ollama/fs/ggml/ggml.go
Devon Rifkin 7c94471d38 ggml: more accurate estimates for head count array case
Also standardized the approach by always treatting `HeadCount()` and
`HeadCountKV()` as arrays by filling them with the same value when
they're a scalar in the original GGUF
2025-04-10 16:28:34 -07:00

851 lines
20 KiB
Go

package ggml
import (
"encoding/binary"
"errors"
"fmt"
"io"
"log/slog"
"reflect"
"slices"
"strings"
"github.com/ollama/ollama/fs/util/bufioutil"
)
type GGML struct {
container
model
}
type model interface {
KV() KV
Tensors() Tensors
}
type KV map[string]any
func (kv KV) Architecture() string {
return kv.String("general.architecture", "unknown")
}
func (kv KV) Kind() string {
return kv.String("general.type", "unknown")
}
func (kv KV) ParameterCount() uint64 {
return keyValue[uint64](kv, "general.parameter_count")
}
func (kv KV) FileType() fileType {
if t := kv.Uint("general.file_type"); t > 0 {
return fileType(t)
}
return fileTypeUnknown
}
func (kv KV) BlockCount() uint64 {
return uint64(kv.Uint("block_count"))
}
func (kv KV) EmbeddingLength() uint64 {
return uint64(kv.Uint("embedding_length"))
}
func (kv KV) HeadCounts() []uint64 {
return kv.UintOrArrayAsArray("attention.head_count", kv.BlockCount(), 1)
}
func (kv KV) HeadCountKVs() []uint64 {
return kv.UintOrArrayAsArray("attention.head_count_kv", kv.BlockCount(), 1)
}
func (kv KV) EmbeddingHeadCount() []uint64 {
headCount := kv.HeadCounts()
embeddingHeadCount := make([]uint64, len(headCount))
for i, heads := range headCount {
if heads == 0 {
embeddingHeadCount[i] = 0
} else {
embeddingHeadCount[i] = kv.EmbeddingLength() / heads
}
}
return embeddingHeadCount
}
func (kv KV) FillArrayOrDefault(key string, defaultValue []uint64) []uint64 {
length := len(defaultValue)
if v, ok := keyValueUntyped(kv, key); ok {
switch v := v.(type) {
case uint32:
return FillArray(uint64(v), length)
case uint64:
return FillArray(v, length)
case int32:
return FillArray(uint64(v), length)
default:
slog.Warn("unsupported type", "key", key, "type", reflect.TypeOf(v))
}
}
return defaultValue
}
func (kv KV) EmbeddingHeadCountK() []uint64 {
return kv.FillArrayOrDefault("attention.key_length", kv.EmbeddingHeadCount())
}
func (kv KV) EmbeddingHeadCountV() []uint64 {
return kv.FillArrayOrDefault("attention.value_length", kv.EmbeddingHeadCount())
}
func (kv KV) GQAMax() uint64 {
heads := kv.HeadCounts()
headsKV := kv.HeadCountKVs()
if len(heads) != len(headsKV) {
slog.Warn("head count and head count kv are not the same length")
return 0
}
if len(heads) == 0 {
slog.Warn("head count is empty")
return 0
}
maxGQA := uint64(0)
for i := range heads {
head := heads[i]
headKV := headsKV[i]
if head == 0 || headKV == 0 {
return 0
}
gqa := head / headKV
if gqa > maxGQA {
maxGQA = gqa
}
}
return maxGQA
}
func (kv KV) ContextLength() uint64 {
return uint64(kv.Uint("context_length"))
}
func (kv KV) ChatTemplate() string {
return kv.String("tokenizer.chat_template")
}
func (kv KV) String(key string, defaultValue ...string) string {
return keyValue(kv, key, append(defaultValue, "")...)
}
func (kv KV) Uint(key string, defaultValue ...uint32) uint32 {
return keyValue(kv, key, append(defaultValue, 0)...)
}
func (kv KV) Float(key string, defaultValue ...float32) float32 {
return keyValue(kv, key, append(defaultValue, 0)...)
}
func (kv KV) Bool(key string, defaultValue ...bool) bool {
return keyValue(kv, key, append(defaultValue, false)...)
}
func (kv KV) UintOrArrayAsArray(key string, n uint64, defaultSingleValue ...uint64) []uint64 {
var singleValue *uint64
if v, ok := keyValueUntyped(kv, key); ok {
switch v := v.(type) {
case *array:
switch v.values[0].(type) {
case int32, uint32, uint64:
values, ok := AsUint64Array(v.values)
if ok {
return values
}
default:
slog.Warn("unexpected array value type", "key", key, "type", reflect.TypeOf(v))
}
case uint32:
val := uint64(v)
singleValue = &val
case int32:
val := uint64(v)
singleValue = &val
}
}
if singleValue == nil {
slog.Warn("falling back to default")
singleValue = &defaultSingleValue[0]
}
values := make([]uint64, n)
for i := range values {
values[i] = *singleValue
}
return values
}
func (kv KV) Strings(key string, defaultValue ...[]string) []string {
r := keyValue(kv, key, &array{})
s := make([]string, r.size)
for i := range r.size {
s[i] = r.values[i].(string)
}
return s
}
func (kv KV) Uints(key string, defaultValue ...[]uint32) []uint32 {
r := keyValue(kv, key, &array{})
s := make([]uint32, r.size)
for i := range r.size {
s[i] = uint32(r.values[i].(int32))
}
return s
}
func (kv KV) Floats(key string, defaultValue ...[]float32) []float32 {
r := keyValue(kv, key, &array{})
s := make([]float32, r.size)
for i := range r.size {
s[i] = float32(r.values[i].(float32))
}
return s
}
func (kv KV) OllamaEngineRequired() bool {
return slices.Contains([]string{
"gemma3",
"mistral3",
}, kv.Architecture())
}
func keyValue[T string | uint32 | uint64 | float32 | *array | bool](kv KV, key string, defaultValue ...T) T {
if val, ok := keyValueUntyped(kv, key); ok {
return val.(T)
}
slog.Warn("key not found", "key", key, "default", defaultValue[0])
return defaultValue[0]
}
func keyValueUntyped(kv KV, key string) (any, bool) {
if !strings.HasPrefix(key, "tokenizer.") && !strings.HasPrefix(key, "general.") {
key = kv.Architecture() + "." + key
}
if val, ok := kv[key]; ok {
return val, true
}
return nil, false
}
type Tensors struct {
items []*Tensor
Offset uint64
}
func (s Tensors) Items(prefix ...string) []*Tensor {
if len(prefix) == 0 {
return s.items
}
var items []*Tensor
for _, t := range s.items {
if strings.HasPrefix(t.Name, prefix[0]) {
items = append(items, t)
}
}
return items
}
func (ts Tensors) GroupLayers() map[string]Layer {
layers := make(map[string]Layer)
for _, t := range ts.items {
parts := strings.Split(t.Name, ".")
if index := slices.IndexFunc(parts, func(s string) bool { return s == "blk" || s == "mm" }); index != -1 {
if len(parts) > index+2 {
// blk and mm should have a number after them, join it
parts = append(
[]string{strings.Join(parts[:index+2], ".")},
parts[index+2:]...)
}
}
if _, ok := layers[parts[0]]; !ok {
layers[parts[0]] = make(Layer)
}
layers[parts[0]][strings.Join(parts[1:], ".")] = t
}
return layers
}
type Layer map[string]*Tensor
func (l Layer) Size() (size uint64) {
for _, t := range l {
size += t.Size()
}
return size
}
type Tensor struct {
Name string `json:"name"`
Kind uint32 `json:"kind"`
Offset uint64 `json:"-"`
// Shape is the number of elements in each dimension
Shape []uint64 `json:"shape"`
io.WriterTo `json:"-"`
}
func (t Tensor) block() (n int) {
if _, err := fmt.Sscanf(t.Name, "blk.%d.", &n); err != nil {
