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Plea for inline expansion of transcendentals.
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Date: -- (:)
From: Xavier Leroy <Xavier.Leroy@i...>
Subject: Re: Plea for inline expansion of transcendentals.
> It seems better to fail in this case, as the part of the number
> which is significant for these periodic functions is completely lost
> by the machine precision, so the renormalization is useless, isn't
> it ?

Yes, the result of sin(2^64) is totally meaningless.  However,
the Single Unix specification doesn't say that there is a range of
values for the argument of "sin" outside of which we can return an
error (however, it says "The sin() function may lose accuracy when its
argument is far from 0.0", which could be interpreted as "we can
return any wrong result"...)

> The best would be to trap and raise an ML exception (Silly_Trigo :-).

The trapping itself isn't trivial and requires a few instructions,
making the inlining of "sin" less interesting.

> Actually ocaml2.04 toplevel (I have not try the compilers) does
> something very silly:
> 
> #  sin(10.0);;
> - : float = -0.544021110889
> # sin(10e21);;
> - : float = 1e+22    
> 
> Using Ocaml I can therefore prove -1 <  1e+22  < 1 .... Whooo :-) 

Nice example.  You must be using RedHat Linux 6 on a PC :-)  The
toplevel and bytecode compiler use whatever "sin" function is provided
by the C compiler and C library.  If the latter is correct, you'll get
correct results.  Your example works fine under Digital Unix, for instance.

But it so happens that under RH 6.1, the "sin" function in the C
library does the right thing (perform the "fsin" instruction, check
for overflow, and normalize and try again if necessary), but "gcc -O"
generates directly an "fsin" instruction -- "gcc" without -O calls the
C library function.  I view this as a gcc bug, though.

- Xavier Leroy