using</span> <span class="n">Gadfly</span>
<span class="n">using</span> <span class="n">WWWClient</span>
<span class="n">using</span> <span class="n">DataFrames</span>
<span class="n">const</span> <span class="n">w</span> <span class="o">=</span> <span class="n">WWWClient</span>
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<pre>
Warning: New definition
round(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
round(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
round(DataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
round(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
round(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
round(DataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
round(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
round(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
round(AbstractDataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
round(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
round(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
round(AbstractDataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
ceil(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
ceil(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
ceil(DataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
ceil(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
ceil(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
ceil(DataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
ceil(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
ceil(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
ceil(AbstractDataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
ceil(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
ceil(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
ceil(AbstractDataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
floor(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
floor(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
floor(DataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
floor(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
floor(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
floor(DataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
floor(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
floor(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
floor(AbstractDataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
floor(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
floor(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
floor(AbstractDataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
trunc(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
trunc(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
trunc(DataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
trunc(DataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
trunc(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
trunc(DataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
trunc(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
trunc(AbstractArray{T&lt;:Real,1},) at operators.jl:236.
To fix, define
trunc(AbstractDataArray{_&lt;:Real,1},)
before the new definition.
Warning: New definition
trunc(AbstractDataArray{T&lt;:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
trunc(AbstractArray{T&lt;:Real,2},) at operators.jl:237.
To fix, define
trunc(AbstractDataArray{_&lt;:Real,2},)
before the new definition.
Warning: New definition
formatter(
</pre>
</div>
</div>
<div class="output_area"><div class="prompt"></div>
<div class="box-flex1 output_subarea output_display_data">
<div class="output_html rendered_html">
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//
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// Construct a callback used to toggle highly-visibility grid lines.
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// Args:
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// Callback function.
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root,
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</div>
<div class="output_area"><div class="prompt"></div>
<div class="box-flex1 output_subarea output_stream output_stderr">
<pre>
Array{T,N},Date{C&lt;:Calendar}...)
is ambiguous with:
formatter(Array{T,N},FloatingPoint...).
To fix, define
formatter(Array{T,N},)
before the new definition.
Warning: New definition
|(SynchronousStepCollection,Any) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:283
is ambiguous with:
|(Any,NAtype) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
To fix, define
|(SynchronousStepCollection,NAtype)
before the new definition.
Warning: New definition
|(Any,SynchronousStepCollection) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:286
is ambiguous with:
|(NAtype,Any) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
To fix, define
|(NAtype,SynchronousStepCollection)
before the new definition.
WARNING: BinDeps.find_library is deprecated, use Base.find_library instead.
WARNING: add_library_mapping is deprecated, use push!(DL_LOAD_PATH,&quot;/path/to/search&quot;) instead.
Warning: New definition
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
+(DataArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
+(AbstractDataArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractArray{T,N},DataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},DataArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractArray{T,N},AbstractDataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
+(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractDataArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
-(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
-(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
-(DataArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
-(AbstractArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
-(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
-(AbstractDataArray{T1&lt;:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2&lt;:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
*(Any,AbstractCalendarDuration) at /Users/kfischer/.julia/Calendar/src/Calendar.jl:341
is ambiguous with:
*(MeasureNil,Any) at /Users/kfischer/.julia/Compose/src/measure.jl:32.
To fix, define
*(MeasureNil,AbstractCalendarDuration)
before the new definition.
Warning: New definition
-(AbstractArray{T1&lt;:CalendarTime,N},AbstractArray{T2&lt;:CalendarTime,N}) at operators.jl:253
is ambiguous with:
-(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
-(DataArray{T1&lt;:CalendarTime,N},AbstractArray{T2&lt;:CalendarTime,N})
before the new definition.
Warning: New definition
-(AbstractArray{T1&lt;:CalendarTime,N},AbstractArray{T2&lt;:CalendarTime,N}) at operators.jl:253
is ambiguous with:
-(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
-(AbstractDataArray{T1&lt;:CalendarTime,N},AbstractArray{T2&lt;:CalendarTime,N})
before the new definition.
