Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p><strong>1. Detecting the overflow</strong>:</p> <pre><code>x = a * b; if (a != 0 &amp;&amp; x / a != b) { // overflow handling } </code></pre> <p>Edit: Fixed division by <code>0</code> (thanks Mark!)</p> <p><strong>2. Computing the carry</strong> is quite involved. One approach is to split both operands into half-words, then apply <a href="https://en.wikipedia.org/wiki/Multiplication_algorithm#Long_multiplication" rel="nofollow noreferrer">long multiplication</a> to the half-words:</p> <pre><code>uint64_t hi(uint64_t x) { return x &gt;&gt; 32; } uint64_t lo(uint64_t x) { return ((1L &lt;&lt; 32) - 1) &amp; x; } void multiply(uint64_t a, uint64_t b) { // actually uint32_t would do, but the casting is annoying uint64_t s0, s1, s2, s3; uint64_t x = lo(a) * lo(b); s0 = lo(x); x = hi(a) * lo(b) + hi(x); s1 = lo(x); s2 = hi(x); x = s1 + lo(a) * hi(b); s1 = lo(x); x = s2 + hi(a) * hi(b) + hi(x); s2 = lo(x); s3 = hi(x); uint64_t result = s1 &lt;&lt; 32 | s0; uint64_t carry = s3 &lt;&lt; 32 | s2; } </code></pre> <p>To see that none of the partial sums themselves can overflow, we consider the worst case:</p> <pre><code> x = s2 + hi(a) * hi(b) + hi(x) </code></pre> <p>Let <code>B = 1 &lt;&lt; 32</code>. We then have</p> <pre><code> x &lt;= (B - 1) + (B - 1)(B - 1) + (B - 1) &lt;= B*B - 1 &lt; B*B </code></pre> <p>I believe this will work - at least it handles Sjlver's test case. Aside from that, it is untested (and might not even compile, as I don't have a C++ compiler at hand anymore).</p>
    singulars
    1. This table or related slice is empty.
    1. POCatch and compute overflow during multiplication of two large integers
      singulars
      1. PTQuestion
    1. PTAnswer
    1. USplasmacel
    1. USmeriton
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. POCatch and compute overflow during multiplication of two large integers
      singulars
      1. PTQuestion
    1. This table or related slice is empty.
    1. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    1. COThe problem with this answer is that signed integer overflow causes undefined behaviour in C - you can't rely on your code continuing to execute correctly (or at all!) after such an event. (On some platforms, overflow triggers a program abort in a similar way to divide-by-zero). sergdev's answer is the right one.
      singulars
      1. PO
      1. UScaf
    2. COcaf’s comment is incorrect. The C99 standard mandates that “A computation involving unsigned operands can never 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 type.” As such, meriton’s solution is valid in theory as well as practice.
      singulars
      1. PO
      1. USJens Ayton
    3. COAre you absolutely sure this is correct? Consider a = 7 and b = 613612691. This computation overflows (for 32 bits), but the carry (according to you) is zero. Sorry to come back to this after more than three years... but it would be sad if StackOverflow had a wrong accepted answer.
      singulars
      1. PO
      1. USSjlver
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload