assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */
  @GwtIncompatible // TODO
  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);

        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */
  @GwtIncompatible // TODO
  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);

 public:
  explicit SqrtGradientFunction(AbstractTensorHandle* sqrt) : sqrt_(sqrt) {
    sqrt->Ref();
  }
  Status Compute(AbstractContext* ctx,
                 absl::Span<AbstractTensorHandle* const> grad_outputs,
                 absl::Span<AbstractTensorHandle*> grad_inputs) override {
    std::string name = "Sqrt_Grad";
    TF_RETURN_IF_ERROR(SqrtGrad(ctx, sqrt_.get(), grad_outputs[0],

  }

  private static final Function<Integer, Double> SQRT_FUNCTION = in -> Math.sqrt(in);

  public void testTransformValues() {
    Map<String, Integer> map = ImmutableMap.of("a", 4, "b", 9);
    Map<String, Double> transformed = transformValues(map, SQRT_FUNCTION);

    assertEquals(ImmutableMap.of("a", 2.0, "b", 3.0), transformed);
  }

  }

  private static final Function<Integer, Double> SQRT_FUNCTION = in -> Math.sqrt(in);

  public void testTransformValues() {
    Map<String, Integer> map = ImmutableMap.of("a", 4, "b", 9);
    Map<String, Double> transformed = transformValues(map, SQRT_FUNCTION);

    assertEquals(ImmutableMap.of("a", 2.0, "b", 3.0), transformed);
  }

 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   if (value < 0) {
 *     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>to be replaced with the more compact
 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);

   * Map<String, Integer> map = ImmutableMap.of("a", 4, "b", 9);
   * Function<Integer, Double> sqrt =
   *     new Function<Integer, Double>() {
   *       public Double apply(Integer in) {
   *         return Math.sqrt((int) in);
   *       }
   *     };
   * Map<String, Double> transformed = Maps.transformValues(map, sqrt);
   * System.out.println(transformed);
   * }</pre>
   *

   *      = ImmutableListMultimap.of("a", 4, "a", 16, "b", 9);
   * Function<Integer, Double> sqrt =
   *     new Function<Integer, Double>() {
   *       public Double apply(Integer in) {
   *         return Math.sqrt((int) in);
   *       }
   *     };
   * ListMultimap<String, Double> transformed = Multimaps.transformValues(map,
   *     sqrt);
   * System.out.println(transformed);
   * }</pre>
   *

assignment context to retrieve both the return value (if any) and the
C errno variable as an error (use _ to skip the result value if the
function returns void). For example:

	n, err = C.sqrt(-1)
	_, err := C.voidFunc()
	var n, err = C.sqrt(1)

Calling C function pointers is currently not supported, however you can
declare Go variables which hold C function pointers and pass them

    }
    // Guess the size is "halfway between" all duplicates and no duplicates, on a log scale.
    return Math.max(
        ImmutableCollection.Builder.DEFAULT_INITIAL_CAPACITY,
        IntMath.sqrt(inputElementsIncludingAnyDuplicates, RoundingMode.CEILING));
  }

  private static final long serialVersionUID = 0xcafebabe;