</pre>
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</div>
<div class="output_area"><div class="prompt output_prompt">
Out[2]:</div>
<div class="box-flex1 output_subarea output_pyout">
<pre>
WWWClient
</pre>
</div>
</div>
</div>
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In&nbsp;[3]:
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<div class="highlight"><pre><span class="n">function</span> <span class="n">DataFrames</span><span class="o">.</span><span class="n">to_io</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">URI</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">IOBuffer</span><span class="p">(</span><span class="n">WWWClient</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="n">x</span><span class="p">,</span><span class="n">nb_available</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">end</span>
</pre></div>
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<div class="output vbox">
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Out[3]:</div>
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<pre>
to_io (generic function with 2 methods)
</pre>
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</div></section>
</section><section>
<section>
<div class="cell border-box-sizing code_cell vbox">
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In&nbsp;[3]:
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<div class="highlight"><pre><span class="n">benchmarks</span> <span class="o">=</span> <span class="n">readtable</span><span class="p">(</span><span class="n">URI</span><span class="p">(</span><span class="s">&quot;http://julialang.org/benchmarks.csv&quot;</span><span class="p">);</span><span class="n">header</span><span class="o">=</span><span class="n">false</span><span class="p">,</span><span class="n">colnames</span><span class="o">=</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">,</span><span class="s">&quot;Benchmark&quot;</span><span class="p">,</span><span class="s">&quot;Time&quot;</span><span class="p">])</span>
<span class="n">benchmarks</span> <span class="o">=</span> <span class="n">join</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="n">subset</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Language</span> <span class="o">.==</span> <span class="s">&quot;c&quot;</span><span class="p">)),</span>
<span class="n">on</span><span class="o">=</span><span class="s">&quot;Benchmark&quot;</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="p">:</span><span class="n">outer</span><span class="p">)</span>
<span class="n">within</span><span class="err">!</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Time</span> <span class="o">./=</span> <span class="n">Time_1</span><span class="p">));</span>
</pre></div>
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In&nbsp;[3]:
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<div class="highlight"><pre><span class="c"># Some cosmetic adjustments. Not essential to the plot, so let&#39;s skip them for the sake of space</span>
<span class="c"># Reorder factors</span>
<span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">PooledDataArray</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">])</span>
<span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">reorder</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">],</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Time&quot;</span><span class="p">])</span>
<span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Benchmark&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">PooledDataArray</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Benchmark&quot;</span><span class="p">])</span>
<span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Benchmark&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">reorder</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Benchmark&quot;</span><span class="p">],</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Time&quot;</span><span class="p">])</span>
<span class="c"># Capitalize</span>
<span class="n">capitalize</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span> <span class="o">=</span> <span class="n">string</span><span class="p">(</span><span class="n">uppercase</span><span class="p">(</span><span class="nb">str</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="p">,</span> <span class="nb">str</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">])</span>
<span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">set_levels</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">],</span>
<span class="n">Dict</span><span class="p">{</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">}(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">],</span>
<span class="p">[</span><span class="n">capitalize</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">&quot;Language&quot;</span><span class="p">]]))</span>
<span class="n">benchmarks</span> <span class="o">=</span> <span class="n">subset</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Language</span> <span class="o">.!=</span> <span class="s">&quot;C&quot;</span><span class="p">))</span>
<span class="n">set_default_plot_size</span><span class="p">(</span><span class="mi">8</span><span class="n">inch</span><span class="p">,</span><span class="mi">8</span><span class="n">inch</span><span class="o">/</span><span class="n">golden</span><span class="p">);</span>
</pre></div>
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In&nbsp;[4]:
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<div class="highlight"><pre><span class="n">p</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="s">&quot;Language&quot;</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="s">&quot;Time&quot;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&quot;Benchmark&quot;</span><span class="p">,</span> <span class="n">Scale</span><span class="o">.</span><span class="n">y_log10</span><span class="p">,</span>
<span class="n">Guide</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">&quot;time relative to C&quot;</span><span class="p">),</span> <span class="n">Guide</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">&quot;smaller is better&quot;</span><span class="p">))</span>
</pre></div>
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<div class="output_area"><div class="prompt"></div>
<div class="box-flex1 output_subarea output_display_data">
<div class="output_html rendered_html">
<div id="gadflyplot-f3tBxMbrYQ18zjgrGj3T"></div>
<script>
function draw_with_data(data, parent_id) {
var g = d3.select(parent_id)
.append("svg")
.attr("width", "203.2mm")
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g.append("defs");
var t = {"scale": 1.0};
(function (g) {
g.attr("class", "plotroot yscalable");
(function (g) {
d3.select("defs")
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.append("svg:path")
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g.append("svg:text")
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<p>Sure, but that's not the main point. So what is? What is different about Julia?</p>
