Functions
Scalar	sin (const Scalar q)
	Sine of a dimensionless quantity.

Scalar	cos (const Scalar q)
	Cosine of a dimensionless quantity.

Scalar	tan (const Scalar q)
	Tangent of a dimensionless quantity.

Scalar	asin (const Scalar q)
	Arc sine (inverse sine)

Scalar	acos (const Scalar q)
	Arc cosine (inverse cosine)

Scalar	atan (const Scalar q)
	Arc tangent (inverse tangent)

Scalar	atan2 (const Scalar y, const Scalar x)
	Two-argument arc tangent (atan2)

Scalar	sinh (const Scalar q)
	Hyperbolic sine.

Scalar	cosh (const Scalar q)
	Hyperbolic cosine.

Scalar	tanh (const Scalar q)
	Hyperbolic tangent.

Scalar	asinh (const Scalar q)
	Inverse hyperbolic sine.

Scalar	acosh (const Scalar q)
	Inverse hyperbolic cosine.

Scalar	atanh (const Scalar q)
	Inverse hyperbolic tangent.

Scalar	log (const Scalar q)
	Natural logarithm (base e)

Scalar	log10 (const Scalar q)
	Base-10 logarithm.

Scalar	log2 (const Scalar q)
	Base-2 logarithm.

Scalar	log1p (const Scalar q)
	log(1 + q) with higher precision for small q

Scalar	exp (const Scalar q)
	Exponential (e^q)

Scalar	expm1 (const Scalar q)
	exp(q) - 1 with higher precision for small q

Scalar	exp2 (const Scalar q)
	Base-2 exponential (2^q)

template<int Power, typename UnitT >
auto	pow (Quantity< UnitT > q)
	Raise a quantity to an integer power.

template<typename UnitT >
auto	square (Quantity< UnitT > q)
	Square of a quantity.

template<typename UnitT >
auto	cube (Quantity< UnitT > q)
	Cube of a quantity.

template<int N, typename UnitT >
auto	root (Quantity< UnitT > q)
	N-th root of a quantity.

template<typename UnitT >
auto	sqrt (Quantity< UnitT > q)
	Square root of a quantity.

template<typename UnitT >
auto	cbrt (Quantity< UnitT > q)
	Cube root of a quantity.

template<typename UnitT >
auto	abs (Quantity< UnitT > q)
	Absolute value of a quantity.

template<typename UnitT >
Quantity< UnitT >	fmod (Quantity< UnitT > x, Quantity< UnitT > y)
	Floating-point remainder of x / y.

template<typename UnitT >
Quantity< UnitT >	modf (Quantity< UnitT > x, Quantity< UnitT > &y)
	Decompose into integer and fractional parts.

template<typename UnitT >
Quantity< UnitT >	max (Quantity< UnitT > x, Quantity< UnitT > y)
	Maximum of two quantities.

template<typename UnitT >
Quantity< UnitT >	min (Quantity< UnitT > x, Quantity< UnitT > y)
	Minimum of two quantities.

template<typename UnitT >
Quantity< UnitT >	clamp (Quantity< UnitT > x, Quantity< UnitT > min, Quantity< UnitT > max)
	Clamp a quantity between min and max bounds.

template<typename UnitT >
Quantity< UnitT >	floor (Quantity< UnitT > x)
	Floor of a quantity (largest integer <= x)

template<typename UnitT >
bool	isnan (Quantity< UnitT > x)
	Determine whether a quantity is nan.

template<typename UnitT >
bool	isfinite (Quantity< UnitT > x)
	Determine whether a quantity is finite.

Function Documentation

◆ abs()

template<typename UnitT >

auto Phyth::Utils::abs ( Quantity< UnitT > q )

Absolute value of a quantity.

Parameters

q	The quantity

Returns: Quantity with the same unit, value = |q.value|

Definition at line 332 of file QuantityFuncs.hpp.

