positional: Multi-Radix Positional Integer

Why

integer is binary and edecimal is decimal. Both are the same idea at a different radix, and hard-coding the radix into each type means the arithmetic gets written twice.

positional parameterises it: a sign-magnitude integer in any radix, with one implementation of the carry-propagating algorithms serving all of them. That makes it the natural type for teaching how positional arithmetic works – showing the same addition in base 2, base 10 and base 16 – and for checking radix-specific code against an independent implementation.

#include <universal/number/positional/positional.hpp>
using namespace sw::universal;

positional<10, 10> a;   // 10 digits, radix 10
positional<16,  2> b;   // 16 digits, radix 2

What

template<unsigned ndigits, unsigned radix>
class positional;

ndigits is the number of digit positions; radix is the base each digit counts in. The value is sign-magnitude, so there is no two’s-complement wrap and no most-negative-value asymmetry – the sign is carried separately from the digits.

Property	Value
Representation	sign + ndigits digits in radix
Width	fixed at compile time
Radix	any, set by template parameter

It is built on blockdigit, the internal digit-vector engine that also backs the decimal types, so a bug fixed in one is fixed in all of them.

Behavioural switches

Like the other fixed-size integer types, positional takes its switches before the header:

• literals in logic and arithmetic operators – enabled by default
• throwing arithmetic exceptions – disabled by default; the default behaviour is a diagnostic on stderr for divide and modulo by zero

Both default inside the core header rather than the umbrella, so a translation unit that includes core.hpp directly gets the same behaviour.

Related

• integer – the binary case, optimised
• edecimal – adaptive-width decimal
• dfixpnt – decimal fixed-point