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<h2 id="Dynamic-Multiple-Dispatch-Everywhere">Dynamic Multiple Dispatch Everywhere<a class="anchor-link" href="#Dynamic-Multiple-Dispatch-Everywhere">&#182;</a></h2>
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convert (generic function with 464 methods)
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+ (generic function with 188 methods)
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<div class="highlight"><pre><span class="nd">@which</span> <span class="n">convert</span><span class="p">(</span><span class="n">Float64</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="nd">@which</span> <span class="mf">1.0</span> <span class="o">+</span> <span class="mi">2</span>
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convert(::Type{Float64},x::Int64) at float.jl:21
+(x::Number,y::Number) at promotion.jl:148
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<h2 id="Basic-Dispatch">Basic Dispatch<a class="anchor-link" href="#Basic-Dispatch">&#182;</a></h2>
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Any</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;fallback&quot;</span>
<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;a and b are both numbers&quot;</span>
<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;a is a number&quot;</span>
<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;b is a number&quot;</span>
<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Integer</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Integer</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;a and b are both integers&quot;</span>
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f (generic function with 5 methods)
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mf">1.5</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
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&quot;a and b are both numbers&quot;
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="s">&quot;bar&quot;</span><span class="p">)</span>
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&quot;a is a number&quot;
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
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&quot;a and b are both integers&quot;
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="s">&quot;foo&quot;</span><span class="p">,[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
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&quot;fallback&quot;
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# 5 methods for generic function &quot;f&quot;:
f(a::Integer,b::Integer) at In[8]:5
f(a::Number,b::Number) at In[8]:2
f(a::Number,b) at In[8]:3
f(a,b::Number) at In[8]:4
f(a,b) at In[8]:1
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<h3 id="Diagonal-Dispatch/Parametric-Dispatch">Diagonal Dispatch/Parametric Dispatch<a class="anchor-link" href="#Diagonal-Dispatch/Parametric-Dispatch">&#182;</a></h3>
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<div class="highlight"><pre><span class="n">f</span><span class="p">{</span><span class="n">T</span><span class="o">&lt;</span><span class="p">:</span><span class="n">Number</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">T</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">T</span><span class="p">)</span> <span class="o">=</span> <span class="s">&quot;a and b are both $(T)s&quot;</span>
<span class="n">f</span><span class="p">{</span><span class="n">T</span><span class="o">&lt;</span><span class="p">:</span><span class="n">Number</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">Vector</span><span class="p">{</span><span class="n">T</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">Vector</span><span class="p">{</span><span class="n">T</span><span class="p">})</span> <span class="o">=</span> <span class="s">&quot;a and b are both vectors of $(T)s&quot;</span>
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f (generic function with 7 methods)
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<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="n">big</span><span class="p">(</span><span class="mf">1.5</span><span class="p">),</span><span class="n">big</span><span class="p">(</span><span class="mf">1.0</span><span class="p">))</span> <span class="c">#Two BigFloats</span>
<span class="n">f</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">],[</span><span class="mf">3.0</span><span class="p">,</span><span class="mf">4.0</span><span class="p">])</span> <span class="c">#Two Array{Float64,1}</span>
<span class="n">f</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">],[</span><span class="mf">3.</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="c">#One Array{Int64,1} &amp; One Array{Float64,1}</span>
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&quot;fallback&quot;
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&quot;a and b are both integers&quot;
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<h3 id="That's-nice,-but-what-does-this-have-to-do-with-speed?">That's nice, but what does this have to do with speed?<a class="anchor-link" href="#That's-nice,-but-what-does-this-have-to-do-with-speed?">&#182;</a></h3>
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<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base.LinAlg.det</span>
<span class="n">function</span> <span class="n">det</span><span class="p">{</span><span class="n">T</span><span class="p">}(</span><span class="n">A</span><span class="p">::</span><span class="n">AbstractArray</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="mi">2</span><span class="p">})</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">size</span><span class="p">(</span><span class="n">A</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">n</span> <span class="o">==</span> <span class="n">size</span><span class="p">(</span><span class="n">A</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span> <span class="o">||</span> <span class="n">error</span><span class="p">(</span><span class="s">&quot;Only square matrices allowed&quot;</span><span class="p">)</span>
<span class="n">n</span> <span class="o">==</span> <span class="mi">2</span> <span class="o">&amp;&amp;</span> <span class="k">return</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">zero</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span><span class="p">:</span><span class="n">n</span>
<span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="o">-</span><span class="n">one</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="o">^</span><span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">det</span><span class="p">(</span><span class="n">hcat</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">,</span><span class="mi">1</span><span class="p">:(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)],</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">,(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span><span class="n">end</span><span class="p">])))</span>
