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Add log2() to Eigen.

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This commit is contained in:
Rasmus Munk Larsen
2020-12-04 21:45:09 +00:00
parent 2dbac2f99f
commit f9fac1d5b0
13 changed files with 160 additions and 12 deletions
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63
Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
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@@ -59,16 +59,16 @@ pldexp_double(Packet a, Packet exponent)
return pmul(a, preinterpret<Packet>(plogical_shift_left<52>(ei)));
}
// Natural logarithm
// Natural or base 2 logarithm.
// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
// be easily approximated by a polynomial centered on m=1 for stability.
// TODO(gonnet): Further reduce the interval allowing for lower-degree
// polynomial interpolants -> ... -> profit!
template <typename Packet>
template <typename Packet, bool base2>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog_float(const Packet _x)
Packet plog_impl_float(const Packet _x)
{
Packet x = _x;
@@ -131,8 +131,13 @@ Packet plog_float(const Packet _x)
x = padd(x, y);
// Add the logarithm of the exponent back to the result of the interpolation.
const Packet cst_ln2 = pset1<Packet>(M_LN2);
x = pmadd(e, cst_ln2, x);
if (base2) {
const Packet cst_log2e = pset1<Packet>(static_cast<float>(M_LOG2E));
x = pmadd(x, cst_log2e, e);
} else {
const Packet cst_ln2 = pset1<Packet>(static_cast<float>(M_LN2));
x = pmadd(e, cst_ln2, x);
}
Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
Packet iszero_mask = pcmp_eq(_x,pzero(_x));
@@ -145,8 +150,23 @@ Packet plog_float(const Packet _x)
por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
}
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog_float(const Packet _x)
{
return plog_impl_float<Packet, /* base2 */ false>(_x);
}
/* Returns the base e (2.718...) logarithm of x.
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog2_float(const Packet _x)
{
return plog_impl_float<Packet, /* base2 */ true>(_x);
}
/* Returns the base e (2.718...) or base 2 logarithm of x.
* The argument is separated into its exponent and fractional parts.
* The logarithm of the fraction in the interval [sqrt(1/2), sqrt(2)],
* is approximated by
@@ -155,16 +175,16 @@ Packet plog_float(const Packet _x)
*
* for more detail see: http://www.netlib.org/cephes/
*/
template <typename Packet>
template <typename Packet, bool base2>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog_double(const Packet _x)
Packet plog_impl_double(const Packet _x)
{
Packet x = _x;
const Packet cst_1 = pset1<Packet>(1.0);
const Packet cst_neg_half = pset1<Packet>(-0.5);
// The smallest non denormalized float number.
// The smallest non denormalized double.
const Packet cst_min_norm_pos = pset1frombits<Packet>( static_cast<uint64_t>(0x0010000000000000ull));
const Packet cst_minus_inf = pset1frombits<Packet>( static_cast<uint64_t>(0xfff0000000000000ull));
const Packet cst_pos_inf = pset1frombits<Packet>( static_cast<uint64_t>(0x7ff0000000000000ull));
@@ -232,8 +252,13 @@ Packet plog_double(const Packet _x)
x = padd(x, y);
// Add the logarithm of the exponent back to the result of the interpolation.
const Packet cst_ln2 = pset1<Packet>(M_LN2);
x = pmadd(e, cst_ln2, x);
if (base2) {
const Packet cst_log2e = pset1<Packet>(M_LOG2E);
x = pmadd(x, cst_log2e, e);
} else {
const Packet cst_ln2 = pset1<Packet>(M_LN2);
x = pmadd(e, cst_ln2, x);
}
Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
Packet iszero_mask = pcmp_eq(_x,pzero(_x));
@@ -246,6 +271,22 @@ Packet plog_double(const Packet _x)
por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
}
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog_double(const Packet _x)
{
return plog_impl_double<Packet, /* base2 */ false>(_x);
}
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
EIGEN_UNUSED
Packet plog2_double(const Packet _x)
{
return plog_impl_double<Packet, /* base2 */ true>(_x);
}
/** \internal \returns log(1 + x) computed using W. Kahan's formula.
See: http://www.plunk.org/~hatch/rightway.php
*/