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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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46
Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
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@@ -126,6 +126,52 @@ Packet plog_float(const Packet _x)
por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
}
/** \internal \returns log(1 + x) computed using W. Kahan's formula.
See: http://www.plunk.org/~hatch/rightway.php
*/
template<typename Packet>
Packet generic_plog1p(const Packet& x)
{
typedef typename unpacket_traits<Packet>::type ScalarType;
const Packet one = pset1<Packet>(ScalarType(1));
Packet xp1 = padd(x, one);
Packet small_mask = pcmp_eq(xp1, one);
Packet log1 = plog(xp1);
// Add a check to handle x == +inf.
Packet pos_inf_mask = pcmp_eq(x, log1);
Packet log_large = pmul(x, pdiv(log1, psub(xp1, one)));
return pselect(por(small_mask, pos_inf_mask), x, log_large);
}
/** \internal \returns exp(x)-1 computed using W. Kahan's formula.
See: http://www.plunk.org/~hatch/rightway.php
*/
template<typename Packet>
Packet generic_expm1(const Packet& x)
{
typedef typename unpacket_traits<Packet>::type ScalarType;
const Packet one = pset1<Packet>(ScalarType(1));
const Packet neg_one = pset1<Packet>(ScalarType(-1));
Packet u = pexp(x);
Packet one_mask = pcmp_eq(u, one);
Packet u_minus_one = psub(u, one);
Packet neg_one_mask = pcmp_eq(u_minus_one, neg_one);
Packet logu = plog(u);
// The following comparison is to catch the case where
// exp(x) = +inf. It is written in this way to avoid having
// to form the constant +inf, which depends on the packet
// type.
Packet pos_inf_mask = pcmp_eq(logu, u);
Packet expm1 = pmul(u_minus_one, pdiv(x, logu));
expm1 = pselect(pos_inf_mask, u, expm1);
return pselect(one_mask,
x,
pselect(neg_one_mask,
neg_one,
expm1));
}
// Exponential function. Works by writing "x = m*log(2) + r" where
// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1).