return -1
}
return
}
func (t Tensor) blockSize() uint64 {
switch t.Kind {
case
0, // F32
1, // F16
24, // I8
25, // I16
26, // I32
27, // I64
28, // F64
30: // BF16
return 1
case
2, // Q4_0
3, // Q4_1
6, // Q5_0
7, // Q5_1
8, // Q8_0
9, // Q8_1
20: // IQ4_NL
return 32
default:
return 256
}
}
func (t Tensor) typeSize() uint64 {
blockSize := t.blockSize()
switch t.Kind {
case 0: // FP32
return 4
case 1: // FP16
return 2
case 2: // Q4_0
return 2 + blockSize/2
case 3: // Q4_1
return 2 + 2 + blockSize/2
case 6: // Q5_0
return 2 + 4 + blockSize/2
case 7: // Q5_1
return 2 + 2 + 4 + blockSize/2
case 8: // Q8_0
return 2 + blockSize
case 9: // Q8_1
return 2 + 2 + blockSize
case 10: // Q2_K
return blockSize/16 + blockSize/4 + 2 + 2
case 11: // Q3_K
return blockSize/8 + blockSize/4 + 12 + 2
case 12: // Q4_K
return 2 + 2 + 12 + blockSize/2
case 13: // Q5_K
return 2 + 2 + 12 + blockSize/8 + blockSize/2
case 14: // Q6_K
return blockSize/2 + blockSize/4 + blockSize/16 + 2
case 15: // Q8_K
return 4 + blockSize + 2*blockSize/16
case 16: // IQ2_XXS
return 2 + 2*blockSize/8
case 17: // IQ2_XS
return 2 + 2*blockSize/8 + blockSize/32
case 18: // IQ3_XXS
return 2 + blockSize/4 + blockSize/8
case 19: // IQ1_S
return 2 + blockSize/8 + blockSize/16
case 20: // IQ4_NL
return 2 + blockSize/2
case 21: // IQ3_S
return 2 + blockSize/4 + blockSize/8 + blockSize/32 + 4
case 22: // IQ2_S
return 2 + blockSize/4 + blockSize/16
case 23: // IQ4_XS
return 2 + 2 + blockSize/2 + blockSize/64
case 24: // I8
return 1
case 25: // I16
return 2
case 26: // I32
return 4
case 27: // I64
return 8
case 28: // F64
return 8
case 29: // IQ1_M
return blockSize/8 + blockSize/16 + blockSize/32
case 30: // BF16
return 2
default:
return 0
}
}
func (t Tensor) parameters() uint64 {
var count uint64 = 1
for _, n := range t.Shape {
count *= n
}
return count
}
func (t Tensor) Size() uint64 {
return t.parameters() * t.typeSize() / t.blockSize()
}
func (t Tensor) Type() string {
return fileType(t.Kind).String()
}
type container interface {
Name() string
Decode(io.ReadSeeker) (model, error)
}
const (
// Magic constant for `ggml` files (unversioned).
FILE_MAGIC_GGML = 0x67676d6c
// Magic constant for `ggml` files (versioned, ggmf).
FILE_MAGIC_GGMF = 0x67676d66
// Magic constant for `ggml` files (versioned, ggjt).
FILE_MAGIC_GGJT = 0x67676a74
// Magic constant for `ggla` files (LoRA adapter).
FILE_MAGIC_GGLA = 0x67676C61
// Magic constant for `gguf` files (versioned, gguf)
FILE_MAGIC_GGUF_LE = 0x46554747
FILE_MAGIC_GGUF_BE = 0x47475546
)
var ErrUnsupportedFormat = errors.New("unsupported model format")
func DetectContentType(b []byte) string {
switch binary.LittleEndian.Uint32(b[:4]) {
case FILE_MAGIC_GGML:
return "ggml"
case FILE_MAGIC_GGMF:
return "ggmf"
case FILE_MAGIC_GGJT:
return "ggjt"
case FILE_MAGIC_GGLA:
return "ggla"
case FILE_MAGIC_GGUF_LE, FILE_MAGIC_GGUF_BE:
return "gguf"
default:
return ""
}
}
// Decode decodes a GGML model from the given reader.
//
// It collects array values for arrays with a size less than or equal to
// maxArraySize. If maxArraySize is 0, the default value of 1024 is used. If
// the maxArraySize is negative, all arrays are collected.
