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However, this raises the even more fundamental question of what *IS* the result of any given computation, not just basic arithmetic operations? Until this question is answered for all cases of interest, I believe it is premature to even consider developing a standard.
Once this question *is* answered, then the only requirement for any implementation is to *enclose the final result* of any given computation. The syntax and semantics of doing so with a given algorithm in any given language can then be addressed, which, along with returned interval width and speed, are simply quality of implementation issues.
The beauty (to me) of such a system is that it leaves totally open just how hardware, language, software, and algorithm developers might choose to increase their quality of implementation, while always enclosing *the* value of the final results of the computation defined by any given code. We do not want a standard that stifles creativity.
Bill Walster On 6/9/11 4:15 AM, Arnold Neumaier wrote:
Dan Zuras Intervals wrote:Folks, The motion is now, & I quote: The Motion: Every IEEE 1788 compliant system SHALL provide the four basic arithmetic operations addition, subtraction, multiplication, and division with rounding downwards and upwards. Type conversions with directed roundings SHALL also be provided.From our point of view (constraint programming and use in global optimization), we often need both rounding directions for the same operations.Thus it would be more useful to have operations that take a list of reals and return a (preferably the tightest) representable interval enclosing the result of an operation with them. Addition and inner product of arbitrarily many inputs, subtraction, division with two arguments, and sqrt with one argument. This fully substitutes for directed rounding (probably at virtually no extra cost if done in hardware). Arnold Neumaier