// If it won't fit in a long, then we store off the intermediate product.
      if (normalizedBits + productBits >= Long.SIZE) {
        bignums.add(BigInteger.valueOf(product));
        product = 1;
        productBits = 0;
      }
      product *= normalizedNum;
      productBits = LongMath.log2(product, FLOOR) + 1;
    }
    // Check for leftovers.
    if (product > 1) {
      bignums.add(BigInteger.valueOf(product));
    }

- Follow through the wizard as above for Veeam Backup and Replication as the steps are the same between both products

- Under Backup Infrastructure -> Backup Repositories, right click and "Add Backup Repository"

- Follow the wizard.  Under the "Object Storage Backup Repository" section, choose the MinIO object storage you created above

## Common Use Cases

### E-commerce Search

```java
// Product search suggestions
SuggestItem product = new SuggestItem(
    new String[]{"iPhone 15 Pro", "Apple iPhone 15 Pro"},
    new String[][]{{"iphone"}, {"apple", "phone"}},
    1.5f,                               // boost popular products
    new String[]{"electronics", "mobile"},
    new String[]{"customer"},
    SuggestItem.Kind.DOCUMENT

    // vol. 2, Knuth, 4.2.2, (16) to the two-variable case. We have two value series x_i and y_i.
    // We define the arithmetic means X_n = 1/n \sum_{i=1}^n x_i, and Y_n = 1/n \sum_{i=1}^n y_i.
    // We also define the sum of the products of the differences from the means
    //           C_n = \sum_{i=1}^n x_i y_i - n X_n Y_n
    // for all n >= 1. Then for all n > 1:
    //       C_{n-1} = \sum_{i=1}^{n-1} x_i y_i - (n-1) X_{n-1} Y_{n-1}

///

## SDK Generators from FastAPI Sponsors { #sdk-generators-from-fastapi-sponsors }

This section highlights **venture-backed** and **company-supported** solutions from companies that sponsor FastAPI. These products provide **additional features** and **integrations** on top of high-quality generated SDKs.

   * }
   * }
   *
   * <p>Note that if any input list is empty, the Cartesian product will also be empty. If no lists
   * at all are provided (an empty list), the resulting Cartesian product has one element, an empty
   * list (counter-intuitive, but mathematically consistent).
   *
   * <p><i>Performance notes:</i> while the cartesian product of lists of size {@code m, n, p} is a

   * }
   * }
   *
   * <p>Note that if any input list is empty, the Cartesian product will also be empty. If no lists
   * at all are provided (an empty list), the resulting Cartesian product has one element, an empty
   * list (counter-intuitive, but mathematically consistent).
   *
   * <p><i>Performance notes:</i> while the cartesian product of lists of size {@code m, n, p} is a

## Враження { #opinions }

"_[...] I'm using **FastAPI** a ton these days. [...] I'm actually planning to use it for all of my team's **ML services at Microsoft**. Some of them are getting integrated into the core **Windows** product and some **Office** products._"

<div style="text-align: right; margin-right: 10%;">Kabir Khan - <strong>Microsoft</strong> <a href="https://github.com/fastapi/fastapi/pull/26"><small>(ref)</small></a></div>

---

## Opinions

"_[...] I'm using **FastAPI** a ton these days. [...] I'm actually planning to use it for all of my team's **ML services at Microsoft**. Some of them are getting integrated into the core **Windows** product and some **Office** products._"

<div style="text-align: right; margin-right: 10%;">Kabir Khan - <strong>Microsoft</strong> <a href="https://github.com/fastapi/fastapi/pull/26"><small>(ref)</small></a></div>

---

## Opinions { #opinions }

"_[...] I'm using **FastAPI** a ton these days. [...] I'm actually planning to use it for all of my team's **ML services at Microsoft**. Some of them are getting integrated into the core **Windows** product and some **Office** products._"

<div style="text-align: right; margin-right: 10%;">Kabir Khan - <strong>Microsoft</strong> <a href="https://github.com/fastapi/fastapi/pull/26"><small>(ref)</small></a></div>

---