func Decode(rs io.ReadSeeker, maxArraySize int) (*GGML, int64, error) {
if maxArraySize == 0 {
maxArraySize = 1024
}
rs = bufioutil.NewBufferedSeeker(rs, 32<<10)
var magic uint32
if err := binary.Read(rs, binary.LittleEndian, &magic); err != nil {
return nil, 0, err
}
var c container
switch magic {
case FILE_MAGIC_GGUF_LE:
c = &containerGGUF{ByteOrder: binary.LittleEndian, maxArraySize: maxArraySize}
case FILE_MAGIC_GGUF_BE:
c = &containerGGUF{ByteOrder: binary.BigEndian, maxArraySize: maxArraySize}
default:
return nil, 0, errors.New("invalid file magic")
}
model, err := c.Decode(rs)
if err != nil {
return nil, 0, err
}
offset, err := rs.Seek(0, io.SeekCurrent)
if err != nil {
return nil, 0, err
}
// final model type
return &GGML{
container: c,
model: model,
}, offset, nil
}
func (f GGML) GraphSize(context, batch uint64, numParallel int, kvCacheType string) (kv []uint64, partialOffload, fullOffload uint64) {
embedding := f.KV().EmbeddingLength()
heads := f.KV().HeadCounts()
headsKV := f.KV().HeadCountKVs()
vocab := uint64(f.KV()["tokenizer.ggml.tokens"].(*array).size)
embeddingHeads := f.KV().EmbeddingHeadCount()
maxEmbeddingHeads, ok := MaxValue(embeddingHeads)
if !ok {
maxEmbeddingHeads = 1
slog.Warn("failed to get max embedding heads")
}
embeddingHeadsK := f.KV().EmbeddingHeadCountK()
maxEmbeddingHeadsK, ok := MaxValue(embeddingHeadsK)
if !ok {
maxEmbeddingHeadsK = 1
slog.Warn("failed to get max embedding headsK")
}
embeddingHeadsV := f.KV().EmbeddingHeadCountV()
layers := f.Tensors().GroupLayers()
bytesPerElement := kvCacheBytesPerElement(kvCacheType)
kv = make([]uint64, f.KV().BlockCount())
for i := range kv {
kv[i] = uint64(float64(context*(embeddingHeadsK[i]+embeddingHeadsV[i])*headsKV[i]) * bytesPerElement)
}
maxHeads, ok := MaxValue(heads)
if !ok {
maxHeads = 1
slog.Warn("failed to get max heads")
}
maxHeadsKV, ok := MaxValue(headsKV)
if !ok {
maxHeadsKV = 1
slog.Warn("failed to get max headsKV")
}
switch f.KV().Architecture() {
case "llama":
fullOffload = max(
4*batch*(1+4*embedding+context*(1+maxHeads)),
4*batch*(embedding+vocab),
)
partialOffload = 4 * batch * embedding
partialOffload += max(
4*batch*(1+embedding+max(context, embedding))+embedding*embedding*9/16+4*context*(batch*maxHeads+maxEmbeddingHeads*maxHeadsKV),
4*batch*(embedding+vocab)+embedding*vocab*105/128,
)
if ffnGateExpsWeight, ok := layers["blk.0"]["ffn_gate_exps.weight"]; ok {
// mixtral 8x22b
ff := uint64(f.KV()["llama.feed_forward_length"].(uint32))
partialOffload = max(
3*ffnGateExpsWeight.Size()+4*batch*(2*ff+maxHeadsKV+embedding+context+maxEmbeddingHeads*maxHeadsKV),
4*(context*batch*maxHeads+context*maxEmbeddingHeads*maxHeadsKV+batch*1024+maxEmbeddingHeads*maxHeadsKV*batch),
)
} else if ffnGateWeight, ok := layers["blk.0"]["ffn_gate.0.weight"]; ok {
// mixtral 8x7b
ffnGateWeight1 := ffnGateWeight.Shape[1]
fullOffload = 4 * batch * (2 + 3*embedding + context*(1+maxHeads) + 2*maxHeadsKV + ffnGateWeight1)
partialOffload = max(
4*batch*(3+maxEmbeddingHeads*maxHeadsKV+embedding+context*(1+maxHeads)+ffnGateWeight1)+(embedding*embedding+3*embedding*maxHeadsKV*ffnGateWeight1)*9/16,
4*batch*(1+2*embedding+context*(1+maxHeads))+embedding*(6*context*maxHeadsKV/maxHeads+embedding*9/16),
)
}
case "mllama":
var visionTokens, tiles uint64 = 1601, 4
crossAttentionLayers := f.KV().Uints("attention.cross_attention_layers")
for i := range kv {
if slices.Contains(crossAttentionLayers, uint32(i)) {
