Operations

Unary operations ℝ → ℝ Binary operations ℝ × ℝ → ℝ Structural properties Status

These operate on a single operand x ∈ decimal_t<T>.

Category	Operation	Symbol / Function	Description	Notes
Arithmetic	Identity	`+x`	Returns `x` unchanged	No-op
Arithmetic	Negation	`-x`	Additive inverse	`x + (-x) = 0`
Root	Square root	`sqrt(x)`	√x	Exact at perfect squares
Exponential	Natural exp	`exp(x)`	e^x
Logarithmic	Natural log	`log(x)`	ln(x)	`log(1)=0`
Logarithmic	Base-10 log	`log10(x)`	log₁₀(x)
Trigonometric	Sine	`sin(x)`	sin(x)
Trigonometric	Cosine	`cos(x)`	cos(x)
Trigonometric	Tangent	`tan(x)`	tan(x)
Hyperbolic	sinh	`sinh(x)`	sinh(x)
Hyperbolic	cosh	`cosh(x)`	cosh(x)
Hyperbolic	tanh	`tanh(x)`	tanh(x)
Inverse trig	arcsin	`asin(x)`	sin⁻¹(x)
Inverse trig	arccos	`acos(x)`	cos⁻¹(x)
Inverse trig	arctan	`atan(x)`	tan⁻¹(x)
Inverse hyperbolic	asinh	`asinh(x)`
Inverse hyperbolic	acosh	`acosh(x)`
Inverse hyperbolic	atanh	`atanh(x)`
Special	Gamma	`tgamma(x)`	Γ(x)
Special	Log Gamma	`lgamma(x)`	log Γ(x)

These operate on two operands x, y ∈ decimal_t<T>.

Category	Operation	Symbol	Description	Algebraic Guarantees
Arithmetic	Addition	`x + y`	Sum	Commutative, associative
Arithmetic	Subtraction	`x - y`	Difference
Arithmetic	Multiplication	`x * y`	Product	Commutative, associative
Arithmetic	Division	`x / y`	Quotient	`x/x = 1` (x ≠ 0)
Assignment	Add assign	`x += y`	In-place addition
Assignment	Sub assign	`x -= y`	In-place subtraction
Assignment	Mul assign	`x *= y`	In-place multiplication	(expected / conventional)
Assignment	Div assign	`x /= y`	In-place division	(expected / conventional)

Enforced where exact arithmetic permits.