ellcomplete_test.jule

// Copyright 2025 mertcandav.
// Use of this source code is governed by a BSD 3-Clause
// license that can be found in the LICENSE file.

use "std/math"
use "std/testing"

// Checks if the Legendre's relation for m=0.0001(0.0001)0.9999
// is satisfied with accuracy 1e-14.
#test
fn testCompleteKE(t: &testing::T) {
	mut m := 1
	for m <= 9999; m++ {
		mf := f64(m) / 10000
		mp := 1 - mf
		K, Kp := CompleteK(mf), CompleteK(mp)
		E, Ep := CompleteE(mf), CompleteE(mp)
		legendre := math::Abs(E*Kp + Ep*K - K*Kp - Pi/2)
		if legendre > 1e-14 {
			t.Errorf("legendre > tol: m={}, legendre={}, tol=1e-14", mf, legendre)
			return
		}
	}
}

// Checks if the relations between two associate elliptic integrals B(m), D(m)
// and more common Legendre's elliptic integrals K(m), E(m) are satisfied with accuracy 1e-14
// for m=0.0001(0.0001)0.9999.
//
// K(m) and E(m) can be computed without cancellation problems as following:
//	K(m) = B(m) + D(m),
//	E(m) = B(m) + (1-m)D(m).
#test
fn testCompleteBD(t: &testing::T) {
	mut m := 1
	for m <= 9999; m++ {
		mf := f64(m) / 10000
		B, D := CompleteB(mf), CompleteD(mf)
		K, E := CompleteK(mf), CompleteE(mf)
		difference1 := math::Abs(K - (B + D))
		difference2 := math::Abs(E - (B + (1-mf)*D))
		if difference1 > 1e-14 {
			t.Errorf("difference1 > tol: m={}, difference1={}, tol=1e-14", mf, difference1)
			return
		}
		if difference2 > 1e-14 {
			t.Errorf("difference2 > tol: m={}, difference2={}, tol=1e-14", mf, difference2)
			return
		}
	}
}