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Implement vectorized versions of log1p and expm1 in Eigen using Kahan's formulas, and change the scalar implementations to properly handle infinite arguments.

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Depending on instruction set, significant speedups are observed for the vectorized path:
log1p wall time is reduced 60-93% (2.5x - 15x speedup)
expm1 wall time is reduced 0-85% (1x - 7x speedup)

The scalar path is slower by 20-30% due to the extra branch needed to handle +infinity correctly.

Full benchmarks measured on Intel(R) Xeon(R) Gold 6154 here: https://bitbucket.org/snippets/rmlarsen/MXBkpM
This commit is contained in:
Rasmus Munk Larsen
2019-08-12 13:53:28 -07:00
parent d55d392e7b
commit a3298b22ec
9 changed files with 95 additions and 6 deletions
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8
Eigen/src/Core/MathFunctions.h
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@@ -501,7 +501,8 @@ namespace std_fallback {
}
EIGEN_USING_STD_MATH(log);
return (u - RealScalar(1)) * x / log(u);
Scalar logu = log(u);
return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu;
}
}
@@ -548,7 +549,10 @@ namespace std_fallback {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_USING_STD_MATH(log);
Scalar x1p = RealScalar(1) + x;
return numext::equal_strict(x1p, Scalar(1)) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) );
Scalar log_1p = log(x1p);
const bool is_inf = numext::equal_strict(x1p, log_1p);
const bool is_small = numext::equal_strict(x1p, Scalar(1));
return (is_inf || is_small) ? x : x * (log_1p / (x1p - RealScalar(1)));
}
}