Aleph::polynomial_detail Namespace Reference

Internal helpers for polynomial operations. More...

Functions
template<typename C >
C	power (C base, size_t exp)
	Fast exponentiation by squaring.
template<typename Int > requires std::is_integral_v<Int>
uint64_t	abs_to_u64 (Int value) noexcept
template<typename Int > requires std::is_integral_v<Int>
uint64_t	normalize_mod_u64 (Int value, const uint64_t modulus) noexcept
template<typename Int > requires std::is_integral_v<Int>
Int	centered_from_mod_u64 (const uint64_t value, const uint64_t modulus) noexcept

Detailed Description

Internal helpers for polynomial operations.

Function Documentation

abs_to_u64()

template<typename Int >
requires std::is_integral_v<Int>

uint64_t Aleph::polynomial_detail::abs_to_u64 ( Int  value )

noexcept

Definition at line 102 of file tpl_polynomial.H.

References Aleph::divide_and_conquer_partition_dp().

Referenced by Aleph::Gen_Polynomial< Coefficient >::factor_mod_p(), Aleph::Gen_Polynomial< Coefficient >::hensel_lift(), Aleph::Gen_Polynomial< Coefficient >::positive_divisors(), TEST(), Aleph::Gen_Polynomial< Coefficient >::try_extract_primitive_cubic_factor(), Aleph::Gen_Polynomial< Coefficient >::try_extract_primitive_quadratic_factor(), and Aleph::Gen_Polynomial< Coefficient >::try_extract_rational_linear_factor().

centered_from_mod_u64()

template<typename Int >
requires std::is_integral_v<Int>

Int Aleph::polynomial_detail::centered_from_mod_u64 ( const uint64_t  value, const uint64_t  modulus  )

noexcept

Definition at line 136 of file tpl_polynomial.H.

References Aleph::divide_and_conquer_partition_dp().

normalize_mod_u64()

template<typename Int >
requires std::is_integral_v<Int>

uint64_t Aleph::polynomial_detail::normalize_mod_u64 ( Int  value, const uint64_t  modulus  )

noexcept

Definition at line 117 of file tpl_polynomial.H.

References Aleph::divide_and_conquer_partition_dp().

Referenced by Aleph::Gen_Polynomial< Coefficient >::eval_mod_u64(), Aleph::Gen_Polynomial< Coefficient >::factor_mod_p(), and Aleph::Gen_Polynomial< Coefficient >::hensel_lift().

power()

template<typename C >

C Aleph::polynomial_detail::power	(	C	base,
		size_t	exp
	)

Fast exponentiation by squaring.

Computes \(\text{base}^{\text{exp}}\) in \(O(\log \text{exp})\) multiplications.

Definition at line 87 of file tpl_polynomial.H.

References exp().

Referenced by Aleph::Gen_Polynomial< Coefficient >::definite_integral(), Aleph::Gen_Polynomial< Coefficient >::horner_eval(), Aleph::Gen_Polynomial< Coefficient >::mignotte_bound(), Aleph::Gen_Polynomial< Coefficient >::pseudo_divmod(), and Aleph::Gen_Polynomial< Coefficient >::sparse_eval().