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Question

Is std::numeric_limits<float>::is_iec559 + std::numeric_limits<float>::digits == 24 enough to ensure(1) that float is binary32(2) in IEEE 754 ? Same for double with ... digits == 53 ?

1. In any case including the weirdest implementations still respecting the C++ standard.
2. "binary32" is a specific representation of floating points in the IEEE 754 standard, I don't mean "stored in 32 bits".

Edit : + std::numeric_limits<float>::max_exponent - 1 == 127

Edit : Are there any other ways ? If yes, which one is "the best" ?

Answer 1

If I understand your question correctly, it boils down to "are there other IEC559/IEEE754 formats besides binary32 which also have a 24 bits mantissa"? The answer to that is No.

You need the iec559 part as that's what connects the C++ standard to the IEC standard. Without it, anything goes. Knowing it's IEC559, the digits test is straightforward.

But you want to make sure that the "24" is actually counted in bits, so you would want to check radix==2 as well. That's the binary in binary32 . Alternatively, you can check if sizeof(float)*CHAR_BIT==32 . If radix is larger than two, you can't fit 24 digits in 32 bits.

Answer 2

You can use traits class to check your representation matches some expectations.

Here are the traits used to test your representation:

namespace num {
    template <std::size_t N> struct ieee754_traits;
    
    template <> struct ieee754_traits<4> {
      using unsigned_type = uint32_t;
      static constexpr std::size_t sign_size = 1;
      static constexpr std::size_t exp_size = 8;
      static constexpr std::size_t mant_size = 23;
      static constexpr std::size_t exp_shift = 127;
      static constexpr int32_t exp_mask = 0xFF;
      static constexpr unsigned_type mant_mask = 0x7FFFFF;
    };
    
    template <> struct ieee754_traits<8> {
      using unsigned_type = uint64_t;
      static constexpr std::size_t sign_size = 1;
      static constexpr std::size_t exp_size = 11;
      static constexpr std::size_t mant_size = 52;
      static constexpr std::size_t exp_shift = 1023;
      static constexpr int32_t exp_mask = 0x7FF;
      static constexpr unsigned_type mant_mask = 0xFFFFFFFFFFFFF;
    };

    template<typename T>
    constexpr bool check_ieee754() {
        // add more check here
        return std::numeric_limits<T>::digits == (num::ieee754_traits<sizeof(T)>::mant_size + 1) &&
           std::numeric_limits<T>::max_exponent == (num::ieee754_traits<sizeof(T)>::exp_mask - num::ieee754_traits<sizeof(T)>::exp_shift);
    }
}

Then, you can check your representation:

static_assert(sizeof(float) == 4 && sizeof(double) == 8);
static_assert(num::check_ieee754<float>(), "does not match ieee754");
static_assert(num::check_ieee754<double>(), "does not match ieee754");