ops_tests.cpp

// Copyright © 2023 Apple Inc.

#include <cmath>
#include <numeric>

#include "doctest/doctest.h"

#include "mlx/mlx.h"

using namespace mlx::core;

TEST_CASE("test copy") {
  array x(1.0);
  auto y = copy(x);
  CHECK_EQ(y.shape(), std::vector<int>{});
  CHECK_NE(y.id(), x.id());
  CHECK_EQ(y.item<float>(), 1.0f);

  x = array({1, 2}, {2, 1});
  y = copy(x);
  CHECK_EQ(y.shape(), std::vector<int>{2, 1});
  CHECK_EQ(y.dtype(), int32);
  CHECK_NE(y.id(), x.id());
  CHECK(array_equal(y, x).item<bool>());
}

TEST_CASE("test reshape") {
  array x(1.0);
  CHECK_EQ(reshape(x, {}).shape(), std::vector<int>{});
  CHECK_THROWS_AS(reshape(x, {2}), std::invalid_argument);
  auto y = reshape(x, {1, 1, 1});
  CHECK_EQ(y.shape(), std::vector<int>{1, 1, 1});
  y = reshape(x, {-1, 1, 1});
  CHECK_EQ(y.shape(), std::vector<int>{1, 1, 1});
  y = reshape(x, {1, 1, -1});
  CHECK_EQ(y.shape(), std::vector<int>{1, 1, 1});
  CHECK_THROWS_AS(reshape(x, {1, -1, -1}), std::invalid_argument);
  CHECK_THROWS_AS(reshape(x, {2, -1}), std::invalid_argument);

  x = zeros({2, 2, 2});
  y = reshape(x, {8});
  CHECK_EQ(y.shape(), std::vector<int>{8});
  CHECK_THROWS_AS(reshape(x, {7}), std::invalid_argument);
  y = reshape(x, {-1});
  CHECK_EQ(y.shape(), std::vector<int>{8});
  y = reshape(x, {-1, 2});
  CHECK_EQ(y.shape(), std::vector<int>{4, 2});
  CHECK_THROWS_AS(reshape(x, {-1, 7}), std::invalid_argument);

  // Works with empty array
  x = array({});
  y = reshape(x, {0, 0, 0});
  CHECK_EQ(y.shape(), std::vector<int>{0, 0, 0});
  y.eval();
  CHECK_EQ(y.size(), 0);
  CHECK_THROWS_AS(reshape(x, {}), std::invalid_argument);
  CHECK_THROWS_AS(reshape(x, {1}), std::invalid_argument);
  y = reshape(x, {1, 5, 0});
  CHECK_EQ(y.shape(), std::vector<int>{1, 5, 0});
}

TEST_CASE("test squeeze and expand") {
  array x = zeros({2, 1, 2, 1, 2, 1});
  CHECK_EQ(squeeze(x).shape(), std::vector<int>{2, 2, 2});
  CHECK_EQ(squeeze(x, {1, 3, 5}).shape(), std::vector<int>{2, 2, 2});
  CHECK_EQ(squeeze(x, {-1, -3, -5}).shape(), std::vector<int>{2, 2, 2});
  CHECK_EQ(squeeze(x, 1).shape(), std::vector<int>{2, 2, 1, 2, 1});
  CHECK_EQ(squeeze(x, -1).shape(), std::vector<int>{2, 1, 2, 1, 2});

  CHECK_THROWS(squeeze(x, 0));
  CHECK_THROWS(squeeze(x, 2));
  CHECK_THROWS(squeeze(x, {1, 3, 1}));
  CHECK_THROWS(squeeze(x, {1, 3, -3}));

  x = zeros({2, 2});
  CHECK_EQ(expand_dims(x, 0).shape(), std::vector<int>{1, 2, 2});
  CHECK_EQ(expand_dims(x, -1).shape(), std::vector<int>{2, 2, 1});
  CHECK_EQ(expand_dims(x, 1).shape(), std::vector<int>{2, 1, 2});
  CHECK_EQ(expand_dims(x, {0, 1, 2}).shape(), std::vector<int>{1, 1, 1, 2, 2});
  CHECK_EQ(
      expand_dims(x, {0, 1, 2, 5, 6, 7}).shape(),
      std::vector<int>{1, 1, 1, 2, 2, 1, 1, 1});

  CHECK_THROWS(expand_dims(x, 3));
  CHECK_THROWS(expand_dims(x, -4));
  CHECK_THROWS(expand_dims(x, {0, 1, 0}));
  CHECK_THROWS(expand_dims(x, {0, 1, -4}));
}

TEST_CASE("test slice") {
  array x = array(3);
  auto out = slice(x, {}, {});
  CHECK_EQ(out.item<int>(), 3);
  CHECK_THROWS_AS(slice(x, {1}, {2}), std::invalid_argument);
  CHECK_THROWS_AS(slice(x, {}, {2}), std::invalid_argument);
  CHECK_THROWS_AS(slice(x, {0}, {}), std::invalid_argument);

  x = array({3});
  out = slice(x, {0}, {1});
  CHECK_EQ(out.item<int>(), 3);
  out = slice(x, {-1}, {1});
  CHECK_EQ(out.item<int>(), 3);

  out = slice(x, {-3}, {10});
  CHECK_EQ(out.item<int>(), 3);

  out = slice(x, {1}, {0});
  eval(out);
  CHECK_EQ(out.shape(), std::vector<int>{0});

  out = slice(x, {0}, {1}, {1});
  CHECK_EQ(out.item<int>(), 3);

  out = slice(x, {0}, {1}, {10});
  CHECK_EQ(out.item<int>(), 3);

  x = array({0, 1, 2, 3, 4, 5, 6, 7}, {2, 4});
  out = slice(x, {0, 0}, {2, 2});
  CHECK(array_equal(out, array({0, 1, 4, 5}, {2, 2})).item<bool>());

  out = slice(x, {0, 0}, {0, 2});
  CHECK(array_equal(out, reshape(array({}), {0, 2})).item<bool>());

  out = slice(x, {0, 2}, {2, 3});
  CHECK(array_equal(out, array({2, 6}, {2, 1})).item<bool>());

  out = slice(x, {0, 0}, {2, 4}, {1, 2});
  CHECK(array_equal(out, array({0, 2, 4, 6}, {2, 2})).item<bool>());
}

TEST_CASE("test split") {
  array x = array(1);
  CHECK_THROWS(split(x, 0));

  x = array({3});
  CHECK_EQ(split(x, 1)[0].item<int>(), 3);

  x = array({0, 1, 2});
  CHECK_THROWS(split(x, 3, 1));
  CHECK_THROWS(split(x, 3, -2));

  auto out = split(x, 3, 0);
  CHECK_EQ(out.size(), 3);

  out = split(x, 3, -1);
  CHECK_EQ(out.size(), 3);
  for (auto i = 0; i < 3; ++i) {
    CHECK_EQ(out[i].shape(), std::vector<int>{1});
    CHECK_EQ(out[i].dtype(), int32);
    CHECK_EQ(out[i].item<int>(), i);
  }

  x = array({0, 1, 2, 3, 4, 5}, {2, 3});
  out = split(x, 2);
  CHECK(array_equal(out[0], array({0, 1, 2}, {1, 3})).item<bool>());
  CHECK(array_equal(out[1], array({3, 4, 5}, {1, 3})).item<bool>());
  out = split(x, 3, 1);
  CHECK(array_equal(out[0], array({0, 3}, {2, 1})).item<bool>());
  CHECK(array_equal(out[1], array({1, 4}, {2, 1})).item<bool>());
  CHECK(array_equal(out[2], array({2, 5}, {2, 1})).item<bool>());

  x = zeros({8, 12});
  out = split(x, 2);
  CHECK_EQ(out.size(), 2);
  CHECK_EQ(out[0].shape(), std::vector<int>{4, 12});
  CHECK_EQ(out[1].shape(), std::vector<int>{4, 12});
  out = split(x, 3, 1);
  CHECK_EQ(out.size(), 3);
  CHECK_EQ(out[0].shape(), std::vector<int>{8, 4});
  CHECK_EQ(out[1].shape(), std::vector<int>{8, 4});
  CHECK_EQ(out[2].shape(), std::vector<int>{8, 4});

  out = split(x, std::vector<int>{});
  CHECK_EQ(out.size(), 1);
  CHECK_EQ(out[0].shape(), x.shape());

  out = split(x, {3, 7});
  CHECK_EQ(out.size(), 3);
  CHECK_EQ(out[0].shape(), std::vector<int>{3, 12});
  CHECK_EQ(out[1].shape(), std::vector<int>{4, 12});
  CHECK_EQ(out[2].shape(), std::vector<int>{1, 12});

  out = split(x, std::vector<int>{20});
  CHECK_EQ(out.size(), 2);
  CHECK_EQ(out[0].shape(), std::vector<int>{8, 12});
  CHECK_EQ(out[1].shape(), std::vector<int>{0, 12});

  // Negative indices
  out = split(x, std::vector<int>{-5});
  CHECK_EQ(out[0].shape(), std::vector<int>{3, 12});
  CHECK_EQ(out[1].shape(), std::vector<int>{5, 12});

  // Different axis
  out = split(x, std::vector<int>{2, 8}, 1);
  CHECK_EQ(out[0].shape(), std::vector<int>{8, 2});
  CHECK_EQ(out[1].shape(), std::vector<int>{8, 6});
  CHECK_EQ(out[2].shape(), std::vector<int>{8, 4});

  // Out of order indices
  x = arange(5);
  out = split(x, std::vector<int>{2, 1, 2});
  CHECK(array_equal(out[0], array({0, 1})).item<bool>());
  CHECK(array_equal(out[1], array({})).item<bool>());
  CHECK(array_equal(out[2], array({1})).item<bool>());
  CHECK(array_equal(out[3], array({2, 3, 4})).item<bool>());
}

TEST_CASE("test transpose") {
  array x(1);
  auto y = transpose(x);
  CHECK_EQ(y.shape(), std::vector<int>{});
  CHECK_EQ(y.item<int>(), 1);
  CHECK_THROWS_AS(transpose(x, {0}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {1}), std::invalid_argument);

  x = array({1}, {1});
  y = transpose(x);
  CHECK_EQ(y.shape(), std::vector<int>{1});
  CHECK_EQ(y.item<int>(), 1);

