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Fix unidirectionally broadcast the shapes steps (#663)
SHA: 4eda710 Reason: push, by fdwr Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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<h3 class="heading settled" data-level="8.1" id="algorithms-broadcasting"><span class="secno">8.1. </span><span class="content">Broadcasting</span><a class="self-link" href="#algorithms-broadcasting"></a></h3>
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<p>Broadcasting refers to how operations treat tensors with different shapes, and follow the precedent set by <a data-link-type="biblio" href="#biblio-numpy-broadcasting-rule" title="General Broadcasting Rules of NumPy">[numpy-broadcasting-rule]</a>.</p>
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<details class="algorithm" data-algorithm="unidirectionally broadcasting the shapes" open>
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<summary> To <dfn class="dfn-paneled" data-dfn-type="dfn" data-lt="unidirectionally broadcasting the shapes" data-noexport id="unidirectionally-broadcasting-the-shapes">unidirectionally broadcast the shapes</dfn> <var>shapeA</var> and <var>shapeB</var>, perform the following steps. <var>shapeA</var> and <var>shapeB</var> are <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤③">lists</a> of positive integers, representing the dimensions of tensors, and the steps return a new <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤④">list</a> of positive integers, or failure. </summary>
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<summary> To <dfn class="dfn-paneled" data-dfn-type="dfn" data-lt="unidirectionally broadcasting the shapes" data-noexport id="unidirectionally-broadcasting-the-shapes">unidirectionally broadcast the shapes</dfn> <var>shapeFrom</var> and <var>shapeTo</var>, perform the following steps. <var>shapeFrom</var> and <var>shapeTo</var> are <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤③">lists</a> of positive integers, representing the dimensions of tensors, and the steps return a new <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤④">list</a> of positive integers, or failure. </summary>
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<ol>
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<li data-md>
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<p>Let <var>sizeA</var> be <var>shapeA</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑥">size</a>.</p>
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<p>Let <var>sizeFrom</var> be <var>shapeFrom</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑥">size</a>.</p>
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<li data-md>
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<p>Let <var>sizeB</var> be <var>shapeB</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑦">size</a>.</p>
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<p>Let <var>sizeTo</var> be <var>shapeTo</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑦">size</a>.</p>
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<p>If <var>sizeB</var> > <var>sizeA</var>, then return failure.</p>
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<p>If <var>sizeFrom</var> > <var>sizeTo</var>, then return failure.</p>
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<li data-md>
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<p>Let <var>paddedB</var> be a <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-clone" id="ref-for-list-clone⑨">clone</a> of <var>shapeB</var>.</p>
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<p>Let <var>paddedShapeFrom</var> be a <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-clone" id="ref-for-list-clone⑨">clone</a> of <var>shapeFrom</var>.</p>
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<li data-md>
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<p>While <var>paddedB</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑧">size</a> is less than <var>sizeA</var>, <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-prepend" id="ref-for-list-prepend">prepend</a> 1 to <var>paddedB</var>.</p>
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<p>While <var>paddedShapeFrom</var>’s <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-size" id="ref-for-list-size④⑧">size</a> is less than <var>sizeTo</var>, <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-prepend" id="ref-for-list-prepend">prepend</a> 1 to <var>paddedShapeFrom</var>.</p>
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<li data-md>
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<p>Let <var>outputShape</var> be a new <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤⑤">list</a>.</p>
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<p><a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-iterate" id="ref-for-list-iterate①⑤">For each</a> <var>index</var> in <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#the-range" id="ref-for-the-range①④">the range</a> 0 to <var>sizeA</var>, exclusive:</p>
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<p><a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-iterate" id="ref-for-list-iterate①⑤">For each</a> <var>index</var> in <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#the-range" id="ref-for-the-range①④">the range</a> 0 to <var>sizeTo</var>, exclusive:</p>
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<p>Let <var>dimA</var> be <var>shapeA</var>[<var>index</var>].</p>
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<p>Let <var>dimFrom</var> be <var>paddedShapeFrom</var>[<var>index</var>].</p>
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<li data-md>
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<p>Let <var>dimB</var> be <var>paddedB</var>[<var>index</var>].</p>
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<p>Let <var>dimTo</var> be <var>shapeTo</var>[<var>index</var>].</p>
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<li data-md>
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<p>If <var>dimA</var> is not equal to <var>dimB</var> and <var>dimA</var> is not equal to 1, then return failure.</p>
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<p>If <var>dimTo</var> is not equal to <var>dimFrom</var> and <var>dimFrom</var> is not equal to 1, then return failure.</p>
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<p><a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-append" id="ref-for-list-append③">Append</a> <var>dimA</var> to <var>outputShape</var>.</p>
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<p><a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list-append" id="ref-for-list-append③">Append</a> <var>dimTo</var> to <var>outputShape</var>.</p>
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<p>Return <var>outputShape</var>.</p>
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</details>
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<p class="algorithm" data-algorithm="unidirectionally broadcastable"> <var>shapeA</var> is <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="unidirectionally-broadcastable">unidirectionally broadcastable</dfn> to <var>shapeB</var> if <a data-link-type="dfn" href="#unidirectionally-broadcasting-the-shapes" id="ref-for-unidirectionally-broadcasting-the-shapes②">unidirectionally broadcasting the shapes</a> <var>shapeA</var> and <var>shapeB</var> does not result in failure. </p>
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<p class="algorithm" data-algorithm="unidirectionally broadcastable"> <var>shapeFrom</var> is <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="unidirectionally-broadcastable">unidirectionally broadcastable</dfn> to <var>shapeTo</var> if <a data-link-type="dfn" href="#unidirectionally-broadcasting-the-shapes" id="ref-for-unidirectionally-broadcasting-the-shapes②">unidirectionally broadcasting the shapes</a> <var>shapeFrom</var> and <var>shapeTo</var> does not result in failure. </p>
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<details class="algorithm" data-algorithm="bidirectionally broadcasting the shapes" open>
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<summary> To <dfn class="dfn-paneled" data-dfn-type="dfn" data-lt="bidirectionally broadcasting the shapes" data-noexport id="bidirectionally-broadcasting-the-shapes">bidirectionally broadcast the shapes</dfn> <var>shapeA</var> and <var>shapeB</var>, perform the following steps. <var>shapeA</var> and <var>shapeB</var> are <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤⑥">lists</a> of positive integers, representing the dimensions of tensors, and the steps return a new <a data-link-type="dfn" href="https://infra.spec.whatwg.org/#list" id="ref-for-list⑤⑦">list</a> of positive integers, or failure. </summary>
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