leading-zero-bit-count.h

//===-- include/flang/Common/leading-zero-bit-count.h -----------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
 
#ifndef FORTRAN_COMMON_LEADING_ZERO_BIT_COUNT_H_
#define FORTRAN_COMMON_LEADING_ZERO_BIT_COUNT_H_
 
// A fast and portable function that implements Fortran's LEADZ intrinsic
// function, which counts the number of leading (most significant) zero bit
// positions in an integer value.  (If the most significant bit is set, the
// leading zero count is zero; if no bit is set, the leading zero count is the
// word size in bits; otherwise, it's the largest left shift count that
// doesn't reduce the number of bits in the word that are set.)
 
#include <cinttypes>
 
namespace Fortran::common {
namespace {
// The following magic constant is a binary deBruijn sequence.
// It has the remarkable property that if one extends it
// (virtually) on the right with 5 more zero bits, then all
// of the 64 contiguous framed blocks of six bits in the
// extended 69-bit sequence are distinct.  Consequently,
// if one shifts it left by any shift count [0..63] with
// truncation and extracts the uppermost six bit field
// of the shifted value, each shift count maps to a distinct
// field value.  That means that we can map those 64 field
// values back to the shift counts that produce them,
// and (the point) this means that we can shift this value
// by an unknown bit count in [0..63] and then figure out
// what that count must have been.
//    0   7   e   d   d   5   e   5   9   a   4   e   2   8   c   2
// 0000011111101101110101011110010110011010010011100010100011000010
static constexpr std::uint64_t deBruijn{0x07edd5e59a4e28c2};
static constexpr std::uint8_t mapping[64]{63, 0, 58, 1, 59, 47, 53, 2, 60, 39,
    48, 27, 54, 33, 42, 3, 61, 51, 37, 40, 49, 18, 28, 20, 55, 30, 34, 11, 43,
    14, 22, 4, 62, 57, 46, 52, 38, 26, 32, 41, 50, 36, 17, 19, 29, 10, 13, 21,
    56, 45, 25, 31, 35, 16, 9, 12, 44, 24, 15, 8, 23, 7, 6, 5};
} // namespace
 
inline constexpr int LeadingZeroBitCount(std::uint64_t x) {
  if (x == 0) {
    return 64;
  } else {
    x |= x >> 1;
    x |= x >> 2;
    x |= x >> 4;
    x |= x >> 8;
    x |= x >> 16;
    x |= x >> 32;
    // All of the bits below the uppermost set bit are now also set.
    x -= x >> 1; // All of the bits below the uppermost are now clear.
    // x now has exactly one bit set, so it is a power of two, so
    // multiplication by x is equivalent to a left shift by its
    // base-2 logarithm.  We calculate that unknown base-2 logarithm
    // by shifting the deBruijn sequence and mapping the framed value.
    int base2Log{mapping[(x * deBruijn) >> 58]};
    return 63 - base2Log; // convert to leading zero count
  }
}
 
inline constexpr int LeadingZeroBitCount(std::uint32_t x) {
  return LeadingZeroBitCount(static_cast<std::uint64_t>(x)) - 32;
}
 
inline constexpr int LeadingZeroBitCount(std::uint16_t x) {
  return LeadingZeroBitCount(static_cast<std::uint64_t>(x)) - 48;
}
 
namespace {
static constexpr std::uint8_t eightBitLeadingZeroBitCount[256]{8, 7, 6, 6, 5, 5,
    5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
    3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
    2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
}
 
inline constexpr int LeadingZeroBitCount(std::uint8_t x) {
  return eightBitLeadingZeroBitCount[x];
}
 
template <typename A> inline constexpr int BitsNeededFor(A x) {
  return 8 * sizeof x - LeadingZeroBitCount(x);
}
} // namespace Fortran::common
#endif // FORTRAN_COMMON_LEADING_ZERO_BIT_COUNT_H_