◆ acos()

Scalar Phyth::Utils::acos ( const Scalar q )

inline

Arc cosine (inverse cosine)

Parameters

q	Value in [-1, 1] (dimensionless)

Returns: Angle in radians (dimensionless)

Definition at line 57 of file QuantityFuncs.hpp.

◆ acosh()

Scalar Phyth::Utils::acosh ( const Scalar q )

inline

Inverse hyperbolic cosine.

Parameters

q	Value (dimensionless)

Returns: acosh(q) as a dimensionless scalar

Definition at line 128 of file QuantityFuncs.hpp.

◆ asin()

Scalar Phyth::Utils::asin ( const Scalar q )

inline

Arc sine (inverse sine)

Parameters

q	Value in [-1, 1] (dimensionless)

Returns: Angle in radians (dimensionless)

Definition at line 47 of file QuantityFuncs.hpp.

◆ asinh()

Scalar Phyth::Utils::asinh ( const Scalar q )

inline

Inverse hyperbolic sine.

Parameters

q	Value (dimensionless)

Returns: asinh(q) as a dimensionless scalar

Definition at line 118 of file QuantityFuncs.hpp.

◆ atan()

Scalar Phyth::Utils::atan ( const Scalar q )

inline

Arc tangent (inverse tangent)

Parameters

q	Value (dimensionless)

Returns: Angle in radians (dimensionless)

Definition at line 67 of file QuantityFuncs.hpp.

◆ atan2()

Scalar Phyth::Utils::atan2	(	const Scalar	y,
		const Scalar	x
	)

inline

Two-argument arc tangent (atan2)

Parameters

y	Y component (dimensionless)
x	X component (dimensionless)

Returns: Angle in radians (dimensionless), in [-pi, pi]

Definition at line 78 of file QuantityFuncs.hpp.

◆ atanh()

Scalar Phyth::Utils::atanh ( const Scalar q )

inline

Inverse hyperbolic tangent.

Parameters

q	Value in (-1, 1) (dimensionless)

Returns: atanh(q) as a dimensionless scalar

Definition at line 138 of file QuantityFuncs.hpp.

◆ cbrt()

template<typename UnitT >

auto Phyth::Utils::cbrt ( Quantity< UnitT > q )

Cube root of a quantity.

Parameters

q	The quantity to take the cube root of

Returns: Quantity with dimension DimT^(1/3)

Definition at line 321 of file QuantityFuncs.hpp.

◆ clamp()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::clamp	(	Quantity< UnitT >	x,
		Quantity< UnitT >	min,
		Quantity< UnitT >	max
	)

Clamp a quantity between min and max bounds.

Parameters

x	Value to clamp
min	Lower bound (inclusive)
max	Upper bound (inclusive)

Returns: If x < min, returns min; if x > max, returns max; otherwise returns x

Definition at line 400 of file QuantityFuncs.hpp.

◆ cos()

Scalar Phyth::Utils::cos ( const Scalar q )

inline

Cosine of a dimensionless quantity.

Parameters

q	Angle in radians (dimensionless)

Returns: cos(q) as a dimensionless scalar

Definition at line 27 of file QuantityFuncs.hpp.

◆ cosh()

Scalar Phyth::Utils::cosh ( const Scalar q )

inline

Hyperbolic cosine.

Parameters

q	Value (dimensionless)

Returns: cosh(q) as a dimensionless scalar

Definition at line 98 of file QuantityFuncs.hpp.

◆ cube()

template<typename UnitT >

auto Phyth::Utils::cube ( Quantity< UnitT > q )

Cube of a quantity.

Template Parameters

UnitT Unit type of the input quantity

Parameters

q	The quantity to cube

Returns: Quantity with dimension DimT^3

Definition at line 271 of file QuantityFuncs.hpp.

◆ exp()

Scalar Phyth::Utils::exp ( const Scalar q )

inline

Exponential (e^q)

Parameters

q	Value (dimensionless)

Returns: e^q as a dimensionless scalar

Definition at line 188 of file QuantityFuncs.hpp.