<span class="n">end</span>
<span class="n">s</span>
<span class="n">end</span>
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det (generic function with 17 methods)
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<div class="highlight"><pre><span class="n">methods</span><span class="p">(</span><span class="n">det</span><span class="p">)</span>
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# 17 methods for generic function &quot;det&quot;:
det(A::Triangular{T&lt;:Number}) at linalg/triangular.jl:63
det(W::Woodbury{T}) at linalg/woodbury.jl:84
det(A::Tridiagonal{T}) at linalg/tridiag.jl:357
det(D::Diagonal{T}) at linalg/diagonal.jl:80
det{T&lt;:Union(Float32,Complex{Float64},Complex{Float32},Float64)}(A::AbstractArray{T&lt;:Union(Float32,Complex{Float64},Complex{Float32},Float64),2}) at linalg/dense.jl:416
det(x::Number) at linalg/dense.jl:419
det{T}(C::Cholesky{T}) at linalg/factorization.jl:44
det{T}(C::CholeskyPivoted{T}) at linalg/factorization.jl:122
det{T}(A::LU{T}) at linalg/factorization.jl:186
det(A::Eigen{T,V}) at linalg/factorization.jl:533
det{T}(lu::LUTridiagonal{T}) at linalg/tridiag.jl:353
det{Tv&lt;:Float64,Ti&lt;:Int32}(lu::UmfpackLU{Tv&lt;:Float64,Ti&lt;:Int32}) at linalg/umfpack.jl:189
det{Tv&lt;:Complex{Float64},Ti&lt;:Int32}(lu::UmfpackLU{Tv&lt;:Complex{Float64},Ti&lt;:Int32}) at linalg/umfpack.jl:197
det{Tv&lt;:Float64,Ti&lt;:Int64}(lu::UmfpackLU{Tv&lt;:Float64,Ti&lt;:Int64}) at linalg/umfpack.jl:189
det{Tv&lt;:Complex{Float64},Ti&lt;:Int64}(lu::UmfpackLU{Tv&lt;:Complex{Float64},Ti&lt;:Int64}) at linalg/umfpack.jl:197
det(L::CholmodFactor{Tv&lt;:Union(Float32,Complex{Float64},Complex{Float32},Float64),Ti&lt;:Union(Int64,Int32)}) at linalg/cholmod.jl:1039
det{T}(A::AbstractArray{T,2}) at In[17]:3
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<h3 id="But-what-about-numbers??">But what about numbers??<a class="anchor-link" href="#But-what-about-numbers??">&#182;</a></h3>
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<div class="highlight"><pre><span class="c"># This code is taken 1:1 from boot.jl</span>
<span class="n">baremodule</span> <span class="n">FakeMain</span>
<span class="n">abstract</span> <span class="n">Number</span>
<span class="n">abstract</span> <span class="n">Real</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Number</span>
<span class="n">abstract</span> <span class="n">FloatingPoint</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Real</span>
<span class="n">abstract</span> <span class="n">Integer</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Real</span>
<span class="n">abstract</span> <span class="n">Signed</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Integer</span>
<span class="n">abstract</span> <span class="n">Unsigned</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Integer</span>
<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Float16</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">FloatingPoint</span>
<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Float32</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">FloatingPoint</span>
<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Float64</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">FloatingPoint</span>
<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Bool</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Integer</span>
<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Char</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Integer</span>
<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Int8</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Signed</span>
<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Uint8</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Unsigned</span>
<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Int16</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Signed</span>
<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Uint16</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Unsigned</span>
<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Int32</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Signed</span>
<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Uint32</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Unsigned</span>
<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Int64</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Signed</span>
<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Uint64</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Unsigned</span>
<span class="n">bitstype</span> <span class="mi">128</span> <span class="n">Int128</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Signed</span>
<span class="n">bitstype</span> <span class="mi">128</span> <span class="n">Uint128</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Unsigned</span>
<span class="n">end</span>
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<h3 id="The-promotion-system">The promotion system<a class="anchor-link" href="#The-promotion-system">&#182;</a></h3>
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<div class="highlight"><pre><span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">+</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
<span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">*</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">-</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
<span class="o">/</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">/</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
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Warning: Method definition +(Number,Number) in module Base at promotion.jl:148 overwritten in module Main at In[20]:1.
Warning: Method definition *(Number,Number) in module Base at promotion.jl:149 overwritten in module Main at In[20]:2.
Warning: Method definition -(Number,Number) in module Base at promotion.jl:150 overwritten in module Main at In[20]:3.
Warning: Method definition /(Number,Number)
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/ (generic function with 79 methods)
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<div class="highlight"><pre><span class="n">baremodule</span> <span class="n">FakeBase</span>
<span class="n">promote_type</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">T</span><span class="p">},</span> <span class="p">::</span><span class="n">Type</span><span class="p">{</span><span class="n">S</span><span class="p">})</span> <span class="o">=</span>
<span class="n">promote_result</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">promote_rule</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">),</span> <span class="n">promote_rule</span><span class="p">(</span><span class="n">S</span><span class="p">,</span><span class="n">T</span><span class="p">))</span>
<span class="n">promote_rule</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span> <span class="o">=</span> <span class="bp">None</span>
