html/latest/harmonics_8h_source.html

// SPDX-FileCopyrightText: 2025-2026 Jonathan Busse <jonathan@jbusse.de>

//

// SPDX-License-Identifier: AGPL-3.0-only


#include "hpdyad.h"


#ifndef EPSTEIN_HARMONICS

#define EPSTEIN_HARMONICS


double coeffs_c_inner(long long n, long long i, long long k, long long dim);


double coeffs_c_outer(long long n, long long k, long long dim);


void coeffs_c_inner_hpdyad(unsigned int n, unsigned int i, unsigned int k,

                           unsigned int dim, hpdyad_t *out);


void harmonic_h_inner_term_scalar_hpdyad(unsigned int n, unsigned int i,

                                         unsigned int k, unsigned int dim,

                                         hpdyad_t *out);


void harmonic_h_inner_term_multi_hpdyad(unsigned int dim, const unsigned int *alpha,

                                        const unsigned int *beta,

                                        const unsigned int *theta1,

                                        const unsigned int *theta2, hpdyad_t *out);


double harmonic_h_inner_sum(unsigned int k, unsigned int dim,

                            const unsigned int *alpha, const unsigned int *gamma,

                            unsigned int alphaAbs);


unsigned long long

precompute_harmonic_h_inner_chunk_size(unsigned int alphaAbs, unsigned int kMax,

                                       unsigned int dim, const unsigned int *alpha,

                                       unsigned long long *chunk_offset,

                                       unsigned long long *valid_count);


void precompute_harmonic_h_inner_sum(unsigned int alphaAbs, unsigned int dim,

                                     const unsigned int *alpha,

                                     const unsigned long long *chunk_offset,

                                     double *coeffs, unsigned int *exponents);


double harmonic_h(unsigned int k, unsigned int dim, const double *z,

                  unsigned int alphaAbs, const unsigned long long *chunk_offset,

                  const unsigned long long *valid_count, const double *coeffs,

                  const unsigned int *exponents);


#endif

coeffs_c_inner
double coeffs_c_inner(long long n, long long i, long long k, long long dim)
Computes cₙ,ᵢ,ₖ＝ ∏_{j=i+1}^{⌊n/2⌋-k} (2n＋d−2−4k−2j).
Definition harmonics.c:23

coeffs_c_inner_hpdyad
void coeffs_c_inner_hpdyad(unsigned int n, unsigned int i, unsigned int k, unsigned int dim, hpdyad_t *out)
Computes cₙ,ᵢ,ₖ＝ ∏_{j=i+1}^{⌊n/2⌋-k} (2n＋d−2−4k−2j) as hpdyad.
Definition harmonics.c:72

harmonic_h_inner_term_multi_hpdyad
void harmonic_h_inner_term_multi_hpdyad(unsigned int dim, const unsigned int *alpha, const unsigned int *beta, const unsigned int *theta1, const unsigned int *theta2, hpdyad_t *out)
Computes binom(i,β) × binom(α,θ₁) × θ₂!/(θ₂−θ₁)! as hpdyad.
Definition harmonics.c:126

coeffs_c_outer
double coeffs_c_outer(long long n, long long k, long long dim)
Computes cₙ,ₖ＝2⁻ᵏ/ cₙ,₀,ₖ ∏ⱼ₌₁ᵏ(2n＋d−2j)∕((2n＋d＋2−4j)(2n＋d−4j)).
Definition harmonics.c:42

harmonic_h_inner_sum
double harmonic_h_inner_sum(unsigned int k, unsigned int dim, const unsigned int *alpha, const unsigned int *gamma, unsigned int alphaAbs)
Computes the inner sum h_inner(α,γ,k) using exact hpdyad arithmetic.
Definition harmonics.c:173

precompute_harmonic_h_inner_chunk_size
unsigned long long precompute_harmonic_h_inner_chunk_size(unsigned int alphaAbs, unsigned int kMax, unsigned int dim, const unsigned int *alpha, unsigned long long *chunk_offset, unsigned long long *valid_count)
Computes chunk offsets and valid entry counts for precomputed inner harmonic sums corresponding to k ...
Definition harmonics.c:282

harmonic_h_inner_term_scalar_hpdyad
void harmonic_h_inner_term_scalar_hpdyad(unsigned int n, unsigned int i, unsigned int k, unsigned int dim, hpdyad_t *out)
Computes (-2)**(-i) · c_{n,i,k} · binom(i+k,k) as hpdyad.
Definition harmonics.c:98

harmonic_h
double harmonic_h(unsigned int k, unsigned int dim, const double *z, unsigned int alphaAbs, const unsigned long long *chunk_offset, const unsigned long long *valid_count, const double *coeffs, const unsigned int *exponents)
Calculates the homogeneous harmonic polynomial h₍α,k₎ of degree |α|−2k such that y^α = ∑ₖ (y·y)^k h₍α...
Definition harmonics.c:399

precompute_harmonic_h_inner_sum
void precompute_harmonic_h_inner_sum(unsigned int alphaAbs, unsigned int dim, const unsigned int *alpha, const unsigned long long *chunk_offset, double *coeffs, unsigned int *exponents)
Precomputes and stores inner harmonic sums h_inner(α,γ,k) and exponents (2γ-α) for all k = 0,...
Definition harmonics.c:328

hpdyad.h
High-precision dyadic number operations.

hpdyad_t
Fixed-size high-precision dyadic number (hpdyad) with separate sign and binary exponent.
Definition hpdyad.h:28