◆ exp2()

Scalar Phyth::Utils::exp2 ( const Scalar q )

inline

Base-2 exponential (2^q)

Parameters

q	Value (dimensionless)

Returns: 2^q as a dimensionless scalar

Definition at line 208 of file QuantityFuncs.hpp.

◆ expm1()

Scalar Phyth::Utils::expm1 ( const Scalar q )

inline

exp(q) - 1 with higher precision for small q

Parameters

q	Value (dimensionless)

Returns: e^q - 1 as a dimensionless scalar

Definition at line 198 of file QuantityFuncs.hpp.

◆ floor()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::floor ( Quantity< UnitT > x )

Floor of a quantity (largest integer <= x)

Parameters

x	Input quantity

Returns: Quantity with the same unit, value = floor(x.value)

Definition at line 412 of file QuantityFuncs.hpp.

◆ fmod()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::fmod	(	Quantity< UnitT >	x,
		Quantity< UnitT >	y
	)

Floating-point remainder of x / y.

Parameters

x	Dividend
y	Divisor

Returns: x - n*y for some integer n, with the same unit as x and y

Definition at line 344 of file QuantityFuncs.hpp.

◆ isfinite()

template<typename UnitT >

bool Phyth::Utils::isfinite ( Quantity< UnitT > x )

Determine whether a quantity is finite.

Parameters

x	Input quantity

Returns: Return value = isfintie(x.value)

Definition at line 434 of file QuantityFuncs.hpp.

◆ isnan()

template<typename UnitT >

bool Phyth::Utils::isnan ( Quantity< UnitT > x )

Determine whether a quantity is nan.

Parameters

x	Input quantity

Returns: Return value = isnan(x.value)

Definition at line 423 of file QuantityFuncs.hpp.

◆ log()

Scalar Phyth::Utils::log ( const Scalar q )

inline

Natural logarithm (base e)

Parameters

q	Positive value (dimensionless)

Returns: ln(q) as a dimensionless scalar

Definition at line 148 of file QuantityFuncs.hpp.

◆ log10()

Scalar Phyth::Utils::log10 ( const Scalar q )

inline

Base-10 logarithm.

Parameters

q	Positive value (dimensionless)

Returns: log10(q) as a dimensionless scalar

Definition at line 158 of file QuantityFuncs.hpp.

◆ log1p()

Scalar Phyth::Utils::log1p ( const Scalar q )

inline

log(1 + q) with higher precision for small q

Parameters

q	Value (dimensionless)

Returns: log(1+q) as a dimensionless scalar

Definition at line 178 of file QuantityFuncs.hpp.

◆ log2()

Scalar Phyth::Utils::log2 ( const Scalar q )

inline

Base-2 logarithm.

Parameters

q	Positive value (dimensionless)

Returns: log2(q) as a dimensionless scalar

Definition at line 168 of file QuantityFuncs.hpp.

◆ max()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::max	(	Quantity< UnitT >	x,
		Quantity< UnitT >	y
	)

Maximum of two quantities.

Parameters

x	First quantity
y	Second quantity

Returns: The larger quantity

Definition at line 373 of file QuantityFuncs.hpp.

◆ min()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::min	(	Quantity< UnitT >	x,
		Quantity< UnitT >	y
	)

Minimum of two quantities.

Parameters

x	First quantity
y	Second quantity

Returns: The smaller quantity

Definition at line 386 of file QuantityFuncs.hpp.

◆ modf()

template<typename UnitT >

Quantity< UnitT > Phyth::Utils::modf	(	Quantity< UnitT >	x,
		Quantity< UnitT > &	y
	)

Decompose into integer and fractional parts.

Parameters

x	Input quantity
y	Output: integer part (same unit as x)

Returns: Fractional part (same unit as x)

Example: auto x = 3.14_m; auto frac = Utils::modf(x, int_part); // int_part = 3_m, frac = 0.14_m

Definition at line 361 of file QuantityFuncs.hpp.