<span class="n">promote_result</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">)</span> <span class="o">=</span> <span class="n">typejoin</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">)</span>
<span class="c"># If no promote_rule is defined, both directions give None. In that</span>
<span class="c"># case use typejoin on the original types instead.</span>
<span class="n">promote_result</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">T</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="n">S</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="bp">None</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="bp">None</span><span class="p">})</span> <span class="o">=</span> <span class="n">typejoin</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
<span class="n">end</span>
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<h3 id="Example:-Modular-Integers">Example: Modular Integers<a class="anchor-link" href="#Example:-Modular-Integers">&#182;</a></h3>
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<div class="highlight"><pre><span class="n">module</span> <span class="n">ModInts</span>
<span class="n">export</span> <span class="n">ModInt</span>
<span class="kn">import</span> <span class="nn">Base</span><span class="p">:</span> <span class="o">-</span><span class="p">,</span> <span class="o">+</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">convert</span><span class="p">,</span> <span class="n">promote_rule</span><span class="p">,</span> <span class="n">show</span><span class="p">,</span> <span class="n">showcompact</span>
<span class="n">immutable</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Integer</span>
<span class="n">k</span><span class="p">::</span><span class="n">Int</span>
<span class="n">ModInt</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">=</span> <span class="n">new</span><span class="p">(</span><span class="n">k</span> <span class="o">%</span> <span class="n">n</span><span class="p">)</span>
<span class="n">end</span>
<span class="o">-</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="o">-</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
<span class="o">+</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">+</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
<span class="o">-</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">-</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
<span class="o">*</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">*</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
<span class="n">convert</span><span class="p">{</span><span class="n">n</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}},</span> <span class="n">i</span><span class="p">::</span><span class="n">Int</span><span class="p">)</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">i</span><span class="p">)</span>
<span class="n">promote_rule</span><span class="p">{</span><span class="n">n</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}},</span> <span class="p">::</span><span class="n">Type</span><span class="p">{</span><span class="n">Int</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}</span>
<span class="n">show</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span> <span class="n">k</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span> <span class="s">&quot;$(k.k) mod $n&quot;</span><span class="p">)</span>
<span class="n">showcompact</span><span class="p">(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span> <span class="n">k</span><span class="p">::</span><span class="n">ModInt</span><span class="p">)</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
<span class="n">end</span> <span class="c"># module</span>
<span class="n">using</span> <span class="n">ModInts</span>
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<div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">11119</span><span class="p">)</span>
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9 mod 11
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<div class="highlight"><pre><span class="n">b</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">12345</span><span class="p">)</span>
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3 mod 11
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<div class="highlight"><pre><span class="n">a</span><span class="o">+</span><span class="n">b</span>
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1 mod 11
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<div class="highlight"><pre><span class="n">a</span><span class="o">*</span><span class="n">b</span>
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5 mod 11
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<div class="highlight"><pre><span class="n">n</span> <span class="o">=</span> <span class="mi">8</span>
<span class="n">A</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span> <span class="n">rand</span><span class="p">(</span><span class="mi">1</span><span class="p">:</span><span class="mi">100</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
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8x8 Array{ModInt{11},2}:
10 1 1 3 1 9 7 0
2 4 9 3 4 3 10 4
4 0 0 0 10 1 10 1
10 9 5 7 2 5 7 0
6 2 10 0 9 4 10 4
0 9 6 2 3 4 1 2
8 6 10 10 1 7 4 5
9 0 7 1 5 4 1 10
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<div class="highlight"><pre><span class="n">A</span><span class="o">^</span><span class="mi">2</span> <span class="o">+</span> <span class="n">A</span> <span class="o">+</span> <span class="mi">4</span>
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8x8 Array{ModInt{11},2}:
3 6 8 6 1 2 4 0
9 5 10 2 10 10 2 2
10 9 1 9 5 5 8 8
4 4 2 10 2 1 4 10
9 2 5 8 8 7 6 6
0 5 3 1 3 6 0 5
8 1 0 9 7 10 2 10
5 8 3 1 0 8 4 0
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<h3 id="Cailey-Hamilton">Cailey-Hamilton<a class="anchor-link" href="#Cailey-Hamilton">&#182;</a></h3>
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<p>Theorem: Every Matrix satisfies its own characteristic polynomial.</p>
<p>Let's Check</p>
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<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
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in module Base at promotion.jl:151 overwritten in module Main at In[20]:4.
Warning: New definition
promote_rule(Type{Poly{T}},Type{T}) at /Users/kfischer/.julia/Polynomial/src/Polynomial.jl:19
is ambiguous with:
promote_rule(Type{T},Type{NAtype}) at /Users/kfischer/.julia/DataFrames/src/natype.jl:32.
To fix, define
promote_rule(Type{Poly{T}},Type{NAtype})
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<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
<span class="err">λ</span> <span class="o">=</span> <span class="n">Poly</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
<span class="n">p</span><span class="o">=</span><span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="o">-</span><span class="nb">map</span><span class="p">(</span><span class="n">x</span><span class="o">-&gt;</span><span class="err">λ</span><span class="o">*</span><span class="n">x</span><span class="p">,</span><span class="n">eye</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">)))</span>
