manual_endres_schindelin = function(p, q) {
  p = p / sum(p)
  q = q / sum(q)
  m = (p + q) / 2

  term = function(a, midpoint) {
    positive = a > 0
    sum(a[positive] * log2(a[positive] / midpoint[positive]))
  }

  sqrt(term(p, m) + term(q, m))
}

test_that("the discrete Endres-Schindelin implementation matches its definition", {
  p = c(0.2, 0.5, 0.3)
  q = c(0.1, 0.7, 0.2)

  expect_equal(
    endresSchindelin_Distribution(p, q),
    manual_endres_schindelin(p, q),
    tolerance = 1e-14
  )
})

test_that("zero-probability components use the 0 log 0 convention", {
  p = c(1, 0, 0)
  q = c(0, 1, 0)

  expect_equal(endresSchindelin_Distribution(p, p), 0)
  expect_equal(
    endresSchindelin_Distribution(p, q),
    sqrt(2),
    tolerance = 1e-14
  )
})

test_that("non-negative counts are normalized before comparison", {
  expect_equal(
    endresSchindelin_Distribution(c(2, 3, 5), c(4, 1, 5)),
    endresSchindelin_Distribution(c(0.2, 0.3, 0.5), c(0.4, 0.1, 0.5))
  )
})

test_that("the discrete distance is symmetric and satisfies a triangle case", {
  p = c(0.7, 0.2, 0.1)
  q = c(0.1, 0.6, 0.3)
  r = c(0.2, 0.2, 0.6)

  dpq = endresSchindelin_Distribution(p, q)
  dqp = endresSchindelin_Distribution(q, p)
  dpr = endresSchindelin_Distribution(p, r)
  drq = endresSchindelin_Distribution(r, q)

  expect_equal(dpq, dqp, tolerance = 1e-14)
  expect_lte(dpq, dpr + drq + 1e-14)
})

test_that("invalid probability vectors are rejected", {
  expect_error(
    endresSchindelin_Distribution(c(1, -0.1), c(1, 0)),
    "negative"
  )
  expect_error(
    endresSchindelin_Distribution(c(0, 0), c(1, 0)),
    "positive finite sum"
  )
  expect_error(
    endresSchindelin_Distribution(c(1, 0), c(1, 0, 0)),
    "same length"
  )
})

test_that("sample-based Endres-Schindelin distances use a common support", {
  skip_if_not_installed("ScatterDensity")

  set.seed(1403)
  x = rnorm(64)
  y = x + 3

  expect_identical(
    endresSchindelin_TwoSamplePDF(x, x, grid.length = 32),
    0
  )

  dxy = endresSchindelin_TwoSamplePDF(x, y, grid.length = 32)
  dyx = endresSchindelin_TwoSamplePDF(y, x, grid.length = 32)

  expect_true(is.finite(dxy))
  expect_gt(dxy, 0)
  expect_equal(dxy, dyx, tolerance = 1e-6)
})