Improve performance of ComputeWinCount

As it turns out `big.Int#Mul` doesn't like it when you reuse input as
output.

```
name         old time/op    new time/op    delta
WinCounts-8    4.56µs ± 1%    3.90µs ± 2%  -14.44%  (p=0.000 n=9+10)

name         old alloc/op   new alloc/op   delta
WinCounts-8    3.50kB ± 0%    1.15kB ± 0%  -67.23%  (p=0.000 n=10+10)

name         old allocs/op  new allocs/op  delta
WinCounts-8      45.0 ± 0%      24.0 ± 0%  -46.67%  (p=0.000 n=10+10)
```

Signed-off-by: Jakub Sztandera <kubuxu@protocol.ai>

chain/types/electionproof.go

@@ -83,11 +83,13 @@ func expneg(x *big.Int) *big.Int {
 
 // polyval evaluates a polynomial given by coefficients `p` in Q.256 format,
 // at point `x` in Q.256 format, output is in Q.256
+
 func polyval(p []*big.Int, x *big.Int) *big.Int {
 	res := new(big.Int).Set(p[0]) // Q.256
+	tmp := new(big.Int)           // big.Int.Mul doesn't like when input is reused as output
 	for _, c := range p[1:] {
-		res = res.Mul(res, x)         // Q.256 * Q.256 => Q.512
-		res = res.Rsh(res, precision) // Q.512 >> 256 => Q.256
+		tmp = tmp.Mul(res, x)         // Q.256 * Q.256 => Q.512
+		res = res.Rsh(tmp, precision) // Q.512 >> 256 => Q.256
 		res = res.Add(res, c)
 	}
 
@@ -129,12 +131,13 @@ func (ep *ElectionProof) ComputeWinCount(power BigInt, totalPower BigInt) uint64
 	rhs = rhs.Lsh(rhs, precision) // Q.256
 	rhs = rhs.Sub(rhs, elam)      // Q.256
 
+	tmp := new(big.Int) // big.Int.Mul doesn't like when input is reused as output
 	var j uint64
 	for lhs.Cmp(rhs) < 0 && j < MaxWinCount {
 		j++
-		pmf = pmf.Mul(pmf, lam)                                 // Q.256 * Q.256 => Q.512
-		pmf = pmf.Rsh(pmf, precision)                           // Q.512 >> 256 => Q.256
 		pmf = pmf.Div(pmf, new(big.Int).SetUint64(j) /* Q.0 */) // Q.256 / Q.0 => Q.256
+		tmp = tmp.Mul(pmf, lam)                                 // Q.256 * Q.256 => Q.512
+		pmf = pmf.Rsh(tmp, precision)                           // Q.512 >> 256 => Q.256
 		rhs = rhs.Sub(rhs, pmf)
 	}
 

chain/types/electionproof_test.go

@@ -18,23 +18,43 @@ func TestElectionLam(t *testing.T) {
 }
 
 func TestElectionExp(t *testing.T) {
-	t.Skip()
+	t.SkipNow()
 	const N = 256
 
 	step := big.NewInt(5)
 	step = step.Lsh(step, 256) // Q.256
 	step = step.Div(step, big.NewInt(N-1))
 
+	f, _ := os.Create("exp.csv")
+
 	x := big.NewInt(0)
 	for i := 0; i < N; i++ {
 		y := expneg(x)
-		fmt.Printf("\"%s\" \"%s\";\n", x, y)
+		fmt.Fprintf(f, "%s,%s\n", x, y)
 		x = x.Add(x, step)
 	}
 }
 
+var Res uint64
+
+func BenchmarkWinCounts(b *testing.B) {
+	totalPower := NewInt(100)
+	power := NewInt(100)
+	ep := &ElectionProof{VRFProof: nil}
+	var res uint64
+
+	b.ResetTimer()
+	b.ReportAllocs()
+	for i := 0; i < b.N; i++ {
+		ep.VRFProof = []byte{byte(i), byte(i >> 8), byte(i >> 16), byte(i >> 24), byte(i >> 32)}
+		j := ep.ComputeWinCount(power, totalPower)
+		res += j
+	}
+	Res += res
+}
+
 func TestWinCounts(t *testing.T) {
-	t.Skip()
+	t.SkipNow()
 	totalPower := NewInt(100)
 	power := NewInt(30)