What's the term for "default rounding mode" for arithmetic ops in IEEE 754?

Question

I know that IEEE 754 is the specification for floating-point number data types, their representation and the semantics of operations on them; but - I'm not knowledgeable in the standard itself.

I also know that IEEE 754 defines the following four rounding modes: to nearest, up, down, to zero; and that in typical environments supporting IEEE 754 you can say "please round x using rounding mode m" (e.g. here's how it's done with glibc). That's all well and good.

However, rounding also happens when you simply perform arithmetic: If you have a single-precision 0.9999999 (or something close to that) and you add this to 100000, you will either get 100001, or something close to 100000.99 .

My question: Is this rounding supposed to be an application of a "default rounding mode"? Is that the IEEE 754 term, or is there another, specific term for what I've described? And are the four rounding modes supposed to be supported for implicit rounding arithmetic, as well?

Answer 1

IEEE 754-2008 does not define “modes” for rounding; it changed the terminology from the 1985 standard to imply more flexibility than a global mode. In clause 4.3.3, it specifies round-to-nearest-ties-to-even as the default method for binary formats. For decimal formats, it says a default is not defined but should be round-to-nearest-ties-to-even.

IEEE 754-2008 subclause 4.3 specifies several rounding-direction attributes. It does not say there has to be a mode that provides a rounding-direction setting. A computing environment could, for example, including the rounding-direction attribute as a parameter on each individual operation. For example, a processor architecture could have separate instructions for add with rounding-to-nearest-ties-to-even, add with rounding toward +∞, add with rounding toward zero, and so on. Or it could include the rounding-direction attribute as a operand to the instruction. Or the instruction could be affected by a global mode set in some special processor register.

Many processor architectures provide rounding mode as a setting in a floating-point control register.

The IEEE 754-1985 standard described rounding modes and defined mode as “A variable that a user may set, sense, save, and restore to control the execution of subsequent arithmetic operations.” This may have influenced the development of rounding modes in control registers, but that has a detrimental effect on performance, as global registers cause dependencies between instructions: Every floating-point instruction depends on that global register, so any change to that register interferes with parallel execution of instructions.

However, it is desirable that the rounding direction be flexible, as one might want to alternately use different modes when implementing interval arithmetic or evaluating complicated routines such as implementations of sine or exponentiation. So the IEEE 754-2008 committee changed the standard not to define global modes. Clause 4 specifies some semantics for attributes, including that languages should provide ways to specify the attributes for all standard operations in a “block.” A block may be an entire program or a single operation; it is language-defined. Subclause 4.2 says languages should provide dynamic ways of specifying the attributes, so they can be determined at run-time.