KDF9

On 19-6-06 05:22, in article

I still have my 40-year old KDF9 Programming Manual:

"(C) All rights reserved English Electric Computers Limited price: five shillings"

I can confirm that the manual says that floating-point exponents are in excess-128 representation. An example shows that fraction parts are in 2's complement representation.

It further says, of double precision floating point:

"The sign digit is D0 of word 1. D0 of the 2nd word is ALWAYS 0 and is ignored. 'p' the exponent: WF is held in D1-D8 of word 1. For engineering purposes p minus 39 is in D1-D8 of word 2. 'f' the fraction: WF is considered to be started in D9-D47 of word 1 and continued in D9-D47 of word 2. If p is less than 39, word 2 is made into all 0's."

Operations with double precision results never rounded, whereas those with single-precision results always did.

I believe that the floating point facilities of KDF9 were heavily influenced by the pioneering work done by Jim Wilkinson on the numerical analysis of error propagation. This led, in particular, to the inclusion of the x+F instruction for forming accurate scalar products by accumulating the sum of products of single-precision vectors in double precision - multiply-and-accumulate, in fact.

-- Bill Findlay