<img class="sponsor-image" src="/img/sponsors/scalar-banner.svg" />
      </a>
    </div>
    <div class="item">
      <a title="Auth, user management and more for your B2B product" style="display: block; position: relative;" href="https://www.propelauth.com/?utm_source=fastapi&utm_campaign=1223&utm_medium=topbanner" target="_blank">
        <span class="sponsor-badge">sponsor</span>

        axesSizeProduct[i] = Math.multiplyExact(axesSizeProduct[i + 1], axes.get(i).size());
      }
    } catch (ArithmeticException e) {
      throw new IllegalArgumentException(
          "Cartesian product too large; must have size at most Integer.MAX_VALUE");
    }
    this.axesSizeProduct = axesSizeProduct;
  }

  private int getAxisIndexForProductIndex(int index, int axis) {

   */
  @InlineMe(replacement = "Math.subtractExact(a, b)")
  public static int checkedSubtract(int a, int b) {
    return Math.subtractExact(a, b);
  }

  /**
   * Returns the product of {@code a} and {@code b}, provided it does not overflow.
   *
   * <p><b>Note:</b> this method is now unnecessary and should be treated as deprecated; use {@link
   * Math#multiplyExact(int, int)} instead.
   *

    img: https://fastapi.tiangolo.com/img/sponsors/scalar.svg
  - url: https://www.propelauth.com/?utm_source=fastapi&utm_campaign=1223&utm_medium=mainbadge
    title: Auth, user management and more for your B2B product
    img: https://fastapi.tiangolo.com/img/sponsors/propelauth.png
  - url: https://zuplo.link/fastapi-gh
    title: 'Zuplo: Deploy, Secure, Document, and Monetize your FastAPI'

    checkState(count() > 1);
    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product.  A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

### Cross-cutting architecture modules

There are some additional cross-cutting architecture modules that aren't themselves platforms:

#### Enterprise integration

Provides cross-cutting integration with Gradle's commercial product.

#### IDE integration

Provides cross-cutting integration with IDEs and other tooling.

#### Build infrastructure

    checkState(count() > 1);
    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

## Cross-cutting architecture modules

There are some additional cross-cutting architecture modules that aren't platforms:

### Enterprise integration

Provides cross-cutting integration with Gradle's commercial product.

### IDE integration

Provides cross-cutting integration with IDEs and other tooling.

### Build infrastructure

        // CSV with numbers and mixed data types - quoted fields keep quotes
        value = "123,\"Product Name\",45.67,\"Description with, comma\"";
        result = KuromojiCSVUtil.parse(value);
        assertEquals(4, result.length);
        assertEquals("123", result[0]);
        assertEquals("Product Name", result[1]);
        assertEquals("45.67", result[2]);
        assertEquals("\"Description with, comma\"", result[3]);