  // Negative indices
  y = transpose(x, {-1});
  CHECK_EQ(y.shape(), std::vector<int>{1});
  CHECK_EQ(y.item<int>(), 1);

  CHECK_THROWS_AS(transpose(x, {1}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {0, 0}), std::invalid_argument);

  // Works with empty array
  x = array({});
  y = transpose(x);
  CHECK_EQ(y.shape(), std::vector<int>{0});
  y.eval();
  CHECK_EQ(y.size(), 0);

  x = array({1, 2, 3, 4, 5, 6}, {2, 3});
  y = transpose(x);
  CHECK_EQ(y.shape(), std::vector<int>{3, 2});
  y = transpose(x, {-1, 0});
  CHECK_EQ(y.shape(), std::vector<int>{3, 2});
  y = transpose(x, {-1, -2});
  CHECK_EQ(y.shape(), std::vector<int>{3, 2});
  y.eval();
  CHECK(array_equal(y, array({1, 4, 2, 5, 3, 6}, {3, 2})).item<bool>());
  y = transpose(x, {0, 1});
  CHECK_EQ(y.shape(), std::vector<int>{2, 3});
  CHECK(array_equal(y, x).item<bool>());
  y = transpose(x, {0, -1});
  CHECK_EQ(y.shape(), std::vector<int>{2, 3});
  CHECK(array_equal(y, x).item<bool>());

  CHECK_THROWS_AS(transpose(x, {}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {0}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {0, 0}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {0, 0, 0}), std::invalid_argument);
  CHECK_THROWS_AS(transpose(x, {0, 1, 1}), std::invalid_argument);

  x = array({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {2, 3, 2});
  y = transpose(x);
  CHECK_EQ(y.shape(), std::vector<int>{2, 3, 2});
  auto expected = array({1, 7, 3, 9, 5, 11, 2, 8, 4, 10, 6, 12}, {2, 3, 2});
  CHECK(array_equal(y, expected).item<bool>());

  y = transpose(x, {0, 1, 2});
  CHECK_EQ(y.shape(), std::vector<int>{2, 3, 2});
  CHECK(array_equal(y, x).item<bool>());
  y = transpose(x, {1, 0, 2});
  CHECK_EQ(y.shape(), std::vector<int>{3, 2, 2});
  expected = array({1, 2, 7, 8, 3, 4, 9, 10, 5, 6, 11, 12}, {3, 2, 2});
  CHECK(array_equal(y, expected).item<bool>());
  y = transpose(x, {0, 2, 1});
  CHECK_EQ(y.shape(), std::vector<int>{2, 2, 3});
  expected = array({1, 3, 5, 2, 4, 6, 7, 9, 11, 8, 10, 12}, {2, 2, 3});
  CHECK(array_equal(y, expected).item<bool>());

  // Check reshaping a transposed array
  x = array({0, 1, 2, 3, 4, 5, 6, 7}, {4, 2});
  x = reshape(transpose(x), {2, 2, 2});
  expected = array({0, 2, 4, 6, 1, 3, 5, 7}, {2, 2, 2});
  CHECK(array_equal(x, expected).item<bool>());

  // Check maintaining contiguous status
  x = array({0, 1, 2, 3, 4, 5, 6, 7}, {1, 4, 1, 2});
  CHECK(x.flags().row_contiguous);
  x = transpose(x, {2, 1, 0, 3});
  eval(x);
  CHECK(x.flags().row_contiguous);
}

TEST_CASE("test comparison ops") {
  // Empty array
  {
    array x({});
    array y({});
    auto z = x == y;
    CHECK_EQ(z.dtype(), bool_);
    CHECK_EQ(z.shape(), std::vector<int>{0});
  }

  // Basic cases
  {
    array x(1.0);
    array y(1.0);
    CHECK(equal(x, y).item<bool>());
    CHECK((x == y).item<bool>());
    CHECK((x == 1.0f).item<bool>());
    CHECK((1.0f == y).item<bool>());

    CHECK(!(x != y).item<bool>());
    CHECK(!not_equal(x, y).item<bool>());
    CHECK(!(1.0f != y).item<bool>());
    CHECK(!(x != 1.0f).item<bool>());

    CHECK(array_equal(x, y).item<bool>());

    x = array(0.0);
    CHECK(!equal(x, y).item<bool>());
    CHECK(!array_equal(x, y).item<bool>());
    CHECK(not_equal(x, y).item<bool>());
  }

  // Greater and less
  {
    array x(1.0);
    array y(0.0);
    CHECK(greater(x, y).item<bool>());
    CHECK((x > 0.0f).item<bool>());
    CHECK((1.0f > y).item<bool>());
    CHECK(greater_equal(x, y).item<bool>());
    CHECK((1.0f >= y).item<bool>());
    CHECK(!(x > 1.0f).item<bool>());
    CHECK((x >= 1.0f).item<bool>());

    CHECK(less(y, x).item<bool>());
    CHECK((y < 1.0).item<bool>());
    CHECK((y <= 1.0f).item<bool>());
    CHECK(!(x < 1.0).item<bool>());
    CHECK((x <= 1.0f).item<bool>());
  }

  // Check array_equal works
  {
    auto x = zeros({5, 5});
    auto y = zeros({5, 5});
    CHECK(array_equal(x, y).item<bool>());

    x = zeros({1, 1});
    CHECK(!array_equal(x, y).item<bool>());

    x = ones({5, 5});
    CHECK(!array_equal(x, y).item<bool>());

    x = array({0.0f, 1.0f, NAN});
    y = array({0.0f, 1.0f, NAN});
    CHECK(!array_equal(x, y).item<bool>());
    CHECK(array_equal(x, y, true).item<bool>());
  }

  // Check other types
  {
    auto x = zeros({5, 5}, int32);
    auto y = zeros({5, 5}, int32);
    CHECK(array_equal(x, y).item<bool>());

    x = ones({5, 5}, bool_);
    y = ones({5, 5}, bool_);
    CHECK(array_equal(x, y).item<bool>());
  }

  // Check type promotion
  {
    array x(1.0f);
    array y(1);
    CHECK_EQ(equal(x, y).item<bool>(), true);

    x = array(true, bool_);
    CHECK_EQ(equal(x, y).item<bool>(), true);
  }

  // Broadcasting works
  {
    auto x = zeros({1, 2});
    auto y = zeros({2, 1});
    auto z = equal(x, y);
    CHECK_EQ(z.dtype(), bool_);
    CHECK_EQ(z.shape(), std::vector<int>{2, 2});
    auto expected = array({true, true, true, true}, {2, 2});
    CHECK(array_equal(z, expected).item<bool>());

    x = array({1.0, 2.0}, {1, 2});
    y = array({1.0, 2.0}, {2, 1});
    z = equal(x, y);
    CHECK_EQ(z.dtype(), bool_);
    CHECK_EQ(z.shape(), std::vector<int>{2, 2});
    expected = array({true, false, false, true}, {2, 2});
    CHECK(array_equal(z, expected).item<bool>());

    expected = array({false, true, false, false}, {2, 2});
    z = greater(x, y);
    CHECK(array_equal(z, expected).item<bool>());

    expected = array({true, true, false, true}, {2, 2});
    z = greater_equal(x, y);
    CHECK(array_equal(z, expected).item<bool>());

    expected = array({false, false, true, false}, {2, 2});
    z = less(x, y);
    CHECK(array_equal(z, expected).item<bool>());

    expected = array({true, false, true, true}, {2, 2});
    z = less_equal(x, y);
    CHECK(array_equal(z, expected).item<bool>());
  }
}

TEST_CASE("test all close") {
  array x(1.0f);
  array y(1.0f);
  CHECK(allclose(x, y).item<bool>());

  y = array(1.1f);
  CHECK_FALSE(allclose(x, y).item<bool>());
  CHECK(allclose(x, y, 0.1).item<bool>());
  CHECK_FALSE(allclose(x, y, 0.01).item<bool>());
  CHECK(allclose(x, y, 0.01, 0.1).item<bool>());
}

TEST_CASE("test reduction ops") {
  // Check shapes and throws correctly
  {
    auto x = array(1);
    auto out = sum(x);
    CHECK_EQ(out.ndim(), 0);
    CHECK_THROWS_AS(sum(x, 0), std::out_of_range);
    CHECK_THROWS_AS(sum(x, -1), std::out_of_range);
    out = sum(x, std::vector<int>{});
    CHECK_EQ(out.shape(), std::vector<int>{});
    CHECK_EQ(out.size(), 1);

    x = array({});
    out = sum(x);
    CHECK_EQ(out.shape(), std::vector<int>{});
    CHECK_EQ(out.size(), 1);
    out = sum(x, true);
    CHECK_EQ(out.shape(), std::vector<int>{1});
    out = sum(x, std::vector<int>{});
    CHECK_EQ(out.shape(), x.shape());

    x = zeros({2});
    out = sum(x);
    CHECK_EQ(out.ndim(), 0);
    out = sum(x, -1);
    CHECK_EQ(out.ndim(), 0);
    out = sum(x, -1, true);
    CHECK_EQ(out.ndim(), 1);
    CHECK_EQ(out.shape(), std::vector<int>{1});

    CHECK_THROWS_AS(sum(x, 1), std::out_of_range);
    CHECK_THROWS_AS(sum(x, -2), std::out_of_range);
    CHECK_THROWS_AS(sum(x, {0, 0}), std::invalid_argument);
    CHECK_THROWS_AS(sum(x, {-1, 0}), std::invalid_argument);

    x = zeros({2, 3, 4});
    out = sum(x, {0, 2});
    CHECK_EQ(out.shape(), std::vector<int>{3});
    out = sum(x, std::vector<int>{});
    CHECK_EQ(out.shape(), x.shape());

    out = sum(x, {0, -1});
    CHECK_EQ(out.shape(), std::vector<int>{3});

    out = sum(x, {0, -1}, true);
    CHECK_EQ(out.shape(), std::vector<int>{1, 3, 1});

    out = sum(x, true);
    CHECK_EQ(out.shape(), std::vector<int>{1, 1, 1});

    out = sum(x);
    CHECK_EQ(out.shape(), std::vector<int>{});

    CHECK_THROWS_AS(sum(x, 3), std::out_of_range);
    CHECK_THROWS_AS(sum(x, -4), std::out_of_range);
    CHECK_THROWS_AS(sum(x, {0, 1, -2}), std::invalid_argument);
  }

