with Licensor regarding such Contributions.

   6. Trademarks. This License does not grant permission to use the trade
      names, trademarks, service marks, or product names of the Licensor,
      except as required for reasonable and customary use in describing the
      origin of the Work and reproducing the content of the NOTICE file.

      with Licensor regarding such Contributions.

   6. Trademarks. This License does not grant permission to use the trade
      names, trademarks, service marks, or product names of the Licensor,
      except as required for reasonable and customary use in describing the
      origin of the Work and reproducing the content of the NOTICE file.

      with Licensor regarding such Contributions.

   6. Trademarks. This License does not grant permission to use the trade
      names, trademarks, service marks, or product names of the Licensor,
      except as required for reasonable and customary use in describing the
      origin of the Work and reproducing the content of the NOTICE file.

      with Licensor regarding such Contributions.

   6. Trademarks. This License does not grant permission to use the trade
      names, trademarks, service marks, or product names of the Licensor,
      except as required for reasonable and customary use in describing the
      origin of the Work and reproducing the content of the NOTICE file.

   */
  @InlineMe(replacement = "Math.subtractExact(a, b)")
  public static long checkedSubtract(long a, long 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

## Враження

"_[...] 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" target="_blank"><small>(ref)</small></a></div>

---

      // whose index in the sorted dataset equals the quotient; if there is a remainder, we
      // interpolate between that and the next value.

      // Since index and (dataset.length - 1) are non-negative ints, their product can be expressed
      // as a long, without risk of overflow:
      long numerator = (long) index * (dataset.length - 1);
      // Since scale is a positive int, index is in [0, scale], and (dataset.length - 1) is a

## 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" target="_blank"><small>(ref)</small></a></div>

---

        return a + b;
    }

    /**
     * Safe integer multiplication with overflow check
     *
     * @param a first operand
     * @param b second operand
     * @return product of a and b
     * @throws ArithmeticException if overflow occurs
     */
    public static int safeMultiply(int a, int b) {
        validateIntegerMultiplication(a, b, "Multiplication");
        return a * b;
    }

      with Licensor regarding such Contributions.

   6. Trademarks. This License does not grant permission to use the trade
      names, trademarks, service marks, or product names of the Licensor,
      except as required for reasonable and customary use in describing the
      origin of the Work and reproducing the content of the NOTICE file.