consensus, core: EIP 100 polishes, fix chain maker diff

This PR polishes the EIP 100 difficulty adjustment algorithm
to match the same mechanisms as the Homestead was implemented
to keep the code uniform. It also avoids a few memory allocs
by reusing big1 and big2, pulling it out of the common package
and into ethash.

The commit also fixes chain maker to forward the uncle hash
when creating a simulated chain (it wasn't needed until now
so we just skipped a copy there).

2 files changed, 39 insertions, 29 deletions

diff --git a/consensus/ethash/consensus.go b/consensus/ethash/consensus.go
index fa2d740e4..01d97a470 100644
--- a/consensus/ethash/consensus.go
+++ b/consensus/ethash/consensus.go
@@ -287,7 +287,7 @@ func (ethash *Ethash) verifyHeader(chain consensus.ChainReader, header, parent *
 // given the parent block's time and difficulty.
 // TODO (karalabe): Move the chain maker into this package and make this private!
 func CalcDifficulty(config *params.ChainConfig, time uint64, parent *types.Header) *big.Int {
-	next := new(big.Int).Add(parent.Number, common.Big1)
+	next := new(big.Int).Add(parent.Number, big1)
 	switch {
 	case config.IsMetropolis(next):
 		return calcDifficultyMetropolis(time, parent)
@@ -301,33 +301,44 @@ func CalcDifficulty(config *params.ChainConfig, time uint64, parent *types.Heade
 // Some weird constants to avoid constant memory allocs for them.
 var (
 	expDiffPeriod = big.NewInt(100000)
+	big1          = big.NewInt(1)
+	big2          = big.NewInt(2)
 	big9          = big.NewInt(9)
 	big10         = big.NewInt(10)
 	bigMinus99    = big.NewInt(-99)
 )
 
+// calcDifficultyMetropolis is the difficulty adjustment algorithm. It returns
+// the difficulty that a new block should have when created at time given the
+// parent block's time and difficulty. The calculation uses the Metropolis rules.
 func calcDifficultyMetropolis(time uint64, parent *types.Header) *big.Int {
+	// https://github.com/ethereum/EIPs/issues/100.
+	// algorithm:
+	// diff = (parent_diff +
+	//         (parent_diff / 2048 * max((2 if len(parent.uncles) else 1) - ((timestamp - parent.timestamp) // 9), -99))
+	//        ) + 2^(periodCount - 2)
+
 	bigTime := new(big.Int).SetUint64(time)
 	bigParentTime := new(big.Int).Set(parent.Time)
 
-	// adj_factor = max((2 if len(parent.uncles) else 1) - ((timestamp - parent.timestamp) // 9), -99)
-	var x *big.Int
+	// holds intermediate values to make the algo easier to read & audit
+	x := new(big.Int)
+	y := new(big.Int)
+
+	// (2 if len(parent_uncles) else 1) - (block_timestamp - parent_timestamp) // 9
+	x.Sub(bigTime, bigParentTime)
+	x.Div(x, big9)
 	if parent.UncleHash == types.EmptyUncleHash {
-		x = big.NewInt(1)
+		x.Sub(big1, x)
 	} else {
-		x = big.NewInt(2)
+		x.Sub(big2, x)
 	}
-	z := new(big.Int).Sub(bigTime, bigParentTime)
-	z.Div(z, big9)
-	x.Sub(x, z)
-
-	// max(1 - (block_timestamp - parent_timestamp) // 10, -99)))
+	// max((2 if len(parent_uncles) else 1) - (block_timestamp - parent_timestamp) // 9, -99)
 	if x.Cmp(bigMinus99) < 0 {
 		x.Set(bigMinus99)
 	}
-
 	// (parent_diff + parent_diff // 2048 * max(1 - (block_timestamp - parent_timestamp) // 10, -99))
-	y := new(big.Int).Div(parent.Difficulty, params.DifficultyBoundDivisor)
+	y.Div(parent.Difficulty, params.DifficultyBoundDivisor)
 	x.Mul(y, x)
 	x.Add(parent.Difficulty, x)
 
