Scaling constants

Functions
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::blue_max () noexcept
	Blue's max constant B for the sum of squares.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::blue_min () noexcept
	Blue's min constant b for the sum of squares.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::blue_scalingMax () noexcept
	Blue's scaling constant for numbers bigger than B.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::blue_scalingMin () noexcept
	Blue's scaling constant for numbers smaller than b.
template<typename real_t >
int	tlapack::digits () noexcept
	Digits.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::safe_max () noexcept
	Safe Maximum.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::safe_min () noexcept
	Safe Minimum.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::ulp () noexcept
	Unit in the Last Place.
template<TLAPACK_REAL real_t>
constexpr real_t	tlapack::uroundoff () noexcept
	Unit roundoff.

Detailed Description

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Function Documentation

blue_max()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::blue_max ( )

constexprnoexcept

Blue's max constant B for the sum of squares.

See also

https://doi.org/10.1145/355769.355771

blue_min()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::blue_min ( )

constexprnoexcept

Blue's min constant b for the sum of squares.

See also

https://doi.org/10.1145/355769.355771

blue_scalingMax()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::blue_scalingMax ( )

constexprnoexcept

Blue's scaling constant for numbers bigger than B.

See also

https://doi.org/10.1145/355769.355771

blue_scalingMin()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::blue_scalingMin ( )

constexprnoexcept

Blue's scaling constant for numbers smaller than b.

See also

https://doi.org/10.1145/355769.355771

Modification introduced in

See also

https://doi.org/10.1145/3061665 to scale denormalized numbers correctly.

digits()

template<typename real_t >

int tlapack::digits ( )

noexcept

Digits.

Number of digits p in the mantissa.

See also

std::numeric_limits<real_t>::digits.

safe_max()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::safe_max ( )

constexprnoexcept

Safe Maximum.

safe_max() := 1/safe_min()

safe_min()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::safe_min ( )

constexprnoexcept

Safe Minimum.

Smallest normal positive power of two such that its inverse (1/safe_min()) is finite.

ulp()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::ulp ( )

constexprnoexcept

Unit in the Last Place.

\[ b^{-(p-1)} \]

where b is the machine base, and p is the number of digits in the mantissa.

uroundoff()

template<TLAPACK_REAL real_t>

constexpr real_t tlapack::uroundoff ( )

constexprnoexcept

Unit roundoff.

\[ b^{-(p-1)} * r \]

where b is the machine base, p is the number of digits in the mantissa, and r is the largest possible rounding error in ULPs (units in the last place) as defined by ISO 10967, which can vary from 0.5 (rounding to the nearest digit) to 1.0 (rounding to zero or to infinity).

See also

https://people.eecs.berkeley.edu/~demmel/cs267/lecture21/lecture21.html