Geoff Barrett. A formal approach to rounding. In Proceedings 8th Symposium on Computer Arithmetic, pages 247--254, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....becoming sufficiently mature to consider the next evolutionary step of integrating formal approaches into the design process. Our focus is to do as much upfront verification as possible to minimize the burden on the designer Previous work has also formally specified IEEE floating point standards [2, 3, 16]. These works have been related together by Miner and Leathrum in [17] in verifying the general class of subtractive division algorithms. Rather than focus on specific floating point algorithms, our current work attempts to develop an environment in which a designer can develop new hardware ....

.... then 2 else 1 endif d(p) subrange( 1,0) if odd (floor(16 p) then 0 else 1 endif e(p) below(2) if odd (floor(16 p) then 1 else 0 endif qsel( D:Dtype) p: ptype(D) subrange( 2,2) let ppindex:int=floor(8 approx(p) Dindex=floor( D 1) 8) in table ppindex, Dindex [ 0 1 2 3 4 5 6 7] 10 2 9 2 2 2 8 2 2 2 2 7 2 2 2 2 2 2 6 2 2 2 2 2 2 2 ....

Geoff Barrett. A formal approach to rounding. In Proceedings 8th Symposium on Computer Arithmetic, pages 247--254, 1987.

....shall be performed as if it first produced an intermediate result correct to infinite precision and with unbounded range, and then that result rounded according to one of the modes . 7, 8] Barrett manually verified a general rounding algorithm with respect to a Z formalization of IEEE 754 [2, 3]. When Barrett performed his verification, there was no machine assisted reasoning for the Z specification language. Some tools for machine assisted application of Z have recently been developed [14] Thus far, these have not been applied to floating point verification. Recently, the microcode ....

....a radix 4 SRT lookup table based on using a signed digit adder for computing the partial remainder. Suppose further, that the implementation is for single precision IEEE 754 arithmetic. The following sequence of PVS declarations provides a verified algorithm for the design: IMPORTING dividetypes[4,2,2], signeddigitlookup qs: qstype[4,2,2] qsel IMPORTING ieeedivide[4,2,2,qs,24,192,127, 126] Theory signed digit lookup contains the definition of an SRT4 lookup table suitable for use with a signed digit adder. It contains the proof that the quotient selection function q sel satisfies type qs ....

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Geoff Barrett. A formal approach to rounding. In Proceedings 8th Symposium on Computer Arithmetic, pages 247--254, 1987.

.... shall be performed as if it first produced an intermediate result correct to infinite precision and with unbounded range, and then that result rounded according to one of the modes : 6, 7] Barrett manually verified a general rounding algorithm with respect to a Z formalization of IEEE 754 [1, 2]. When Barrett performed his verification, there was no machine assisted reasoning for the Z specification language. Some tools for machine assisted application of Z have recently been developed [13] Thus far, these have not been applied to floating point verification. Recently, the microcode for ....

Geoff Barrett. A formal approach to rounding. In Proceedings 8th Symposium on Computer Arithmetic, pages 247--254, 1987.

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