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can generate_canonical return 1.0 exactly?

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The text in 26.5.7.2 [rand.util.canonical] says that 0 <= tj < 1.  But
it seems to me that if arithmetic with RealType can round upwards,
then a result of 1.0 is possible.  All that's required is for the
conversion of (gi - g.min()) to RealType to round up to R.

Here's a demonstration, using gcc-4.9.0.  I expect it to hold on any
machine with IEEE floats.


drdlogin0039$ cat canbeone.cpp
#include <random>
#include <iostream>

int main(int argc, char **argv){
    std::mt19937 e, f;
    unsigned long long n = 60571531ull;

    e.discard(n);
    unsigned u = e();
    std::cout << "after discard(" << n << ") engine returns " <<
std::hex << u << "\n";

    f.discard(n);
    std::cout << "calling std::generate_canonical<float, 32>:\n";
    float v = std::generate_canonical<float, 32>(f);
    if( v == 1.0f ){
        std::cout << "v==1.0f exactly\n";
    }else{
        std::cout << "v=" << v << "\n";
    }
    return 0;
}
drdlogin0039$ dw -m gcc/4.9.0-28B/bin g++ canbeone.cpp -std=c++11 -Wall
drdlogin0039$ ./a.out
after discard(60571531) engine returns ffffffe1
calling std::generate_canonical<float, 32>:
v==1.0f exactly
drdlogin0039$


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can generate_canonical return 1.0 exactly? john.salmon@googlemail.com - 2014-05-30 15:33 -0600

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