assertThat(manyValuesAccumulatorByAddAllPartitionedPairedStats.populationCovariance())
        .isWithin(ALLOWED_ERROR)
        .of(MANY_VALUES_SUM_OF_PRODUCTS_OF_DELTAS / MANY_VALUES_COUNT);
    // For datasets of many double values, we test many combinations of finite and non-finite
    // x-values:
    for (ManyValues values : ALL_MANY_VALUES) {
      PairedStatsAccumulator accumulator =

Because of this, **FastAPI** itself provides an alternative API documentation (using ReDoc), which you can access at <a href="http://127.0.0.1:8000/redoc" class="external-link" target="_blank">http://127.0.0.1:8000/redoc</a>:

<img src="/img/tutorial/path-params/image02.png">

The same way, there are many compatible tools. Including code generation tools for many languages.

to generate a trusted root certificate, an intermediate certificate, and a server certificate.
We use `certificateAuthority(int)` to create certificates that can sign other certificates. The
int specifies how many intermediate certificates are allowed beneath it in the chain.

```java
HeldCertificate rootCertificate = new HeldCertificate.Builder()
    .certificateAuthority(1)
    .build();

	user.Pets = append(user.Pets, &pet)
	CheckUser(t, user2, user)

	AssertAssociationCount(t, user, "Pets", 3, "AfterAppend")

	pets2 := []Pet{{Name: "pet-has-many-append-1-1"}, {Name: "pet-has-many-append-1-1"}}

	if err := DB.Model(&user2).Association("Pets").Append(&pets2); err != nil {
		t.Fatalf("Error happened when append pet, got %v", err)
	}

	for _, pet := range pets2 {
		pet := pet
		if pet.ID == 0 {

   * non-nullable {@code cause}, as many users expect to find one.
   */
  public ExecutionError(@Nullable String message, @Nullable Error cause) {
    super(message, cause);
  }

  /**
   * Creates a new instance with {@code null} as its detail message and the given cause. Prefer to
   * provide a non-nullable {@code cause}, as many users expect to find one.
   */

package tests_test

import (
	"testing"

	"gorm.io/gorm"
	. "gorm.io/gorm/utils/tests"
)

func TestUpdateHasManyAssociations(t *testing.T) {
	user := *GetUser("update-has-many", Config{})

	if err := DB.Create(&user).Error; err != nil {
		t.Fatalf("errors happened when create: %v", err)
	}

	user.Pets = []*Pet{{Name: "pet1"}, {Name: "pet2"}}
	if err := DB.Save(&user).Error; err != nil {

When you check the benchmarks, it is common to see several tools of different types compared as equivalent.

Specifically, to see Uvicorn, Starlette and FastAPI compared together (among many other tools).

The simpler the problem solved by the tool, the better performance it will get. And most of the benchmarks don't test the additional features provided by the tool.

The hierarchy is like:

        return value;
      }
    }
    return null;
  }

  /**
   * A sensible definition of {@link #clear} in terms of the {@code iterator} method of {@link
   * #entrySet}. In many cases, you may wish to override {@link #clear} to forward to this
   * implementation.
   *
   * @since 7.0
   */
  protected void standardClear() {
    Iterators.clear(entrySet().iterator());
  }

        value = "${spaces}";
        assertEquals("   ", ResourceUtil.resolve(value));

        // Test long property name
        System.setProperty("very.long.property.name.with.many.dots", "long");
        value = "${very.long.property.name.with.many.dots}";
        assertEquals("long", ResourceUtil.resolve(value));

        // Test multiple occurrences of same variable
        System.setProperty("repeat", "X");

# Generating SDKs { #generating-sdks }

Because **FastAPI** is based on the **OpenAPI** specification, its APIs can be described in a standard format that many tools understand.

This makes it easy to generate up-to-date **documentation**, client libraries (<abbr title="Software Development Kits">**SDKs**</abbr>) in multiple languages, and **testing** or **automation workflows** that stay in sync with your code.