Math Functions

Constexpr mathematical functions with no standard library dependency. More...

Functions
template<typename T >
constexpr T	consteig::abs (const T x)
	Absolute value of a real number.
template<typename T >
constexpr Complex< T >	consteig::csqrt (const T x)
	Complex-valued square root of a real number.
template<typename T >
constexpr auto	consteig::exp (const T x) noexcept
	Computes the exponential of a real number.
template<typename T >
constexpr T	consteig::pow (const T x, const unsigned int n)
	Raise x to an unsigned integer power via exponentiation by squaring.
template<typename T >
constexpr T	consteig::pow (const T x, const int n)
	Raise x to a signed integer power.
template<typename T >
constexpr T	consteig::sgn (const T x)
	Signum function: returns +1, -1, or 0.
template<typename T >
constexpr T	consteig::sqrt (const T x)
	Constexpr square root.
template<typename T >
constexpr auto	consteig::sin (const T x) noexcept
	Computes the sine of x (in radians).
template<typename T >
constexpr auto	consteig::cos (const T x) noexcept
	Computes the cosine of x (in radians).
template<typename T >
constexpr auto	consteig::tan (const T x) noexcept
	Computes the tangent of x (in radians) as sin_series(r) / cos_series(r), where r = trig_reduce(x).
template<typename T >
constexpr bool	consteig::is_float (T const &)
	Returns true if T is a floating-point type (value overload).
template<typename T >
constexpr bool	consteig::is_float ()
	Returns true if T is a floating-point type (type-only overload).
template<typename T >
constexpr T	consteig::epsilon ()
	Machine epsilon for type T.

Detailed Description

Constexpr mathematical functions with no standard library dependency.

Function Documentation

abs()

template<typename T >

constexpr T consteig::abs ( const T x )

constexpr

Absolute value of a real number.

Returns |x|. Handles signed zero correctly (returns positive zero).

Template Parameters

T	Numeric type.

Parameters

x	Input value.

Returns

Non-negative absolute value of x.

csqrt()

template<typename T >

constexpr Complex< T > consteig::csqrt ( const T x )

constexpr

Complex-valued square root of a real number.

For non-negative x, returns {sqrt(x), 0}. For negative x, returns {0, sqrt(|x|)} (purely imaginary result). Use this instead of sqrt when the input may be negative.

Template Parameters

T	Numeric type.

Parameters

x	Input value (may be negative).

Returns

Complex<T> square root.

pow() [1/2]

template<typename T >

constexpr T consteig::pow ( const T x, const unsigned int n )

constexpr

Raise x to an unsigned integer power via exponentiation by squaring.

Template Parameters

T	Numeric type.

Parameters

x	Base value.
n	Non-negative exponent.

Returns

x^n.

pow() [2/2]

template<typename T >

constexpr T consteig::pow ( const T x, const int n )

constexpr

Raise x to a signed integer power.

Negative exponents compute 1 / x^|n|.

Template Parameters

T	Numeric type.

Parameters

x	Base value.
n	Integer exponent (may be negative).

Returns

x^n.

sgn()

template<typename T >

constexpr T consteig::sgn ( const T x )

constexpr

Signum function: returns +1, -1, or 0.

Template Parameters

T	Numeric type.

Parameters

x	Input value.

Returns

+1 if x > 0, -1 if x < 0, 0 if x == 0.

sqrt()

template<typename T >

constexpr T consteig::sqrt ( const T x )

constexpr

Constexpr square root.

For floating-point types, uses Newton's method with range reduction. For integer types, returns the floor of the exact square root. Negative inputs produce a poison value (compile-time error in constexpr context); use csqrt if the input may be negative.

Template Parameters

T	Numeric type.

Parameters

x	Non-negative input value.

Returns

Square root of x.

tan()

template<typename T >

constexpr auto consteig::tan ( const T x )

constexprnoexcept

Computes the tangent of x (in radians) as sin_series(r) / cos_series(r), where r = trig_reduce(x).

NOTE: tan has singularities where cos_series(r) == 0 (x = pi/2 + k*pi for integer k). Near these points the result can be very large, +/-infinity, or NaN. This function does not clamp or guard against those cases.

is_float() [1/2]

template<typename T >

constexpr bool consteig::is_float ( T const & )

constexpr

Returns true if T is a floating-point type (value overload).

Template Parameters

T	Type to test.

is_float() [2/2]

template<typename T >

constexpr bool consteig::is_float ( )

constexpr

Returns true if T is a floating-point type (type-only overload).

Recognized floating-point types: float, double, long double. All other types (including integer types) return false.

Template Parameters

T	Type to test.

static_assert(consteig::is_float<double>(), "");
static_assert(!consteig::is_float<int>(), "");

epsilon()

template<typename T >

constexpr T consteig::epsilon ( )

constexpr

Machine epsilon for type T.

Returns the smallest value eps such that 1 + eps != 1 in type T. Hardcoded for float and double to IEEE 754 values for O(1) constexpr performance. Falls back to iterative computation for long double and other types.

For non-floating-point types, returns T(0).

Template Parameters

T	Numeric type.

Returns

Machine epsilon, or T(0) for integer types.