constants¶
scalar_constants class¶
template <typename T> scalar_constants
pi variable (scalar_constants::pi)¶
constexpr static T pi =
static_cast<T>(3.1415926535897932384626433832795)
The mathematical constant π (pi).
Template param T The numeric type.
sqr_pi variable (scalar_constants::sqr_pi)¶
constexpr static T sqr_pi =
static_cast<T>(9.8696044010893586188344909998762)
The square of π (pi²).
Template param T The numeric type.
recip_pi variable (scalar_constants::recip_pi)¶
constexpr static T recip_pi =
static_cast<T>(0.31830988618379067153776752674503)
The reciprocal of π (1/π).
Template param T The numeric type.
degtorad variable (scalar_constants::degtorad)¶
constexpr static T degtorad = static_cast<T>(pi / 180)
Degrees to radians conversion factor (π / 180).
Template param T The numeric type.
radtodeg variable (scalar_constants::radtodeg)¶
constexpr static T radtodeg = static_cast<T>(pi * 180)
Radians to degrees conversion factor (π * 180).
Template param T The numeric type.
e variable (scalar_constants::e)¶
constexpr static T e =
static_cast<T>(2.718281828459045235360287471352662)
The mathematical constant e (Euler's number).
Template param T The numeric type.
recip_log_2 variable (scalar_constants::recip_log_2)¶
constexpr static T recip_log_2 = static_cast<T>(
1.442695040888963407359924681001892137426645954)
The reciprocal of the natural logarithm of 2 (1 / ln(2)).
Template param T The numeric type.
recip_log_10 variable (scalar_constants::recip_log_10)¶
constexpr static T recip_log_10 =
static_cast<T>(0.43429448190325182765112891891661)
The reciprocal of the natural logarithm of 10 (1 / ln(10)).
Template param T The numeric type.
log_2 variable (scalar_constants::log_2)¶
constexpr static T log_2 =
static_cast<T>(0.69314718055994530941723212145818)
The natural logarithm of 2 (ln(2)).
Template param T The numeric type.
log_10 variable (scalar_constants::log_10)¶
constexpr static T log_10 =
static_cast<T>(2.3025850929940456840179914546844)
The natural logarithm of 10 (ln(10)).
Template param T The numeric type.
sqrt_2 variable (scalar_constants::sqrt_2)¶
constexpr static T sqrt_2 =
static_cast<T>(1.4142135623730950488016887242097)
The square root of 2 (√2).
Template param T The numeric type.
epsilon variable (scalar_constants::epsilon)¶
constexpr static T epsilon =
std::numeric_limits<T>::epsilon()
The machine epsilon — the smallest value such that 1 + epsilon ≠ 1.
Template param T The numeric type.
infinity variable (scalar_constants::infinity)¶
constexpr static T infinity =
std::numeric_limits<T>::infinity()
The representation of positive infinity for the type T.
Template param T The numeric type.
neginfinity variable (scalar_constants::neginfinity)¶
constexpr static T neginfinity =
-std::numeric_limits<T>::infinity()
The representation of negative infinity for the type T.
Template param T The numeric type.
qnan variable (scalar_constants::qnan)¶
constexpr static T qnan =
std::numeric_limits<T>::quiet_NaN()
A quiet NaN (Not-a-Number) value for the type T.
This value does not raise floating-point exceptions.
Template param T The numeric type.
constants class¶
template <typename T> constants
c_pi variable¶
template <typename T, int m = 1, int d = 1>
constexpr inline subtype<T> c_pi =
subtype<T>(3.1415926535897932384626433832795 * m / d)
The mathematical constant π (pi), scaled by m/d.
Template param T The numeric type.
Template param m Numerator multiplier (default is 1).
Template param d Denominator divisor (default is 1).
Note Examples:
- c_pi<f64, 4> = 4π
- c_pi<f64, 3, 4> = 3/4π
c_sqr_pi variable¶
template <typename T, int m = 1, int d = 1>
constexpr inline subtype<T> c_sqr_pi =
subtype<T>(9.8696044010893586188344909998762 * m / d)
The square of π (pi²), scaled by m/d.
Template param T The numeric type.
Template param m Numerator multiplier (default is 1).
Template param d Denominator divisor (default is 1).