  // Test sum
  {
    auto x = array({});
    CHECK_EQ(sum(x).item<float>(), 0.0f);

    x = array({1, 2, 3});
    CHECK_EQ(sum(x).item<int>(), 6);
    CHECK(array_equal(sum(x, std::vector<int>{}), x).item<bool>());

    x = ones({2, 3});
    CHECK(array_equal(sum(x, 1), full({2}, 3.0f)).item<bool>());
    CHECK(array_equal(sum(x, 0), full({3}, 2.0f)).item<bool>());
    CHECK_EQ(sum(x, {0, 1}).item<float>(), 6.0f);

    x = ones({2, 3, 4});
    CHECK(array_equal(sum(x, 0), full({3, 4}, 2.0f)).item<bool>());
    CHECK(array_equal(sum(x, 1), full({2, 4}, 3.0f)).item<bool>());
    CHECK(array_equal(sum(x, 2), full({2, 3}, 4.0f)).item<bool>());
    CHECK(array_equal(sum(x, {0, 1}), full({4}, 6.0f)).item<bool>());
    CHECK(array_equal(sum(x, {0, 2}), full({3}, 8.0f)).item<bool>());
    CHECK(array_equal(sum(x, {1, 2}), full({2}, 12.0f)).item<bool>());

    // Output for bool gets higher precision
    x = array({true, true, true});
    CHECK_EQ(sum(x).item<int32_t>(), 3);

    x = array(2.0f);
    x = broadcast_to(x, {2, 2, 2});
    CHECK_EQ(sum(x).item<float>(), 16.0f);

    // Tests with non-uniform results after reduction
    x = array({1.0f, 1.0f, 1.0f, 2.0f, 2.0f, 2.0f}, {2, 3});
    CHECK(array_equal(sum(x, 0), full({3}, 3.0f)).item<bool>());
    CHECK(array_equal(sum(x, 1), array({3.0f, 6.0f}, {2})).item<bool>());
  }

  // Test prod
  {
    auto x = array({});
    CHECK_EQ(prod(x).item<float>(), 1.0f);

    x = array({2, 2, 2});
    CHECK_EQ(prod(x).item<int>(), 8);
    CHECK(array_equal(prod(x, std::vector<int>{}), x).item<bool>());

    x = full({2, 3}, 2.0f);
    CHECK(array_equal(prod(x, 1), full({2}, 8.0f)).item<bool>());
    CHECK(array_equal(prod(x, 0), full({3}, 4.0f)).item<bool>());
    CHECK_EQ(prod(x, {0, 1}).item<float>(), 64.0f);

    x = full({2, 3, 4}, 2.0f);
    CHECK(array_equal(prod(x, 0), full({3, 4}, 4.0f)).item<bool>());
    CHECK(array_equal(prod(x, 1), full({2, 4}, 8.0f)).item<bool>());
    CHECK(array_equal(prod(x, 2), full({2, 3}, 16.0f)).item<bool>());
    CHECK(array_equal(prod(x, {0, 1}), full({4}, 64.0f)).item<bool>());
    CHECK(array_equal(prod(x, {0, 2}), full({3}, 256.0f)).item<bool>());
    CHECK(array_equal(prod(x, {1, 2}), full({2}, 4096.0f)).item<bool>());

    // Tests with non-uniform results after reduction
    x = array({1.0f, 1.0f, 1.0f, 2.0f, 2.0f, 2.0f}, {2, 3});
    CHECK(array_equal(prod(x, 0), full({3}, 2.0f)).item<bool>());
    CHECK(array_equal(prod(x, 1), array({1.0f, 8.0f}, {2})).item<bool>());

    x = array({true, true, true, false, true, false}, {2, 3});
    CHECK(array_equal(prod(x, 0), array({false, true, false})).item<bool>());
    CHECK(array_equal(prod(x, 1), array({true, false})).item<bool>());
  }

  // Test all
  {
    auto x = array({});
    CHECK_EQ(all(x).item<bool>(), true);

    x = array({2, 2, 2});
    CHECK_EQ(all(x).item<bool>(), true);
    auto out = all(x, std::vector<int>{});
    CHECK(array_equal(out, array({true, true, true})).item<bool>());

    x = array({0, 2, 2});
    CHECK_EQ(all(x).item<bool>(), false);

    x = array({true, true, true, false, true, false}, {2, 3});
    CHECK(array_equal(all(x, 1), array({true, false})).item<bool>());
    CHECK(array_equal(all(x, 0), array({false, true, false})).item<bool>());
  }

  // Test any
  {
    auto x = array({});
    CHECK_EQ(any(x).item<bool>(), false);

    x = array({0, 0, 0});
    CHECK_EQ(any(x).item<bool>(), false);

    x = array({0, 2, 0});
    CHECK_EQ(any(x).item<bool>(), true);
    auto out = any(x, std::vector<int>{});
    CHECK(array_equal(out, array({false, true, false})).item<bool>());

    x = array({true, false, true, false, false, false}, {2, 3});
    CHECK(array_equal(any(x, 1), array({true, false})).item<bool>());
    CHECK(array_equal(any(x, 0), array({true, false, true})).item<bool>());
  }

  // Test max and min
  {
    auto x = array({});
    CHECK_THROWS(max(x));
    CHECK_THROWS(min(x));

    x = array({1.0f, 2.0f, 3.0f});
    CHECK_EQ(max(x).item<float>(), 3.0f);
    CHECK_EQ(min(x).item<float>(), 1.0f);

    x = array({-2.0f, -1.0f});
    CHECK_EQ(max(x).item<float>(), -1.0f);
    CHECK_EQ(min(x).item<float>(), -2.0f);

    constexpr float inf = std::numeric_limits<float>::infinity();
    x = array({inf});
    CHECK_EQ(min(x).item<float>(), inf);

    x = array({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f}, {2, 3});
    CHECK(array_equal(max(x, 0), array({4.0f, 5.0f, 6.0f})).item<bool>());
    CHECK(array_equal(max(x, 1), array({3.0f, 6.0f})).item<bool>());
    CHECK(array_equal(min(x, 0), array({1.0f, 2.0f, 3.0f})).item<bool>());
    CHECK(array_equal(min(x, 1), array({1.0f, 4.0f})).item<bool>());

    x = array({1u, 2u, 3u});
    CHECK_EQ(max(x).item<uint32_t>(), 3u);
    CHECK_EQ(min(x).item<uint32_t>(), 1u);

    x = array({1u, 2u, 3u, 4u, 5u, 6u}, {2, 3});
    CHECK(array_equal(max(x, 0), array({4u, 5u, 6u})).item<bool>());
    CHECK(array_equal(max(x, 1), array({3u, 6u})).item<bool>());
    CHECK(array_equal(min(x, 0), array({1u, 2u, 3u})).item<bool>());
    CHECK(array_equal(min(x, 1), array({1u, 4u})).item<bool>());

    x = array({true, false, true, false, false, false}, {2, 3});
    CHECK(array_equal(max(x, 1), array({true, false})).item<bool>());
    CHECK(array_equal(max(x, 0), array({true, false, true})).item<bool>());

    x = array({true, true, true, false, true, false}, {2, 3});
    CHECK(array_equal(min(x, 1), array({true, false})).item<bool>());
    CHECK(array_equal(min(x, 0), array({false, true, false})).item<bool>());
  }

  // Test logsumexp
  {
    auto x = array({});
    CHECK_THROWS(logsumexp(x));

    constexpr float inf = std::numeric_limits<float>::infinity();

    x = array({-inf, -inf});
    WARN_EQ(logsumexp(x).item<float>(), -inf);

    x = array({0.0f, -inf});
    CHECK_EQ(logsumexp(x).item<float>(), 0.0f);

    x = array({0.0f, inf});
    WARN_EQ(logsumexp(x).item<float>(), inf);

    x = reshape(arange(6, float32), {2, 3});

    std::vector<float> nums = {0.0f, 1.0f, 2.0f, 3.0f};
    x = array(nums.data(), {2, 2});
    auto y = logsumexp(x, {0, 1}, true);
    CHECK_EQ(y.shape(), std::vector<int>{1, 1});
    auto result = std::log(
        std::exp(nums[0]) + std::exp(nums[1]) + std::exp(nums[2]) +
        std::exp(nums[3]));
    CHECK(y.item<float>() == doctest::Approx(result));
    auto expected = array(
        {std::log(std::exp(nums[0]) + std::exp(nums[2])),
         std::log(std::exp(nums[1]) + std::exp(nums[3]))});
    CHECK(allclose(logsumexp(x, 0), expected).item<bool>());

    expected = array(
        {std::log(std::exp(nums[0]) + std::exp(nums[1])),
         std::log(std::exp(nums[2]) + std::exp(nums[3]))});
    CHECK(allclose(logsumexp(x, 1), expected).item<bool>());
  }

  // Test softmax
  {
    auto x = array({0., 0., 0., 0.});
    auto y = array({0.25, 0.25, 0.25, 0.25});
    CHECK(array_equal(y, softmax(x)).item<bool>());
    CHECK(array_equal(y, softmax(x, -1)).item<bool>());
    CHECK(array_equal(y, softmax(x, std::vector<int>{-1})).item<bool>());
    CHECK(array_equal(y, softmax(x, std::vector<int>{0})).item<bool>());
  }
}

TEST_CASE("test irregular binary ops") {
  // 1D strided
  {
    auto x = full({128}, 1.0f);
    auto y = full({64}, 1.0f);
    x = slice(x, {0}, {128}, {4});
    y = slice(y, {0}, {64}, {2});
    CHECK(array_equal(add(x, y), full({32}, 2.0f)).item<bool>());
  }

  // 2D broadcasts
  {
    auto x = full({32, 32}, 4.0f);
    auto y = full({32}, 4.0f);
    CHECK(array_equal(add(x, y), full({32, 32}, 8.0f)).item<bool>());
    y = reshape(y, {32, 1});
    CHECK(array_equal(add(x, y), full({32, 32}, 8.0f)).item<bool>());
    CHECK(array_equal(subtract(y, x), zeros({32, 32})).item<bool>());
  }
}

TEST_CASE("test arithmetic unary ops") {
  // Test negative
  {
    array x(1.0f);
    CHECK_EQ(negative(x).item<float>(), -1.0f);
    CHECK_EQ((-x).item<float>(), -1.0f);

    // works on empty array
    CHECK(array_equal(-array({}), array({})).item<bool>());

