From f9fac1d5b044afb8104ecb5c1e5183c309bafca4 Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Fri, 4 Dec 2020 21:45:09 +0000
Subject: Add log2() to Eigen.

---
 .../Core/arch/Default/GenericPacketMathFunctions.h | 63 ++++++++++++++++++----
 1 file changed, 52 insertions(+), 11 deletions(-)

(limited to 'Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h')

diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 60db2e12f..c6bb89b05 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -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);
+}
+
+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...) logarithm of 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
  */
-- 
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