Note Examples:
- c_sqr_pi<f64, 4> = 4π²
- c_sqr_pi<f64, 3, 4> = 3/4π²
c_recip_pi variable¶
template <typename T, int m = 1, int d = 1>
constexpr inline subtype<T> c_recip_pi =
subtype<T>(0.31830988618379067153776752674503 * m / d)
The reciprocal of π (1/π), scaled by m/d.
Template param T The numeric type.
Template param m Numerator multiplier (default is 1).
Template param d Denominator divisor (default is 1).
Note Examples:
- c_recip_pi<f64> = 1/π
- c_recip_pi<f64, 4> = 4/π
c_degtorad variable¶
template <typename T>
constexpr inline subtype<T> c_degtorad = c_pi<T, 1, 180>
Degrees to radians conversion factor (π / 180).
Template param T The numeric type.
c_radtodeg variable¶
template <typename T>
constexpr inline subtype<T> c_radtodeg = c_recip_pi<T, 180>
Radians to degrees conversion factor (180 / π).
Template param T The numeric type.
c_e variable¶
template <typename T, int m = 1, int d = 1>
constexpr inline subtype<T> c_e =
subtype<T>(2.718281828459045235360287471352662 * m / d)
The mathematical constant e (Euler's number), scaled by m/d.
Template param T The numeric type.
Template param m Numerator multiplier (default is 1).
Template param d Denominator divisor (default is 1).
c_mantissa_bits variable¶
template <typename T>
constexpr inline unsigned c_mantissa_bits =
sizeof(subtype<T>) == 32 ? 23 : 52
The number of mantissa bits for the given floating-point type.
Template param T The numeric type.
c_mantissa_mask variable¶
template <typename T>
constexpr inline subtype<T> c_mantissa_mask =
(subtype<T>(1) << c_mantissa_bits<T>)-1
The bitmask for the mantissa of the floating-point representation.
Template param T The numeric type.
c_epsilon variable¶
template <typename T>
constexpr inline subtype<T> c_epsilon =
(std::numeric_limits<subtype<T>>::epsilon())
The machine epsilon — the smallest value such that 1 + epsilon ≠ 1.
Template param T The numeric type.
c_infinity variable¶
template <typename T>
constexpr inline subtype<T> c_infinity =
std::numeric_limits<subtype<T>>::infinity()
Positive infinity representation.
Template param T The numeric type.
c_neginfinity variable¶
template <typename T>
constexpr inline subtype<T> c_neginfinity =
-std::numeric_limits<subtype<T>>::infinity()
Negative infinity representation.
Template param T The numeric type.
c_qnan variable¶
template <typename T>
constexpr inline subtype<T> c_qnan =
std::numeric_limits<subtype<T>>::quiet_NaN()
A quiet NaN (Not-a-Number) value.
Template param T The numeric type.
c_recip_log_2 variable¶
template <typename T>
constexpr inline subtype<T> c_recip_log_2 = subtype<T>(
1.442695040888963407359924681001892137426645954)
The reciprocal of the natural logarithm of 2 (1 / ln(2)).
Template param T The numeric type.
c_recip_log_10 variable¶
template <typename T>
constexpr inline subtype<T> c_recip_log_10 =
subtype<T>(0.43429448190325182765112891891661)
The reciprocal of the natural logarithm of 10 (1 / ln(10)).
Template param T The numeric type.
c_log_2 variable¶
template <typename T>
constexpr inline subtype<T> c_log_2 =
subtype<T>(0.69314718055994530941723212145818)
The natural logarithm of 2 (ln(2)).
Template param T The numeric type.
c_log_10 variable¶
template <typename T>
constexpr inline subtype<T> c_log_10 =
subtype<T>(2.3025850929940456840179914546844)
The natural logarithm of 10 (ln(10)).
Template param T The numeric type.
c_sqrt_2 variable¶
template <typename T, int m = 1, int d = 1>
constexpr inline subtype<T> c_sqrt_2 =
subtype<T>(1.4142135623730950488016887242097 * m / d)
The square root of 2 (√2), scaled by m/d.
Template param T The numeric type.
Template param m Numerator multiplier (default is 1).
Template param d Denominator divisor (default is 1).
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