Create denormalized (subnormal) floating point values in C++

Question

For testing purposes I need to create one positive and one negative denormalized (aka subnormal) float and double number in C++.

How can I write/produce such a number?

Answer 1

You could use -std::numeric_limits<T>::denorm_min() and std::numeric_limits<T>::denorm_min(). It is just incidental that the produced denormalized values have a special characteristic. If you don't want that, multiply by some reasonably small integer value.

Answer 2

For full flexibility and coverage, create a union with an unsigned integer value and a floating-point value of the same size. Probably unsigned int + float for 32-bit values, and unsigned long + double for 64-bit values. Store your desired denorm value in the integer field, and read out the corresponding floating-point value. If you want to get fancy, specify the integer with bit fields, for the sign, exponent and fraction portions of your floating point number.

32-bit denorms are in the range [0x00000001, 0x007fffff] for positive values, and [0x80000001, 0x807fffff] for negative denorms.

64-bit denorms are in the range [0x0000000000000001, 0x000fffffffffffff] for positive values, and [0x8000000000000001, 0x800fffffffffffff] for negative denorms.

If you use bit fields in your translation union, then the sign bit is arbitrary, exponent is zero, and the fraction can be any value but zero.