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copied!<p>After reading the standard a bit more and thinking about this, I believe I have the best answer, but I am not certain.</p> <p>First, the definition of <code>digits</code>, taken from the latest C++14 draft standard, N3797, § 18.3.2.4:</p> <blockquote> <p><code>static constexpr int digits;</code></p> <p>8 Number of <code>radix</code> digits that can be represented without change.</p> <p>9 For integer types, the number of non-sign bits in the representation.</p> <p>10 For floating point types, the number of <code>radix</code> digits in the mantissa</p> </blockquote> <p>The case of <code>bounded::integer<-100, 5></code> is the same as for <code>bounded::integer<0, 5></code>, which would give a value of <code>2</code>.</p> <p>For the case of <code>bounded::integer<16, 19></code>, <code>digits</code> should be defined as <code>0</code>. Such a class cannot even represent a 1-bit number (since <code>0</code> and <code>1</code> aren't in the range), and according to 18.3.2.7.1:</p> <blockquote> <p>All members shall be provided for all specializations. However, many values are only required to be meaningful under certain conditions (for example, <code>epsilon()</code> is only meaningful if <code>is_integer</code> is <code>false</code>). Any value that is not "meaningful" shall be set to 0 or false.</p> </blockquote> <p>I believe that any integer-like class which does not have <code>0</code> as a possible value cannot meaningfully compute <code>digits</code> and <code>digits10</code>.</p> <p>Another possible answer is to use an information theoretic definition of digits. However, this is not consistent with the values for the built-in integers. The description explicitly leaves out sign bits, but those would still be considered a single bit of information, so I feel that rules out this interpretation. It seems that this exclusion of the sign bit also means that I have to take the smaller in magnitude of the negative end and the positive end of the range for the first number, which is why I believe that the first question is equivalent to <code>bounded::integer<0, 5></code>. This is because you are only guaranteed 2 bits can be stored without loss of data. You can potentially store up to 6 bits as long as your number is negative, but in general, you only get 2.</p> <p><code>bounded::integer<16, 19></code> is much trickier, but I believe the interpretation of "not meaningful" makes more sense than shifting the value over and giving the same answer as if it were <code>bounded::integer<0, 3></code>, which would be <code>2</code>.</p> <p>I believe this interpretation follows from the standard, is consistent with other integer types, and is the least likely to confuse the users of such a class.</p> <p>To answer the question of the use cases of <code>digits</code>, a commenter mentioned radix sort. A base-2 radix sort might expect to use the value in <code>digits</code> to sort a number. This would be fine if you set <code>digits</code> to <code>0</code>, as that indicates an error condition for attempting to use such a radix sort, but can we do better while still being in line with built-in types?</p> <p>For unsigned integers, radix sort that depends on the value of <code>digits</code> works just fine. <code>uint8_t</code> has <code>digits == 8</code>. However, for signed integers, this wouldn't work: <code>std::numeric_limits<int8_t>::digits == 7</code>. You would also need to sort on that sign bit, but <code>digits</code> doesn't give you enough information to do so.</p>

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