RC-1

internal/core/core.go

@@ -0,0 +1,88 @@
+package core
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"encoding/base64"
+	"fmt"
+	"math"
+	"math/big"
+)
+
+func RandomDecimal(bits int) (string, error) {
+	max := new(big.Int).Lsh(big.NewInt(1), uint(bits))
+	n, err := rand.Int(rand.Reader, max)
+	if err != nil {
+		return "", err
+	}
+	return n.String(), nil
+}
+
+func RandomSeed() (string, error) {
+	b := make([]byte, 32)
+	if _, err := rand.Read(b); err != nil {
+		return "", err
+	}
+	return base64.RawURLEncoding.EncodeToString(b), nil
+}
+
+func ExpectedGuess(taskID, seed, clientID string, seq int64, bits int) string {
+	h := sha256.Sum256([]byte(fmt.Sprintf("%s|%s|%s|%d", taskID, seed, clientID, seq)))
+	n := new(big.Int).SetBytes(h[:])
+	mod := new(big.Int).Lsh(big.NewInt(1), uint(bits))
+	n.Mod(n, mod)
+	return n.String()
+}
+
+func Distance(a, b string) (*big.Int, error) {
+	x, ok := new(big.Int).SetString(a, 10)
+	if !ok {
+		return nil, fmt.Errorf("invalid integer")
+	}
+	y, ok := new(big.Int).SetString(b, 10)
+	if !ok {
+		return nil, fmt.Errorf("invalid integer")
+	}
+	d := new(big.Int).Sub(x, y)
+	d.Abs(d)
+	return d, nil
+}
+
+func log2Big(x *big.Int) float64 {
+	if x.Sign() <= 0 {
+		return 0
+	}
+	n := x.BitLen()
+	if n <= 53 {
+		return math.Log2(float64(x.Uint64()))
+	}
+	shift := n - 53
+	top := new(big.Int).Rsh(new(big.Int).Set(x), uint(shift))
+	return math.Log2(float64(top.Uint64())) + float64(shift)
+}
+
+func Score(distance *big.Int, bits int) float64 {
+	if distance.Sign() == 0 {
+		return 100
+	}
+	s := 100 * (1 - log2Big(new(big.Int).Add(distance, big.NewInt(1)))/float64(bits))
+	if s < 0 {
+		return 0
+	}
+	if s > 100 {
+		return 100
+	}
+	return s
+}
+
+func Position(clientID string, score float64) (float64, float64, float64) {
+	h := sha256.Sum256([]byte(clientID))
+	f := func(i int) float64 { v := uint16(h[i])<<8 | uint16(h[i+1]); return float64(v)/65535*2 - 1 }
+	x, y, z := f(0), f(2), f(4)
+	norm := math.Sqrt(x*x + y*y + z*z)
+	if norm < 0.001 {
+		norm = 1
+	}
+	r := 0.25 + 13*(1-score/100)
+	return r * x / norm, r * y / norm, r * z / norm
+}

internal/core/core_test.go

@@ -0,0 +1,29 @@
+package core
+
+import (
+	"math/big"
+	"testing"
+)
+
+func TestExpectedGuessDeterministic(t *testing.T) {
+	a := ExpectedGuess("task_x", "seed", "client", 7, 28)
+	b := ExpectedGuess("task_x", "seed", "client", 7, 28)
+	if a != b {
+		t.Fatalf("not deterministic: %s != %s", a, b)
+	}
+	n, ok := new(big.Int).SetString(a, 10)
+	if !ok || n.Sign() < 0 || n.BitLen() > 28 {
+		t.Fatalf("guess outside range: %s", a)
+	}
+}
+
+func TestScore(t *testing.T) {
+	if Score(big.NewInt(0), 32) != 100 {
+		t.Fatal("exact hit must score 100")
+	}
+	near := Score(big.NewInt(1), 32)
+	far := Score(new(big.Int).Lsh(big.NewInt(1), 30), 32)
+	if near <= far {
+		t.Fatalf("near score %f should exceed far %f", near, far)
+	}
+}