    // Throws on bool
    CHECK_THROWS(negative(array(true)));
  }

  // Test logical not
  {
    array x(false);
    CHECK_EQ(logical_not(x).item<bool>(), true);

    x = array(1.0f);
    auto y = logical_not(x);
    CHECK_EQ(y.dtype(), bool_);
    CHECK_EQ(y.item<bool>(), false);

    x = array(0);
    y = logical_not(x);
    CHECK_EQ(y.dtype(), bool_);
    CHECK_EQ(y.item<bool>(), true);
  }

  // Test abs
  {
    array x({-1.0f, 0.0f, 1.0f});
    CHECK(array_equal(abs(x), array({1.0f, 0.0f, 1.0f})).item<bool>());

    // works on empty array
    CHECK(array_equal(abs(array({})), array({})).item<bool>());

    // int32
    x = array({-1, 0, 1});
    CHECK(array_equal(abs(x), array({1, 0, 1})).item<bool>());

    // uint32
    x = array({1u, 0u, 1u});
    CHECK(array_equal(abs(x), array({1u, 0u, 1u})).item<bool>());

    // bool
    x = array({false, true});
    CHECK(array_equal(abs(x), array({false, true})).item<bool>());
  }

  // Test sign
  {
    array x({-1.0f, 0.0f, 1.0f});
    CHECK(array_equal(sign(x), x).item<bool>());

    // works on empty array
    CHECK(array_equal(sign(array({})), array({})).item<bool>());

    // int32
    x = array({-1, 0, 1});
    CHECK(array_equal(sign(x), x).item<bool>());

    // uint32
    x = array({1u, 0u, 1u});
    CHECK(array_equal(sign(x), x).item<bool>());

    // bool
    x = array({false, true});
    CHECK(array_equal(sign(x), x).item<bool>());
  }

  constexpr float neginf = -std::numeric_limits<float>::infinity();

  // Test exponential
  {
    array x(0.0);
    CHECK_EQ(exp(x).item<float>(), 1.0);

    x = array(2.0);
    CHECK_EQ(exp(x).item<float>(), std::exp(2.0f));

    CHECK(array_equal(exp(array({})), array({})).item<bool>());

    x = array(neginf);
    CHECK_EQ(exp(x).item<float>(), 0.0f);

    // Integer input type
    x = array(2);
    CHECK_EQ(x.dtype(), int32);
    CHECK_EQ(exp(x).item<float>(), std::exp(2.0f));

    // Input is irregularly strided
    x = broadcast_to(array(1.0f), {2, 2, 2});
    CHECK(array_equal(exp(x), full({2, 2, 2}, std::exp(1.0f))).item<bool>());

    x = split(array({0.0f, 1.0f, 2.0f, 3.0f}, {2, 2}), 2, 1)[0];
    auto expected = array({std::exp(0.0f), std::exp(2.0f)}, {2, 1});
    CHECK(array_equal(exp(x), expected).item<bool>());
  }

  // Test sine
  {
    array x(0.0);
    CHECK_EQ(sin(x).item<float>(), 0.0);

    x = array(M_PI_2);
    CHECK(sin(x).item<float>() == doctest::Approx(std::sin(M_PI_2)));

    CHECK(array_equal(sin(array({})), array({})).item<bool>());

    // Integer input type
    x = array(0);
    CHECK_EQ(x.dtype(), int32);
    CHECK_EQ(sin(x).item<float>(), std::sin(0.0f));

    // Input is irregularly strided
    x = broadcast_to(array(1.0f), {2, 2, 2});
    CHECK(allclose(sin(x), full({2, 2, 2}, std::sin(1.0f))).item<bool>());

    x = split(array({0.0f, 1.0f, 2.0f, 3.0f}, {2, 2}), 2, 1)[0];
    auto expected = array({std::sin(0.0f), std::sin(2.0f)}, {2, 1});
    CHECK(allclose(sin(x), expected).item<bool>());
  }

  // Test cos
  {
    array x(0.0);
    CHECK_EQ(cos(x).item<float>(), doctest::Approx(1.0));

    x = array(M_PI_2);
    CHECK(cos(x).item<float>() == doctest::Approx(std::cos(M_PI_2)));

    CHECK(array_equal(cos(array({})), array({})).item<bool>());

    // Integer input type
    x = array(0);
    CHECK_EQ(x.dtype(), int32);
    CHECK(cos(x).item<float>() == doctest::Approx(std::cos(0.0f)));

    // Input is irregularly strided
    x = broadcast_to(array(1.0f), {2, 2, 2});
    CHECK(allclose(cos(x), full({2, 2, 2}, std::cos(1.0f))).item<bool>());

    x = split(array({0.0f, 1.0f, 2.0f, 3.0f}, {2, 2}), 2, 1)[0];
    auto expected = array({std::cos(0.0f), std::cos(2.0f)}, {2, 1});
    CHECK(allclose(cos(x), expected).item<bool>());
  }

  // Test log
  {
    array x(0.0);
    CHECK_EQ(log(x).item<float>(), neginf);

    x = array(1.0);
    CHECK_EQ(log(x).item<float>(), log(1.0f));

    // Integer input type
    x = array(1);
    CHECK_EQ(log(x).dtype(), float32);
    CHECK_EQ(log(x).item<float>(), log(1.0f));

    // Input is irregularly strided
    x = broadcast_to(array(1.0f), {2, 2, 2});
    CHECK(array_equal(log(x), full({2, 2, 2}, std::log(1.0f))).item<bool>());

    x = split(array({1.0f, 2.0f, 3.0f, 4.0f}, {2, 2}), 2, 1)[0];
    auto expected = array({std::log(1.0f), std::log(3.0f)}, {2, 1});
    CHECK(array_equal(log(x), expected).item<bool>());
  }

  // Test log2
  {
    array x(0.0);
    CHECK_EQ(log2(x).item<float>(), neginf);

    x = array(1.0);
    CHECK_EQ(log2(x).item<float>(), 0.0f);

    x = array(1024.0f);
    CHECK_EQ(log2(x).item<float>(), 10.0f);
  }

  // Test log10
  {
    array x(0.0);
    CHECK_EQ(log10(x).item<float>(), neginf);

    x = array(1.0);
    CHECK_EQ(log10(x).item<float>(), 0.0f);

    x = array(1000.0f);
    CHECK_EQ(log10(x).item<float>(), 3.0f);
  }

  // Test log1p
  {
    array x(-1.0f);
    CHECK_EQ(log1p(x).item<float>(), neginf);

    x = array(1.0f);
    CHECK_EQ(log1p(x).item<float>(), std::log1pf(1.0f));

    // Integer input type
    x = array(1);
    CHECK_EQ(log1p(x).dtype(), float32);
    CHECK_EQ(log1p(x).item<float>(), std::log1pf(1.0f));

    // Input is irregularly strided
    x = broadcast_to(array(1.0f), {2, 2, 2});
    CHECK(
        array_equal(log1p(x), full({2, 2, 2}, std::log1pf(1.0f))).item<bool>());

    x = split(array({1.0f, 2.0f, 3.0f, 4.0f}, {2, 2}), 2, 1)[0];
    auto expected = array({std::log1pf(1.0f), std::log1pf(3.0f)}, {2, 1});
    CHECK(array_equal(log1p(x), expected).item<bool>());
  }

  // Test sigmoid
  {
    array x(0.0);
    CHECK_EQ(sigmoid(x).item<float>(), 0.5f);

    // Integer input type
    x = array(0);
    CHECK_EQ(sigmoid(x).dtype(), float32);
    CHECK_EQ(sigmoid(x).item<float>(), 0.5f);

    constexpr auto inf = std::numeric_limits<float>::infinity();
    x = array(inf);
    CHECK_EQ(sigmoid(x).item<float>(), 1.0f);
    x = array(-inf);
    CHECK_EQ(sigmoid(x).item<float>(), 0.0f);
  }

  // Test square
  {
    array x(3.0);
    CHECK_EQ(square(x).item<float>(), 9.0);

    x = array(2);
    CHECK_EQ(square(x).item<int>(), 4);

    x = full({3, 3}, 2.0f);
    CHECK(array_equal(square(x), full({3, 3}, 4.0f)).item<bool>());
  }

  // Test sqrt and rsqrt
  {
    array x(4.0);
    CHECK_EQ(sqrt(x).item<float>(), 2.0);
    CHECK_EQ(rsqrt(x).item<float>(), 0.5);

    x = full({3, 3}, 9.0f);
    CHECK(array_equal(sqrt(x), full({3, 3}, 3.0f)).item<bool>());

    x = array(4, int32);
    CHECK_EQ(sqrt(x).item<float>(), 2.0f);
    CHECK_EQ(rsqrt(x).item<float>(), 0.5f);
  }

  // Test reciprocal
  {
    array x(8.0);
    CHECK_EQ(reciprocal(x).item<float>(), 0.125f);

    x = array(2);
    auto out = reciprocal(x);
    CHECK_EQ(out.dtype(), float32);
    CHECK_EQ(out.item<float>(), 0.5f);

    x = full({3, 3}, 2.0f);
    CHECK(array_equal(reciprocal(x), full({3, 3}, 0.5f)).item<bool>());
  }
}

TEST_CASE("test error functions") {
  constexpr float inf = std::numeric_limits<float>::infinity();
  array x(0.0f);
  CHECK_EQ(erf(x).item<float>(), 0.0f);
  x = array(inf);
  CHECK_EQ(erf(x).item<float>(), 1.0f);
  x = array(-inf);
  CHECK_EQ(erf(x).item<float>(), -1.0f);

  x = array(1, int32);
  CHECK_EQ(erf(x).dtype(), float32);

  x = array(0.0f);
  CHECK_EQ(erfinv(x).item<float>(), 0.0f);
  x = array(1.0f);
  CHECK_EQ(erfinv(x).item<float>(), inf);
  x = array(-1.0f);
  CHECK_EQ(erfinv(x).item<float>(), -inf);

  x = array(1, int32);
  CHECK_EQ(erfinv(x).dtype(), float32);

  x = array(2.0f);
  CHECK(std::isnan(erfinv(x).item<float>()));
  x = array(-2.0f);
  CHECK(std::isnan(erfinv(x).item<float>()));

  auto vals = {0.9f, 0.5f, 0.1f, -0.1f, -0.5f, -0.9f};
  // Expected values are generated from scipy's error function:
  //   python -c "import scipy.special as ss;
  //   vals = [0.9, 0.5, 0.1, -0.1, -0.5, -0.9];
  //   print([ss.erf(x) for x in vals])"
  {
    auto expected = {
        0.7969082124228322,
        0.5204998778130465,
        0.1124629160182849,
        -0.1124629160182849,
        -0.5204998778130465,
        -0.7969082124228322};
    for (int i = 0; i < vals.size(); ++i) {
      x = array(vals.begin()[i]);
      CHECK_EQ(erf(x).item<float>(), doctest::Approx(expected.begin()[i]));
    }
  }