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Poly(-7 mod 11 + 10 mod 11x^2 + -1 mod 11x^3 + -7 mod 11x^4 + 9 mod 11x^5 + -8 mod 11x^6 + -4 mod 11x^7 + x^8)
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<div class="highlight"><pre><span class="n">papply</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
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8x8 Array{ModInt{11},2}:
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 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 0 0 0 0 0 0
0 0 0 0 0 0 0 0
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<h3 id="Or-with-Smileys">Or with Smileys<a class="anchor-link" href="#Or-with-Smileys">&#182;</a></h3>
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<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base</span><span class="p">:</span> <span class="n">promote_rule</span><span class="p">,</span> <span class="n">convert</span><span class="p">,</span> <span class="n">show</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span>
<span class="n">immutable</span> <span class="n">Face</span> <span class="o">&lt;</span><span class="p">:</span> <span class="n">Number</span>
<span class="n">v</span><span class="p">::</span><span class="n">Bool</span>
<span class="n">end</span>
<span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">v</span><span class="err">$</span><span class="n">y</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
<span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">v</span><span class="o">&amp;</span><span class="n">y</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>
<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
<span class="n">one</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">})</span> <span class="o">=</span> <span class="err">☺</span>
<span class="n">zero</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">})</span> <span class="o">=</span> <span class="err">☹</span>
<span class="n">Base</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span><span class="n">f</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span><span class="n">f</span><span class="o">.</span><span class="n">v</span><span class="err">?</span><span class="s">&#39;☺&#39;</span><span class="p">:</span><span class="s">&#39;☹&#39;</span><span class="p">)</span>
<span class="n">Base</span><span class="o">.</span><span class="n">convert</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">},</span><span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">convert</span><span class="p">(</span><span class="n">Bool</span><span class="p">,</span><span class="n">x</span><span class="p">))</span>
<span class="n">Base</span><span class="o">.</span><span class="n">convert</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Bool</span><span class="p">},</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">v</span>
<span class="n">const</span> <span class="err">☺</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">true</span><span class="p">)</span>
<span class="n">const</span> <span class="err">☹</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">false</span><span class="p">)</span>
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☹
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<div class="highlight"><pre><span class="n">n</span><span class="o">=</span><span class="mi">8</span>
<span class="n">A</span><span class="o">=</span><span class="nb">map</span><span class="p">(</span><span class="n">Face</span><span class="p">,</span><span class="n">randbool</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
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8x8 Array{Face,2}:
☹ ☹ ☹ ☹ ☹ ☺ ☹ ☹
☺ ☺ ☹ ☹ ☹ ☺ ☺ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☺ ☹ ☹ ☹ ☺ ☺ ☹ ☺
☹ ☹ ☺ ☺ ☹ ☹ ☹ ☺
☺ ☺ ☺ ☺ ☺ ☹ ☹ ☺
☹ ☺ ☹ ☺ ☹ ☹ ☺ ☺
☺ ☺ ☺ ☹ ☹ ☹ ☹ ☺
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<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
<span class="err">λ</span> <span class="o">=</span> <span class="n">Poly</span><span class="p">([</span><span class="err">☹</span><span class="p">,</span><span class="err">☺</span><span class="p">])</span>
<span class="err">λ</span><span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">x</span><span class="o">-&gt;</span><span class="err">λ</span><span class="o">*</span><span class="n">x</span><span class="p">,</span><span class="n">eye</span><span class="p">(</span><span class="n">Face</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
<span class="n">p</span><span class="o">=</span><span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="o">-</span><span class="err">λ</span><span class="n">I</span><span class="p">)</span>
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Poly(x^3 + x^5 + x^7 + x^8)
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<div class="highlight"><pre><span class="n">papply</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
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8x8 Array{Face,2}:
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
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<h1 id="How-does-it-work?">How does it work?<a class="anchor-link" href="#How-does-it-work?">&#182;</a></h1>
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<div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">11119</span><span class="p">)</span>
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9 mod 11
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<div class="highlight"><pre><span class="n">b</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">12345</span><span class="p">)</span>
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3 mod 11
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<div class="highlight"><pre><span class="n">a</span><span class="o">+</span><span class="n">b</span>
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1 mod 11
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<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="o">+</span><span class="p">,(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}))</span>
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before the new definition.
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; Function Attrs: sspreq
define %ModInt @&quot;julia_+6067&quot;(%ModInt, %ModInt) #2 {
top:
%2 = extractvalue %ModInt %0, 0, !dbg !27934
%3 = extractvalue %ModInt %1, 0, !dbg !27934
%4 = add i64 %3, %2, !dbg !27934
%5 = srem i64 %4, 11, !dbg !27934
%6 = insertvalue %ModInt undef, i64 %5, 0, !dbg !27934, !julia_type !27939
ret %ModInt %6, !dbg !27934
}
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<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="o">+</span><span class="p">,</span> <span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}))</span>
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.section __TEXT,__text,regular,pure_instructions
