aerobus::polynomial< Ring >::val< coeffN, coeffs > Struct Template Reference

values (seen as types) in polynomial ring More...

#include <aerobus.h>

Public Types
using	ring_type = Ring
	ring coefficients live in
using	enclosing_type = polynomial< Ring >
	enclosing ring type
using	aN = coeffN
	heavy weight coefficient (non zero)
using	strip = val< coeffs... >
	remove largest coefficient
using	is_zero_t = std::bool_constant<(degree==0) &&(aN::is_zero_t::value)>
	true_type if polynomial is constant zero
template<size_t index>
using	coeff_at_t = typename coeff_at< index >::type
	type of coefficient at index
template<typename x >
using	value_at_t = horner_reduction_t< val > ::template inner< 0, degree+1 > ::template type< typename Ring::zero, x >

Static Public Member Functions
static std::string	to_string ()
	get a string representation of polynomial
template<typename arithmeticType >
static constexpr DEVICE INLINED arithmeticType	eval (const arithmeticType &x)
	evaluates polynomial seen as a function operating on arithmeticType
template<typename arithmeticType >
static DEVICE INLINED arithmeticType	compensated_eval (const arithmeticType &x)
	Evaluate polynomial on x using compensated horner scheme.

Static Public Attributes
static constexpr size_t	degree = sizeof...(coeffs)
	degree of the polynomial
static constexpr bool	is_zero_v = is_zero_t::value
	true if polynomial is constant zero

Detailed Description

template<typename Ring>
template<typename coeffN, typename... coeffs>
struct aerobus::polynomial< Ring >::val< coeffN, coeffs >

values (seen as types) in polynomial ring

Template Parameters

coeffN	high degree coefficient
...coeffs	lower degree coefficients

Examples

examples/compensated_horner.cpp.

Member Typedef Documentation

aN

template<typename Ring >

template<typename coeffN , typename... coeffs>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::aN = coeffN

heavy weight coefficient (non zero)

coeff_at_t

template<typename Ring >

template<typename coeffN , typename... coeffs>

template<size_t index>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::coeff_at_t = typename coeff_at<index>::type

type of coefficient at index

Template Parameters

index

enclosing_type

template<typename Ring >

template<typename coeffN , typename... coeffs>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::enclosing_type = polynomial<Ring>

enclosing ring type

is_zero_t

template<typename Ring >

template<typename coeffN , typename... coeffs>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::is_zero_t = std::bool_constant<(degree == 0) && (aN::is_zero_t::value)>

true_type if polynomial is constant zero

ring_type

template<typename Ring >

template<typename coeffN , typename... coeffs>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::ring_type = Ring

ring coefficients live in

strip

template<typename Ring >

template<typename coeffN , typename... coeffs>

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::strip = val<coeffs...>

remove largest coefficient

value_at_t

template<typename Ring >

template<typename coeffN , typename... coeffs>

template<typename x >

using aerobus::polynomial< Ring >::val< coeffN, coeffs >::value_at_t = horner_reduction_t<val> ::template inner<0, degree + 1> ::template type<typename Ring::zero, x>

Member Function Documentation

compensated_eval()

template<typename Ring >

template<typename coeffN , typename... coeffs>

template<typename arithmeticType >

static DEVICE INLINED arithmeticType aerobus::polynomial< Ring >::val< coeffN, coeffs >::compensated_eval ( const arithmeticType &  x )

inlinestatic

Evaluate polynomial on x using compensated horner scheme.

This is twice as accurate as simple eval (horner) but cannot be constexpr

Please note this makes no sense on integer types as arithmetic on integers is exact in IEEE

WARNING : this does not work with gcc with -O3 optimization level because gcc does illegal stuff with floating point arithmetic

Template Parameters

arithmeticType

float for example

Parameters

x

eval()

template<typename Ring >

template<typename coeffN , typename... coeffs>

template<typename arithmeticType >

static constexpr DEVICE INLINED arithmeticType aerobus::polynomial< Ring >::val< coeffN, coeffs >::eval ( const arithmeticType &  x )

inlinestaticconstexpr

evaluates polynomial seen as a function operating on arithmeticType

Template Parameters

arithmeticType

usually float or double

Parameters

x

value

Returns

P(x)

to_string()

template<typename Ring >

template<typename coeffN , typename... coeffs>

static std::string aerobus::polynomial< Ring >::val< coeffN, coeffs >::to_string ( )

inlinestatic

get a string representation of polynomial

Returns

something like a_n X^n + ... + a_1 X + a_0

Member Data Documentation

degree

template<typename Ring >

template<typename coeffN , typename... coeffs>

constexpr size_t aerobus::polynomial< Ring >::val< coeffN, coeffs >::degree = sizeof...(coeffs)

staticconstexpr

degree of the polynomial

is_zero_v

template<typename Ring >

template<typename coeffN , typename... coeffs>

constexpr bool aerobus::polynomial< Ring >::val< coeffN, coeffs >::is_zero_v = is_zero_t::value

staticconstexpr

true if polynomial is constant zero

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The documentation for this struct was generated from the following file:

• src/aerobus.h