  // Expected values are generated from scipy's inverse error function:
  //   python -c "import scipy.special as ss;
  //   vals = [0.9, 0.5, 0.1, -0.1, -0.5, -0.9];
  //   print([ss.erfinv(x) for x in vals])"
  {
    auto expected = {
        1.1630871536766738,
        0.4769362762044699,
        0.08885599049425778,
        -0.08885599049425769,
        -0.4769362762044699,
        -1.1630871536766743};
    for (int i = 0; i < vals.size(); ++i) {
      x = array(vals.begin()[i]);
      CHECK_EQ(erfinv(x).item<float>(), doctest::Approx(expected.begin()[i]));
    }
  }

  // float16_t
  {
    array x(0.0f, float16);
    auto out = erf(x);
    CHECK_EQ(out.dtype(), float16);
    CHECK_EQ(out.item<float16_t>(), 0.0f);

    out = erfinv(x);
    CHECK_EQ(out.dtype(), float16);
    CHECK_EQ(out.item<float16_t>(), 0.0f);
  }

  // bfloat
  {
    array x(0.0f, bfloat16);
    auto out = erf(x);
    CHECK_EQ(out.dtype(), bfloat16);
    CHECK_EQ(out.item<bfloat16_t>(), 0.0f);

    out = erfinv(x);
    CHECK_EQ(out.dtype(), bfloat16);
    CHECK_EQ(out.item<float16_t>(), 0.0f);
  }
}

TEST_CASE("test arithmetic binary ops") {
  array x(1.0);
  array y(1.0);
  auto z = add(x, y);
  CHECK_EQ(z.item<float>(), 2.0);
  z = x + y;
  CHECK_EQ(z.item<float>(), 2.0);
  z = add(z, x);
  CHECK_EQ(z.item<float>(), 3.0);
  z.eval(); // No-op
  CHECK_EQ(z.item<float>(), 3.0);

  // Chain a few adds:
  auto out = x;
  for (int i = 0; i < 10; ++i) {
    out = add(out, x);
  }
  CHECK_EQ(out.item<float>(), 11.0);

  // Works for different shapes
  x = array({1.0, 2.0, 3.0}, {1, 3});
  y = array({1.0, 2.0, 3.0}, {1, 3});
  z = add(x, y);
  CHECK_EQ(z.shape(), std::vector<int>{1, 3});
  auto eq = array_equal(z, array({2.0, 4.0, 6.0}, {1, 3}));
  CHECK(eq.item<bool>());

  // Works with scalars
  x = array({1.0, 2.0, 3.0}, {1, 3});
  y = x + 2.0;
  CHECK_EQ(y.dtype(), float32);
  eq = array_equal(y, array({3.0, 4.0, 5.0}, {1, 3}));
  CHECK(eq.item<bool>());
  y = 2.0 + x;
  CHECK_EQ(y.dtype(), float32);
  eq = array_equal(y, array({3.0, 4.0, 5.0}, {1, 3}));
  CHECK(eq.item<bool>());

  // Check type promotion
  y = 2 + x;
  CHECK_EQ(y.dtype(), float32);

  y = 2.0 + array({1, 2, 3});
  CHECK_EQ(y.dtype(), float32);
  CHECK(array_equal(y, array({3.0, 4.0, 5.0})).item<bool>());

  // Broadcasting works
  x = broadcast_to(array({1.0}), {10});
  y = broadcast_to(array({2.0}), {10});
  z = add(x, y);
  CHECK(array_equal(z, full({10}, 3.0)).item<bool>());

  x = array({1.0, 2.0}, {1, 2});
  y = array({1.0, 2.0}, {2, 1});
  z = add(x, y);
  CHECK_EQ(z.shape(), std::vector<int>{2, 2});
  eq = array_equal(z, array({2.0, 3.0, 3.0, 4.0}, {2, 2}));
  CHECK(eq.item<bool>());

  x = ones({3, 2, 1});
  z = x + 2.0;
  CHECK_EQ(z.shape(), std::vector<int>{3, 2, 1});
  eq = array_equal(z, array({3.0, 3.0, 3.0, 3.0, 3.0, 3.0}, {3, 2, 1}));
  CHECK(eq.item<bool>());

  // Works for empty arrays
  x = array({});
  y = array({});
  z = x + y;
  z.eval();
  CHECK_EQ(z.size(), 0);
  CHECK_EQ(z.shape(), std::vector<int>{0});

  // Check subtraction
  x = array({3, 2, 1});
  y = array({1, 1, 1});
  CHECK(array_equal(x - y, array({2, 1, 0})).item<bool>());

  // Check multiplication
  x = array({1, 2, 3});
  y = array({2, 2, 2});
  CHECK(array_equal(x * y, array({2, 4, 6})).item<bool>());

  // Check division
  x = array(1);
  y = array(1);
  CHECK_EQ(divide(x, y).item<float>(), 1.0f);

  x = array(1);
  y = array(0.5);
  CHECK_EQ(divide(x, y).item<float>(), 2.0f);

  x = array(1);
  y = array(4);
  CHECK_EQ(divide(x, y).item<float>(), 0.25f);

  x = array(true);
  y = array(true);
  CHECK_EQ(divide(x, y).item<float>(), 1.0f);

  x = array(false);
  y = array(true);
  CHECK_EQ(divide(x, y).item<float>(), 0.0f);

  x = array(true);
  y = array(false);
  CHECK(std::isinf(divide(x, y).item<float>()));

  x = array(false);
  y = array(false);
  CHECK(std::isnan(divide(x, y).item<float>()));

  // Check maximum and minimum
  x = array(1.0f);
  y = array(0.0f);
  CHECK_EQ(maximum(x, y).item<float>(), 1.0f);
  CHECK_EQ(minimum(x, y).item<float>(), 0.0f);
  y = array(2.0f);
  CHECK_EQ(maximum(x, y).item<float>(), 2.0f);
  CHECK_EQ(minimum(x, y).item<float>(), 1.0f);

  // Check logaddexp
  x = array(0.0f);
  y = array(0.0f);
  CHECK_EQ(logaddexp(x, y).item<float>(), std::log(2.0f));

  x = array(0u);
  y = array(10000u);
  CHECK_EQ(logaddexp(x, y).item<float>(), 10000.0f);

  constexpr float inf = std::numeric_limits<float>::infinity();
  x = array(inf);
  y = array(3.0f);
  CHECK_EQ(logaddexp(x, y).item<float>(), inf);

  x = array(-inf);
  y = array(3.0f);
  CHECK_EQ(logaddexp(x, y).item<float>(), 3.0f);

  x = array(-inf);
  y = array(-inf);
  CHECK_EQ(logaddexp(x, y).item<float>(), -inf);

  x = array(inf);
  y = array(inf);
  CHECK_EQ(logaddexp(x, y).item<float>(), inf);

  x = array(-inf);
  y = array(inf);
  CHECK_EQ(logaddexp(x, y).item<float>(), inf);
}

TEST_CASE("test broadcast") {
  auto s = broadcast_shapes({1}, {1, 2});
  CHECK_EQ(s, std::vector<int>{1, 2});

  s = broadcast_shapes({1, 2}, {1});
  CHECK_EQ(s, std::vector<int>{1, 2});

  s = broadcast_shapes({2, 2}, {});
  CHECK_EQ(s, std::vector<int>{2, 2});

  s = broadcast_shapes({}, {1, 1});
  CHECK_EQ(s, std::vector<int>{1, 1});

  s = broadcast_shapes({1, 2, 1}, {2});
  CHECK_EQ(s, std::vector<int>{1, 2, 2});

  s = broadcast_shapes({2}, {1, 2, 1});
  CHECK_EQ(s, std::vector<int>{1, 2, 2});

  s = broadcast_shapes({2, 2, 2}, {1, 2, 1});
  CHECK_EQ(s, std::vector<int>{2, 2, 2});

  s = broadcast_shapes({2, 2, 2, 1}, {1, 2, 1});
  CHECK_EQ(s, std::vector<int>{2, 2, 2, 1});

  s = broadcast_shapes({0}, {0, 0});
  CHECK_EQ(s, std::vector<int>{0, 0});

  CHECK_EQ(broadcast_shapes({}, {0}), std::vector<int>{0});

  s = broadcast_shapes({5, 0}, {0, 5, 0});
  CHECK_EQ(s, std::vector<int>{0, 5, 0});

  CHECK_EQ(broadcast_shapes({}, {0}), std::vector<int>{0});
  CHECK_EQ(broadcast_shapes({1}, {0}), std::vector<int>{0});
  CHECK_EQ(broadcast_shapes({1}, {0}), std::vector<int>{0});
  CHECK_EQ(broadcast_shapes({1}, {0, 0}), std::vector<int>{0, 0});
  CHECK_EQ(broadcast_shapes({1, 1}, {0}), std::vector<int>{1, 0});
  CHECK_EQ(broadcast_shapes({1, 1}, {0, 0}), std::vector<int>{0, 0});
  CHECK_EQ(broadcast_shapes({2, 1}, {1, 0}), std::vector<int>{2, 0});
  CHECK_EQ(broadcast_shapes({2, 1}, {2, 0}), std::vector<int>{2, 0});
  CHECK_EQ(broadcast_shapes({2, 1}, {1, 2, 0}), std::vector<int>{1, 2, 0});
  CHECK_THROWS_AS(broadcast_shapes({2}, {0}), std::invalid_argument);
  CHECK_THROWS_AS(broadcast_shapes({2, 1}, {0, 0}), std::invalid_argument);

  CHECK_THROWS_AS(broadcast_shapes({3}, {2}), std::invalid_argument);
  CHECK_THROWS_AS(broadcast_shapes({1, 3}, {2}), std::invalid_argument);
  CHECK_THROWS_AS(broadcast_shapes({3}, {1, 2}), std::invalid_argument);
  CHECK_THROWS_AS(
      broadcast_shapes({1, 3, 2}, {1, 2, 2}), std::invalid_argument);

  auto x = full({1, 1}, 2.3f);
  CHECK_EQ(broadcast_to(x, {1, 1}).item<float>(), 2.3f);

  x = broadcast_to(x, {5, 1});
  CHECK_EQ(x.shape(), std::vector<int>{5, 1});
  x.eval();
  CHECK_EQ(x.strides(), std::vector<size_t>{0, 0});