Filename: In[22]
Source line: 11
push rbp
mov rbp, rsp
sub rsp, 16
mov rcx, rdi
Source line: 11
movabs rdi, 4348774360
mov rax, qword ptr [rdi]
mov qword ptr [rbp - 8], rax
add rcx, rsi
movabs rdx, 3353953467947191203
mov rax, rcx
imul rdx
mov rax, qword ptr [rdi]
cmp rax, qword ptr [rbp - 8]
jne 29
mov rax, rdx
shr rax, 63
sar rdx
add rdx, rax
imul rax, rdx, 11
sub rcx, rax
mov rax, rcx
add rsp, 16
pop rbp
ret
movabs rax, 140735631254601
call rax
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<h3 id="Parsing">Parsing<a class="anchor-link" href="#Parsing">&#182;</a></h3>
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<div class="highlight"><pre><span class="n">poly</span> <span class="o">=</span> <span class="p">:(</span><span class="n">A</span><span class="o">^</span><span class="mi">3</span><span class="o">+</span><span class="mi">2</span><span class="n">A</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
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:(-(+(^(A,3),*(2,A)),1))
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<div class="highlight"><pre><span class="n">ex</span> <span class="o">=</span> <span class="p">:(</span><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="err">$</span><span class="n">poly</span><span class="p">)</span>
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:(evaluate_a_polynomial(A) = -(+(^(A,3),*(2,A)),1))
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<div class="highlight"><pre><span class="n">dump</span><span class="p">(</span><span class="n">ex</span><span class="p">)</span>
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Expr
head: Symbol =
args: Array(Any,(2,))
1: Expr
head: Symbol call
args: Array(Any,(2,))
1: Symbol evaluate_a_polynomial
2: Symbol A
typ: Any
2: Expr
head: Symbol call
args: Array(Any,(3,))
1: Symbol -
2: Expr
head: Symbol call
args: Array(Any,(3,))
typ: Any
3: Int64 1
typ: Any
typ: Any
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evaluate_a_polynomial (generic function with 1 method)
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<div class="highlight"><pre><span class="n">evaluate_a_polynomial</span> <span class="o">|&gt;</span> <span class="n">methods</span>
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# 1 method for generic function &quot;evaluate_a_polynomial&quot;:
evaluate_a_polynomial(A)
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Array{Face,2}
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ModInt{11} (constructor with 1 method)
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<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
return -(+(^(A,3),*(2,A)),1)
end)))
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<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
return -(+(^(A,3),*(2,A)),1)
end)))
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<h2 id="So-if-there's-no-difference,-why-pass-in-the-type?">So if there's no difference, why pass in the type?<a class="anchor-link" href="#So-if-there's-no-difference,-why-pass-in-the-type?">&#182;</a></h2>
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<div class="highlight"><pre><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="o">=</span> <span class="mi">14</span><span class="n">x</span><span class="o">^</span><span class="mi">6</span><span class="o">+</span><span class="mi">3</span><span class="n">x</span><span class="o">^</span><span class="mi">2</span><span class="o">+</span><span class="mi">2</span><span class="n">x</span><span class="o">+</span><span class="mi">3</span>
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evaluate_a_polynomial (generic function with 2 methods)
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<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:x}, {{},{{:x,:Any,0}},{}}, quote # In[50], line 1:
return +(*(14,^(x,6)),*(3,^(x,2)),*(2,x),3)
end)))
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<div class="highlight"><pre><span class="n">function</span> <span class="n">a_more_complicated_function</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">sum</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">A</span><span class="p">))</span> <span class="o">&gt;</span> <span class="mi">0</span>
<span class="k">return</span> <span class="p">:</span><span class="n">ok</span>
<span class="k">else</span>
<span class="k">return</span> <span class="mi">0</span>
<span class="n">end</span>
<span class="n">end</span>
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a_more_complicated_function (generic function with 1 method)
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<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">a_more_complicated_function</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote # In[52], line 2:
unless &gt;(sum(sum(A)),0) goto 0 # line 3:
return :ok
goto 1
0: # In[52], line 5:
return 0
1:
end)))
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<h1 id="Type-inference">Type inference<a class="anchor-link" href="#Type-inference">&#182;</a></h1>
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<div class="highlight"><pre><span class="n">code_typed</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote
return -(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None
end)))
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<div class="highlight"><pre><span class="n">foo</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="n">a_more_complicated_function</span><span class="p">(</span><span class="n">det</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">A</span><span class="p">)))</span>
<span class="n">code_typed</span><span class="p">(</span><span class="n">foo</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote # In[55], line 1:
return a_more_complicated_function(det(-(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None)::None)::None
end)))
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<h1 id="LLVM-IR-Generation">LLVM IR Generation<a class="anchor-link" href="#LLVM-IR-Generation">&#182;</a></h1>
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<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
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; Function Attrs: sspreq
define %ModInt @julia_evaluate_a_polynomial(%ModInt) #2 {
top:
%1 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 6), !dbg !28559, !julia_type !28564
%2 = extractvalue %ModInt %1, 0, !dbg !28559
%3 = mul i64 %2, 3, !dbg !28559
%4 = srem i64 %3, 11, !dbg !28559
%5 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 2), !dbg !28559, !julia_type !28564
%6 = extractvalue %ModInt %5, 0, !dbg !28559
%7 = mul i64 %6, 3, !dbg !28559
%8 = srem i64 %7, 11, !dbg !28559
%9 = add i64 %8, %4, !dbg !28559
%10 = srem i64 %9, 11, !dbg !28559
%11 = extractvalue %ModInt %0, 0, !dbg !28559
%12 = shl i64 %11, 1, !dbg !28559
%13 = srem i64 %12, 11, !dbg !28559
%14 = add i64 %13, %10, !dbg !28559
%15 = srem i64 %14, 11, !dbg !28559
%16 = add i64 %15, 3, !dbg !28559
%17 = srem i64 %16, 11, !dbg !28559
