Proposed resolution:

This wording is relative to N4849.

1. Modify [rand.req.urng] as follows:

   1 A uniform random bit generator g of type G is a function object returning unsigned integer values such that each value in the range of possible results has (ideally) equal probability of being returned. [Note: The degree to which g's results approximate the ideal is often determined statistically.—end note]

   template<class G>
     concept uniform_random_bit_generator =
       invocable<G&> && unsigned_integral<invoke_result_t<G&>> &&
       requires {
         { G::min() } -> same_as<invoke_result_t<G&>>;
         { G::max() } -> same_as<invoke_result_t<G&>>;
         requires bool_constant<(G::min() < G::max())>::value;
       };
   

   -2- Let g be an object of type G. G models uniform_random_bit_generator only if

   (2.1) — both G​::​min() and G​::​max() are constant expressions ([expr.const]),

   (2.2) — G​::​min() < G​::​max(),

   (2.3) — G​::​min() <= g(),

   (2.4) — g() <= G​::​max(), and

   (2.5) — g() has amortized constant complexity.

   3 A class G meets the uniform random bit generator requirements if G models uniform_random_bit_generator, invoke_­result_­t<G&> is an unsigned integer type ([basic.fundamental]), and G provides a nested typedef-name result_­type that denotes the same type as invoke_­result_­t<G&>.

[ 2020-02 Status to Immediate on Thursday night in Prague. ]

[ 2020-02-13; Prague ]

LWG provided some improved wording.

[ 2018-08-20 Priority set to 3 after reflector discussion ]

This wording is relative to N4791.

1. Modify [rand.req.urng] as follows:

   1 A uniform random bit generator g of type G is a function object returning unsigned integer values such that each value in the range of possible results has (ideally) equal probability of being returned. [Note: The degree to which g's results approximate the ideal is often determined statistically.—end note]

   template<auto> struct require-constant; // exposition-only
   
   template<class G>
     concept UniformRandomBitGenerator =
       Invocable<G&> && UnsignedIntegral<invoke_result_t<G&>> &&
       requires {
         { G::min() } -> Same<invoke_result_t<G&>>;
         { G::max() } -> Same<invoke_result_t<G&>>;
         typename require-constant<G::min()>;
         typename require-constant<G::max()>;
         requires G::min() < G::max();
       };
   

   2 Let g be an object of type G. G models UniformRandomBitGenerator only if

   (2.1) — both G​::​min() and G​::​max() are constant expressions ([expr.const]),

   (2.2) — G​::​min() < G​::​max(),

   (2.3) — G​::​min() <= g(),

   (2.4) — g() <= G​::​max(), and

   (2.5) — g() has amortized constant complexity.

   3 A class G meets the uniform random bit generator requirements if G models UniformRandomBitGenerator, invoke_­result_­t<G&> is an unsigned integer type ([basic.fundamental]), and G provides a nested typedef-name result_­type that denotes the same type as invoke_­result_­t<G&>.

[rand.req.urng] paragraph 2 specifies axioms for the UniformRandomBitGenerator concept:

2 Let g be an object of type G. G models UniformRandomBitGenerator only if

(2.1) — both G::min() and G::max() are constant expressions ([expr.const]),

(2.2) — G::min() < G::max(),

(2.3) — G::min() <= g(),

(2.4) — g() <= G::max(), and

(2.5) — g() has amortized constant complexity.

Bullets 2.1 and 2.2 are both compile-time requirements that ought to be validated by the concept.