bitset signed vs unsigned

bug.cpp

#include <bitset>
#include <cmath>
#include <cstdint>
#include <iostream>

void demo_8() {
  const unsigned bit_kind = 8;
  uint8_t a_ui = 129;
  int8_t a_i = 129;
  uint8_t a_ui_from_i = 127;
  std::bitset<bit_kind> b;

  std::cout << " bitkind " << bit_kind << std::endl;
  std::cout << " std::pow(2,7) + 1 = " << std::pow(2, 7) + 1 << std::endl;
  b = a_ui;
  std::cout << " uint" << bit_kind << "_t " << static_cast<int>(a_ui);
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;

  b = a_i;
  std::cout << " int" << bit_kind << "_t " << static_cast<int>(a_i);
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;

  b = a_ui_from_i;
  std::cout << " uint_t from int_t " << static_cast<int>(a_ui_from_i);
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;
  std::cout << std::endl;
}
void demo_64() {
  const unsigned bit_kind = 64;
  uint64_t a_ui = 9223372036854775809;
  int64_t a_i = 9223372036854775809;
  uint64_t a_ui_from_i = 9223372036854775807;
  std::bitset<bit_kind> b;

  std::cout << " bitkind " << bit_kind << std::endl;
  uint64_t pow_val = std::pow(2, 63);
  pow_val += 1;
  std::cout << " std::pow(2,63) + 1 = " << std::fixed << pow_val << std::endl;
  b = a_ui;
  std::cout << " uint" << bit_kind << "_t " << a_ui;
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;

  b = a_i;
  std::cout << " int" << bit_kind << "_t " << a_i;
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;

  b = a_ui_from_i;
  std::cout << " uint_t from int_t " << a_ui_from_i;
  std::cout << " bitset<bitkind> " << b;
  std::cout << std::endl;
  std::cout << std::endl;
}

int main() {
  std::cout << "Highest occ orbtial bug!" << std::endl;
  demo_8();
  demo_64();
  return 0;
}

Highest occ orbtial bug!
 bitkind 8
 std::pow(2,7) + 1 = 129
 uint8_t 129 bitset<bitkind> 10000001
 int8_t -127 bitset<bitkind> 10000001
 uint_t from int_t 127 bitset<bitkind> 01111111

 bitkind 64
 std::pow(2,63) + 1 = 9223372036854775809
 uint64_t 9223372036854775809 bitset<bitkind> 1000000000000000000000000000000000000000000000000000000000000001
 int64_t -9223372036854775807 bitset<bitkind> 1000000000000000000000000000000000000000000000000000000000000001
 uint_t from int_t 9223372036854775807 bitset<bitkind> 0111111111111111111111111111111111111111111111111111111111111111