%18 = insertvalue %ModInt undef, i64 %17, 0, !dbg !28559, !julia_type !28564
ret %ModInt %18, !dbg !28559
}
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<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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; Function Attrs: sspreq
define %jl_value_t* @julia_evaluate_a_polynomial6230(%jl_value_t*, %jl_value_t**, i32) #2 {
top:
%3 = alloca [4 x %jl_value_t*], align 8
%.sub = getelementptr inbounds [4 x %jl_value_t*]* %3, i64 0, i64 0
%4 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 2, !dbg !28571
store %jl_value_t* inttoptr (i64 4 to %jl_value_t*), %jl_value_t** %.sub, align 8
%5 = load %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
%6 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 1, !dbg !28571
%.c = bitcast %jl_value_t** %5 to %jl_value_t*, !dbg !28571
store %jl_value_t* %.c, %jl_value_t** %6, align 8, !dbg !28571
store %jl_value_t** %.sub, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
store %jl_value_t* null, %jl_value_t** %4, align 8
%7 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 3
store %jl_value_t* null, %jl_value_t** %7, align 8
%8 = load %jl_value_t** %1, align 8, !dbg !28571
%9 = call %jl_value_t* @&quot;julia_^6025&quot;(%jl_value_t* %8, i64 3), !dbg !28571
store %jl_value_t* %9, %jl_value_t** %4, align 8, !dbg !28571
call void @&quot;julia_.*6231&quot;(i64 2, %jl_value_t* %8), !dbg !28571
store %jl_value_t* inttoptr (i64 140620606479776 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
%10 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629152784 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
store %jl_value_t* %10, %jl_value_t** %4, align 8, !dbg !28571
store %jl_value_t* inttoptr (i64 140620605942320 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
%11 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629567872 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
%12 = load %jl_value_t** %6, align 8, !dbg !28571
%13 = getelementptr inbounds %jl_value_t* %12, i64 0, i32 0, !dbg !28571
store %jl_value_t** %13, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
ret %jl_value_t* %11, !dbg !28571
}
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<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
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.section __TEXT,__text,regular,pure_instructions
Filename: no file
Source line: 0
push rbp
mov rbp, rsp
push r15
push r14
push r12
push rbx
sub rsp, 48
movabs r14, 4348774360
mov rax, qword ptr [r14]
mov qword ptr [rbp - 40], rax
mov qword ptr [rbp - 72], 4
Source line: 0
movabs r15, 4348775232
mov rax, qword ptr [r15]
mov qword ptr [rbp - 64], rax
lea rax, qword ptr [rbp - 72]
mov qword ptr [r15], rax
vxorps xmm0, xmm0, xmm0
vmovups xmmword ptr [rbp - 56], xmm0
movabs rax, 4380607552
mov rbx, qword ptr [rsi]
mov rdi, rbx
mov esi, 3
call rax
movabs rcx, 4380609184
mov qword ptr [rbp - 56], rax
mov edi, 2
mov rsi, rbx
call rcx
lea rbx, qword ptr [rbp - 56]
movabs r12, 4318407168
movabs rax, 140620606479776
mov qword ptr [rbp - 48], rax
movabs rdi, 140620629152784
mov rsi, rbx
mov edx, 2
call r12
movabs rcx, 140620605942320
mov qword ptr [rbp - 56], rax
mov qword ptr [rbp - 48], rcx
movabs rdi, 140620629567872
mov rsi, rbx
mov edx, 2
call r12
mov rcx, qword ptr [rbp - 64]
mov qword ptr [r15], rcx
mov rcx, qword ptr [r14]
cmp rcx, qword ptr [rbp - 40]
jne 13
add rsp, 48
pop rbx
pop r12
pop r14
pop r15
pop rbp
ret
movabs rax, 140735631254601
call rax
</pre>
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<h3 id="Calling-C-and-Fortran">Calling C and Fortran<a class="anchor-link" href="#Calling-C-and-Fortran">&#182;</a></h3>
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<div class="highlight"><pre><span class="n">pid</span><span class="p">()</span> <span class="o">=</span> <span class="n">ccall</span><span class="p">(:</span><span class="n">getpid</span><span class="p">,</span> <span class="n">Int32</span><span class="p">,</span> <span class="p">())</span>
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pid (generic function with 1 method)
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<div class="highlight"><pre><span class="n">pid</span><span class="p">()</span>
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46441
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<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">pid</span><span class="p">,())</span>
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; Function Attrs: sspreq
define i32 @julia_pid6253() #2 {
top:
%0 = call i32 @getpid(), !dbg !28644
ret i32 %0, !dbg !28644
}
</pre>
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<h1 id="Integrating-LLVM-and-Julia">Integrating LLVM and Julia<a class="anchor-link" href="#Integrating-LLVM-and-Julia">&#182;</a></h1>
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<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base.llvmcall</span>
<span class="n">simd</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">})</span> <span class="o">=</span> <span class="n">llvmcall</span><span class="p">(</span>
<span class="sd">&quot;&quot;&quot;</span>
<span class="sd">%3 = add &lt;4 x i64&gt; %1, %0</span>
<span class="sd">ret &lt;4 x i64&gt; %3</span>
<span class="sd">&quot;&quot;&quot;</span><span class="p">,</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">}),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">),</span><span class="n">x</span><span class="p">)</span>
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simd (generic function with 1 method)
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<div class="highlight"><pre><span class="n">simd</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
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(3,5,7,9)
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<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">simd</span><span class="p">,(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},))</span>
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; Function Attrs: sspreq
define &lt;4 x i64&gt; @julia_simd6273(&lt;4 x i64&gt;) #2 {
top:
%1 = add &lt;4 x i64&gt; %0, &lt;i64 1, i64 2, i64 3, i64 4&gt;
ret &lt;4 x i64&gt; %1, !dbg !28729
}
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<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="n">simd</span><span class="p">,(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},))</span>
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.section __TEXT,__text,regular,pure_instructions
Filename: In[62]
Source line: 2
push rbp
mov rbp, rsp
sub rsp, 16
movabs rax, 4348774360
mov rcx, qword ptr [rax]
mov qword ptr [rbp - 8], rcx
movabs rcx, 4624115088
vpaddq xmm1, xmm0, xmmword ptr [rcx]
mov rax, qword ptr [rax]
cmp rax, qword ptr [rbp - 8]
jne 32
vextractf128 xmm0, ymm0, 1
movabs rax, 4624115072
vpaddq xmm0, xmm0, xmmword ptr [rax]
vinsertf128 ymm0, ymm1, xmm0, 1
Source line: 2
add rsp, 16
pop rbp
ret
movabs rax, 140735631254601
vzeroupper
call rax
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