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    <p>If <code>x</code> is our input...</p> <p>If <code>x &gt; INT_MAX</code>, we want to find a constant <code>k</code> such that <code>0</code> &lt; <code>x - k*INT_MAX</code> &lt; <code>INT_MAX</code>.</p> <p>This is easy -- <code>unsigned int k = x / INT_MAX;</code>. Then, let <code>unsigned int x2 = x - k*INT_MAX;</code></p> <p>We can now cast <code>x2</code> to <code>int</code> safely. Let <code>int x3 = static_cast&lt;int&gt;(x2);</code></p> <p>We now want to subtract something like <code>UINT_MAX - k * INT_MAX + 1</code> from <code>x3</code>, if <code>k &gt; 0</code>.</p> <p>Now, on a 2s complement system, so long as <code>x &gt; INT_MAX</code>, this works out to:</p> <pre><code>unsigned int k = x / INT_MAX; x -= k*INT_MAX; int r = int(x); r += k*INT_MAX; r -= UINT_MAX+1; </code></pre> <p>Note that <code>UINT_MAX+1</code> is zero in C++ guaranteed, the conversion to int was a noop, and we subtracted <code>k*INT_MAX</code> then added it back on "the same value". So an acceptable optimizer should be able to erase all that tomfoolery!</p> <p>That leaves the problem of <code>x &gt; INT_MAX</code> or not. Well, we create 2 branches, one with <code>x &gt; INT_MAX</code>, and one without. The one without does a strait cast, which the compiler optimizes to a noop. The one with ... does a noop after the optimizer is done. The smart optimizer realizes both branches to the same thing, and drops the branch.</p> <p>Issues: if <code>UINT_MAX</code> is really large relative to <code>INT_MAX</code>, the above might not work. I am assuming that <code>k*INT_MAX &lt;= UINT_MAX+1</code> implicitly.</p> <p>We could probably attack this with some enums like:</p> <pre><code>enum { divisor = UINT_MAX/INT_MAX, remainder = UINT_MAX-divisor*INT_MAX }; </code></pre> <p>which work out to 2 and 1 on a 2s complement system I believe (are we guaranteed for that math to work? That's tricky...), and do logic based on these that easily optimize away on non-2s complement systems...</p> <p>This also opens up the exception case. It is only possible if UINT_MAX is much larger than (INT_MIN-INT_MAX), so you can put your exception code in an if block asking exactly that question somehow, and it won't slow you down on a traditional system.</p> <p>I'm not exactly sure how to construct those compile-time constants to deal correctly with that.</p>
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    1. POEfficient unsigned-to-signed cast avoiding implementation-defined behavior
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    1. USYakk - Adam Nevraumont
    1. USYakk - Adam Nevraumont
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    1. CO`UINT_MAX` cannot be small relative to `INT_MAX`, because the spec guarantees that every positive signed int is representable as an unsigned int. But `UINT_MAX+1` is zero on every system; unsigned arithmetic is always modulo `UINT_MAX+1`. Still there might be a kernel of a workable approach here...
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      1. USNemo
    2. CO@Nemo Just following this thread, so pardon my potentially obvious question: Is your statement "`UINT_MAX+1` is zero on every system` established in the '03-spec? If so, is there a specific subsection I should be looking under? Thanks.
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      1. USWhozCraig
    3. CO@WhozCraig: Section 3.9.1 paragraph 4: "Unsigned integers, declared unsigned, shall obey the laws of arithmetic modulo 2^n where n is the number of bits in the value representation of that particular size of integer", with a footnote saying "This implies that unsigned arithmetic does not overflow because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the largest value that can be represented by the resulting unsigned integer type." Basically unsigned is specified to work the way you want/expect.
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      1. USNemo
 

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