[Cfp-interest 3146] thoughts on linear interpolations

[David Hough CFP]

Following 

https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0811r3.html

the problem is to compute, correctly rounded

 (1-t)*a + t*b  OR  a + t*(b-a)

if t is in [0.5,2] 
	then 1-t is exact ; compute (1-t)*a + t*b as 2 dprods and an addtosingle

a + t * (b-a)    
if a/b is in [0.5,2] (determined conservatively as same signs, 
			exponents differ by 0 or 1)
	then b-a is exact ; compute a + t * (b-a) as 2 dprods and addtosingle

otherwise triple addition of a - t*a + t*b - as 2 dprods and add3tosingle

To be clear, dprod(x,y) returns x*y in a precision higher enough to always hold that product exactly, probably double precision

addtosingle(x,y) for x and y in that higher precision, returns x+y rounded once
to the original precision of a and b

add3tosingle(x,y,z) for x, y, and z in that higher precision, returns their
sum rounded once to the original precision.    That's a tall order for the
hardware department and resistance is to be expected.    

And all the
conditionals impede performance, even with the hardware suppport.
It's hard to imagine
an application that could make use of a very slow correctly-rounded software
implementation.

So from my point of view, that argues against standardization in general
purpose languages.   A language could specify an algorithm rather than 
explicit properties of results, with the risk that somebody cleverer might
come up later with an algorithm that is faster and more correct.