  CHECK_THROWS_AS(broadcast_to(x, {1, 5}), std::invalid_argument);
  x = broadcast_to(x, {5, 5});
  CHECK_EQ(x.shape(), std::vector<int>{5, 5});

  x = zeros({2, 1, 2});
  x = broadcast_to(x, {4, 2, 1, 2});
  CHECK_EQ(x.shape(), std::vector<int>{4, 2, 1, 2});
  x.eval();
  CHECK_EQ(x.strides(), std::vector<size_t>{0, 2, 0, 1});

  // Broadcast on empty arrays works as expected
  x = array({});
  CHECK_THROWS_AS(broadcast_to(x, {1}), std::invalid_argument);

  // Broadcast to empty array works as expected
  x = array({1});
  auto y = broadcast_to(x, {0});
  eval(y);
  CHECK_EQ(y.size(), 0);
  CHECK_EQ(y.shape(), std::vector<int>{0});

  x = array({1, 2}, {2, 1});
  y = broadcast_to(x, {2, 0});
  eval(y);
  CHECK_EQ(y.size(), 0);
  CHECK_EQ(y.shape(), std::vector<int>{2, 0});

  // Check repeat application works
  x = zeros({2});
  x = broadcast_to(broadcast_to(x, {2, 2}), {2, 2});
  CHECK_EQ(x.shape(), std::vector<int>{2, 2});
  x.eval();
  CHECK_EQ(x.strides(), std::vector<size_t>{0, 1});
  x = broadcast_to(broadcast_to(x, {2, 2}), {2, 2, 2});
  CHECK_EQ(x.shape(), std::vector<int>{2, 2, 2});
  x.eval();
  CHECK_EQ(x.strides(), std::vector<size_t>{0, 0, 1});

  // Broadcast on transposed arrray works
  x = array({0, 1, 2, 3, 4, 5}, {2, 3});
  x = broadcast_to(transpose(x), {2, 3, 2});
  CHECK_EQ(x.shape(), std::vector<int>{2, 3, 2});
  y = broadcast_to(array({0, 3, 1, 4, 2, 5}, {3, 2}), {2, 3, 2});
  CHECK(array_equal(x, y).item<bool>());

  // Reshape on broadcasted array works
  x = array(1.0);
  x = broadcast_to(x, {2});
  x = reshape(x, {1, 2});
  CHECK(array_equal(x, ones({1, 2})).item<bool>());
}

TEST_CASE("test gather") {
  // More indices than dimensions
  CHECK_THROWS(gather(array(0), array({1}), 0, {1}));

  // Mismatch dimensions and indices
  CHECK_THROWS(gather(array({0}), {array({0})}, {0, 1}, {1}));
  CHECK_THROWS(gather(array({0}), array({0}), -1, {1}));

  // Repeat dimensions
  CHECK_THROWS(
      gather(array({0}, {1, 1}), {array({0}), array({0})}, {0, 0}, {1, 1}));

  // Slice sizes incorrect
  CHECK_THROWS(gather(array({0}), array({0}), 0, {2}));
  CHECK_THROWS(gather(array({0}), array({0}), 0, {0, 0}));
  CHECK_THROWS(gather(array({0}), array({0}), 0, {-1}));

  // Wrong index type
  CHECK_THROWS(gather(array({0}), array({0.0f}), 0, {0}));
  CHECK_THROWS(
      gather(array({0}, {1, 1}), {array({0}), array({0.0f})}, {0, 1}, {1, 1}));

  // Index arrays must be broadcastable
  CHECK_THROWS(gather(
      array({0}, {1, 1}),
      {array({0, 0, 0}, {3}), array({0, 0}, {2})},
      {0, 1},
      {1, 1}));

  // Basic test of correctness with 1D input
  auto x = arange(20);
  auto y = arange(10);
  auto out = gather(x, y, 0, {1});
  CHECK_EQ(out.shape(), std::vector<int>{10, 1});
  CHECK(array_equal(reshape(out, {-1}), y).item<bool>());

  out = gather(x, array({15}, uint32), 0, {1});
  CHECK_EQ(out.shape(), std::vector<int>{1, 1});
  CHECK_EQ(out.item<int32_t>(), 15);

  // No index gather works
  out = gather(x, {}, std::vector<int>{}, {10});
  CHECK_EQ(out.shape(), std::vector<int>{10});
  CHECK(array_equal(out, arange(10)).item<bool>());

  // Basic test of correctness with 2D input
  x = arange(128);
  x = reshape(x, {4, 32});
  y = array({0, 1}, uint32);
  out = gather(x, y, 0, {1, 32});
  CHECK_EQ(out.shape(), std::vector<int>{2, 1, 32});
  CHECK(array_equal(reshape(out, {64}), arange(64)).item<bool>());

  x = reshape(x, {64, 2});
  y = array({0}, uint32);
  out = gather(x, y, 0, {64, 1});
  CHECK_EQ(out.shape(), std::vector<int>{1, 64, 1});
  CHECK(array_equal(out, reshape(arange(0, 128, 2), {1, 64, 1})).item<bool>());

  // Basic test of correctness with 3D input
  x = arange(256);
  x = reshape(x, {8, 4, 8});
  y = array({0}, uint32);
  out = gather(x, y, 0, {8, 1, 1});
  CHECK_EQ(out.shape(), std::vector<int>{1, 8, 1, 1});
  CHECK(
      array_equal(out, reshape(arange(0, 256, 32), {1, 8, 1, 1})).item<bool>());

  x = broadcast_to(array({1, 2}), {20, 2});
  out = gather(x, array({5}), 0, {1, 1});
  CHECK_EQ(out.item<int>(), 1);
  out = gather(x, {array({5}), array({1})}, {0, 1}, {1, 1});
  CHECK_EQ(out.item<int>(), 2);
}

TEST_CASE("test take") {
  // Empty takes
  auto empty = astype(array({}), int32);
  auto z = take(array({1}), empty);
  CHECK_EQ(z.shape(), std::vector<int>{0});
  empty = reshape(empty, {1, 0, 1});
  z = take(array({1}), empty);
  CHECK_EQ(z.shape(), std::vector<int>{1, 0, 1});

  CHECK_THROWS(take(array({}), array(1)));

  z = take(array({}), empty);
  CHECK_EQ(z.size(), 0);

  // Take a single row
  auto x = reshape(arange(256), {8, 4, 8});
  z = take(x, array({0}, uint32), 0);
  CHECK_EQ(z.shape(), std::vector<int>{1, 4, 8});
  z = reshape(z, {32});
  CHECK(array_equal(z, arange(32)).item<bool>());

  z = take(x, array({1}, uint32), 0);
  z = reshape(z, {32});
  CHECK(array_equal(z, arange(32, 64)).item<bool>());

  // Take multiple rows
  x = arange(256);
  x = reshape(x, {8, 4, 8});
  z = take(x, array({0, 1}, uint32), 0);
  z = reshape(z, {64});
  CHECK(array_equal(z, arange(64)).item<bool>());

  // Take along middle axis
  x = reshape(arange(8), {2, 2, 2});
  z = take(x, array({0}), 1);
  CHECK(array_equal(z, array({0, 1, 4, 5}, {2, 1, 2})).item<bool>());

  // Irregular strides test
  auto a = array({1, 2, 3}, float32);
  auto indices = broadcast_to(array(0), {10});
  auto b = take(a, indices);
  CHECK(array_equal(b, ones({10})).item<bool>());

  // Take with 0 dim index
  z = take(array({0, 1, 2}), array(0));
  CHECK_EQ(z.item<int>(), 0);
  CHECK_EQ(z.ndim(), 0);

  // Check take with float indices crashes
  CHECK_THROWS(take(array({}), array({})));
  CHECK_THROWS(take(a, array({1.0, 2.0, 3.0})));

  // Check axis
  a = array({1, 2, 3, 4}, {2, 2});
  CHECK_THROWS(take(a, array({1}), -3));
  CHECK_THROWS(take(a, array({1}), 2));

  // Check negative indices
  a = array({1, 2, 3, 4}, {2, 2});
  CHECK_EQ(take(a, array({-1})).item<int>(), 4);
  CHECK(array_equal(take(a, array({1, -1})), array({2, 4})).item<bool>());
  CHECK(array_equal(take(a, array(-1), 0), array({3, 4})).item<bool>());

  // Check shapes
  a = zeros({2, 1, 1});
  auto out = take(a, array({1}), 0);
  CHECK(array_equal(out, zeros({1, 1, 1})).item<bool>());
  out = take(a, array({0}), 1);
  CHECK(array_equal(out, zeros({2, 1, 1})).item<bool>());
  out = take(a, array({0}), 1);
  CHECK(array_equal(out, zeros({2, 1, 1})).item<bool>());
  a = zeros({1, 2, 1});
  out = take(a, array({0}), 0);
  CHECK(array_equal(out, zeros({1, 2, 1})).item<bool>());
  out = take(a, array({0}), 1);
  CHECK(array_equal(out, zeros({1, 1, 1})).item<bool>());
  out = take(a, array({0, 1}), 1);
  CHECK(array_equal(out, zeros({1, 2, 1})).item<bool>());
}

TEST_CASE("test take along axis") {
  // No zero dim arrays
  auto a = array(1);
  CHECK_THROWS(take_along_axis(a, array(0), 0));

  // Index and array size mismatches
  a = arange(5);
  CHECK_THROWS(take_along_axis(a, array({1}), 1));
  CHECK_THROWS(take_along_axis(a, array({1}, {1, 1}), 0));
  CHECK_THROWS(take_along_axis(a, array(1), -1));

  auto out = take_along_axis(a, array({1}), 0);
  CHECK_EQ(out.item<int>(), 1);
  out = take_along_axis(a, array({1}), -1);
  CHECK_EQ(out.item<int>(), 1);

  // Indices have wrong shape
  a = zeros({2, 3, 4});
  CHECK_THROWS(take(a, zeros({1, 3, 4}), 1));
  CHECK_THROWS(take(a, zeros({2, 3, 7}), 1));
  CHECK_THROWS(take(a, zeros({2, 3, 2}), 0));

