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The << operator in C++ is a binary operator that serves two distinct structural purposes depending on its operand types: natively, it functions as the bitwise left shift operator for integral types, and through operator overloading, it acts as the stream insertion operator for output streams.

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1. Bitwise Left Shift (Native Behavior)

When both operands are integral or unscoped enumeration types, << performs a bitwise left shift. It shifts the binary representation of the left-hand side (LHS) operand to the left by the number of positions specified by the right-hand side (RHS) operand. Mechanics:
  • Zero-filling: Vacated bit positions on the right are filled with zeros.
  • Promotion: Integer promotions are performed on both operands before the shift. The return type is the type of the promoted LHS operand.
  • Mathematical Equivalence: Shifting left by nn positions is mathematically equivalent to multiplying the LHS by 2n2^n, provided no overflow occurs.
  • Undefined Behavior (UB): The operation results in UB if the RHS is negative, or if the RHS is greater than or equal to the bit-width of the promoted LHS type.
#include <cstdint>

int main() {
    uint8_t a = 0b00001101; // Decimal 13
    
    // 'a' undergoes integer promotion to 'int' before the shift.
    // The result is explicitly cast back to uint8_t for this assignment.
    uint8_t b = static_cast<uint8_t>(a << 2); // Evaluates to 0b00110100 (Decimal 52)
    
    return 0;
}

​
2. Stream Insertion (Overloaded Behavior)

When the LHS operand is an instance of std::ostream (such as std::cout), the << operator is overloaded to perform stream insertion. It formats the RHS operand into a sequence of characters and inserts them into the stream buffer. The standard library implements this via two mechanisms:
  1. Member function overloads: Used for fundamental types (e.g., int, double, bool) and const void*.
  2. Non-member function overloads: Used for standard library types (e.g., std::string, const char*) to allow the stream to remain the LHS operand without modifying the std::ostream class itself.
Mechanics:
  • Return by Reference: The operator strictly returns a reference to the LHS std::ostream object (std::ostream&), which enables operator chaining.
  • Associativity vs. Evaluation Order: The left-to-right associativity of << dictates the parsing and grouping of the expression (i.e., a << b << c parses as (a << b) << c). However, associativity does not govern the evaluation order of the operands. Prior to C++17, the evaluation of arguments in a chained << expression was unsequenced. Since C++17, the << operator guarantees strict left-to-right sequential evaluation of its operands.
#include <iostream>
#include <string>

// Example of a user-defined non-member overload
struct CustomData { int id; };
std::ostream& operator<<(std::ostream& os, const CustomData& data) {
    return os << data.id; 
}

int main() {
    int var1 = 42;
    std::string var2 = " items: ";
    CustomData data{7};

    // Chaining stream insertions
    std::cout << var1 << var2 << data << '\n';

    // Structural equivalent demonstrating parsing and overload resolution:
    // 1. std::cout.operator<<(var1) -> member overload for 'int'
    // 2. operator<<(..., var2)      -> non-member overload for 'std::string'
    // 3. operator<<(..., data)      -> user-defined non-member overload
    // 4. operator<<(..., '\n')      -> non-member overload for 'char'
    operator<<(
        operator<<(
            operator<<(
                std::cout.operator<<(var1), 
            var2), 
        data), 
    '\n');

    return 0;
}

​
Precedence and Associativity

Regardless of whether it is used for bitwise shifting or stream insertion, the << operator maintains the same parsing rules in the C++ grammar:
  • Associativity: Left-to-right.
  • Precedence: It sits below arithmetic operators (+, -, *, /) but above relational operators (<, >, <=, >=) and equality operators (==, !=).
Because of this precedence level, arithmetic expressions on the RHS of a stream insertion do not require parentheses, whereas bitwise operations, relational operations, or equality operations passed into a stream do require parentheses to prevent compilation errors or unintended parsing. 
#include <iostream>

int main() {
    int val = 4;
    int a = 1;
    int b = 1;

    // Precedence mechanics
    std::cout << 5 + 3 << '\n';       // Valid: Evaluates as std::cout << (5 + 3)
    std::cout << (val << 1) << '\n';  // Parentheses required: Bitwise shift inside stream insertion
    std::cout << (a == b) << '\n';    // Parentheses required: Equality operation inside stream insertion

    return 0;
}
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