kv[i] = headsKV[i] * (embeddingHeadsK[i] + embeddingHeadsV[i]) *
4 * // sizeof(float32)
visionTokens *
tiles
}
}
fullOffload = max(
4*batch*(2+3*embedding+maxEmbeddingHeadsK*maxHeads+context*(1+maxHeads)),
// vocab graph
4*batch*(embedding+vocab),
)
var ropeFreqsCount uint64
if ropeFreqs, ok := f.Tensors().GroupLayers()["rope_freqs"]; ok {
if ropeFreqsWeights, ok := ropeFreqs["weights"]; ok {
ropeFreqsCount = ropeFreqsWeights.parameters()
}
}
partialOffload = max(
4*(batch*
(2*embedding+1+context*(1+maxHeads)+maxEmbeddingHeadsK*maxHeads)+
ropeFreqsCount+
maxEmbeddingHeadsK*context*maxHeadsKV),
// vocab graph
4*batch*(embedding+vocab)+embedding*vocab*105/128,
)
case "gemma", "gemma2", "gemma3":
fullOffload = max(
4*batch*(embedding+vocab),
4*batch*(2+context+context*maxHeads+2*embedding+2*maxEmbeddingHeadsK*maxHeads),
)
partialOffload = max(
4*embedding*batch+embedding*vocab*105/128+4*vocab*batch,
4*batch*(2*embedding+1+2*maxEmbeddingHeadsK*maxHeads+context+context*maxHeads)+
4*maxEmbeddingHeadsK*context*8+
embedding*embedding*maxEmbeddingHeadsK*maxHeads*9/16,
)
// Gemma2 also has sliding window attention but we only have an optimized implementation in the Ollama
// engine. Gemma3 always uses the Ollama engine.
if f.KV().Architecture() == "gemma3" {
const gemma3GlobalCacheCount = 6
slidingWindow := (uint64(numParallel) * uint64(f.KV().Uint("attention.sliding_window"))) + batch
for i := range kv {
// Every 6th layer is a global layer, which is the full context size that has already been set. The other
// layers are the smaller local (sliding) layers.
if (i+1)%gemma3GlobalCacheCount != 0 {
kv[i] = uint64(float64(slidingWindow*(embeddingHeadsK[i]+embeddingHeadsV[i])*headsKV[i]) * bytesPerElement)
}
}
}
case "command-r":
fullOffload = max(
4*batch*(embedding+vocab),
4*batch*(2+4*embedding+context*(1+maxHeads)),
)
partialOffload = max(
4*batch*(embedding+vocab)+embedding*vocab*105/128,
4*batch*(1+2*embedding+context*(1+maxHeads))+4*embedding*context+embedding*embedding*9/16,
)
case "qwen2":
fullOffload = max(
4*batch*(embedding+vocab),
4*batch*(1+2*embedding+context+context*maxHeads),
)
partialOffload = max(
4*batch*(embedding+vocab)+embedding*vocab*105/128,
4*(batch*(1+2*embedding+context*(1+maxHeads))+embedding*(1+context)),
)
case "phi2":
fullOffload = max(
4*batch*(embedding+vocab),
4*batch*(1+4*embedding+context+context*maxHeads),
)
partialOffload = max(
4*batch*(2*embedding+vocab)+embedding*vocab*105/128,
4*batch*(2+3*embedding+context+context*maxHeads),
)
case "stablelm":
fullOffload = 4 * batch * (context*(1+maxHeads) + 3*embedding + 2)
partialOffload = max(
4*batch*(vocab+2*embedding),
fullOffload,
)
case "deepseek2":
fullOffload = max(
4*batch*(3*embedding+vocab),
4*batch*(3*embedding+2+context*(1+maxHeadsKV)+2*maxEmbeddingHeadsK*maxHeadsKV),
)
partialOffload = max(
4*batch*(3*embedding+vocab)+embedding*vocab*105/128,
4*batch*(2*embedding+1+2*maxEmbeddingHeadsK*maxHeadsKV+context+context*maxHeadsKV)+4*maxEmbeddingHeadsK*context*maxHeadsKV+embedding*embedding*maxEmbeddingHeadsK*maxHeadsKV*9/16,
)
case "chatglm":
fullOffload = 4 * batch * (embedding + vocab)
partialOffload = 4*batch*(embedding+vocab) + embedding*vocab*105/128
if qkvBias, ok := layers["blk.0"]["attn_qkv.bias"]; ok {
fullOffload = max(
fullOffload,
4*batch*(2+
2*embedding+
context+
context*maxHeads+
maxEmbeddingHeadsK*maxHeads+
qkvBias.Shape[0]),
)
partialOffload = max(