  // Empty arrays
  a = reshape(array({}), {1, 0});
  CHECK_THROWS(take_along_axis(a, array({1}), 0));

  out = take_along_axis(a, reshape(array({1}), {1, 1}), 0);
  eval(out); // Make sure it runs
  CHECK_EQ(out.shape(), std::vector<int>{1, 0});

  auto inds = reshape(astype(array({}), int32), {1, 0});
  out = take_along_axis(a, inds, 0);
  eval(out); // Make sure it runs
  CHECK_EQ(out.shape(), std::vector<int>{1, 0});

  a = array({1, 2, 3, 4}, {2, 2});
  inds = array({0, 1}, {1, 2});
  out = take_along_axis(a, inds, 0);
  CHECK(array_equal(out, array({1, 4}, {1, 2})).item<bool>());

  inds = array({0, 1, 0, 1, 0, 0, 1, 0}, {4, 2}, int32);
  out = take_along_axis(a, inds, 0);
  CHECK(array_equal(out, array({1, 4, 1, 4, 1, 2, 3, 2}, {4, 2})).item<bool>());

  inds = array({0, 1}, {2, 1});
  out = take_along_axis(a, inds, 1);
  CHECK(array_equal(out, array({1, 4}, {2, 1})).item<bool>());

  // Broadcasting works
  inds = array({0}, {1, 1});
  out = take_along_axis(a, inds, 0);
  CHECK(array_equal(out, array({1, 2}, {1, 2})).item<bool>());
  out = take_along_axis(a, inds, 1);
  CHECK(array_equal(out, array({1, 3}, {2, 1})).item<bool>());

  inds = array({0, 1, 1, 0, 0, 1}, {2, 3}, int32);
  out = take_along_axis(a, inds, 1);
  CHECK(array_equal(out, array({1, 2, 2, 3, 3, 4}, {2, 3})).item<bool>());

  a = reshape(arange(8), {2, 2, 2});
  inds = array({0, 1, 0, 0, 1, 0, 0, 1}, {2, 2, 2});
  out = take_along_axis(a, inds, 0);
  CHECK(array_equal(out, array({0, 5, 2, 3, 4, 1, 2, 7}, {2, 2, 2}))
            .item<bool>());
  out = take_along_axis(a, inds, 1);
  CHECK(array_equal(out, array({0, 3, 0, 1, 6, 5, 4, 7}, {2, 2, 2}))
            .item<bool>());
  out = take_along_axis(a, inds, 2);
  CHECK(array_equal(out, array({0, 1, 2, 2, 5, 4, 6, 7}, {2, 2, 2}))
            .item<bool>());
}

TEST_CASE("test scatter") {
  // More indices than dimensions
  CHECK_THROWS(scatter(array(0), array({1}), array(1), 0));

  // Mismatch dimensions and indices
  CHECK_THROWS(scatter(array({0}), {array({0})}, array({1}, {1, 1}), {0, 1}));
  CHECK_THROWS(scatter(array({0}), array({0}), array({1}, {1, 1}), -1));

  // Repeat dimensions
  CHECK_THROWS(scatter(
      array({0}, {1, 1}), {array({0}), array({0})}, array({1}), {0, 0}));

  // Update sizes incorrect
  CHECK_THROWS(scatter(array({0}), array({0}), array({0, 1}), 0));
  CHECK_THROWS(scatter(array({0}), array({0}), array({0, 1}, {2, 1}), 0));
  CHECK_THROWS(scatter(array({0}, {1}), array({0}), array({0, 1}, {1, 2}), 0));

  // Wrong index type
  CHECK_THROWS(scatter(array({0}), array({0.0f}), array({0}, {1, 1}), 0));
  CHECK_THROWS(scatter(
      array({0}, {1, 1}),
      {array({0}), array({0.0f})},
      array({1}, {1, 1, 1}),
      {0, 1}));

  // Index arrays must be broadcastable
  CHECK_THROWS(scatter(
      array({0}, {1, 1}),
      {array({0, 0, 0}, {3}), array({0, 0}, {2})},
      ones({3, 2, 1, 1}),
      {0, 1}));

  // Single element scatter
  auto in = zeros({4}, float32);
  auto inds = arange(2);
  auto updates = ones({2, 1}, float32);
  auto out = scatter(in, inds, updates, 0);
  CHECK(array_equal(out, array({1.0f, 1.0f, 0.0f, 0.0f})).item<bool>());

  // Single element scatter add
  in = ones({4}, float32);
  inds = array({0, 0, 3});
  updates = ones({3, 1}, float32);
  out = scatter_add(in, inds, updates, 0);
  CHECK(array_equal(out, array({3.0f, 1.0f, 1.0f, 2.0f})).item<bool>());

  // Single element scatter prod
  in = ones({4}, float32);
  inds = array({0, 0, 3});
  updates = full({3, 1}, 2.0f, float32);
  out = scatter_prod(in, inds, updates, 0);
  CHECK(array_equal(out, array({4.0f, 1.0f, 1.0f, 2.0f})).item<bool>());

  // Single element scatter max
  in = ones({4}, float32);
  inds = array({0, 0, 3});
  updates = array({1.0f, 6.0f, -2.0f}, {3, 1});
  out = scatter_max(in, inds, updates, 0);
  CHECK(array_equal(out, array({6.0f, 1.0f, 1.0f, 1.0f})).item<bool>());

  // Single element scatter min
  in = ones({4}, float32);
  inds = array({0, 0, 3});
  updates = array({1.0f, -6.0f, 2.0f}, {3, 1});
  out = scatter_min(in, inds, updates, 0);
  CHECK(array_equal(out, array({-6.0f, 1.0f, 1.0f, 1.0f})).item<bool>());

  // Empty scatter
  in = arange(4, float32);
  inds = astype(array({}), uint32);
  updates = reshape(array({}), {0, 1});
  out = scatter(in, inds, updates, 0);
  CHECK(array_equal(out, in).item<bool>());

  // Array scatters
  in = zeros({4, 4}, float32);
  inds = array({0, 1, 2, 3});
  updates = reshape(arange(16, float32), {4, 1, 4});
  out = scatter(in, inds, updates, 0);
  CHECK(array_equal(out, reshape(arange(16, float32), {4, 4})).item<bool>());

  // Irregular strided index and reduce collison test
  in = zeros({10}, float32);
  inds = broadcast_to(array(3), {10});
  updates = ones({10, 1}, float32);
  out = scatter_add(in, inds, updates, 0);
  CHECK_EQ(take(out, array(3)).item<float>(), 10);

  // 1 element array with 0 dim index
  in = array({1}, int32);
  updates = array({2}, int32);
  out = scatter_max(in, array(0), updates, 0);
  CHECK_EQ(out.item<int>(), 2);

  // No index arrays or axes
  out = scatter_max(array(1), {}, array(2), std::vector<int>{});
  CHECK_EQ(out.item<int>(), 2);

  // Irregularaly strided updates test
  in = ones({3, 3});
  updates = broadcast_to(array({0, 0, 0}), {1, 3, 3});
  inds = array({0});
  out = scatter(in, inds, updates, 0);
  CHECK(array_equal(out, zeros({3, 3})).item<bool>());

  // Along different axis
  in = zeros({2, 3});
  updates = array({1, 2, 3, 4}, {2, 2, 1});
  inds = array({0, 2});
  out = scatter(in, inds, updates, 1);
  auto expected = array({1, 0, 3, 2, 0, 4}, {2, 3});
  CHECK(array_equal(out, expected).item<bool>());

  // Multiple index arrays
  in = zeros({2, 2});
  updates = array({1, 2}, {2, 1, 1});
  inds = array({0, 1});
  out = scatter(in, {inds, inds}, updates, {0, 1});
  CHECK(array_equal(out, array({1, 0, 0, 2}, {2, 2})).item<bool>());

  // Broadcasted indices
  in = zeros({2, 2});
  updates = array({5, 2, 9, 1}, {2, 2, 1, 1});
  auto inds0 = array({0, 1}, {2, 1});
  auto inds1 = array({0, 1}, {1, 2});
  out = scatter(in, {inds0, inds1}, updates, {0, 1});
  CHECK(array_equal(out, array({5, 2, 9, 1}, {2, 2})).item<bool>());

  // Brodacasted operand
  in = broadcast_to(array({0, 0}), {2, 2});
  updates = array({1, 1}, {2, 1, 1});
  inds = array({0, 1});
  out = scatter_add(in, inds, updates, 0);
  CHECK(array_equal(out, array({1, 0, 1, 0}, {2, 2})).item<bool>());
}

TEST_CASE("test complex ops") {
  //  Creation ops
  {
    auto x = full({2, 2}, complex64_t{1, 1});
    CHECK_EQ(x.dtype(), complex64);
    std::initializer_list<complex64_t> expected = {
        {1, 1}, {1, 1}, {1, 1}, {1, 1}};
    CHECK(array_equal(x, array(expected, {2, 2})).item<bool>());
  }

  // Unary ops
  {
    std::initializer_list<complex64_t> vals = {{0, 1}, {1, 0}, {1, 1}};
    auto x = array(vals);

    auto y = abs(x);
    CHECK_EQ(y.dtype(), float32);
    CHECK(array_equal(y, array({1.0f, 1.0f, std::sqrt(2.0f)})).item<bool>());

    y = negative(x);
    std::initializer_list<complex64_t> expected = {{0, -1}, {-1, 0}, {-1, -1}};
    CHECK(array_equal(y, array(expected)).item<bool>());

    y = exp(x);
    {
      std::initializer_list<complex64_t> expected = {
          {0.54030231, 0.84147098}, {2.71828183, 0.}, {1.46869394, 2.28735529}};
      CHECK(allclose(y, array(expected)).item<bool>());
    }

    y = sin(x);
    {
      std::initializer_list<complex64_t> expected = {
          {0., 1.17520119}, {0.84147098, 0.}, {1.29845758, 0.63496391}};
      CHECK(allclose(y, array(expected)).item<bool>());
    }

    y = cos(x);
    {
      std::initializer_list<complex64_t> expected = {
          {1.54308063, -0.}, {0.54030231, -0.}, {0.83373003, -0.98889771}};
      CHECK(allclose(y, array(expected)).item<bool>());
    }
  }

