tree c6159df39c7a3ac9f1eb99ea6973a799a68ad484
parent 1e13ccd477067cf984e4659c444497706935cda7
author Sameer Agarwal <sameeragarwal@google.com> 1792627592 -0700
committer Sameer Agarwal <sameeragarwal@google.com> 1792714029 -0700

Precompute scalar derivatives in Jet elementary functions

Compute cbrt(f) using a single cbrt(f.a) call with f.v / (3 * r * r),
avoiding both the second cbrt evaluation and f.a * f.a overflow or
underflow at extreme magnitudes. Precompute the scalar derivative factor
in erf(x) and erfc(x) using a compile-time constant for 2 / sqrt(pi)
before multiplying x.v so Eigen evaluates a single scalar-vector product
instead of scaling x.v twice. Parenthesize (T(1.0) / log(T(10.0))) / f.a
in log10 and (T(1.0) / log(T(2.0))) / f.a in log2 so the reciprocal
constant folds at compile time, and use T(0.5) / tmp in sqrt. Standardize
on floating-point T(...) constants and left-multiplication by scalar
derivatives across elementary functions in jet.h.

Benchmark (Apple M1 Pro):
----------------------------------------------------------------------
Benchmark                                     Before    After   Change
----------------------------------------------------------------------
Cbrt<3>/1000                                 11.7 us  7.29 us   -37.7%
Cbrt<10>/1000                                15.9 us  11.5 us   -27.6%
Cbrt<32>/1000                                29.9 us  25.7 us   -14.0%
Erf<3>/1000                                  23.8 us  21.1 us   -11.3%
Erf<32>/1000                                 39.9 us  32.8 us   -17.8%
Erfc<3>/1000                                 23.1 us  20.2 us   -12.6%
Erfc<32>/1000                                39.8 us  32.7 us   -17.8%
Sqrt<15>/1000                                4.50 us  4.38 us    -2.7%
Sqrt<32>/1000                                12.5 us  12.4 us    -0.8%
----------------------------------------------------------------------

Change-Id: I2a4ceebad76cbb0eddc42be6368872a9e5543b70