◆ pow()

template<int Power, typename UnitT >

auto Phyth::Utils::pow ( Quantity< UnitT > q )

Raise a quantity to an integer power.

The resulting dimension is the original dimension raised to the power.

Template Parameters

Power	Integer exponent (can be negative)
UnitT	Unit type of the input quantity

Parameters

q	The quantity to raise

Returns: Quantity with dimension DimT^Power

Example: auto t = 2.0_s; auto t2 = Utils::pow<2>(t); // 4 s^2 auto inv_t = Utils::pow<-1>(t); // 0.5 s^-1

Definition at line 228 of file QuantityFuncs.hpp.

◆ root()

template<int N, typename UnitT >

auto Phyth::Utils::root ( Quantity< UnitT > q )

N-th root of a quantity.

Template Parameters

N	Root index (positive integer)
UnitT	Unit type of the input quantity

Parameters

q	The quantity to take the root of

Returns: Quantity with dimension DimT^(1/N)

Example: auto area = 9.0_m2; auto length = Utils::root<2>(area); // 3.0_m

Definition at line 291 of file QuantityFuncs.hpp.

◆ sin()

Scalar Phyth::Utils::sin ( const Scalar q )

inline

Sine of a dimensionless quantity.

Parameters

q	Angle in radians (dimensionless)

Returns: sin(q) as a dimensionless scalar

Definition at line 17 of file QuantityFuncs.hpp.

◆ sinh()

Scalar Phyth::Utils::sinh ( const Scalar q )

inline

Hyperbolic sine.

Parameters

q	Value (dimensionless)

Returns: sinh(q) as a dimensionless scalar

Definition at line 88 of file QuantityFuncs.hpp.

◆ sqrt()

template<typename UnitT >

auto Phyth::Utils::sqrt ( Quantity< UnitT > q )

Square root of a quantity.

Parameters

q	The quantity to take the square root of

Returns: Quantity with dimension DimT^(1/2)

Example: auto area = 9.0_m2; auto length = Utils::sqrt(area); // 3.0_m

Definition at line 310 of file QuantityFuncs.hpp.

◆ square()

template<typename UnitT >

auto Phyth::Utils::square ( Quantity< UnitT > q )

Square of a quantity.

Template Parameters

UnitT Unit type of the input quantity

Parameters

q	The quantity to square

Returns: Quantity with dimension DimT^2

Example: auto t = 2.0_s; auto t2 = Utils::square(t); // 4 s^2

Definition at line 256 of file QuantityFuncs.hpp.

◆ tan()

Scalar Phyth::Utils::tan ( const Scalar q )

inline

Tangent of a dimensionless quantity.

Parameters

q	Angle in radians (dimensionless)

Returns: tan(q) as a dimensionless scalar

Definition at line 37 of file QuantityFuncs.hpp.

◆ tanh()

Scalar Phyth::Utils::tanh ( const Scalar q )

inline

Hyperbolic tangent.

Parameters

q	Value (dimensionless)

Returns: tanh(q) as a dimensionless scalar

Definition at line 108 of file QuantityFuncs.hpp.

Functions

Function Documentation

◆ abs()

◆ acos()

◆ acosh()

◆ asin()

◆ asinh()

◆ atan()

◆ atan2()

◆ atanh()

◆ cbrt()

◆ clamp()

◆ cos()

◆ cosh()

◆ cube()

◆ exp()

◆ exp2()

◆ expm1()

◆ floor()

◆ fmod()

◆ isfinite()

◆ isnan()

◆ log()

◆ log10()

◆ log1p()

◆ log2()

◆ max()

◆ min()

◆ modf()

◆ pow()

◆ root()

◆ sin()

◆ sinh()

◆ sqrt()

◆ square()

◆ tan()

◆ tanh()