[PIP-0002]: Migration from BTC-Style Difficulty Adjustment Algorithm to ASERT

consensus/xhash/asert.go

@@ -0,0 +1,124 @@
+package xhash
+
+import (
+	"math/big"
+)
+
+// ASERT params
+const (
+	asertIdealBlockTime = int64(600)     // seconds
+	asertHalflife       = int64(172800)  // 2 days in seconds
+	asertRadix          = int64(1 << 16) // fixed-point radix (2^16)
+)
+
+// Polynomial coefficients for 2^x cubic approximation (from BCH spec)
+const (
+	asertPolyA = uint64(195766423245049)
+	asertPolyB = uint64(971821376)
+	asertPolyC = uint64(5127)
+)
+
+// ASERTNextTarget computes the next target using the aserti3-2d algorithm.
+// All math here is integer-only and matches the BCH specification.
+//
+// anchorHeight      = height of anchor block
+// anchorParentTime  = timestamp (Unix seconds) of parent of anchor block
+// anchorTarget      = integer target value of anchor block
+// evalHeight        = height of evaluation block
+// evalTime          = timestamp of evaluation block
+// maxTarget         = maximum allowed target (easiest difficulty)
+//
+// Returns the target for the next block after the evaluation block.
+func ASERTNextTarget(
+	anchorHeight int64,
+	anchorParentTime int64,
+	anchorTarget *big.Int,
+	evalHeight int64,
+	evalTime int64,
+	maxTarget *big.Int,
+) *big.Int {
+	if anchorHeight <= 0 {
+		panic("ASERTNextTarget: anchorHeight must be > 0")
+	}
+	if anchorTarget.Sign() <= 0 {
+		panic("ASERTNextTarget: anchorTarget must be > 0")
+	}
+	if maxTarget.Sign() <= 0 {
+		panic("ASERTNextTarget: maxTarget must be > 0")
+	}
+
+	timeDelta := evalTime - anchorParentTime
+	heightDelta := evalHeight - anchorHeight
+
+	// Use truncating integer division (Go's / on ints already truncates toward zero)
+	numBlocks := heightDelta + 1
+	exponent := ((timeDelta - asertIdealBlockTime*numBlocks) * asertRadix) / asertHalflife
+
+	numShifts := exponent >> 16
+
+	// Keep 16-bit fractional part
+	exponent -= numShifts * asertRadix
+
+	// Now compute the cubic approximation factor in 16.16 fixed point.
+	// We interpret exponent as a signed 64-bit, but pass it to the poly as uint64
+	// so we get the same 2's-complement behavior as the BCH reference.
+	ux := uint64(exponent)
+
+	// factor = ((A*x + B*x^2 + C*x^3 + 2^47) >> 48) + 2^16
+	// This yields a multiplier in 16.16 fixed point.
+	x2 := ux * ux
+	x3 := x2 * ux
+
+	poly := asertPolyA*ux + asertPolyB*x2 + asertPolyC*x3 + (uint64(1) << 47)
+	factor := (poly >> 48) + uint64(asertRadix) // + 2^16
+
+	next := new(big.Int).Mul(anchorTarget, new(big.Int).SetUint64(factor))
+
+	// Apply the 2^numShifts factor:
+	if numShifts < 0 {
+		// Right-shift by -numShifts
+		next.Rsh(next, uint(-numShifts))
+	} else if numShifts > 0 {
+		// Left-shift by numShifts
+		next.Lsh(next, uint(numShifts))
+	}
+
+	// Divide by 2^16 to remove fixed-point scaling
+	next.Rsh(next, 16)
+
+	// Clamp to valid range
+	if next.Sign() <= 0 {
+		next.SetInt64(1)
+		return next
+	}
+	if next.Cmp(maxTarget) > 0 {
+		next = new(big.Int).Set(maxTarget)
+	}
+	return next
+}
+
+// difficultyToTarget: target = floor((2^256-1) / difficulty)
+func difficultyToTarget(d *big.Int) *big.Int {
+	if d.Sign() <= 0 {
+		// avoid div by zero; treat as max difficulty → min target
+		return new(big.Int).SetInt64(1)
+	}
+	t := new(big.Int).Div(new(big.Int).Set(two256m1), d)
+	if t.Sign() <= 0 {
+		t.SetInt64(1)
+	}
+	return t
+}
+
+// targetToDifficulty: difficulty = floor((2^256-1) / target)
+func targetToDifficulty(t *big.Int) *big.Int {
+	if t.Sign() <= 0 {
+		// avoid div by zero; treat as easiest target → difficulty = 1
+		return big.NewInt(1)
+	}
+	d := new(big.Int).Div(new(big.Int).Set(two256m1), t)
+	if d.Sign() <= 0 {
+		d.SetInt64(1)
+	}
+	return d
+}