partialOffload,
4*batch*(1+
2*embedding+
maxEmbeddingHeadsK*maxHeads+
context+
context*maxHeads)+
4*maxEmbeddingHeadsK*context+
4*context*maxEmbeddingHeadsK+
4*qkvBias.Shape[0],
)
}
}
return
}
func (llm GGML) VisionGraphSize() (weights, graphSize uint64) {
if llm.KV().Uint("vision.block_count") == 0 {
return
}
for name, layer := range llm.Tensors().GroupLayers() {
if name == "v" || strings.HasPrefix(name, "v.") {
for _, tensor := range layer {
weights += tensor.Size()
}
}
}
imageSize := uint64(llm.KV().Uint("vision.image_size"))
patchSize := uint64(llm.KV().Uint("vision.patch_size"))
if patchSize == 0 {
slog.Warn("unknown patch size for vision model")
return
}
numChannels := uint64(llm.KV().Uint("vision.num_channels"))
numPatches := (imageSize / patchSize) * (imageSize / patchSize)
if _, ok := llm.Tensors().GroupLayers()["v"]["class_embd"]; ok {
numPatches++
}
headCount := uint64(llm.KV().Uint("vision.attention.head_count"))
embeddingLength := uint64(llm.KV().Uint("vision.embedding_length"))
switch llm.KV().Architecture() {
case "mllama":
numPaddedPatches := numPatches + 8 - (numPatches%8)%8
maxNumTiles := uint64(llm.KV().Uint("vision.max_num_tiles"))
graphSize = 4 * (8 +
imageSize*imageSize*numChannels*maxNumTiles +
embeddingLength*numPatches*maxNumTiles +
9*embeddingLength*numPaddedPatches*maxNumTiles +
numPaddedPatches*maxNumTiles*numPaddedPatches*maxNumTiles*headCount)
case "gemma3", "mistral3":
graphSize = 4 * (imageSize*imageSize*numChannels +
embeddingLength*patchSize +
numPatches*numPatches*headCount)
}
return weights, graphSize
}
// SupportsKVCacheType checks if the requested cache type is supported
func (f GGML) SupportsKVCacheType(cacheType string) bool {
return slices.Contains([]string{"f16", "q8_0", "q4_0"}, cacheType)
}
// SupportsFlashAttention checks if the model supports flash attention
func (f GGML) SupportsFlashAttention() bool {
_, isEmbedding := f.KV()[fmt.Sprintf("%s.pooling_type", f.KV().Architecture())]
if isEmbedding {
return false
}
// Check head counts match and are non-zero
headCount := f.KV().HeadCounts()
embeddingHeadCountK := f.KV().EmbeddingHeadCountK()
embeddingHeadCountV := f.KV().EmbeddingHeadCountV()
for i := range headCount {
if embeddingHeadCountK[i] != embeddingHeadCountV[i] {
return false
}
}
return true
}
// kvCacheBytesPerElement returns the number of bytes per element for a given KV cache type
func kvCacheBytesPerElement(cacheType string) float64 {
switch cacheType {
case "q8_0":
return 1 // 1/2 of fp16
case "q4_0":
return 0.5 // 1/4 of fp16
default:
return 2 // f16 (default)
}
}
func AsUint64Array(v []any) ([]uint64, bool) {
switch v[0].(type) {
case uint32:
values := make([]uint64, len(v))
for i, v := range v {
values[i] = uint64(v.(uint32))
}
return values, true
case uint64:
values := make([]uint64, len(v))
for i, v := range v {
values[i] = v.(uint64)
}
return values, true
case int32:
values := make([]uint64, len(v))
for i, val := range v {
val := val.(int32)
if val < 0 {
slog.Warn("negative value in int32 array", "value", val)
return nil, false
}
values[i] = uint64(val)
}
return values, true
}
return nil, false
}
func MaxValue(values []uint64) (uint64, bool) {
if len(values) == 0 {
return 0, false
}
max := values[0]
for _, v := range values {
if v > max {
max = v
}
}
return max, true
}
func FillArray[T any](value T, n int) []T {
values := make([]T, n)
for i := range values {
values[i] = value
}
return values
}