  // Binary ops
  {
    std::initializer_list<complex64_t> vals_x = {{0, 1}, {1, 0}, {1, 1}};
    auto x = array(vals_x);

    std::initializer_list<complex64_t> vals_y = {{2, 0}, {1, 1}, {0, 1}};
    auto y = array(vals_y);

    auto z = add(x, y);
    {
      std::initializer_list<complex64_t> expected = {{2, 1}, {2, 1}, {1, 2}};
      CHECK(array_equal(z, array(expected)).item<bool>());
    }

    z = subtract(x, y);
    {
      std::initializer_list<complex64_t> expected = {{-2, 1}, {0, -1}, {1, 0}};
      CHECK(array_equal(z, array(expected)).item<bool>());
    }

    z = multiply(x, y);
    {
      std::initializer_list<complex64_t> expected = {{0, 2}, {1, 1}, {-1, 1}};
      CHECK(array_equal(z, array(expected)).item<bool>());
    }

    z = maximum(x, y);
    {
      std::initializer_list<complex64_t> expected = {{2, 0}, {1, 1}, {1, 1}};
      CHECK(array_equal(z, array(expected)).item<bool>());
    }
  }

  // Reductions
  if (default_device() == Device::cpu) {
    std::initializer_list<complex64_t> vals = {{0, 0}, {1, 0}, {0, 1}};
    auto x = array(vals);
    CHECK_EQ(max(x).item<complex64_t>(), complex64_t{1, 0});
    CHECK_EQ(min(x).item<complex64_t>(), complex64_t{0, 0});
    CHECK_EQ(sum(x).item<complex64_t>(), complex64_t{1, 1});
    CHECK_EQ(prod(x).item<complex64_t>(), complex64_t{0, 0});
  }
}

TEST_CASE("test as_strided op") {
  auto x = arange(10);
  auto y = as_strided(x, {3, 3}, {1, 1}, 0);
  auto expected = array({0, 1, 2, 1, 2, 3, 2, 3, 4}, {3, 3});
  CHECK(array_equal(y, expected).item<bool>());

  y = as_strided(x, {3, 3}, {0, 3}, 0);
  expected = array({0, 3, 6, 0, 3, 6, 0, 3, 6}, {3, 3});
  CHECK(array_equal(y, expected).item<bool>());

  x = reshape(x, {2, 5}); // 0 1 2 3 ...
  x = transpose(x, {1, 0}); // 0 5 1 6 2 7 ...
  y = as_strided(x, {3, 3}, {2, 1}, 1);
  expected = array({5, 1, 6, 6, 2, 7, 7, 3, 8}, {3, 3});
  CHECK(array_equal(y, expected).item<bool>());
}

TEST_CASE("test scan op") {
  auto x = array({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f}, {2, 3});
  auto y = cumsum(x, 1, false, true);
  auto expected = array({1.0f, 3.0f, 6.0f, 4.0f, 9.0f, 15.0f}, {2, 3});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 1, false, false);
  expected = array({0.0f, 1.0f, 3.0f, 0.0f, 4.0f, 9.0f}, {2, 3});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 1, true, true);
  expected = array({6.0f, 5.0f, 3.0f, 15.0f, 11.0f, 6.0f}, {2, 3});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 1, true, false);
  expected = array({5.0f, 3.0f, 0.0f, 11.0f, 6.0f, 0.0f}, {2, 3});
  CHECK(array_equal(y, expected).item<bool>());

  x = array({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f}, {2, 2, 2});
  y = cumsum(x, 0, false, true);
  expected =
      array({1.0f, 2.0f, 3.0f, 4.0f, 6.0f, 8.0f, 10.0f, 12.0f}, {2, 2, 2});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 1, false, true);
  expected =
      array({1.0f, 2.0f, 4.0f, 6.0f, 5.0f, 6.0f, 12.0f, 14.0f}, {2, 2, 2});
  CHECK(array_equal(y, expected).item<bool>());

  x = array({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f}, {2, 2, 2});
  y = cumsum(x, 0, true, true);
  expected =
      array({6.0f, 8.0f, 10.0f, 12.0f, 5.0f, 6.0f, 7.0f, 8.0f}, {2, 2, 2});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 1, true, true);
  expected =
      array({4.0f, 6.0f, 3.0f, 4.0f, 12.0f, 14.0f, 7.0f, 8.0f}, {2, 2, 2});
  CHECK(array_equal(y, expected).item<bool>());

  x = reshape(x, {4, 2});
  y = cumsum(x, 0, false, false);
  expected = array({0.0f, 0.0f, 1.0f, 2.0f, 4.0f, 6.0f, 9.0f, 12.0f}, {4, 2});
  CHECK(array_equal(y, expected).item<bool>());

  y = cumsum(x, 0, true, false);
  expected =
      array({15.0f, 18.0f, 12.0f, 14.0f, 7.0f, 8.0f, 0.0f, 0.0f}, {4, 2});
  CHECK(array_equal(y, expected).item<bool>());

  // Check the vmap implementation
  auto fun = [](array x) { return cumsum(x, 0, false, true); };
  y = vmap(fun, 0, 0)(x);
  expected = array({1.0f, 3.0f, 3.0f, 7.0f, 5.0f, 11.0f, 7.0f, 15.0f}, {4, 2});
  CHECK(array_equal(y, expected).item<bool>());

  y = vmap(fun, 1, 1)(x);
  expected = array({1.0f, 2.0f, 4.0f, 6.0f, 9.0f, 12.0f, 16.0f, 20.0f}, {4, 2});
  CHECK(array_equal(y, expected).item<bool>());
}

TEST_CASE("test pad") {
  auto x = zeros({1, 2, 3});
  CHECK_EQ(pad(x, 1).shape(), std::vector<int>{3, 4, 5});
  CHECK_EQ(pad(x, {0, 1}).shape(), std::vector<int>{2, 3, 4});
  CHECK_EQ(pad(x, {{1, 1}, {1, 2}, {3, 1}}).shape(), std::vector<int>{3, 5, 7});
}

TEST_CASE("test power") {
  CHECK_EQ(power(array(1), array(2)).item<int>(), 1);
  CHECK_EQ((array(1) ^ 2).item<int>(), 1);
  CHECK_EQ((1 ^ array(2)).item<int>(), 1);
  CHECK_EQ((array(-1) ^ 2).item<int>(), 1);
  CHECK_EQ((array(-1) ^ 3).item<int>(), -1);

  // TODO Throws but exception not caught from calling thread
  // CHECK_THROWS((x^-1).item<int>());

  CHECK_EQ((array(true) ^ array(false)).item<bool>(), true);
  CHECK_EQ((array(false) ^ array(false)).item<bool>(), true);
  CHECK_EQ((array(true) ^ array(true)).item<bool>(), true);
  CHECK_EQ((array(false) ^ array(true)).item<bool>(), false);

  auto x = array(2.0f);
  CHECK_EQ((x ^ 0.5).item<float>(), std::pow(2.0f, 0.5f));
  CHECK_EQ((x ^ 2.0f).item<float>(), 4.0f);

  CHECK(std::isnan((array(-1.0f) ^ 0.5).item<float>()));

  auto a = complex64_t{0.5, 0.5};
  auto b = complex64_t{0.5, 0.5};
  auto expected = std::pow(a, b);
  auto out = (array(a) ^ array(b)).item<complex64_t>();
  CHECK(abs(out.real() - expected.real()) < 1e-7);
  CHECK(abs(out.imag() - expected.imag()) < 1e-7);
}

TEST_CASE("test where") {
  array condition(true);
  array x(1.0f);
  array y(0.0f);
  auto out = where(condition, x, y);
  CHECK_EQ(out.dtype(), float32);
  CHECK_EQ(out.item<float>(), 1.0f);

  x = array({1, 2}, {2, 1});
  y = array({3, 4}, {1, 2});
  CHECK(array_equal(where(condition, x, y), broadcast_to(x, {2, 2}))
            .item<bool>());

  condition = array(false);
  CHECK(array_equal(where(condition, x, y), broadcast_to(y, {2, 2}))
            .item<bool>());

  condition = array({true, false});
  out = where(condition, x, y);
  auto expected = array({1, 4, 2, 4}, {2, 2});
  CHECK(array_equal(where(condition, x, y), expected).item<bool>());

  condition = array({true, false, false, true}, {2, 2});
  out = where(condition, x, y);
  expected = array({1, 4, 3, 2}, {2, 2});
  CHECK(array_equal(where(condition, x, y), expected).item<bool>());

  x = array(1);
  y = array(2);
  out = where(condition, x, y);
  expected = array({1, 2, 2, 1}, {2, 2});
  CHECK(array_equal(where(condition, x, y), expected).item<bool>());
}

TEST_CASE("test eye") {
  auto eye_3 = eye(3);
  CHECK_EQ(eye_3.shape(), std::vector<int>{3, 3});
  auto expected_eye_3 =
      array({1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f}, {3, 3});
  CHECK(array_equal(eye_3, expected_eye_3).item<bool>());

  auto eye_3x2 = eye(3, 2);
  CHECK_EQ(eye_3x2.shape(), std::vector<int>{3, 2});
  auto expected_eye_3x2 = array({1.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f}, {3, 2});
  CHECK(array_equal(eye_3x2, expected_eye_3x2).item<bool>());
}

TEST_CASE("test identity") {
  auto id_4 = identity(4);
  CHECK_EQ(id_4.shape(), std::vector<int>{4, 4});
  auto expected_id_4 = array(
      {1.0f,
       0.0f,
       0.0f,
       0.0f,
       0.0f,
       1.0f,
       0.0f,
       0.0f,
       0.0f,
       0.0f,
       1.0f,
       0.0f,
       0.0f,
       0.0f,
       0.0f,
       1.0f},
      {4, 4});
  CHECK(array_equal(id_4, expected_id_4).item<bool>());
}

TEST_CASE("test eye with positive k offset") {
  auto eye_3_k1 = eye(3, 4, 1);
  CHECK_EQ(eye_3_k1.shape(), std::vector<int>{3, 4});
  auto expected_eye_3_k1 = array(
      {0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f},
      {3, 4});
  CHECK(array_equal(eye_3_k1, expected_eye_3_k1).item<bool>());
}

TEST_CASE("test eye with negative k offset") {
  auto eye_4_k_minus1 = eye(4, 3, -1);
  CHECK_EQ(eye_4_k_minus1.shape(), std::vector<int>{4, 3});
  auto expected_eye_4_k_minus1 = array(
      {0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f},
      {4, 3});
  CHECK(array_equal(eye_4_k_minus1, expected_eye_4_k_minus1).item<bool>());
}