Denormal Numbers

A normalized number is a number for which both the exponent (including bias) and the most significant bit of the mantissa are non-zero. For such numbers, all the bits of the mantissa contribute to the precision of the representation.

The smallest normalized single-precision floating-point number greater than zero is about 1.1754943^-38. Smaller numbers are possible, but those numbers must be represented with a zero exponent and a mantissa whose leading bit(s) are zero, which leads to a loss of precision. These numbers are called denormalized numbers or denormals (newer specifications refer to these as subnormal numbers).

Denormal computations use hardware and/or operating system resources to handle denormals; these can cost hundreds of clock cycles. Denormal computations take much longer to calculate than normal computations.

There are several ways to avoid denormals and increase the performance of your application:

• Scale the values into the normalized range.
• Use a higher precision data type with a larger range.
• Flush denormals to zero.