// n: expected insertions
  // b: m/n, bits per insertion
  // p: expected false positive probability
  //
  // 1) Optimal k = b * ln2
  // 2) p = (1 - e ^ (-kn/m))^k
  // 3) For optimal k: p = 2 ^ (-k) ~= 0.6185^b
  // 4) For optimal k: m = -nlnp / ((ln2) ^ 2)

  /**
   * Computes the optimal number of hash functions (k) for a given false positive probability (p).
   *

alias kv-pairify='yq ".configuration[]" | jq ".[]" | jq -r ".name + \"=\" + .value"'
```

Let's take for example a set of 12 compute nodes with an aggregate memory of _1.2TiB_, we need to do following settings for optimal results. Add the following optimal entries for _core-site.xml_ to configure _s3a_ with **MinIO**. Most important options here are

```
cat ${HADOOP_CONF_DIR}/core-site.xml | kv-pairify | grep "mapred"

	maxPartsCount             = 10000
	maxPartSize               = 1024 * 1024 * 1024 * 5
	minPartSize               = 1024 * 1024 * 128 // chosen by us to be optimal for HDDs
)

// optimalPartInfo - calculate the optimal part info for a given
// object size.
//
// NOTE: Assumption here is that for any object to be uploaded to any S3 compatible
// object storage it will have the following parameters as constants.

final class SingletonImmutableSet<E> extends ImmutableSet<E> {
  // We deliberately avoid caching the asList and hashCode here, to ensure that with
  // compressed oops, a SingletonImmutableSet packs all the way down to the optimal 16 bytes.

  final transient E element;

  SingletonImmutableSet(E element) {
    this.element = Preconditions.checkNotNull(element);
  }

  @Override
  public int size() {
    return 1;
  }

Example: Limit a MinIO cluster to accept at max 1600 simultaneous S3 API requests across all nodes of the cluster.

```sh
export MINIO_API_REQUESTS_MAX=1600

# MinIO Server Limits Per Tenant

For optimal production setup MinIO recommends Linux kernel version 4.x and later.

## Erasure Code (Multiple Drives / Servers)

| Item                                                            | Specification |
|:----------------------------------------------------------------|:--------------|
| Maximum number of servers per cluster                           | no-limit      |

final class SingletonImmutableSet<E> extends ImmutableSet<E> {
  // We deliberately avoid caching the asList and hashCode here, to ensure that with
  // compressed oops, a SingletonImmutableSet packs all the way down to the optimal 16 bytes.

  final transient E element;

  SingletonImmutableSet(E element) {
    this.element = Preconditions.checkNotNull(element);
  }

  @Override
  public int size() {
    return 1;
  }

list_quorum                     (string)    set the acceptable quorum expected for list operations e.g. "optimal", "reduced", "disk", "strict", "auto" (default: 'strict')
replication_priority            (string)    set replication priority (default: 'auto')

type endpointSet struct {
	argPatterns []ellipses.ArgPattern
	endpoints   []string   // Endpoints saved from previous GetEndpoints().
	setIndexes  [][]uint64 // All the sets.
}

// Supported set sizes this is used to find the optimal
// single set size.
var setSizes = []uint64{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

// getDivisibleSize - returns a greatest common divisor of
// all the ellipses sizes.

	// to derive & seal the key-encryption-key and to en/decrypt the object data.
	// This algorithm should not be used for new objects because its key derivation
	// is not optimal. See: https://github.com/minio/minio/pull/6121
	InsecureSealAlgorithm = "DARE-SHA256"
)

// Type represents an AWS SSE type:
//   - SSE-C
//   - SSE-S3
//   - SSE-KMS
type Type interface {
	fmt.Stringer