The FixedMath library meticulously handles the addition of fixed-point numbers (fixed_t), ensuring precision and correctness across various operations. This includes support for mixed-type arithmetic involving fixed_t, integers, and floating-point numbers.
fixed_additioni(fixed_t lh, fixed_t rh) noexcept: This function calculates the sum of two fixed_t values, employing checks to prevent overflow and underflow. If the sum exceeds the representable range, it returns NaN to signal an error in the operation.Promotion to Double: For operations involving a double, the fixed_t value is promoted to double precision before the addition, ensuring that the operation leverages floating-point precision.
Promotion to Fixed: If an arithmetic operation involves types other than fixed_t, the non-fixed type is promoted to fixed_t using promote_to_fixed, allowing the operation to proceed with fixed-point precision.
Operator +=: Modifies the left-hand operand by adding the right-hand operand to it. The operand on the right can be any arithmetic type, and the operation is conducted with appropriate type promotions to maintain precision.
Operator +: Defines addition between two operands of potentially mixed types. The result is either a fixed_t or a double, depending on whether any operand is a double, to ensure the operation’s precision is optimized for the operand types.
promoted_double_addition: Specifically handles addition where at least one of the operands is a double, promoting the operation to double precision.
promoted_fixed_addition: Manages the addition of two arithmetic values, promoting them to fixed_t if necessary, to perform the operation within the fixed-point domain.
The FixedMath addition operations are designed with an emphasis on safety, ensuring that any potential overflow or underflow conditions are handled gracefully, returning NaN where appropriate.
fixed_t a = ...; // Initialize with some value
fixed_t b = ...; // Another fixed_t value
fixed_t result = a + b; // Addition of two fixed_t values
int scalar = 5;
fixed_t result2 = a + scalar; // Addition with an integer scalar
double d = 2.0;
auto result3 = a + d; // Addition with a double, result is promoted to double