Re: libm trigonometric functions and i387

[Taylor R Campbell <campbell%mumble.net@localhost>]

   Date: Tue, 24 Feb 2009 10:42:49 -0700
   From: Sverre Froyen <sverre%viewmark.com@localhost>

   How do you accurately pass an argument of 2^63 to libm's trig functions?  A 
   quick look suggests your only choices are float or double.  For an argument 
   value of 2^63, the uncertainty exceeds 2*pi by several orders of magnitute.

That's not the point.  Each (numeric) floating-point value has a
unique associated real number, and each real number has a unique sine,
cosine, or tangent.  While the sine, cosine, and tangent of most real
numbers are not exactly representable in floating-point, there are
good approximations and there are bad approximations.  There is code
in NetBSD's libm to compute good approximations, and there is (rather
silly) code to compute bad approximations.  I want to invoke the code
that computes good approximations, just like I'd get for addition,
multiplication, square roots, &c., in the IEEE standard.  (If I wanted
bad approximations, again, I could just pass the flags -ffast-math and
-funsafe-math-optimizations to GCC.)  I also don't want to edit
/etc/ld.so.conf.

There are plenty of eminently Googlable arguments on the intertubes
about the uncertainty you mention, and about the merit or numerical
stability of algorithms that might try to compute the sine of 1e22.
That's not what I'm interested in, but I'm sure you can Google up
plenty of entertaining discussions about it if it is what you're
interested in.