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The <= (less than or equal to) operator is a binary relational operator that evaluates whether its left-hand operand is strictly less than or mathematically equivalent to its right-hand operand. It yields a bool prvalue (true or false). 
lhs <= rhs

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Type Mechanics and Evaluation

The behavior of the <= operator depends strictly on the types of the operands provided:
  • Arithmetic Types: If the operands are of different numeric types (e.g., int and double), the compiler performs standard arithmetic conversions (typically promoting the narrower type to the wider type) before executing the comparison.
  • Pointers: When applied to pointers, <= compares memory addresses. This comparison is strictly defined by the C++ standard in two primary scenarios:
    1. Both pointers point to elements within the same array (or to one past the last element of that array).
    2. Both pointers point to non-static data members of the same object. In this case, the later-declared member compares greater, provided both members share the same access control (e.g., both public) and are not part of a union.
    Comparing pointers to unrelated objects results in unspecified behavior.
  • Standard Library Types: For containers (like std::vector) and strings (std::string), the <= operator performs a lexicographical comparison. Prior to C++20, containers like std::vector rely on std::lexicographical_compare, which uses the elements’ operator< to determine ordering and equivalence (where a and b are equivalent if !(a < b) && !(b < a)). Conversely, std::string’s relational operators call std::string::compare, which delegates to std::char_traits<char>::compare. This determines ordering directly (often using memcmp or built-in character comparisons) rather than relying on the character type’s operator<. In C++20 and later, standard library types utilize the three-way comparison operator (operator<=>).

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Operator Overloading (Pre-C++20)

For user-defined types, <= can be overloaded. Best practice dictates implementing it as a non-member function to allow symmetric implicit conversions on both the left-hand and right-hand sides. To maintain logical consistency, it should be implemented strictly in terms of a custom operator<. 
class CustomType {
    int data;
public:
    // Implicit conversion allowed for symmetric comparisons
    CustomType(int val) : data(val) {}

    // Define the primary relational operator
    friend bool operator<(const CustomType& lhs, const CustomType& rhs) {
        return lhs.data < rhs.data;
    }

    // Implement <= strictly in terms of operator<
    friend bool operator<=(const CustomType& lhs, const CustomType& rhs) {
        return !(rhs < lhs); 
    }
};

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C++20 Synthesis via Three-Way Comparison (<=>)

In modern C++ (C++20 and later), explicitly overloading the <= operator is largely obsolete. The compiler will automatically resolve <= operations if the three-way comparison operator (the “spaceship” operator, <=>) is defined. When the compiler encounters lhs <= rhs, it does not generate a standalone operator<= function. Instead, it resolves the operation by rewriting the expression at the call site as (lhs <=> rhs) <= 0. 
#include <compare>

class ModernType {
    int data;
public:
    // Defaulting <=> implicitly declares a defaulted operator==.
    // Operations for <=, <, >, >=, and != are resolved via compiler rewrites at the call site.
    auto operator<=>(const ModernType&) const = default;
};

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Operator Precedence and Associativity

  • Precedence: The <= operator has higher precedence than equality operators (==, !=) but lower precedence than the three-way comparison operator (<=>) and arithmetic operators (+, -, *, /).
  • Associativity: It evaluates left-to-right. However, chaining relational operators (e.g., a <= b <= c) does not behave mathematically. The expression a <= b evaluates to a bool prvalue, which is then implicitly converted to an integer (0 or 1) and compared against c.
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