The prelude's declare surface was five f32 functions, and the five were there
because somebody needed each one. Everything else a caller wanted was written
as a declare at the top of their own file -- the identical libm call with none
of the caveats written down.
So the rest of libm is here: tan, the three inverses, the three logarithms,
exp, fmod, hypot, cbrt, fabs, and an f64 face for every one of them including
the five that already existed. A declare is a line, a symbol already on the
link, and nothing in either backend, which is why this was cheap enough to do
completely rather than one function at a time.
The f64 half is not decoration. f32 is what a position is; f64 is what a
measurement is -- the clock, parse-f64, format-f64, any sum over more than a
few thousand terms -- and having only the f32 face forced a cast down and back
at each of those boundaries, which is where the precision went.
The paragraph the sqrt note draws for itself is now drawn once for the family:
IEEE-754 specifies sqrt, fabs, floor, ceil, round and fmod as exact or
correctly rounded, so those agree bit for bit across glibc, musl and
wasi-libc; it requires nothing of the rest, so the sand-grid rule covers all
of them unchanged. floor, ceil and round are Flan at f32 and libm at f64, and
that is not an inconsistency: the f32 bodies work because every f32 with a
fraction fits in an i32, and at f64 that trick is gone.
abs-i32 and abs-i64 are Flan, one per width because min and max are builtins
and no generic covers the numeric types. pi and tau at both widths, written
out rather than derived so the compiler rounds each literal once.
programs/math3.flan covers it at values that are exact in binary, so nothing
pins one libm's last bit. The -O0 case is the one that matters: at -O2 LLVM
folds a call over two literals and leaves no symbol to resolve, which is how a
missing -lm hid the first time.
