Hacker's Delight

Chapter 15. Floating-Point

God created the integers, all else is the work of man.

—Leopold Kronecker

Operating on floating-point numbers with integer arithmetic and logical instructions is often a messy proposition. This is particularly true for the rules and formats of the IEEE Standard for Binary Floating-Point Arithmetic, IEEE Std. 754-1985, commonly known as “IEEE arithmetic.” It has the NaN (not a number) and infinities, which are special cases for almost all operations. It has plus and minus zero, which must compare equal to one another. It has a fourth comparison result, “unordered.” The most significant bit of the fraction is not explicitly present in “normal” numbers, but it is in “denormalized” or “subnormal” numbers. The fraction ...