libm trigonometric functions and i387

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

The i387 trigonometric instructions are broken by design: they return
wildly incorrect values for arguments outside a very small range,
because they reduce arguments based on an approximation of pi that is
too coarse.  For example, on 2^62, the FSIN instruction gives about
-0.70713 whereas the correct answer is closer to -0.70292.  Helpfully,
when the arguments exceed about 2^63 in absolute value, the i387
instructions set a processor flag that means `sorry, this hardware is
too broken to give any remotely sensible answer'.  What NetBSD's libm
does with this flag doesn't help the situation, though -- it proceeds
to use other i387 instructions to reduce arguments in exactly the same
way, with exactly the same approximation of pi, that the i387 said
wouldn't give a remotely sensible answer.  For the sine of 1e22, this
yields about 0.8740281, whereas the correct answer is closer to
-0.8522008 (!).

Looking at the source to NetBSD's libm, I see that there is one
directory src/lib/libm/arch/i387/ for i387 miscomputations, and
another directory src/lib/libm/src/ with C code to compute what
appears to be better argument reduction based on 1584 bits of 2/pi,
rather than the 66 or so bits of pi that the i387 uses.  However,
/etc/ld.so.conf persuades the linker to favour libm387 over libm.
This, I think, is a mistake, first of all: programmers who want their
programs to use the i387's fast and loose trigonometric routines can
always compile their programs with -ffast-math and -mfancy-math-387,
but right now the default is to give wildly bogus answers.  Setting
aside, though, the issue of whether NetBSD's libm should be fast or
correct, how do I tell the linker that I want libm, not libm387,
without editing /etc/ld.so.conf?

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