<div dir="ltr"><div>Right, these issues were discussed when the proposal was introduced and reviewed three times. In brief, what was once proposed as `Integer` was renamed `BinaryInteger` to avoid confusion in name between `Integer` and `Int`. It was also found to better reflect the semantics of the protocol, as certain functions treated the value not merely as an integer but operated specifically on its binary representation (for instance, the bitwise operators).</div><div><br></div><div>Do not confuse integers from their representation. Integers have no intrinsic radix and all integers have a binary representation. This is distinct from floating-point protocols, because many real values representable exactly as a decimal floating-point value cannot be represented exactly as a binary floating-point value.</div><div><br></div><div>To your specific question about bitwise operators: their semantics are with respect to the two's-complement binary representation of the integer regardless of the actual internal representation. `~` returns the one's complement of the two's-complement binary representation of the integer. FWIW, this is exactly what `mpn_com()` does in GNU MP for arbitrary-precision integers.</div><div><br></div><div><br></div>On Tue, Oct 31, 2017 at 7:23 PM, Max Moiseev via swift-evolution <span dir="ltr"><<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>></span> wrote:<br><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word;line-break:after-white-space">Just for the reference. There was a lengthy discussion here in the mailing list back when the proposal was introduced:<div><a href="https://lists.swift.org/pipermail/swift-evolution/Week-of-Mon-20170109/thread.html#30191" target="_blank">https://lists.swift.org/<wbr>pipermail/swift-evolution/<wbr>Week-of-Mon-20170109/thread.<wbr>html#30191</a></div><div><br></div><div>Max</div><div><div class="h5"><div><br></div><div><div><blockquote type="cite"><div>On Oct 31, 2017, at 5:15 PM, Daryle Walker via swift-evolution <<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:</div><br class="m_6876455343630890721Apple-interchange-newline"><div><div>Looking at Apple’s Swift (4) docs at their SDK site, shouldn’t there be an “Integer” protocol between Numeric and BinaryInteger? Without that, there’s no solution for Integer types that are either a non-binary radix or a non-radix system (besides being over-broad with Numeric).<br><br>What would move there are: isSigned, quotientAndRemainder, signum, %, %=, /, and /=.<br><br>Also, how is ~ supposed to work in a BinaryInteger that is not a FixedWidthInteger? Extend the high bits to infinity? Maybe that operator should move to the derived protocol.<br><br>Oh, why can’t a non-binary Integer type be fixed-width? FixedWidthInteger should be renamed “FixedWidthBinaryInteger,” which derives from BinaryInteger and a new version of FixedWidthInteger. The new version peels off: max, min, addingReportingOverflow, dividedReportingOverflow, dividingFullWidth, multipliedFullWidth, multipliedReportingOverflow, remainderReportingOverflow, and subtractingReportingOverflow. There’s also a “digitWidth” type property, analogous to “bitWidth”.<br><br>Sent from my iPad<br>______________________________<wbr>_________________<br>swift-evolution mailing list<br><a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a><br><a href="https://lists.swift.org/mailman/listinfo/swift-evolution" target="_blank">https://lists.swift.org/<wbr>mailman/listinfo/swift-<wbr>evolution</a><br></div></div></blockquote></div><br></div></div></div></div><br>______________________________<wbr>_________________<br>
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