@@ -335,19 +346,17 @@ func calcDifficultyMetropolis(time uint64, parent *types.Header) *big.Int {
 	if x.Cmp(params.MinimumDifficulty) < 0 {
 		x.Set(params.MinimumDifficulty)
 	}
-
 	// for the exponential factor
-	periodCount := new(big.Int).Add(parent.Number, common.Big1)
+	periodCount := new(big.Int).Add(parent.Number, big1)
 	periodCount.Div(periodCount, expDiffPeriod)
 
 	// the exponential factor, commonly referred to as "the bomb"
 	// diff = diff + 2^(periodCount - 2)
-	if periodCount.Cmp(common.Big1) > 0 {
-		y.Sub(periodCount, common.Big2)
-		y.Exp(common.Big2, y, nil)
+	if periodCount.Cmp(big1) > 0 {
+		y.Sub(periodCount, big2)
+		y.Exp(big2, y, nil)
 		x.Add(x, y)
 	}
-
 	return x
 }
 
@@ -368,12 +377,12 @@ func calcDifficultyHomestead(time uint64, parent *types.Header) *big.Int {
 	x := new(big.Int)
 	y := new(big.Int)
 
-	// 1 - (block_timestamp -parent_timestamp) // 10
+	// 1 - (block_timestamp - parent_timestamp) // 10
 	x.Sub(bigTime, bigParentTime)
 	x.Div(x, big10)
-	x.Sub(common.Big1, x)
+	x.Sub(big1, x)
 
-	// max(1 - (block_timestamp - parent_timestamp) // 10, -99)))
+	// max(1 - (block_timestamp - parent_timestamp) // 10, -99)
 	if x.Cmp(bigMinus99) < 0 {
 		x.Set(bigMinus99)
 	}
@@ -387,14 +396,14 @@ func calcDifficultyHomestead(time uint64, parent *types.Header) *big.Int {
 		x.Set(params.MinimumDifficulty)
 	}
 	// for the exponential factor
-	periodCount := new(big.Int).Add(parent.Number, common.Big1)
+	periodCount := new(big.Int).Add(parent.Number, big1)
 	periodCount.Div(periodCount, expDiffPeriod)
 
 	// the exponential factor, commonly referred to as "the bomb"
 	// diff = diff + 2^(periodCount - 2)
-	if periodCount.Cmp(common.Big1) > 0 {
-		y.Sub(periodCount, common.Big2)
-		y.Exp(common.Big2, y, nil)
+	if periodCount.Cmp(big1) > 0 {
+		y.Sub(periodCount, big2)
+		y.Exp(big2, y, nil)
 		x.Add(x, y)
 	}
 	return x
@@ -421,12 +430,12 @@ func calcDifficultyFrontier(time uint64, parent *types.Header) *big.Int {
 		diff.Set(params.MinimumDifficulty)
 	}
 
-	periodCount := new(big.Int).Add(parent.Number, common.Big1)
+	periodCount := new(big.Int).Add(parent.Number, big1)
 	periodCount.Div(periodCount, expDiffPeriod)
-	if periodCount.Cmp(common.Big1) > 0 {
+	if periodCount.Cmp(big1) > 0 {
 		// diff = diff + 2^(periodCount - 2)
-		expDiff := periodCount.Sub(periodCount, common.Big2)
-		expDiff.Exp(common.Big2, expDiff, nil)
+		expDiff := periodCount.Sub(periodCount, big2)
+		expDiff.Exp(big2, expDiff, nil)
 		diff.Add(diff, expDiff)
 		diff = math.BigMax(diff, params.MinimumDifficulty)
 	}
diff --git a/core/chain_makers.go b/core/chain_makers.go
index 38a69d42a..976a8114d 100644
--- a/core/chain_makers.go
+++ b/core/chain_makers.go
@@ -218,6 +218,7 @@ func makeHeader(config *params.ChainConfig, parent *types.Block, state *state.St
 			Number:     parent.Number(),
 			Time:       new(big.Int).Sub(time, big.NewInt(10)),
 			Difficulty: parent.Difficulty(),
+			UncleHash:  parent.UncleHash(),
 		}),
 		GasLimit: CalcGasLimit(parent),
 		GasUsed:  new(big.Int),