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To: andy kelly who wrote (55845)	5/21/1998 2:12:00 AM
From: Paul Engel	Read Replies (2) of 186894

Andy - Re: "I have seen you refer to "double precision capability" in talking about the Katmai device. Could you please explain what this means?" Intel's current MMX technology is implemented using only integer data types and operations. The new Katmai MMX instructions incorporate double precision FLOATING POINT data types. For reference, AMD's K6-2 implements SINGLE PRECISION Data types and operations. A single precision data type uses 32 binary bits for encoding and has a range from 1.18 x 10(-38) to 3.40 x 10 (+38) (Decimal Notation). Now, these look like big numbers (positive OR negative) and indeed they are. However, the size is only one issue. Single precision numbers have precision of only 24 bits - NOT 32! The remaining 8 bits are assigned to the Exponent if the number. That is, the number itself has a resolution of 2^24 or roughly 16 million parts. Even this seems quite adequate, except when you consider division of one SMALL single precision number by another, or subtraction of a very small single precision number from a large one. In these cases, ROUNDING errors occur and the loss of precision can lead to curious artifacts when mathematical operations are performed widely different sized numbers. On the other hand, double precision numbers use 64 binary bits to represent numbers in the range 2.23 x 10 (-308) to 1.79 x 10 (308) Decimal. These numbers assign 11 bits to the exponent and 53 binary bits to the precision of the number. Thus, the precision of the number represented in double precision notation is 2^53 or about 1 part in 10^16 - a very large degree of precision. Mathematical operations on double precision numbers, or BETWEEN double precision numbers, will result in very low rounding errors. Paul

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