// It's definitely safe to multiply into numerator and denominator.
              numerator *= n;
              denominator *= i;
              numeratorBits += nBits;
            } else {
              // It might not be safe to multiply into numerator and denominator,
              // so multiply (numerator / denominator) into result.

      for (long b : TEST_LONGS) {
        UnsignedLong aUnsigned = UnsignedLong.fromLongBits(a);
        UnsignedLong bUnsigned = UnsignedLong.fromLongBits(b);
        long expected =
            aUnsigned.bigIntegerValue().multiply(bUnsigned.bigIntegerValue()).longValue();
        UnsignedLong unsignedMul = aUnsigned.times(bUnsigned);
        assertThat(unsignedMul.longValue()).isEqualTo(expected);
      }
    }
  }

  @AndroidIncompatible // presumably slow
  public void testCheckedMultiply() {
    for (int a : ALL_INTEGER_CANDIDATES) {
      for (int b : ALL_INTEGER_CANDIDATES) {
        BigInteger expectedResult = valueOf(a).multiply(valueOf(b));
        boolean expectedSuccess = fitsInInt(expectedResult);
        try {
          assertEquals(a * b, IntMath.checkedMultiply(a, b));
          assertTrue(expectedSuccess);

     */
    open fun header(
      name: String,
      value: String,
    ) = apply {
      headers[name] = value
    }

    /**
     * Adds a header with [name] and [value]. Prefer this method for multiply-valued
     * headers like "Cookie".
     *
     * Note that for some headers including `Content-Length` and `Content-Encoding`,
     * OkHttp may replace [value] with a header derived from the request body.
     */

     */
    open fun header(
      name: String,
      value: String,
    ) = apply {
      headers[name] = value
    }

    /**
     * Adds a header with [name] to [value]. Prefer this method for multiply-valued
     * headers like "Set-Cookie".
     */
    open fun addHeader(
      name: String,
      value: String,
    ) = apply {
      headers.add(name, value)
    }

  // These fields must satisfy the requirements of Stats' constructor as well as those of the stat
  // methods of this class.
  private long count = 0;
  private double mean = 0.0; // any finite value will do, we only use it to multiply by zero for sum
  private double sumOfSquaresOfDeltas = 0.0;
  private double min = NaN; // any value will do
  private double max = NaN; // any value will do

  /** Adds the given value to the dataset. */

func (v *projP2) FromP1xP1(p *projP1xP1) *projP2 { v.X.Multiply(&p.X, &p.T) v.Y.Multiply(&p.Y, &p.Z) v.Z.Multiply(&p.Z, &p.T) return v } func (v *projP2) FromP3(p *Point) *projP2 { v.X.Set(&p.x) v.Y.Set(&p.y) v.Z.Set(&p.z) return v } func (v *Point) fromP1xP1(p *projP1xP1) *Point { v.x.Multiply(&p.X, &p.T) v.y.Multiply(&p.Y, &p.Z) v.z.Multiply(&p.Z, &p.T) v.t.Multiply(&p.X, &p.Y) return v } func (v *Point) fromP2(p *projP2) *Point { v.x.Multiply(&p.X, &p.Z) v.y.Multiply(&p.Y, &p.Z) v.z.Square(&p.Z)...

func (v *projP2) FromP1xP1(p *projP1xP1) *projP2 { v.X.Multiply(&p.X, &p.T) v.Y.Multiply(&p.Y, &p.Z) v.Z.Multiply(&p.Z, &p.T) return v } func (v *projP2) FromP3(p *Point) *projP2 { v.X.Set(&p.x) v.Y.Set(&p.y) v.Z.Set(&p.z) return v } func (v *Point) fromP1xP1(p *projP1xP1) *Point { v.x.Multiply(&p.X, &p.T) v.y.Multiply(&p.Y, &p.Z) v.z.Multiply(&p.Z, &p.T) v.t.Multiply(&p.X, &p.Y) return v } func (v *Point) fromP2(p *projP2) *Point { v.x.Multiply(&p.X, &p.Z) v.y.Multiply(&p.Y, &p.Z) v.z.Square(&p.Z)...

* **Deep Learning**: this is a sub-field of Machine Learning, so, the same applies. It's just that there is not a single spreadsheet of numbers to multiply, but a huge set of them, and in many cases, you use a special processor to build and / or use those models.

### Concurrency + Parallelism: Web + Machine Learning { #concurrency-parallelism-web-machine-learning }

			res[i] = &di
		}
	}
	return res
}

// hasSpaceFor returns whether the disks in `di` have space for and object of a given size.
func hasSpaceFor(di []*DiskInfo, size int64) (bool, error) {
	// We multiply the size by 2 to account for erasure coding.
	size *= 2
	if size < 0 {
		// If no size, assume diskAssumeUnknownSize.
		size = diskAssumeUnknownSize
	}

	var available uint64
	var total uint64