[cfp-interest 3391] Re: Math Functions in Programming Languages Standards

[Paul Zimmermann]

       Hi David,

I agree with you. I don't know the arguments for standardizing linear
interpolation, but I would prefer operations like a*b+c*d to be
standardized, which would be very useful to compute products of
complex numbers.

Also, what would be the semantics of the new functions? Would correct rounding
be required?

Paul

> Date: Thu, 13 Feb 2025 15:18:42 -0800 (PST)
> From: David Hough CFP  <pcfp at oakapple.net>
> 
> 
> Here is a draft of a response to my very long-standing action item for
> recommendations to C about C++ midpoint and linear interpolation.
> 
> https://754r.ucbtest.org/background/math-functions-languages.txt
> 
> 		Math Functions in Programming Languages Standards
> 
> Question: 
> C++ proposes to standardize midpoint and linear interpolation functions.
> Should C follow?
> 
> General comments:
> Programming language standards are big and getting bigger.    It seems likely
> that not all standards groups have equal expertise in what functions 
> applications require.
> 
> If they are going to put additional functions in programming language
> standards, how do they decide which ones are worthwhile?
> 
> Perhaps they should limit themselves to new functions that can be 
> implemented in a single instruction no more complex than an FMA.
> Or to new functions that are the solutions to very simple differential
> equations (e.g. exp/sin/cos), and their inverses - especially avoiding new
> transcendental functions - note that in floating-point arithmetic, 
> the results of x**y and kindred functions are always algebraic numbers
> rather than transcendental numbers.
> 
> LAPACK, or even the BLAS, are very widely used, but that doesn't make them
> good candidates for language standardization.    There are other groups
> better equipped to do that work.
> 
> Specific comments:
> If I had been present at Creation, I would have advised putting gamma or
> lgamma or bessel functions in C.    But here they are, and there's little to
> be gained by taking them out.
> 
> Note that midpoint, in binary, is hardly different from a normal subtraction,
> and would easily make a simple machine instruction.    But that ease does
> not apply to any other radix, 10 or 16 in particular.
> 
> That case against linear interpolation is even stronger.
> 
> One benefit of standardization is uniformity of syntax.   But uniformity of
> semantics is even more important, especially for exceptions.    But different
> application areas have vastly different requirements for exceptions.   Perhaps
> the semantics are best specified by application-oriented groups rather than
> language committees.
> 
> Conclusion:
> My suggestion for C would be to not standardize midpoint and linear
> interpolation, but if it is done, limit the specification to syntax and
> just those semantics that all stakeholders can agree on.
> 
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